MEASURING THE STRUCTURE AND COMPOSITION OF CIRCUMSTELLAR DEBRIS DISKS

Transcription

1 MEASURING THE STRUCTURE AND COMPOSITION OF CIRCUMSTELLAR DEBRIS DISKS by Nicholas Paul Ballering Copyright c Nicholas Paul Ballering 2016 A Dissertation Submitted to the Faculty of the DEPARTMENT OF ASTRONOMY In Partial Fulfillment of the Requirements For the Degree of DOCTOR OF PHILOSOPHY In the Graduate College THE UNIVERSITY OF ARIZONA 2016

2 2 THE UNIVERSITY OF ARIZONA GRADUATE COLLEGE As members of the Dissertation Committee, we certify that we have read the dissertation prepared by Nicholas Paul Ballering, titled Measuring the Structure and Composition of Circumstellar Debris Disks and recommend that it be accepted as fulfilling the dissertation requirement for the Degree of Doctor of Philosophy. George Rieke Date: 9 August 2016 Kate Su Date: 9 August 2016 Daniel Apai Date: 9 August 2016 Glenn Schneider Date: 9 August 2016 Phil Hinz Date: 9 August 2016 Final approval and acceptance of this dissertation is contingent upon the candidate s submission of the final copies of the dissertation to the Graduate College. I hereby certify that I have read this dissertation prepared under my direction and recommend that it be accepted as fulfilling the dissertation requirement. Dissertation Director: George Rieke Date: 9 August 2016

3 3 STATEMENT BY AUTHOR This dissertation has been submitted in partial fulfillment of requirements for an advanced degree at the University of Arizona and is deposited in the University Library to be made available to borrowers under rules of the Library. Brief quotations from this dissertation are allowable without special permission, provided that accurate acknowledgment of source is made. Requests for permission for extended quotation from or reproduction of this manuscript in whole or in part may be granted by the head of the major department or the Dean of the Graduate College when in his or her judgment the proposed use of the material is in the interests of scholarship. In all other instances, however, permission must be obtained from the author. SIGNED: Nicholas Paul Ballering

4 4 ACKNOWLEDGEMENTS First, I would like to thank my advisor, George Rieke. Your patience and encouragement gave me the freedom to lead my own explorations into the fascinating world of debris disks, while your insight and wisdom guided each project to a successful conclusion. I could not have asked for a better mentor. I also thank Kate Su and Andras Gaspar. I ve learned a tremendous amount from you both, and working together has been a true pleasure. Thank you Buell Januzzi for all your work to make the department a fun, friendly, and productive environment. Its clear to me that you care about the success and well-being of everyone here. I m proud to have spent the formative years of my academic career at Steward. I would not be where I am today without my family. Thank you, mom and dad, for your unconditional support. You raised me to have the confidence and dedication I needed to make this dissertation a success. Thanks to my dog, Carly, for reminding me to take breaks from work and go hiking. Jessica, I thank you for your tremendous patience, trust, encouragement, and understanding over these last six years. Finally, I thank my daughter Margot. Your curiosity and sense of wonder at the world remind me of what science is really all about.

5 5 DEDICATION For my family.

6 6 TABLE OF CONTENTS LIST OF FIGURES LIST OF TABLES ABSTRACT CHAPTER 1 INTRODUCTION Debris Disks and Planet Formation Dust Production The Grain Size Distribution The Stirring of Planetesimals Debris Disk Evolution Signposts of Unseen Planets Optical Properties of Dust Dust Temperature Radiation Forces on Dust Observing Debris Disks SEDs Imaging Thermal Emission Imaging Scattered Light Components of Debris Disks Cold Components Blowout Halos Warm Components Exozodiacal Dust (Exozodi) Very Hot Dust Gas in Debris Disks CHAPTER 2 A TREND BETWEEN COLD DEBRIS DISK TEMPERA- TURE AND STELLAR TYPE: IMPLICATIONS FOR THE FORMATION AND EVOLUTION OF WIDE-ORBIT PLANETS Introduction Methods Target Selection Photometry IRS Data Reduction

7 7 TABLE OF CONTENTS Continued Photosphere Model Black Body Fitting Results Discussion Conclusions CHAPTER 3 PROBING THE TERRESTRIAL REGIONS OF PLANETARY SYSTEMS: WARM DEBRIS DISKS WITH EMISSION FEATURES Introduction Methods Target Selection IRS Data Reduction Model Fitting Results A Window to Terrestrial Zones Notes on Specific Targets Discussion Conclusions CHAPTER 4 WHAT SETS THE RADIAL LOCATIONS OF WARM DEBRIS DISKS? Introduction Methods Target Selection IRS Data IR and Sub-mm Photometry Modeling dust emission Fitting Models to the Observed SEDs Analysis and Results Discussion of Outlier Systems Summary CHAPTER 5 A COMPREHENSIVE DUST MODEL APPLIED TO THE RE- SOLVED BETA PICTORIS DEBRIS DISK FROM OPTICAL TO RADIO WAVELENGTHS Introduction Stellar Properties Data HST/STIS HST/WFC

8 8 TABLE OF CONTENTS Continued Spitzer/MIPS Herschel/PACS at 70 µm ALMA Model Images The Dust Spatial Distribution The Dust Composition Fitting Procedure Results with 100% Astronomical Silicates Results with Generic Optical Constants Results with Mixtures of Common Materials SED Discussion Sub-blowout Grains The Dust Composition Summary CHAPTER 6 SUMMARY AND FUTURE PROSPECTS Cold Belts Exozodi Warm Disks Dust Composition Gas in Debris Disks Modeling with Non-Spherical Grains Global Debris Disk Simulations APPENDIX A DERIVING PHOTOSPHERE [24] APPENDIX B TARGET PROPERTIES AND RESULTS FROM CHAPTER APPENDIX C PLOTS OF WARM BELT FITS FROM CHAPTER APPENDIX D TARGETS PROPERTIES AND FITTING RESULTS FROM CHAPTER APPENDIX E β PIC MODEL COMPARED WITH ADDITIONAL DATA 236 E.1 The SW Side E.2 Gemini/T-ReCS E.3 Scattered Light Color

9 9 TABLE OF CONTENTS Continued APPENDIX F OPTICAL CONSTANTS OF β PIC DUST MODEL REFERENCES

10 10 LIST OF FIGURES 1.1 The evolutionary stages of young stellar objects The decay of debris disks around A stars The Fomalhaut disk in scattered light and sub-mm emission The five debris disk dust components Gallery of two-component systems Gallery of cold-component systems Gallery of warm-component systems Histogram of component temperatures Cold disk temperature vs. stellar temperature Bayesian posterior distributions Cold disk temperature vs. age One-belt fits to emission features Continuation of Figure Continuation of Figure Two-belt fits to emission features Continuation of Figure Continuation of Figure Continuation of Figure Continuation of Figure Continuation of Figure Equilibrium temperatures of detected exozodi belts a min vs a BOS for detected exozodi belts Stellar type and age of detected exozodi belts The fraction of warm disks with emission features vs. stellar type The fraction of warm disks with emission features vs. age The brightness and age of warm disks with and without features Warm dust location vs. stellar mass for single-component systems Bootstrap results Warm dust location vs. stellar mass for two-component systems Dust location distribution around the trend line Disk brightness vs. dust location residual from trend HST /STIS radial profiles HST /WFC3 difference images

11 11 LIST OF FIGURES Continued 5.3 HST /WFC3 radial profiles Spitzer/MIPS 24 µm image Spitzer/MIPS radial profiles Herschel/PACS radial profiles ALMA radial profiles Constraints on the spatial parameters Fit to data assuming 100% astronomical silicates Fit to data using generic optical constants Constraints on the dust composition and grain size parameters Best fit model compared to data Optical constants of the best fit model Thermal SED of the best fit model A.1 Distribution around photosphere [24] prediction C.1 Fits to single-component systems C.2 Continuation of Figure C C.3 Continuation of Figure C C.4 Fits to two-component systems C.5 Continuation of Figure C C.6 Continuation of Figure C C.7 Continuation of Figure C C.8 Continuation of Figure C E.1 Model compared to SW side data E.2 T-ReCS radial profiles E.3 Best fit model compared to T-ReCS data E.4 Scattered light color images of the best fit model E.5 Best fit model compared to observed scattered light colors E.6 Scattered light SED of the best fit model

12 12 LIST OF TABLES 2.1 Photometry Band Properties Target Properties One Belt Fitting Results Two Belt Fitting Results: Inner Belt Properties Broadband SED Photometry Data Properties of the Best Fit Model (of the NE side) B.1 Target Properties B.2 Photometry and IR Excess Properties D.1 Target Properties D.2 Target Photometry D.3 Single-Component Fit Results D.4 Two-Component Fit Results F.1 Optical Constants of the Best Fit Model

13 13 ABSTRACT In this dissertation, I measure the structure and composition of circumstellar debris disks to probe the underlying planetary systems. In Chapter 1, I provide an introduction to the field of debris disks. I highlight our current observational and theoretical understanding of the field, rather than providing a detailed history. This is intended to give the reader context and motivation for the subsequent chapters. I also describe important developments in debris disk science that are not the focus of this dissertation, but are nevertheless vital for a complete overview. In Chapter 2, I describe my analysis of a large sample of cold ( 130 K) debris disks seen in Spitzer/IRS data. Previous work had suggested a common temperature for these disk components, regardless of spectral type. I find that there is trend with spectral type and argue that the locations of cold disks are not set by snow lines, but more likely by the formation/evolution of planets. This work was published in Ballering et al. (2013). In Chapter 3, I turn my focus to the warm ( 190 K) debris components identified in Chapter 2 specifically those exhibiting silicate emission features. I show that these features arise from exozodiacal dust in the habitable zones around these stars. This was published in Ballering et al. (2014). In Chapter 4, I examine the remainder of the warm disks to investigate what mechanism sets their location. I find that for many systems, the locations trace the water snow line in the primordial protoplanetary disk, rather than the current snow line. This favors the interpretation that warm debris components arise from asteroid belts in these systems. This study will be published soon. In Chapter 5, I analyze images of the debris disk around β Pictoris at five different wavelengths, including in thermal emission and scattered light. I find that matching the disk brightness at all wavelengths constrains the composition of the

14 14 dust, with a mixture of astronomical silicates and organic refractory material fitting the data well. This was published in Ballering et al. (2016). In Chapter 6, I conclude with a summary of this dissertation and prospects for future progress in these areas.

15 15 CHAPTER 1 INTRODUCTION 1.1 Debris Disks and Planet Formation The process of star formation naturally results in a young stellar object surrounded by a disk of gas and dust. The star and surrounding material evolve through a series of stages (designated class 0 through class III), as summarized in Figure 1.1. In the protostellar phase (class 0 and I) the disk and star continue to accumulate material from the surrounding envelope, and the protostar itself is heated by this accretion. The spectral energy distributions (SEDs) of these systems are dominated by emission from the disk and envelope in the far-ir and sub-mm. Eventually the protostar blows away the surrounding envelope and the young stellar object enters the pre-main sequence phase as a class II object. The star is heated by its own contraction while continuing to accrete material through the disk (called a protoplanetary disk). The star is now much more prominent in the SED, although emission from the disk is still strong in the infrared and sub-mm. The transition from class II to III occurs as the protoplanetary disk disperses, accretion drops, and the star begins fusing hydrogen in its core and arrives at the main sequence. The lifetime of a protoplanetary disk is typically less than 10 Myr. Planets form from the material in the protoplanetary disk. The most widelyaccepted theory for the formation of giant planets is core accretion (Pollack et al., 1996). This is a bottom-up process starting with the collisional growth of dust grains into pebbles and eventually into 1 km sized planetesimals. Several theoretical barriers exist in the planetesimal formation process, so this is an area of much active research. The planetesimals collide and grow into a 10M solid core, which then accretes gas from the disk. This process must proceed quickly enough to reach the gas accretion stage before the protoplanetary disk disperses. Terrestrial planets

16 Figure 1.1: The evolutionary stages of young stellar objects. The right column shows a cartoon of the system at each stage, while the left column shows a representative SED. This figure is from Dauphas and Chaussidon (2011). 16

17 17 also form from the planetesimals, but because they do not accrete a large quantity of gas, the final stages of their formation can proceed for tens of Myr after disk dispersal. After disk dispersal, the star may be orbited by planets (giant and/or terrestrial) and residual planetesimals. These residual planetesimals constitute the parent bodies of a debris disk. Although the planetesimals cannot be detected with current technology, collisions among the planetesimals produce dust, which can be observed. Dust grains are removed from the system by radiation pressure and drag forces on timescales shorter than the age of most debris disk systems, meaning there must be a continuous supply of new dust strong evidence for the presence of the parent bodies. Debris disks are qualitatively different from protoplanetary disks in that their dust represents the breakup and decay of larger bodies, whereas protoplanetary dust is primordial and is seen as an ingredient for the construction of larger bodies. Protoplanetary disks have large amounts of gas (gas/dust 100 by mass), while debris disks have, at most, trace amounts of gas. There is also a quantitative difference in the amount of dust; protoplanetary disks have tens or hundreds of M of dust, while debris disk have < 1 M of dust. Debris disks are optically thin at all wavelengths, whereas protoplanetary disks are only optically thin in the sub-mm and radio. Debris disks are a natural product of the planet formation process, so observations of these disks are valuable to the study of planet formation. While the total mass in a debris disk is less than the mass in planets, the total surface area of the debris dust is much greater than that of the planets, making debris disks much easier to observe. To first order, the existence of a debris disk is confirmation that the initial stage of planet formation planetesimal formation was successful. Furthermore, a planet s gravity will shape or clear the material around it, so the spatial distribution of the debris can reveal where planets formed (or at least where they currently reside). Finally, by measuring the composition of debris disk dust we can infer the composition of the parent body planetesimals and thus also the composi-

18 18 tion of the solid components of planets, which formed from the planetesimals. The diversity in the structure and composition of debris disks may reflect the degree of diversity in planet formation, elucidating how typical or rare are planetary systems like our own. 1.2 Dust Production Debris disk dust is produced from parent body planetesimals by a collisional cascade. Collisions among particles of all sizes result in the breakup or erosion of larger particles into smaller ones. The largest particles involved are the parent body planetesimals while the smallest are µm sized dust grains that are still large enough to resist being blown out of the system by radiation pressure. The cascade persists in a steady state, although the total mass in all particle sizes will slowly decline as the parent bodies are depleted and collisions become less frequent. While collisional cascades are the favored mechanism to produce dust in the majority of debris disks, there are other possibilities. The collisions of planetesimals during terrestrial planet formation produce dust (Kenyon and Bromley, 2004), which could account for dust seen in young systems when this phase of planet formation is expected to occur. Another possibility is a period of dynamical instability among the planets in the system that scatters many of the residual planetesimals and causes a transient spike in collisional activity, analogues to the Late Heavy Bombardment in the solar system. The Late Heavy Bombardment occurred when the solar system was Myr old, but such an event could be triggered in a system of any age. Additionally, a single giant collision between protoplanets could create a significant amount of debris, which then evolves via a collisional cascade (Kenyon and Bromley, 2005; Jackson and Wyatt, 2012). Such collisions may be associated with the final stages of terrestrial planet formation (like the Moon-forming event) or with dynamical instability in the system. A discrete cloud of dust and gas was imaged within the large debris disk around β Pictoris; this cloud may be the result of a giant collision (Telesco et al., 2005; Dent et al., 2014). Finally, dust could

19 19 be produced from the disintegration of comets, which is the mechanism thought to supply the zodiacal dust in the inner part of the solar system (Nesvorný et al., 2010) The Grain Size Distribution An important property of a debris disk is the distribution of the dust grain sizes. The distribution is most often quantified as a power law, n(a) a q, where a is the grain radius and n(a)da is the volume number density of grains with sizes between a and a + da. The distribution cuts off at the small end where particles are removed from the system by radiation pressure, and at the large end by the largest body that has undergone a collision (collisions among large objects are less frequent, so the very largest bodies may not yet have undergone any collisions). The total mass is dominated by the largest particles in the distribution, while the total surface area is dominated by the smallest. Knowing the value of q is important for accurately interpreting debris disk observations. It also reveals deeper insights into the nature of the dust-producing collisions and the material properties of the debris. A value of q = 3.5 was derived by Dohnanyi (1969) assuming a collisional cascade in steady-state with particles of all sizes having the same strengths and velocities. Newer simulations relax these assumptions and find that the distribution does not follow a perfectly smooth power law (rather, the distribution is wavy), and the effective q can take values between 3 and 4, depending on the specifics of the simulations (Gáspár et al., 2012; Pan and Schlichting, 2012). Observationally, q can be measured from the spectral slope of the dust s thermal emission at sub-mm/radio wavelengths (Draine, 2006). Measurements, too, find values between 3 and 4, although there is some disagreement among studies as to the best specific value, e.g. MacGregor et al. (2016) found q = 3.36 while Gáspár et al. (2012) found q = 3.65.

20 The Stirring of Planetesimals In order for a population of parent body planetesimals to collide and produce dust, they must have relative velocities of >1 10 m/s, corresponding to eccentricities of e > Perhaps the planetesimals have this eccentricity initially, in which case the disk is considered pre-stirred. Otherwise, a stirring mechanism must be invoked (Kenyon and Bromley, 2008). Two such mechanisms have been proposed: stirring by planets or self-stirring. For the first mechanism, gravitational perturbations from planets in the system stir the planetesimals (Mustill and Wyatt, 2009). If this were the dominant case, then the presence of an observable debris disk would be an indication of planets in the system. Detailed simulations of the β Pic debris disk found that the known giant planet in that system can be responsible for stirring the outer planetesimals (Nesvold and Kuchner, 2015). In the self-stirring model, the disk is stirred by the largest bodies within the planetesimal disk (those with size 2000 km, comparable to the size of Pluto in the solar system) (Kenyon and Bromley, 2008; Kennedy and Wyatt, 2010). Large bodies in the planetesimal belt may take some time to form, predicting a delay before debris disks begin producing dust. Stirring by planets may also result in a delay, so both these theories have been termed delayed-stirring models. Plotting observed debris disk infrared brightness or frequency vs. age shows some evidence for a rise until an age of Myr then a decline for older systems, consistent with delayed-stirring (Hernández et al., 2006; Currie et al., 2008a,b) Debris Disk Evolution Beyond the possible rise in the first 10 Myr discussed in Section 1.2.2, the observed brightness and frequency of debris disks do clearly decline with age (Rieke et al., 2005; Su et al., 2006; Siegler et al., 2007; Meyer et al., 2008; Trilling et al., 2008; Sierchio et al., 2014). The decline roughly follows the relation t 0 /t, and the timescale of the decline (t 0 ) depends on stellar type and the temperature of the debris being

21 21 considered. Around A stars, the warm debris detected at 24 µm decays significantly faster (t 0 =150 Myr) than the cold debris detected at 70 µm (t 0 >400 Myr). For FGK stars, the 24 µm excess decays quite fast (perhaps faster than for A stars (Wyatt, 2008)), while the 70 µm excess decays more slowly, with excess seen in some very old (>5 Gyr) systems (Wyatt, 2008; Sierchio et al., 2014). Disks detected in scattered light also exhibit a decline in brightness with age (Schneider et al., 2016). The observed decline is in-line with expectations from a steady-state collisional cascade (Wyatt et al., 2007b), see Figure 1.2. The theory of steady-state decay predicts a maximum disk brightness for any given age, regardless of the disk s initial mass (Wyatt et al., 2007a). This is because more massive disks will simply decay faster and converge to the brightness evolution of initially less massive disks. The handful of disks observed to be brighter than this limit must have dust produced by transient events, e.g. gravitational instabilities or giant collisions. Although young stars host the highest disk frequency and the brightest disks, there are also a number of young stars that show no signs of having a debris disk (Rieke et al., 2005). This suggests that much of the variation among debris disks arises from their initial conditions rather than different evolutionary pathways. Wyatt et al. (2007b) found that the observed distribution of disk brightnesses at all ages can arise from variations in the initial disk masses. Gáspár et al. (2016) found that the brightness (mass) of debris disks is correlated with the metallicity of the host star. This suggests that some of the variance in the initial disk masses arises from the level of solids available in the material from which the star and planetary system formed. 1.3 Signposts of Unseen Planets Various features of debris disks are connected to the presence of planets, and a great motivation to study debris disks is their ability to reveal the presence and properties of unseen planets. As already discussed, planets may be responsible for stirring debris disks. However, other stirring mechanisms are possible, so this not a

22 Figure 1.2: The left panels show the brightness of warm (top) and cold (bottom) debris disks around A stars vs. their ages. The black points are detected disks, the red circles are systems with no disk detected, and the green dots the results of a steady-state collisional cascade simulation. Both warm and cold disks decay with time, although the warm disks decay faster. There is significant scatter in disk brightness at any age, but this scatter is reproduced well in the simulation, which starts from disks with a distribution of initial masses. The right panels show the results from the left panels after binning in both age and disk brightness ( small, medium, and large excesses), clarifying the good match between the data and simulation. This figure was taken from Wyatt (2008) and is originally from Wyatt et al. (2007b). 22

23 23 definitive signature of planets. Many debris disks have a cold outer belt with a region cleared of debris interior to it. Some systems also have an inner warm debris component with a clearing between it and the outer belt. One or more planets may be responsible for maintaining this clearing (Su et al., 2013). While planets are a promising explanation, other processes, such as the location of snow lines in the protoplanetary disk, could also yield belts at one or two specific locations. The detailed morphology of disks from spatially resolved imaging can reveal much more about the presence of planets. A planet located interior to a debris belt will sculpt the inner edge of belt. In the solar system, Neptune sculpts the inner edge of the Kuiper belt (Liou and Zook, 1999). The sharpness of the inner edge constrains the mass and location of the planet (Quillen, 2006; Chiang et al., 2009; Boley et al., 2012; Rodigas et al., 2014b). A planet on an eccentric orbit will also force the debris belt to be eccentric, which is observable as an offset in the location of the star from the geometric center of the debris belt. Such offsets have been seen in Fomalhaut (Kalas et al., 2005), HR 4796 (Schneider et al., 2009), and HD (Krist et al., 2012). An eccentric debris disk can also be detected by an effect called pericenter glow, where the disk-star offset causes one side of the disk to be nearer to the star and thus brighter than the other side (Wyatt et al., 1999). However, asymmetric features can also arise from interactions between the disk and the interstellar medium (Kalas, 2005; Maness et al., 2009). Other features such as clumps and warps may result from the influence of planets. The warp in the β Pic disk can be explained by the known planet, although the clump in that disk might instead be the result of a giant collision. 1.4 Optical Properties of Dust Light can interact with a dust grain by absorption/emission or by scattering. The efficiency of these processes is described by Q abs (λ, a) and Q sca (λ, a), which are the ratio of the effective grain cross-sections of absorption/emission and scattering,

24 24 respectively, to the geometric cross-section. While absorption/emission is isotropic, scattering is not. The distribution of scattering angles is described by the scattering phase function of the grain. These quantities depend on the composition, grain size, grain shape, and wavelength of light. The composition sets the optical constants, n(λ) and k(λ), which are the real and imaginary components of the index of refraction of the dust material. The optical constants are a function of wavelength, but do not depend on grain size. n(λ) and k(λ) are not independent of each other; they can be related by the Kramers-Kronig relations, but deriving one from the other requires knowing either n(λ) or k(λ) over all wavelengths. If grains are assumed to be spherical, Q abs (λ, a), Q sca (λ, a), and the scattering phase function can be derived from n(λ) and k(λ) using Mie theory. To model non-spherical or aggregate grains, several techniques exist, each with their own assumptions, pros, and cons (Fogel and Leung, 1998; Min, 2009). For dust much larger than the wavelength of light, the grains are in the geometric limit where Q abs (λ, a) and Q sca (λ, a) approach unity. When a λ, they can exceed unity and show distinctive variations with wavelength. For dust smaller than the wavelength, the efficiencies drop to very low values. Light scattered from a grain can become polarized. The degree of polarization depends on the grain properties, wavelength, and scattering angle, and can also be derived from Mie theory for spherical particles. Measuring polarization, when combined with measurements of the total amount of scattered light and thermal emission, provides additional constraints on the grain properties (Perrin et al., 2009). Polarized light can also reveal the overall geometry of the disk, and enhance the signal of the disk relative to un-polarized starlight Dust Temperature Because debris disk dust is heated and cooled by the absorption and emission of radiation, the optical properties play an important role in setting the dust temperature. Grains typically have sizes comparable to or larger than wavelengths where starlight

25 25 peaks, so they heat efficiently. Their temperatures are low enough, however, that for small grains the peak wavelength of their blackbody thermal emission is greater than their size, so they cool inefficiently. The net result is that small grains achieve a temperature greater than would be predicted for a perfect blackbody receiving the same stellar flux. It is important to account for this effect when interpreting unresolved observations of a debris disk s SED and inferring the dust location from its temperature Radiation Forces on Dust Stellar radiation will impart momentum on dust grains, impacting their orbits. The key parameter is β, the ratio of the radiation force to the gravitational force on a grain (Burns et al., 1979). β is independent of location, as both forces scale inversely with grain-star distance squared. For large grains, β is typically small so the radiation force does not have a large effect. Smaller grains have large β, but β can decrease again for very small grains. When β > 0.5, the grains are unbound from the star and leave the system on hyperbolic orbits. The grain size where β = 0.5 is called the blowout size and is thought to characterize the smallest grains in the collisional cascade. Grains slightly larger than the blowout size (β slightly smaller than 0.5) end up on eccentric orbits. β depends on the grain composition via the radiation pressure efficiency, Q pr (λ, a), which can be derived from the optical constants by, e.g., Mie theory for spherical grains. Stellar radiation also causes dust to slowly spiral inwards toward the star by Poynting-Robertson (P-R) drag. The strength of the effect is also governed by β. P- R drag is most effective for intermediate-sized particles, those too large to be blown out or put on eccentric orbits, but small enough to have non-zero β. In most debris disks, P-R drag occurs slowly enough such that grains typically collide and break up before they can move inwards, that is, disks are collision-dominated rather than drag-dominated (Wyatt, 2005). However, Kennedy and Piette (2015) note that it is inevitable that some amount of dust will manage to be dragged inwards, unless other forces such as gravitational perturbations from planets stop it. Stellar wind

26 26 drag (although not a radiative force) can also cause dust grains to spiral inwards in an analogous manner to P-R drag. 1.5 Observing Debris Disks SEDs The majority of debris disks have been detected via the infrared radiation they emit in excess of that expected from the star alone. Essentially, the signal from the star and that from the disk are decomposed spectrally, rather than spatially. These observations were made possible chiefly due to mid- and far- infrared space missions such as the Infrared Astronomical Satellite (IRAS), the Infrared Space Observatory (ISO), the Spitzer Space Telescope, and the Herschel Space Observatory. The brightest cold disks can also be detected via their excess at sub-mm/radio wavelengths from ground-based facilities. With photometry from Spitzer s Multiband Imaging Photometer (MIPS) playing such a prominent role in detecting debris disks, excess at 24 µm has come to be synonymous with warm dust and excess at 70 µm with cold dust. Greater spectral coverage, such as offered by Spitzer s Infrared Spectrograph (IRS), is required to accurately decompose an SED into its multiple components and measure their temperatures. The SEDs of most debris disks show a cold component (T < 130 K), a warm component (T 190 K), or both, which can be fit well by blackbody functions (Morales et al., 2009, 2011; Ballering et al., 2013; Chen et al., 2014; Kennedy and Wyatt, 2014). A minority of debris disks show spectral emission features from the dust, which provide additional constraints on the dust location, grain sizes, and composition (e.g. Chen et al., 2006; Lisse et al., 2007, 2008; Ballering et al., 2014; Mittal et al., 2015).

27 Imaging Thermal Emission Single-dish imaging in the infrared has been able to resolve the largest debris disks. This has been done from space with Spitzer (e.g. Su et al., 2005, 2008, 2009; Ballering et al., 2016) and Herschel (e.g. Acke et al., 2012; Booth et al., 2013; Matthews et al., 2014a; Pawellek et al., 2014). Ground-based observations in the mid-ir, although not as sensitive as those from space, have obtained higher-resolution observations of bright disks (e.g. Telesco et al., 2005; Moerchen et al., 2010, 2011). Thermal images have yielded a number of important results. By measuring the location of the dust, and comparing with SEDs, Booth et al. (2013) found that the minimum grain sizes are consistent with the expected blowout sizes. Thermal images have allowed for the identification of blowout halos (Su et al., 2005) and asymmetric features (Telesco et al., 2005; Moerchen et al., 2011). Comparing the brightness in thermal images to the brightness in scattered light can constrain the grain composition (Ballering et al., 2016). Higher resolution can be achieved with interferometry in the sub-mm/radio. This has been done successfully with the Submillimeter Array (SMA) and especially with the Atacama Large Millimeter/submillimeter Array (ALMA). Here, the resolution is good enough to determine not just the overall size of the disk, but also to measure the width and radial profile of outer belts (e.g. Boley et al., 2012; Marino et al., 2016), comparable to what is possible in scattered light (see Figure 1.3). Sub-mm/radio emission traces large grains that are not influenced by radiation forces, meaning the dust is tracing the parent body belt, whereas short wavelength (scattered light) images trace the small grains. Nulling interferometry is performed at λ 10 µm to search for dust in the terrestrial/habitable regions of nearby planetary systems (exozodiacal dust, or exozodi ). Although clear images of the dust are not produced by this technique, very faint quantities of dust can be identified by spatially separating the starlight from the dust emission. There are two prominent nulling projects: the Keck Interferometrer Nuller (KIN), which detected exozodi around five stars (Mennesson et al.,

28 Figure 1.3: The outer cold belt around the nearby star Fomalhaut. The blue shows the disk observed in scattered light with HST (Kalas et al., 2008), and the orange shows the disk s thermal emission in the sub-mm seen with ALMA (Boley et al., 2012). The detection of large grains confirms the presence of an underlying belt of parent body planetesimals here, since the large grains are not expected to move from their birth location. Also, for the same reason, the properties of the planet(s) that may be sculpting this disk can more accurately be constrained from the sub-mm profile. 28

29 ), and the Large Binocular Telescope Interferometer (LBTI, Hinz et al., 2014), which is currently surveying many nearby stars (Weinberger et al., 2015) and has begun to return results (Defrère et al., 2015) Imaging Scattered Light Images in scattered light have been successfully performed from space with the Hubble Space Telescope (HST ) (e.g. Golimowski et al., 2006; Schneider et al., 2014; Apai et al., 2015), and from the ground with typically 6 8 meter class telescopes with advanced adaptive optics systems (e.g. Buenzli et al., 2010; Rodigas et al., 2014a, 2015). The primary challenge is separating the disk signal from that of the star amid instrumental artifacts in the image. Coronography, angular differential imaging (ADI), polarized differential imaging (PDI), and various stellar point spread function subtraction techniques are common tools used to overcome this challenge. Scattered light images trace small grains, and thus show the effects of radiation (and other) forces on the dust, such as the presence of blowout halos (Apai et al., 2015). The color of the dust in scattered light as well as the relative brightness of scattered light vs. thermal emission constrain the grain sizes and composition (Debes et al., 2008; Rodigas et al., 2015; Ballering et al., 2016). The dust properties can also be constrained by measuring the scattering phase function (and polarization, if observing in polarized light), although the range of scattering angles that can be sampled depends on the disk s inclination. The dust properties may also complicate the interpretation of a scattered light image, as features in the observed disk could arise from structure in the density distribution of the dust or from the dust optical properties. This is especially true in polarized light when the observations do not recover all of the Stokes parameters (Perrin et al., 2015). A catalog of imaged disks (in scattered light or thermal emission) is currently maintained online at

30 30 Figure 1.4: An edge-on schematic of the five dust components a debris disk can possess (not all disks have all of these components). In order of increasing stellocentric distance, these components are: very hot dust, exozodiacal dust, warm dust, cold dust, and the blowout halo. This figure is from (Su and Rieke, 2014). 1.6 Components of Debris Disks Su and Rieke (2014) identified five distinct dust components that a debris disk could have. These are illustrated in Figure Cold Components These are the most commonly detected components in debris disk SEDs and have typical temperatures < 130 K. They are also the most commonly detected components in resolved images. The images in the sub-mm confirm that cold dust originates in-situ from an outer belt of parent body planetesimals, perhaps analogous to the Kuiper belt in the solar system. Some cold components are seen to be narrow rings (e.g. Fomalhaut, HR 4796), while others are radially broad (β Pic, HR 8799). The location of the cold belts may be set by snow lines or by planets in

31 31 which case they may trace the outer limits of efficient planet formation, beyond which only planetesimals formed. Chapter 2 addresses cold belts in more detail Blowout Halos Some systems (e.g. Vega, β Pic) show very extended distributions of dust consisting of small grains likely originating from a cold belt that are influenced by radiation pressure. Whether the majority of the grains in the halo are on bound-but-eccentric orbits or are truly unbound is not known. Why some bright debris disks have very prominent halos while others do not is also not known, although perhaps halos are a transient phenomenon (Su et al., 2005). The β Pic halo is examined in more detail in Chapter Warm Components Warm disks are also readily inferred from debris disk SEDs and have temperatures 190 K. They are too near their host stars to be easily imaged, so less is known about their properties and origins. They likely arise from a parent body population analogous to the asteroid belt or from material originating in an outer cold belt. I address this question further in Chapter Exozodiacal Dust (Exozodi) Exozodi is dust in the terrestrial/habitable zones of other stars, and has a temperature of 300 K. It is unlikely to result from a steady-state collisional cascade at those corresponding locations. It could be dust that flows inward from an asteroid belt (Su et al., 2016), it could originate from an outer cold belt, or it may be the result of terrestrial planet formation or giant collisions. Exozodi is of particular interest because its presence may interfere with our ability to image Earth-like planets in these systems (Roberge et al., 2012). This concern has motivated the nulling projects discussed in Section Exozodi is also of interest in that it may represent the veneer of materials delivered to terrestrial planets. Exozodi is the

32 32 subject of Chapter Very Hot Dust Very hot dust is seen in near-ir interferometric observations of some stars (Absil et al., 2013; Ertel et al., 2014). This dust likely consists of nano-grains (the product of dust sublimation very near the star) that become eletrically charged and trapped in the star s magnetic field (Rieke et al., 2016) Gas in Debris Disks Gas is seen in some massive debris disks. Gas is detected in UV absorption lines for edge-on disks (Roberge et al., 2006), from [OI] and [CII] forbidden lines at 63 and 158 µm with Herschel (Roberge et al., 2013; Donaldson et al., 2013; Riviere-Marichalar et al., 2014), and from CO emission lines in the sub-mm, especially with ALMA (Dent et al., 2014; Marino et al., 2016). Because the distribution of gas is seen to trace the distribution of dust in these systems, this gas like the dust is thought to be created via collisions of larger bodies, rather than being leftover primordial gas. One exception is HD 21997, which may contain leftover protoplanetary gas (Moór et al., 2011a). UV absorption lines may result from gas released by evaporating comets (so called falling evaporating bodies ). In theory, residual gas can interact with the dust, creating structure in its spatial distribution (Besla and Wu, 2007; Lyra and Kuchner, 2013).

33 33 CHAPTER 2 A TREND BETWEEN COLD DEBRIS DISK TEMPERATURE AND STELLAR TYPE: IMPLICATIONS FOR THE FORMATION AND EVOLUTION OF WIDE-ORBIT PLANETS Cold debris disks trace the limits of planet formation or migration in the outer regions of planetary systems, and thus have the potential to answer many of the outstanding questions in wide-orbit planet formation and evolution. We characterized the infrared excess spectral energy distributions of 174 cold debris disks around 543 main-sequence stars observed by both Spitzer IRS and MIPS. We found a trend between the temperature of the inner edges of cold debris disks and the stellar type of the stars they orbit. This argues against the importance of strictly temperaturedependent processes (e.g. non-water ice lines) in setting the dimensions of cold debris disks. Also, we found no evidence that delayed stirring causes the trend. The trend may result from outward planet migration that traces the extent of the primordial protoplanetary disk, or it may result from planet formation that halts at an orbital radius limited by the efficiency of core accretion. 2.1 Introduction From the sizes of protoplanetary disks, we expect planets to form out to tens of au. The many giant planets found on small orbits by radial velocity and transit techniques are believed to have formed beyond the water ice lines of their stars and migrated inward. Inward migration of massive planets can have a profound (and usually destructive) effect on the smaller objects in a planetary system, such as Earth-sized planets within the habitable zones. It is therefore important to determine how many systems retain their giant planets on wide orbits. Direct detection of these planets is limited to the most massive examples. Indirect detection through

34 34 the use of debris disks addresses this limitation. A debris disk consists of the circumstellar solid material that remains after the protoplanetary disk gas has dispersed and giant planets might have formed. Although most of the mass in a debris disk is harbored by the parent bodies (planetesimals), dust generated in their collisions accounts for the majority of the disk s surface area, and observations of debris disks via their thermal emission or reflected stellar radiation trace this dust. While tens of debris disks have been spatially resolved, the majority are detected only as an infrared excess in the spectral energy distribution (SED) of their star. Typical debris disk temperatures are tens to a few hundred kelvins, emitting as modified blackbodies that peak in the mid to far infrared. These wavelengths are well-suited for study with the Spitzer Space Telescope (Werner et al., 2004) Infrared Spectrograph (IRS; Houck et al., 2004) and Multiband Imaging Photometer for Spitzer (MIPS; Rieke et al., 2004). Other instruments suitable for studying debris disks in the infrared include the Herschel Space Observatory and the Wide-field Infrared Survey Explorer (WISE). For recent reviews of debris disks, see Wyatt (2008) and Matthews et al. (2014b). Debris disks often appear constrained to one or two discrete rings. This is evident from images of resolved disks such as Fomalhaut (Kalas et al., 2008; Boley et al., 2012), and from SEDs of unresolved debris disks that are fit well by one or two blackbody functions, corresponding to dust at one or two distinct radial locations. Of the 28 disks without strong emission features presented by Chen et al. (2006), all but one were fit better with a blackbody function than with a continuous disk model. The exception was HR8799, which was later determined to be best modelled by two blackbodies (Chen et al., 2009; Su et al., 2009). Morales et al. (2009) originally fit some excess SEDs with a power law, representing a continuous radial distribution of dust; however, Morales et al. (2011) argued that these power law fits require the optical depth of the disk to increase with orbital radius (which is theoretically implausible), and they found that these targets can be fit well by two blackbodies instead. These warm and cold debris disk components may be analogous to the asteroid belt and Kuiper belt in the Solar System.

35 35 Why do rings form, and what sets their location? Ice lines are one possibility. During the protoplanetary disk phase, a radial pressure gradient in the gas partially counteracts the gravitational force on the gas, allowing it to rotate at a sub-keplerian velocity. Solid particles orbit at Keplerian rates, and thus experience a head wind that slows their rotation and makes them spiral inwards. When these solids reach the ice line, the volatile component sublimates, producing a local pressure increase that counteracts the overall pressure gradient. This creates a zone where the particles can settle without a headwind. Thus, there is a tendency to have a planetesimal belt near the ice line, and this belt can then produce grains that assume a specific temperature. Morales et al. (2011) found similar warm disk temperatures (190 K) around stars of different stellar types. This can potentially be explained by the presence of the water ice line at K. Dodson-Robinson et al. (2009b) argue that ice lines of other species (e.g. CO, CH 4, N 2 ) at lower temperatures may play an important role in planet formation in the outer Solar System. If ice lines are also responsible for setting the location of the cold components, we would expect these components to have similar temperatures over a range of stellar types. Planets may also cause the discrete ring structures. Planetesimals will be scattered away once a planet is massive enough to dominate the gravity in its vicinity. Observations support the expected relation between planets and disk structure: the four giant planets imaged around HR 8799 (Marois et al., 2010) are located in the gap between the warm and cold debris disk components (Su et al., 2009); the imaged planet orbiting β Pic appears to sculpt the inner edge of its debris disk (Lagrange et al., 2010); the well-resolved cold debris ring around Fomalhaut is likely confined by planets (Kalas et al., 2008; Boley et al., 2012); and in the Solar System, Neptune sculpts the inner edge of the Kuiper belt (Liou and Zook, 1999). If the locations of debris disks are set by planets, we can use cold debris disks to investigate wide-orbit planets, which are not easily studied by other means. Of the over 850 confirmed exoplanets, 35 have orbits larger than 5 au, and only 17 have orbits larger than 10 au (NASA Exoplanet Archive 1, as of March 2013). This 1

36 36 is likely due to the observational biases of the radial velocity and transit detection techniques. Direct imaging can detect wide-orbit planets, but the current technology is only sensitive to very massive planets around young, nearby stars. Uranus and Neptune, for instance, could not be directly detected from outside the Solar System. The planet formation processes beyond 5-10 au are poorly understood. For example, did the planets around HR 8799 form at their current locations or did they (or at least their cores) form on smaller orbits, then migrate outwards via scattering interactions with other planets or planetesimals? Cold debris disks provide an observational test of these planet formation and migration theories. Planet formation by core accretion becomes less efficient farther from the star due to a radial increase in the dynamical timescale and decline in the surface density of solids in the protoplanetary disk (Mordasini et al., 2008; Dodson-Robinson et al., 2009a). Therefore, the inner edge of a cold debris disk may represent the outer limit of efficient core accretion (Kennedy and Wyatt, 2010; Dodson-Robinson et al., 2011). A planet migrating outwards into a debris disk will push the inner edge of the disk outward as well. Uranus and Neptune may have formed on smaller orbits and migrated into the Kuiper belt (Tsiganis et al., 2005). In this alternate scenario, the inner edge of a cold debris disk may represent the limits of outward migration. In this chapter, we focus on Spitzer measurements of cold debris disks, showing how their temperatures vary with the temperature of their central star and what this implies about planet formation and migration on wide-orbits. First, we describe the selection of our target stars ( 2.2.1). Then, we outline our photometric ( 2.2.2) and IRS ( 2.2.3) data acquisition/reduction. Next, we detail our modeling of the stellar photosphere SED ( 2.2.4), our derivation of the infrared excess, and our fitting of blackbodies to the excess ( 2.2.5). Finally, we analyze the results ( 2.3) and discuss the implications for wide-orbit planet formation and migration ( 2.4), before offering a summary and concluding remarks ( 2.5).

37 Methods Target Selection We searched the Spitzer observers log for main-sequence stars that were observed with the IRS Long Low (LL) module (both orders) in staring mode and with MIPS at 24 µm and 70 µm, and we accumulated a sample of 543 targets. The stellar properties of our target list are summarized in Table B.1. After reducing and analyzing the data, we refined the sample as described in This yielded 225 stars with significant excess (of which 174 had cold components), which are detailed in Table B.2. It is important to note that our sample comprised stars from a variety of Spitzer observational programs, each having targets selected in a different manner (e.g. nearby stars, stars with previously detected infrared excess, stars with RV-detected planets, etc.). Hence, our sample was not selected to be statistically representative in any one sense; rather, it was designed to include as many relevant targets as possible. We calculated the stellar temperature, T, from the star s V-K s color using tabulated values for main-sequence stars (or interpolations between these values) from Cox (2000), and we estimated a 200 K one-sigma uncertainty on these values. T is listed for targets with significant excess in Table B.2. Over the range of spectral types and metallicities of our sample of stars, V-K s is an accurate indicator of stellar effective temperature, with a peak-to-peak scatter of less than ± 1.5% and weak metallicity dependence (Masana et al., 2006). We use T to parametrize stellar type, and this degree of accuracy is sufficient for our purpose. Some of the uncertainty in T reflects the effect of interstellar reddening on V-K s, although the great majority of stars in this sample are within the Local Bubble and therefore should not be strongly reddened (of the 174 targets for which we detect cold components, only 29 are beyond 100 pc, 19 are beyond 120 pc, and 4 are beyond 150 pc). Ages for these stars were estimated from a combination of chromospheric activity measurements, x-ray emission, placement on the HR diagram, surface gravity,

38 38 membership in clusters and associations, and gyrochronology collected from the literature. Sierchio et al. (2014) describe the intercomparison of these methods and how they are applied, and the quoted ages are on the scale calibrated by Mamajek and Hillenbrand (2008). The ages are listed in Table B.1, along with references for the measurements used to derive the ages and a quality flag for the age accuracy (ranging from 0 if no age could be determined to 3 if there were three or more age measurements with good agreement) Photometry Although we built our target list around the Spitzer IRS spectra, we supported these spectra in our analysis with a suite of photometric data. The properties of the photometric systems we used are summarized in Table 2.1 and the photometric data for the targets with significant excess (see 2.2.5) are given in Table B.2. MIPS photometry at 24 µm provided an important calibration reference for the IRS data ( 2.2.3), while 70 µm photometry provided a crucial constraint on the temperature of cold debris disks ( 2.2.5). We used our in-house debris disk pipeline to reduce and extract photometry for the MIPS data as part of the effort to preserve the legacy of Spitzer measurements on debris disk studies (Su et al., 2010; K. Su et al. 2016, in prep). Basic reduction (up to the post-bcd mosaics) and calibrations of the MIPS data follow the descriptions by Engelbracht et al. (2007) and Gordon et al. (2007). In addition, the extraction of the 24 µm photometry was briefly described in Urban et al. (2012), where the source position at 24 µm is determined by a combination of PSF fitting and 2D Gaussian fitting. Both PSF fitting and aperture photometry 2 were performed, and we preferentially used the aperture photometry at 24 µm because this was used to calibrate the photosphere model at 24 µm, as described in and the Appendix (the PSF and aperture photometry agree to within a few percent). We then used the 24 µm source position to perform PSF fitting for data at 70 µm by minimizing the residual signal at the 2 The 24 µm aperture photometry used an aperture radius of 6.255, a sky annulus of , and an aperture correction factor of

39 39 source position (for details, see K. Su et al. 2016, in prep). For faint sources located in areas with structured background, the resultant 70 µm photometry can be negative, which reflects non-detection. The 1σ photometry uncertainty (listed in Table B.2) includes the pixel-to-pixel variation near the source of interest, and detector repeatability (1% and 5% of the source flux at 24 and 70 µm, respectively). MIPS photometry data for all of our targets can be found in Gáspár et al. (2013), Sierchio et al. (2014), and K. Su et al. (2016, in prep). V, J, H, and K s photometry were used to model the stellar photosphere SED ( 2.2.4) and to estimate T ( 2.2.1). We obtained Hipparcos V band (ESA, 1997) and 2MASS J, H, and K band photometry (Cutri et al., 2003) from the VizieR online database. Many of the targets in the sample are nearby stars and are severely saturated in the 2MASS data. To overcome this, we used heritage aperture photometry, which we transformed to match the 2MASS system. When both 2MASS and transformed heritage photometry of high quality were available, we averaged them. The references for the heritage photometry are in Table B.2. IRAC photometry (3.6 µm) was also used to model the stellar photosphere SED ( 2.2.4). These data were taken in Spitzer cycle 7 (PID 70076, PI: Su). All the IRAC data were taken in subarray mode with four dithered positions to avoid saturation. We used the Basic Calibrated Data (BCD) products provided by the Spitzer Science Center (pipeline version S18.18), and performed the necessary steps (pixel solid angle correction and pixel phase correction; K. Su et al. 2016, in prep) to extract the photometry. Aperture photometry was used for each individual data frame (64 frames per dithered position); and the final quoted flux density is the median value of all measurements per star. WISE data (Cutri et al., 2012) were obtained from VizieR, but are not included in Table B.2. Because WISE photometry is less accurate than Spitzer photometry, we did not use it quantitatively. Instead, we used it as a qualitative confirmation of our Spitzer data.

40 IRS Data Reduction Our IRS reduction started with the Level 1 BCD products, downloaded from the Spitzer Heritage Archive. In addition to IRS LL data, we also reduced Short Low (SL) module data, when available, and included them in our analysis. The Astronomical Observation Requests (AORs) used for each target are listed in Table B.1. The basic reduction was performed using the Spectroscopic Modeling Analysis and Reduction Tool (SMART) software package (Higdon et al., 2004), scripted into a series of automated routines. For each spectral order of each IRS AOR, three files (2D spectra, uncertainty, and mask) were combined into a single 3-plane file. Bad and rogue pixels were removed by the routine IRSCLEAN with the clean parameter set to 4096 (pixels with this value or higher were included in the clean). Next, when available, multiple Data Collection Events (DCEs) for the same nod position were combined, and then the background was removed from each 2D spectrum by subtraction of the opposite nod. The 2D spectra were then converted into 1D spectra using SMART s optimal 2 nod extraction (Lebouteiller et al., 2010). The 1D spectra from both nods were combined. The result was a wavelength, flux density, and uncertainty vector of each spectral order for each AOR. The bonus third order data were not used. The remainder of the data reduction and analysis was performed with the MATLAB software package. IRS data at wavelengths near the order edges often were of poor quality, so data longward of 38 µm and shortward of µm were discarded from the LL first order, data shortward of 14.3 µm were discarded from the LL second order, data longward of 14.7 µm and shortward of 7.55 µm were discarded from the SL first order, and data shortward of 5.25 µm were discarded from the SL second order. Systematic offsets in flux density existed between IRS orders, which we fixed by applying a multiplicative correction factor to the LL first order spectrum and to both SL order spectra (if they existed), in order to align them with the LL second order flux density. Initially, we determined the order correction factors using an automated routine, but due to the variety of shapes of the spectra and the presence

41 41 of outlying data points, we found that fine-tuning these factors by eye was more reliable. The data from all available orders and modules were then combined into a single spectrum. Next, we cut outlying data points from the spectrum in an iterative process. The spectrum was fit with a polynomial and the standard deviation of residual flux density values around the fit was calculated. Points lying more than three standard deviations from the fit were discarded. This process was iterated six times. Because the scatter of the data generally increased towards longer wavelengths, we applied this process separately to the short and long ends of our spectrum; if SL data were available, the two sections were divided at 14 µm and each section fit with a fourth degree polynomial, whereas if no SL data were available, the sections were divided at 25 µm and each section was fit with a second degree polynomial. This procedure, on average, cut 10 data points from each spectrum, with the first iteration typically cutting five points, and the sixth iteration only cutting zero, one, or two points (nearly 90% of spectra had no points cut in the sixth iteration). Before cutting, the spectra had 181, 296, or 373 points, depending on the available orders. After the outliers were cut, the spectrum was smoothed by binning to a wavelength resolution of 0.7 µm. The absolute calibration of IRS data is only accurate to 10%, whereas the MIPS calibration is accurate to 2% (Engelbracht et al., 2007). To reduce systematic errors in our IRS data, we multiplicatively scaled our spectrum to be consistent with the measured MIPS 24 µm flux density for each target. The IRS spectra were calibrated as point sources, so if a source was slightly extended, it would have an incorrect slit-loss correction. The stellar photospheres (point-like) are dominant in the IRS spectra for the majority of sources in the sample; therefore, this has no significant impact on the result. If the MIPS photometry for a source was contaminated by background emission, this contamination would be passed to the IRS spectrum of the source through this scaling (the IRS data may or may not have picked up the contamination, depending on the slit orientation). Nevertheless, an additional multiplicative factor was later applied to the IRS data (see 2.2.4), which

42 42 corrected any lingering errors from this process. Some targets were observed with more than one IRS AOR. We combined the spectra from these AORs, interleaving their data points, then re-smoothing to a spectral resolution of 0.7 µm Photosphere Model Although the spectrum of a main-sequence star peaks in the visible or near-ir, the stellar photosphere can still be the dominant source of flux density in the mid-ir. Thus, to extract the thermal emission of the debris disk (the infrared excess), an accurate model spectrum of the stellar photosphere must be generated and subtracted from the data. It is common to use photosphere spectra from detailed numerical models of stellar structures, such as KURUCZ/ATLAS9 (Castelli and Kurucz, 2004). However, these models are not well-tested in the mid- and far-infrared. Sinclair et al. (2010) compared various families of models (KURUCZ/ATLAS9, MARCS, and NEXTGEN/PHOENIX) and found that the choice of model family can affect whether a star is determined to have an infrared excess or not. We opted for a simpler model, a Rayleigh-Jeans relation given by F ν (λ) = RJ/λ 2, where RJ is an amplitude scale factor. This model is appropriate for wavelengths beyond 5 µm because stars in this study, mostly A through K dwarfs, have virtually no spectral features in the mid-ir, behaving as blackbodies in the Rayleigh- Jeans regime. For example, in the range of most interest for this study, the departure of a reference A0 star spectrum (Rieke et al., 2008) from a Rayleigh-Jeans fit between 15 and 30 µm is no more than ± 0.3%, and the ATLAS9 (Castelli, 2013) solar model follows Rayleigh-Jeans behavior to within ± 0.24% from 20 to 40 µm. However, the theoretical spectra show minor systematic differences from the observations (Rieke et al., 2008), so use of them to improve the knowledge of the SEDs would be risky. Modeling the photosphere thus came down to finding the appropriate scale factor (RJ) for each star in our sample. We used a set of color relations (derived from a

43 43 sample of stars known to have no IR excess) to predict the MIPS 24 µm magnitude of the photosphere, [24], from measured V, J, H, K s, and IRAC magnitudes bands where IR excesses due to very close-in dust are very rare. The details of these relations are described in the Appendix. This procedure estimates the 24 µm photospheric outputs to about 2% rms, based solely on data at wavelengths short of 4 µm. We then converted [24] to flux density units and used it to find the scaling factor for the photosphere model, which is given in Table B.2 for targets with significant excess (see 2.2.5). We finally applied a small multiplicative factor to the IRS data if it clearly looked slightly offset from the photosphere model. Then, we subtracted the photosphere model from the IRS spectra and MIPS 70 µm point to obtain the infrared excess, F ν excess (λ) = F ν (λ) F ν (λ). The photosphere model was assumed to have an uncertainty of 2%, thus the uncertainty in the excess flux density was σ excess (λ) = σ (λ) 2 + [0.02F ν (λ)] Black Body Fitting To interpret the excesses in a general way, we needed to assign them fiducial temperatures. The emission of disk grains is a function of their optical constants; however, as discussed in 2.1, debris disks radiate like blackbodies at one or two temperatures. The simplest possible description of the emission is in terms of these temperatures. In this section, we describe how we determined if each target had significant excess and whether the excess was best described by one or two blackbodies. We fit F ν excess (λ) with a one component blackbody model F ν model1 (λ) = c one F ν BB (λ, T one ) (2.1) where F ν BB (λ, T ) is the Planck Function. The best-fit parameters, c one and T one

44 44 HIP HIP11360 F (Jy) F (Jy) F (Jy) F (Jy) F (Jy) F (Jy) ν ν ν ν ν ν Warm (153 K) Cold (53 K) Warm + Cold Warm (255 K) Cold (83 K) Warm + Cold Warm (222 K) Cold (53 K) Warm + Cold Warm (297 K) Cold (115 K) Warm + Cold Warm (186 K) Cold (51 K) Warm + Cold Warm (174 K) Cold (71 K) Warm + Cold HIP26796 HIP41081 HIP58720 HIP75077 HIP λ (µm) Excess F ν (Jy) Excess F ν (Jy) Excess F ν (Jy) Excess F ν (Jy) Excess F ν (Jy) Excess F ν (Jy) HIP HIP HIP HIP HIP λ (µm) Figure 2.1: A gallery of six targets from our sample found to have two components. The left panels include the photosphere, while the right panels show the excess above the photosphere. IRS data are black points, MIPS data are magenta squares, and WISE data are magenta triangles. The black dashed line is the photosphere, the red and blue lines are the warm and cold components of the model, respectively, and the green line is the total model. Note that error bars are omitted from the left panels for clarity. WISE and MIPS 24 µm data are omitted from the right panels, as these points were not used to constrain the fits.

45 45 were found by minimizing the reduced chi-squared, { χ 2 ν = 1 N [F ν excess (λ i ) F ν model (λ i )] 2 ν σ excess (λ i ) 2 i + 28 [F ν excess (70µm) F ν model (70µm)] 2 σ excess (70µm) 2 }, (2.2) where ν = N + 28 n 1, N is the number of data points in the IRS excess data, and n is the number of free parameters in the fit (n=2). The MIPS 70 µm data point was weighted in the fit as 28 IRS data points, equivalent to the number of IRS data points (0.7 µm resolution) that would fit inside the equivalent width of the MIPS 70 µm spectral response function (19.65 µm). The fit was performed using MATLAB s lsqcurvefit algorithm. T one was constrained to between 0 and 500 K. While c one represents the amplitude of the debris disk emission, a more useful measure of a debris disk s brightness is the fractional excess, f L excess /L. We calculated f according to f = ( Fν excess max F ν max ) ( λ max λ excess max ), (2.3) from Equation 2 of Wyatt (2008). F ν excess max and F ν max are the peak flux density values of the disk emission and stellar photosphere emission, respectively, which occur at wavelengths λ excess max and λ max. While the peak flux densities for the disk components were easily calculated from our best fit model, the Rayleigh-Jeans stellar photosphere model had no maximum. To overcome this, we created a blackbody function using the temperature of the star from Table B.1, and scaled it to match the flux density of our Rayleigh-Jeans model at 24 µm. From this representation of the photosphere, we found the maximum flux density, and calculated f. With our best fits in hand, we refined our sample to only those targets with statistically significant excess. First, we inspected all fits by eye and discarded targets with poor quality data that resulted in clearly unrealistic fits. Second, we discarded targets with excess that was too faint, f < Third, we inspected the fits and identified all targets whose excess relied solely on the MIPS 70 µm data point (i.e. there was no excess in the IRS data). For these cases, we required

46 46 HIP HIP43797 F (Jy) F (Jy) F (Jy) F (Jy) F (Jy) F (Jy) ν ν ν ν ν ν Cold (89 K) Cold (104 K) Cold (110 K) Cold (28 K) Cold (71 K) Cold (49 K) HIP57632 HIP64184 HIP71395 HIP HIP λ (µm) Excess F ν (Jy) Excess F ν (Jy) Excess F ν (Jy) Excess F ν (Jy) Excess F ν (Jy) Excess F ν (Jy) HIP HIP HIP HIP HIP λ (µm) Figure 2.2: A gallery of six targets from our sample found to have only a cold component. The left panels include the photosphere, while the right panels show the excess above the photosphere. IRS data are black points, MIPS data are magenta squares, and WISE data are magenta triangles. The black dashed line is the photosphere and the blue line is the model cold component. Note that error bars are omitted from the left panels for clarity. WISE and MIPS 24 µm data are omitted from the right panels, as these points were not used to constrain the fits.

47 47 this MIPS point to represent a significant excess, so we discarded targets where F ν excess (70µm)/σ excess (70µm) < 3 or where F ν excess (70µm)/F ν (70µm) < 1. This process resulted in 318 of the original 543 stars having no significant excess. Of the remaining 225 targets with significant excess, we next determined whether the excess consisted of one or two components. To do this, we fit the excess SED of each target with a model consisting of the sum of two blackbodies, F ν model2 (λ) = c cold F ν BB (λ, T cold ) + c warm F ν BB (λ, T warm ). (2.4) Finding the optimal set of the four parameters c cold, T cold, c warm, and T warm was again done by minimizing the reduced chi-squared (Equation 2.2), now with n=4. Our definition of cold was the coldest well-detected component of the excess that was below 130 K. Morales et al. (2011) found a continuous distribution of warm components above 130 K, centered around 190 K, whose temperatures were set by the water ice line. Thus, any component above 130 K was considered warm for the purposes of this study. A component with a temperature of 110 K, for example, would be considered warm if another, colder temperature component was also detected, but would be considered cold if no colder component was detected. To implement this, we fit each target once using 100 K as the division between warm and cold, and again with the division at 130 K. We then selected the better of these two cases (based on reduced chi-squared) to represent the best two-component model. For many targets, these two cases yielded identical fits. In both cases, the minimum cold temperature allowed by the fit was 0 K, and the maximum allowed warm temperature was 500 K. Deciding if each target warranted a two-component model was a two-step process. First, we required that the reduced chi-squared of the two-component fit be at least three times better than that of the one-component fit (i.e. all targets where χ 2 ν1/χ 2 ν2 < 3 were deemed to be better fit by a single component). Second, for the remaining targets, we identified those for which the presence of the cold component relied entirely on the MIPS 70 µm point, meaning the IRS excess was entirely fit

48 48 HIP HIP1473 F ν (Jy) Warm (133 K) HIP43121 Excess F ν (Jy) HIP43121 F (Jy) F (Jy) F (Jy) F (Jy) F (Jy) ν ν ν ν ν Warm (158 K) Warm (194 K) Warm (250 K) Warm (156 K) Warm (178 K) HIP57971 HIP64053 HIP64877 HIP74824 λ (µm) Excess F ν (Jy) Excess F ν (Jy) Excess F ν (Jy) Excess F ν (Jy) Excess F ν (Jy) HIP HIP HIP HIP λ (µm) Figure 2.3: A gallery of six targets from our sample found to have only a warm component. The left panels include the photosphere, while the right panels show the excess above the photosphere. IRS data are black points, MIPS data are magenta squares, and WISE data are magenta triangles. The black dashed line is the photosphere and the red line is the model warm component. Note that error bars are omitted from the left panels for clarity. WISE and MIPS 24 µm data are omitted from the right panels, as these points were not used to constrain the fits.

49 49 by the warm component. For these targets to have significant cold components, we required their MIPS 70 µm excess to fall more than 3σ above the excess predicted by the warm component. That is, if one of these targets had F ν excess (70µm) c warm F ν BB (70µm, T warm ) σ excess (70µm) < 3, we concluded that it was best fit by one component. This step was analogous to the third step we performed when deciding if each target had excess or not. The targets that passed both of these criteria were deemed to have two components. This process identified 100 single-component cold disks, 51 single-component warm disks, and 74 two-component disks. We found only one target (HIP45585) that required two warm components (both >130 K) to fit properly, and we discarded this target from our results as it had no cold components (it is counted in the 318 targets that we discarded). We found no targets requiring two components colder than 100 K. Our methods were insensitive to possible additional cold components below 50 K. We concluded that our fitting procedure allowed us to find all cold components above this limit. Equivalently, our method reliably fit the inner edges of the cold disks. For the two-component disks, we calculated the fractional excesses for the warm and cold components, f warm and f cold, using Equation 2.3. One-component excesses were deemed warm or cold depending if they had temperatures above or below 130 K. The verdicts for all targets are given in Table B.1 and the parameters of our best fits for targets with significantly-detected components are listed in Table B.2. We estimated that the uncertainty in T cold was 10 K. This estimate was conservative; warmer cold components had more IRS data points in excess of the photosphere, so their fits were more constrained, with a temperature uncertainty of 3 to 7 K. We were unable to accurately constrain the temperatures of very cold components, which were detected only at 70 µm. With only one data point, blackbodies at a wide range of cold temperatures could be given the amplitude necessary to match the point, so a degeneracy existed between T and f in blackbody fits to the excess

50 Warm Components Cold Components Number Disk Temperature (K) Figure 2.4: Histograms of the warm and cold debris disk temperatures found in this sample. The bar left of 45 K contains all of the upper limit cold components.

51 51 SED. We made this distinction at 45 K; above this temperature there was enough information in the IRS spectra to constrain the temperature. Cold temperatures above 45 K were considered true detections, while cold temperatures below 45 K were considered unconstrained and were replaced with upper limits at 45 K. By using the 70 µm data to determine if such targets had significant excesses, we ensured that these disks were truly very cold, rather than warm but very faint. Of the 174 cold components in our sample, 25 had temperature upper limits. Some IRS spectra exhibit mineralogical emission features (e.g. HIP41081, HIP57971). Our model did not explicitly account for these features, but they peak sharply at 10 µm and do not resemble blackbody functions. These features did not influence our fits, except to raise the value of the minimum reduced chi-squared. The data and best fits for a small sample of our targets are shown in Figures 2.1, 2.2, and 2.3 (for targets with two components, one cold component, and one warm component, respectively). The left panels in all of these figures show the measured data with the photosphere and blackbody models, while the right panels illustrate the excess data and models with the photosphere subtracted. Histograms of the significant warm and cold debris disk temperatures are shown in Figure Results Morales et al. (2011) studied the behavior of the warm disk components in detail, but their sample (restricted to stars with ages less than 1 Gyr) had too few 70 µm detections of solar-type stars (9) to determine any trends between the cold component temperature and stellar type. To look for such a trend in our larger sample, we plot the cold component temperature versus stellar temperature in Figure 2.5. Well-constrained disk temperatures are black circles (open circles are young systems with age less than 25 Myr), and upper limits are downward facing blue triangles. Although there is substantial scatter in the cold component temperatures, a positive correlation between cold debris disk temperature and stellar temperature is evident.

52 Detections Detections (Age < 25 Myr) Upper Limits Best Fit Trend Line 110 Cold Disk Temperature (K) Stellar Temperature (K) Figure 2.5: The temperature of the cold disk component versus the temperature of the disk s host star. Black circles are well-determined disk temperatures (open circles are young systems), and blue triangles are upper limits. Although there is substantial scatter in the cold component temperatures, a correlation between cold debris disk temperature and stellar temperature is evident. Note, for example, that there are no disks colder than 50 K around stars hotter than 8500 K, in comparison with the large number of disks with temperature < 45 K around cooler stars. The green line is the best fit trend to the data, determined by a Bayesian linear regression, T cold = T A representative error bar is in the lower right.

53 53 To quantify this trend, we fit a linear relation to the data by Bayesian analysis using the routine linmix err 3. The routine properly handles upper-limits, and it uses uncertainties in both x and y directions (we assumed an uncertainty of 10 K in T cold and 200 K in T ). In its model, the routine also includes the normallydistributed intrinsic scatter of the data around the trend. The posterior distributions of the slope, intercept, and intrinsic scatter from the Bayesian regression are show in Figure 2.6. The slope of the linear regression was ± , thus the existence of a trend between T cold and T is significant at level greater than 4.5σ. The 1σ intrinsic scatter around the trend was 19.0 ± 1.46 K. The best-fit trend line from the Bayesian analysis, T cold = T , is plotted in green in Figure 2.5. The choice of a linear fit is not physically motivated; its purpose is to show that to first order there is a correlation between cold debris disk temperature and stellar type. A significant source of scatter around the trend results from the 10 targets with T < 7000 K and T cold > 100 K. Six of these stars (HIP560, HIP64184, HIP64995, HIP65875, HIP67497, and HIP78663) are less than 25 Myr old (most are part of the Scorpius-Centaurus Association). Although we show in 2.4 that there is no significant trend in T cold with age across the broad range of stellar ages in our sample, the excesses of these targets may be a product of their relatively young ages. They represent a period (5-50 Myr) when considerable collisional activity may still be occurring as a result of planet building (Kenyon and Bromley, 2008). 2.4 Discussion We now consider what determines the temperature of cold debris disks and how a trend with stellar type might arise. As discussed in 1, Morales et al. (2011) found similar warm disk temperatures (190 K) around stars of different stellar types, and they attributed the effect to a particle trap at the water ice line. If ice lines of other species set the location of cold 3 err.pro

54 Counts from Posterior Distribution Trend Line Slope x Trend Line Intercept Intrinsic Scatter Around Trend Figure 2.6: Histograms of samples from the Bayesian posterior distributions of the T cold vs. T trend slope, intercept, and intrinsic scatter, generated by the linmix err routine.

55 55 debris disks, we would expect cold disks around different type stars to have a common temperature. However, the trend of cold component temperature with stellar type (Figure 2.5) is inconsistent with any strictly temperature-dependent mechanism for setting the location of cold debris disks. Kennedy and Kenyon (2008) show that during the protoplanetary disk phase, the water ice line location is time dependent, and predicting it requires accounting for viscous heating in the disk, as well as the evolution of the pre-main-sequence stellar luminosity. Such considerations have not been applied to potential ice lines of species other than water, and we do not consider this level of detail here. Delayed stirring, in which the radial location of dust in a debris disk moves outwards with time, is a postulated mechanism for debris disk evolution (Kennedy and Wyatt, 2010). This could occur if the parent bodies are distributed in a broad ring. Particles in a debris disk collide and grind into dust faster on smaller orbits where the dynamical timescale is shorter. Thus, the location of the emitting dust moves outward with time, and, therefore, becomes cooler with time. Because late type stars have longer lifetimes than early type stars, the late type stars in our sample are generally older than the early type stars. If delayed stirring occurs, then this age bias in our sample could explain the observed trend in T cold with T. To test this hypothesis, we plot T cold against the age of the system (if available) for targets in three T bins (5000 to 6000 K, 6000 to 7000 K, and 7500 to 9500 K), shown in Figure 2.7. We see no trend in T cold with age in any bin, suggesting that delayed stirring does not produce the trend of disk temperature with stellar type. Perhaps cold debris disks are all at roughly the same orbital distance, regardless of stellar type. Assuming the disk is heated to its equilibrium temperature, the relation between the disk s temperature, location, and stellar type is given by T disk R 1/2 disk L1/4 R 1/2 disk M (2.5) R 1/2 disk T 2. The second and third lines of Equation 2.5 are derived assuming L M 4 and

56 < T * < 6000 K Cold Disk Temperature (K) K < T * < 7000 K K < T * < 9500 K Age (Gyr) Figure 2.7: T cold is plotted against the age of the system for targets in three T bins. No trend is seen with age, suggesting age does not play a confounding role in our discovered T cold vs. T trend. This also argues against the occurrence of delayed stirring.

57 57 L T 8 (valid in the roughly solar mass range). So with R disk constant, early type stars would host warmer disks. Kenyon and Bromley (2008) perform detailed simulations of the evolution of debris disks with inner and outer edges at 30 and 150 au, respectively, around stars with mass ranging from 1 to 3 M. Their models output the disk emission at 24 and 70 µm, which show that the (color) temperature of these cold debris disks does increase with stellar mass, in agreement with this expectation. But is the orbital location of cold debris disks truly constant with stellar type? If the size of cold debris disks traces the size of the original protoplanetary disks, we can use observations of the latter to address this question. Andrews et al. (2010) find that protoplanetary disk mass and radius are related by Furthermore, observations (Scholz et al., 2006) show that Combining these relations yields M disk R 1.6 disk. (2.6) M disk M. (2.7) R disk M 0.63, (2.8) so protoplanetary disk size does increase with earlier stellar type, albeit slowly. How quickly must the disk size increase for it to maintain a constant temperature? From Equation 2.5, R disk (T disk = const) M 2. (2.9) Although the size of disks does increase with earlier spectral type, it does so more slowly than required to maintain a constant temperature, thus disks are expected to be warmer around early type stars, consistent with our findings. Substituting Equation 2.8 into Equation 2.5 reveals how the disk temperature would vary with

58 58 spectral type in this case: T disk L 0.17 M 0.69 (2.10) T New results from Mohanty et al. (2013) suggest that Equation 2.7 may hold only for M 1M, with disk mass constant or possibly even decreasing as M disk M 1/2 for higher mass stars. If this were true and translated into a flat or decreasing R disk with M, then the disk temperature would increase even faster with spectral type than derived in Equation Is it plausible that the inner edge of cold debris disks scales with the size of the original protoplanetary disk? Some mechanism must clear the material inside cold debris disks and set their inner edge, and planets are a common explanation. An outwardly migrating planet would set an inner edge, but migration from planet-planet scattering can be a chaotic and unpredictable phenomenon; simulations show that the planet s final location depends sensitively on the initial conditions of the system (Tsiganis et al., 2005). This suggests that a trend with stellar temperature would not arise. Outward migration via scattering through a smooth disk of planetesimals would proceed in a more orderly manner, and the planet would halt its migration when the surface density of planetesimals decreased below a certain threshold, at a location that scales with the size of the original protoplanetary disk. Planet formation by core accretion (without migration) would also clear debris inside the cold component and create its inner edge. Planetesimals would be either incorporated into the planets as they formed, or scattered away once the planets became massive enough to dominate the gravitational field in their vicinity. mentioned in 2.1, core accretion efficiency declines with increasing orbital radius, leaving an outer zone of planetesimals beyond the planets. The timescale for the formation of a planet with a given mass scales as As t P/Σ, (2.11)

59 59 where P is the orbital period and Σ is the surface density of solids. Substituting Kepler s Third Law, P a 3/2 M 1/2, (2.12) (a is the orbital distance) and the typical protoplanetary disk structure, Σ a 3/2 M, (2.13) (Weidenschilling, 1977; Kenyon and Bromley, 2008) into Equation 2.11 gives t a 3 M 3/2. (2.14) After a time (t) planets will have formed out to a given orbital location (a), which sets the inner edge of the cold debris disk. So setting t constant and a = R disk predicts that the size of the disk would scale with spectral type as R disk M 1/2. (2.15) By comparing this with Equation 2.9, we see that in this case as well, the size of the disk grows more slowly with stellar type than required to maintain a constant equilibrium temperature, consistent with our observational results. Substituting Equation 2.15 into Equation 2.5 shows how the disk temperature would vary with stellar type if its inner edge were set by the limits of planet formation: T disk L 3/16 M 3/4 (2.16) T 3/ Conclusions We studied the circumstellar environment of 543 main-sequence stars via the mid infrared emission of their debris disks, as measured by the Spitzer Space Telescope. After subtracting a model of the flux density expected from the stellar photosphere, we obtained an SED of the infrared excess for each target. We found 225 targets

60 60 with significant excess: 100 with a single cold component, 51 with a single warm component, and 74 with two components. Examining the results revealed a trend between the temperature of the inner edge of the cold debris disk component and that of its host star 4. This trend is inconsistent with theories that predict the location of cold debris disks to be strictly temperature-dependent, i.e. we rule out the dominance of ice lines in sculpting the outer regions of planetary systems. We also rule out delayed stirring as the source of this trend. The trend can potentially be explained if the outward migration of planets traces the extent of the primordial protoplanetary disk, which tends to be limited to warmer equilibrium temperatures for hotter stars. The trend can also be explained if planets form in situ out to a distance where the core accretion efficiency drops below a certain threshold, leaving a cold debris disk that is warmer around earlier type stars. 4 There is a suggestion that this trend is not well-established for systems less than 25 Myr old.

61 61 Table 2.1. Photometry Band Properties Band λ (µm) Zero Point (Jy) Hipparcos V MASS J MASS H MASS K s WISE WISE WISE WISE IRAC MIPS MIPS Note. Properties of photometry bands that were used. J, H, and K s properties are from Rieke et al. (2008), V band properties are from Holberg and Bergeron (2006), and WISE properties are from Jarrett et al. (2011). An IRAC 1 zero point of Jy is typical, but we adjusted it to to bring our newlyreduced IRAC magnitudes in line with an older IRAC reduction, from which Equation A.7 was derived.

62 62 CHAPTER 3 PROBING THE TERRESTRIAL REGIONS OF PLANETARY SYSTEMS: WARM DEBRIS DISKS WITH EMISSION FEATURES Observations of debris disks allow for the study of planetary systems, even where planets have not been detected. However, debris disks are often only characterized by unresolved infrared excesses that resemble featureless blackbodies, and the location of the emitting dust is uncertain due to a degeneracy with the dust grain properties. Here we characterize the Spitzer IRS spectra of 22 debris disks exhibiting 10 micron silicate emission features. Such features arise from small warm dust grains, and their presence can significantly constrain the orbital location of the emitting debris. We find that these features can be explained by the presence of an additional dust component in the terrestrial zones of the planetary systems, i.e. an exozodiacal belt. Aside from possessing exozodiacal dust, these debris disks are not particularly unique; their minimum grain sizes are consistent with the blowout sizes of their systems, and their brightnesses are comparable to those of featureless warm debris disks. These disks are in systems with a range of ages, although the older systems with features are found only around A-type stars. The features in young systems may be signatures of terrestrial planet formation. Analyzing the spectra of unresolved debris disks with emission features may be one of the simplest and most accessible ways to study the terrestrial regions of planetary systems. 3.1 Introduction Terrestrial regions of planetary systems are not well studied. The majority of known exoplanets were discovered using the radial velocity and transit techniques, which are biased to massive and very short-period planets. While some rocky planets have now been discovered in the terrestrial zone (e.g. Kepler-186f; Quintana et al., 2014) their

63 63 frequency and statistical properties can only be estimated by extrapolation from planets nearer their stars (e.g. Petigura et al., 2013). Direct imaging of exoplanets, on the other hand, is currently limited to massive planets on wide orbits outside of the terrestrial zone. Observations of debris disks provide an alternative method to study planetary systems. Debris disks are the results of the collisional processing of the solid material left over from planet formation, and their locations may be gravitationally influenced by unseen planets (for a recent review of debris disks, see Matthews et al., 2014b). The disks are often partitioned into concentric components, and it is useful to categorize these components by equilibrium temperature (Su and Rieke, 2014). Cold components ( 100 K), located in the outer parts of planetary systems, are analogous to the Solar System s Kuiper Belt and may trace the radial limits of planet formation or migration (Ballering et al., 2013). Warm components ( 200 K) are analogous to the asteroid belt in the Solar System, and their locations may be set by the water ice line (Morales et al., 2011). Very hot components ( 1000 K) trace small refractory dust grains located very near to the star (e.g. Absil et al., 2013). Between the very hot and warm components lies the hot component ( 300 K), also referred to as the terrestrial zone. Dust in this zone may be analogous to the zodiacal dust in the Solar System, likely brought inward from Jupiter Family comets and the main asteroid belt (Nesvorný et al., 2010). Studying the terrestrial regions of planetary systems via observations of exozodiacal dust is the subject of this chapter. Debris in terrestrial zones has been largely inaccessible to observation. The Herschel and Spitzer space telescopes have imaged disks at mid- to far-ir wavelengths (e.g., Su et al., 2005; Su et al., 2008; Booth et al., 2013; Morales et al., 2013), but the resolution of these telescopes is not sufficient to resolve the terrestrial regions of these systems. The Atacama Large Millimeter/sub-millimeter Array (ALMA) has high resolution, but works at sub-mm and radio wavelengths so it is primarily sensitive to cold components. Debris disks have also been imaged via the starlight they scatter in the visible and near-infrared by the Hubble Space Telescope (e.g. Kalas

64 64 et al., 2005; Schneider et al., 2009; Soummer et al., 2014) and large ground-based telescopes equipped with advanced adaptive optics systems (e.g. Buenzli et al., 2010; Currie et al., 2012; Rodigas et al., 2014a), but current scattered light observations are limited to regions outside the terrestrial zone by the high dust/star contrast and small inner working angles required. Interferometric observations in the near-infrared have detected very hot dust around some stars (see the current list of detections in van Lieshout et al., 2014), but this material resides nearer to the star than the terrestrial region. A promising method to spatially resolve dust in terrestrial regions is interferometry at λ 10 µm, such as the detections of exozodiacal dust around η Crv (Millan-Gabet et al., 2011). A large program to expand such results is being undertaken with the Large Binocular Telescope Interferometer (LBTI), although it will be limited to relatively nearby stars (Hinz, 2009). The study of exozodiacal dust presented in this chapter is complementary to these interferometric observations. Debris disk characteristics around many stars have been inferred through their spectral energy distributions (SEDs) that show infrared flux density in excess of that from the star s photosphere. SED studies, using data primarily from Spitzer and Herschel, have succeeded in discovering and characterizing hundreds of debris disks (Morales et al., 2011; Ballering et al., 2013; Chen et al., 2014). These studies classify disks by temperature and find that they consist of cold components, warm components, or both. However, these components are usually colder than 300 K, which is the characteristic temperature expected for dust in the terrestrial zone. 1 Conversion of the apparent temperature of a debris disk to its orbital location is uncertain, as there is a degeneracy between the distance from the star and the optical and physical properties of the dust (minimum grain size, grain size distribution, and grain composition). The degeneracy arises from small grains that are superheated above their equilibrium temperatures because they absorb visible starlight more efficiently than they cool by emitting longer wavelength radiation. Booth et al. 1 The recent analysis by Chen et al. (2014) shows some components reaching higher temperatures.

65 65 (2013) resolve several cold debris belts with Herschel and find that they can be up to 2.5 times further from the star than predicted by blackbody fits to their SEDs. Rodriguez and Zuckerman (2012) find that the disk orbital radii can be up to 5 times their blackbody radii. The degree of difference between the true location of a debris disk and that derived from the SED-measured dust temperature is likely not uniform for all disks, as the size of the smallest grains in a system is determined by the radiation forces exerted on them by the central star and by the collisional and dynamical processes occurring in the system. These uncertainties make it difficult to determine whether or not warm dust is located in the terrestrial zone. Furthermore, this degeneracy operates such that debris disk components seem to be nearer to their stars than they actually are because grains tend to be warmer than their equilibrium blackbody temperatures. Because most warm components have measured temperatures less than 300 K, this degeneracy makes it unlikely that these components are probing the terrestrial zones. While the emitted flux density of most debris disks can be well modelled with one or two blackbody functions, a minority of disks show solid-state emission features in their spectra, most prominently at 10 µm and 18 µm from Si-O stretching and O-Si-O bending vibrations in the silicate material, respectively. These features only arise from warm, small (sub-µm to few-µm) grains. By using the extra information present in the emission features, the degeneracies in modelling a debris disk SED are broken, and the location of the disk and its grain properties can be more accurately determined. At least sixteen warm debris disks with prominent spectral features have been studied. These include: HR3927 (Chen et al., 2006), η Crv (Chen et al., 2006; Lisse et al., 2012), HD (Chen et al., 2006; Lisse et al., 2008; Olofsson et al., 2012; Smith et al., 2012; Olofsson et al., 2013), HD (Chen et al., 2006; Lisse et al., 2009; Smith et al., 2012; Johnson et al., 2012a), η Tel (Chen et al., 2006; Smith et al., 2009), HD69830 (Beichman et al., 2005; Lisse et al., 2007; Beichman et al., 2011; Olofsson et al., 2012), BD (Song et al., 2005; Weinberger et al., 2011; Olofsson et al., 2012), HD15407A (Melis et al., 2010; Fujiwara et al., 2012; Olofsson

66 66 et al., 2012), HD (Moór et al., 2009; Olofsson et al., 2012), [GBR2007] ID8 (Meng et al., 2012; Olofsson et al., 2012), EF Cha (Rhee et al., 2007a; Currie et al., 2011), HD (Honda et al., 2004), HD (Fujiwara et al., 2010), HD23514 (Meng et al., 2012; Rhee et al., 2008), HD72905 (Beichman et al., 2006), and the very well-studied debris disk around β Pic (Telesco and Knacke, 1991; Knacke et al., 1993; Okamoto et al., 2004; Chen et al., 2007; Li et al., 2012). In general, it has been concluded that these are exceptional systems, in many cases possibly the sites of elevated dynamical activity that has temporarily boosted the amount of very small dust in their debris systems. Here we present 22 additional warm debris disks with evidence for silicate emission features in their Spitzer Infrared Spectrograph (IRS; Houck et al., 2004) data. The presence of a warm debris disk component was previously known to exist around these stars, but no analysis of their spectral features has been published 2. The large number of new detections of features implies that such behavior is not exceptional. We fit to each spectrum physically-motivated SED models and determine the disk location and grain properties. We find that the locations of these disks can be well constrained, and that they are probing dust in the terrestrial regions of these systems. That is, analysis of subtle silicate features can be used to probe the terrestrial zones in many warm debris disks. 3.2 Methods Target Selection For stars identified in Ballering et al. (2013) to host warm debris disk components, we inspected the IRS data for signs of spectral features. We limited our search to targets with data available from all four IRS low-resolution spectral orders (LL1, LL2, SL1, and SL2). We found 22 targets with signs of features out of the 106 warm components that had all four spectral orders; Ballering et al. (2013) identified One exception is HIP Morales et al. (2013) created a model for this system that does reproduce the IRS emission feature, as we discuss in 3.3.2

67 67 total targets with warm components. The stars in our sample range in spectral type from B9 to F7, and their properties are given in Table 3.1. We inferred T and M from the known spectral types according to the tabulated values (or interpolations between those values) from Carroll and Ostlie (2006). L values were computed from the bolometric magnitudes, as L = (Mbol 4.74) L, where M bol = V 5 log 10 (D) + 5 A V + BC and A V = 1.15(V K (V K) 0 ). BC is the bolometric correction inferred from the spectral type according to Carroll and Ostlie (2006), and (V K) 0 is the intrinsic color inferred from the spectral type according to Cox (2000). We computed R from T and L using the Stefan- Boltzmann Law. MIPS 24 µm flux density values were taken from Ballering et al. (2013). We used stellar ages from Ballering et al. (2013) when available. These were estimated by combining chromospheric activity, x-ray emission, placement on the HR diagram, surface gravity, membership in clusters and associations, and gyrochronology. The references for these measurements are given in Table 3.1. We also provide a quality flag for the age accuracy, giving the number of independent age measurements with good agreement. When ages were not available from Ballering et al. (2013), we found age references in the literature from studies that used reliable HR diagram fitting (Nielsen et al., 2013; Zorec and Royer, 2012; Chen et al., 2014). For these targets, the age uncertainty can be large, sometimes 50%. Zorec and Royer (2012) provided ages in terms of the fraction of the main sequence lifetime; we obtained total main sequence lifetimes for these targets from Table 45 of Schaller et al. (1992), the M versus main sequence lifetime relation for the stellar evolution models employed by Zorec and Royer (2012). We used M values for our targets from Zorec and Royer (2012) when using this table IRS Data Reduction The IRS Astronomical Observation Requests (AORs) for our targets are listed in Table 3.1. The basic reduction was performed using the Spectroscopic Modeling Analysis and Reduction Tool (SMART) software package (Higdon et al., 2004), as

68 68 detailed in Ballering et al. (2013). In summary, bad pixels were removed using IRSCLEAN, multiple Data Collection Events (DCEs) for each nod position were combined, the background was removed from each 2D spectrum by subtraction of the opposite nod, the 2D spectra were converted into 1D spectra using optimal 2 nod extraction (Lebouteiller et al., 2010), and the 1D spectra from both nods were combined. The result was a wavelength, flux density, and uncertainty vector of each spectral order for each AOR. The bonus third order data were not used. We compared our results with the reduction provided by the Cornell AtlaS of Spitzer/IRS Sources 3 (CASSIS; Lebouteiller et al., 2011) to check that any structures in our spectra potential spectral features were not unique to our reduction procedure. We found no serious discrepancies between the two reductions, although there was typically a systematic difference in the absolute flux density level. We used the MATLAB software package for subsequent data reduction and analysis. We examined each spectral order and trimmed data from the ends, where the data are less reliable. The exact location of the trimming was determined individually for each target by eye, although we ensured some degree of overlap remained between adjacent orders. Next, we cut outlying data points from each order. To do this, we fit each spectral order with a third-degree polynomial, calculated the standard deviation of the residuals around this fit, and then discarded points lying more than three standard deviations from the fit. In practice, this process removed very few data points (primarily large outliers). We avoided a more aggressive cutting procedure as we did not want to erase any signs of emission features from our data. We corrected flux density offsets between the orders by applying a multiplicative correction factor to the LL1, SL1, and SL2 flux density values to bring them in line with the LL2 data and with each other. These corrections were determined by eye, and were typically less than 5% and almost always less than 10%. We combined the data from the four orders by interleaving the data at the overlapping regions and then smoothing the entire spectrum by binning to a wavelength resolution of 3 The Cornell Atlas of Spitzer/IRS Sources (CASSIS) is a product of the Infrared Science Center at Cornell University, supported by NASA and JPL.

69 µm. The silicate features we found are in the middle of the SL1 and LL2 wavelength coverages so they are not significantly affected by the order matching procedure. We then normalized the entire IRS spectrum to agree with the measured Multiband Imaging Photometer for Spitzer (MIPS; Rieke et al., 2004) flux density at 24 µm, as the absolute calibration of MIPS is known to be more accurate than that of IRS. With reduced IRS data in hand, we used a variety of empirical fitting approaches that indicated the presence of features roughly at the positions expected for silicate emission. The features were generally too weak to detect when simply viewing the data by eye they only became evident after subtracting the contribution from the stellar photosphere. We set out to confirm the signs of features by fitting the spectra with physically-motivated disk models capable of reproducing the emission features. We present the details of our model fitting procedure in the following section Model Fitting To explore the location of the dust grains producing the emission features, we carried out fits to the debris disk spectra, as discussed below. In summary, we found that fitting with a single dust belt almost always resulted in a belt so broad that a better physical explanation would be two belts, and for 9 of the sources single belt models could not even produce acceptable fits. We therefore fit all the systems with two debris belts. These fits indicate that the features arise from fairly narrow rings, which, as we show in 3.3.1, are largely confined to the terrestrial zones around these stars. The observed flux density from a single dust grain is given by ( a ) 2 F ν (λ, a, T d ) = Qabs (λ, a)πb ν (λ, T d ), (3.1) D where D is the distance to the system, a is the grain size, T d is the temperature of the dust grain, and B ν is the blackbody function. Q abs (λ, a) is the efficiency at which a dust grain absorbs and emits light, which depends on the dust composition. We assumed that all dust grains were composed of amorphous olivine (MgFeSiO 4 ), and

70 70 we obtained the optical constants (n, k) for this material as a function of wavelength from 0.2 to 500 µm from Dorschner et al. (1995). We then used the Mie Theory code miex (Wolf and Voshchinnikov, 2004) with these optical constants to compute Q abs (λ, a) for a range of grain sizes. The dust temperature is set by the energy balance of absorbed and emitted stellar radiation, ( ) 2 R πa 2 Q abs(λ, a)πb λ (λ, T ) dλ = 4πa 2 Q abs (λ, a)πb λ (λ, T d ) dλ, (3.2) r 0 where r is the distance between the dust grain and the star. This equation cannot be solved explicitly for T d, however it can be solved for r: r = R Q abs (λ, a)b λ (λ, T ) dλ 0 Q abs (λ, a)b λ (λ, T d ) dλ. (3.3) For each target in our sample, we computed r over a grid of input a and T d values. We then inverted the tabulated results to find T d (a, r). The integrals in Equation 3.3 were carried out using MATLAB s trapz function with 200 wavelength values logarithmically spaced between 0.2 and 500 µm. When generating models we checked that no dust grains reached temperatures above 1550 K, olivine s sublimation temperature. We assumed the dust grains were distributed in a ring between r in and r out with surface density Σ(r) r q. We also assumed that the grain size distribution was n(a) a p from a min to a max, and was identical at all r. The total flux density from a debris belt is then F ν,belt (λ) = A amax rout a min r in ( a D ) 2 Qabs (λ, a)πb ν (λ, T d )(2πr)r q a p dr da. (3.4) When generating models, we evaluated Equation 3.4 by summing the integrand in bins in r and a, distributed logarithmically between the maximum and minimum values. The normalization A was set so that the total mass of dust represented by the model was M. We tested our procedure by comparing our models with those generated by the Debris Disk Radiative Transfer Simulator 4 4

71 71 (DDS; Wolf and Hillenbrand, 2005). We found a very good agreement between the resulting theoretical spectra. Because we had SL IRS data at wavelengths as short as 5 µm, and the infrared excess generally arose at somewhat longer wavelengths, our spectra provided sufficient information to determine the brightness of the stellar photosphere without relying on photometry from other instruments at shorter wavelengths. Thus, we modelled the photosphere and the excess together, and the normalization of the photosphere was included as a free parameter in our fits. The stellar photosphere was assumed to emit as a blackbody of temperature T. A blackbody is appropriate because the stars in our sample, mostly A and F types, have virtually no spectral features in the mid-ir. First, we attempted to fit our data with the stellar photosphere plus a single belt model. We limited the number of free parameters by fixing the grain size distribution exponent to p = 3.65, as suggested by Gáspár et al. (2012). We also fixed the maximum grain size to a max = 1000 µm, as the largest grains in a disk generally contribute little to the total flux at these wavelengths, making this parameter difficult to constrain. We limited q to vary from 0 to 2. Thus, the form of our model was F ν,model (λ) = C p B ν (λ, T ) + C 0 F ν,belt (λ, r in, r out, q, a min ), (3.5) with six free parameters r in, r out, q, a min, C p, and C 0. Our fitting procedure entailed first defining a broad 4D grid of belt parameters and generating the model spectra for all points in this grid. We then found the best fit to the data (the optimal C p and C 0 ) for each model using MATLAB s lsqcurvefit algorithm by minimizing the standard χ 2 metric (calculated in linear space). The parameter set corresponding to the lowest overall χ 2 was deemed the best model. We examined how the minimum χ 2 varied with each disk parameter to determine if we had located a global minimum in parameter space. We then created a revised parameter grid with greater precision centered on the previous minimum and repeated the fitting procedure, iterating this process until we were confident that the overall best fit was found. We found acceptable one-belt fits to 13 of the

72 72 22 targets. The parameters of the best fits for these targets are given in Table 3.2, and the the fits are shown in Figure 3.1. The IRS SL1 order can show spurious excess signal at 13.5 to 15 µm due to the SL 14 micron teardrop effect (IRS Instrument Handbook). This artifact is thought to be caused by an internal reflection in the instrument, and is evident as a teardrop shape overlapping and slightly to the left of the spectral trace on the detector. We examined the 2D spectra of several sources and noticed signs of this effect. To avoid mistaking the teardrop signal for an emission feature, we excluded the 13.5 to 15 µm data for all of our targets when fitting models. However, in general the models fit this spectral range reasonably well (see Figures 3.1 and 3.4) and including it in our χ 2 minimization would not have modified the fits significantly. For the targets that could not be fit by one-belt models, the difficulty arose because the structure of the features at 10 µm and the levels of continuum excess at longer wavelengths could not both be reproduced with a single belt. Furthermore, the best fitting single-belt models were generally very large in radial extent, whereas many spatially resolved images of debris disks reveal them to be comprised of multiple, narrower belts. In fact, although all of the fits have inner radii within the terrestrial zones of the stars, 10 of the 13 fits have outer radii beyond 30 au. Realistically, all of these fits could just as well be described as two-belt fits, since it is not plausible that there is a single component that is so broad. Therefore, we next fit all of our targets with two-belt models. We again fixed p = 3.65 and a max = 1000 µm for both belts, and the form of the model was F ν,model (λ) = C p B ν (λ, T ) + C 1 F ν,belt (λ, r in1, r out1, q 1, a min1 ) + C 2 F ν,belt (λ, r in2, r out2, q 2, a min2 ), (3.6) with eleven free parameters r in1, r out1, q 1, a min1, r in2, r out2, q 2, a min2, C p, C 1, and C 2. The fitting again entailed defining a 4D grid of parameters for the inner belt and for the outer belt and generating the single-belt model spectra for all points in these grids. We found the best fit to the data (the optimal C p, C 1, and C 2 ) for each

73 HIP2578 (HD3003, HR136) 200 F ν (mjy) AU, amin = 2.2 µm Excess F ν (mjy) HIP27288 (ζ Lep, HD38678, HR1998) F ν (mjy) 10 3 Excess F ν (mjy) AU, amin = 3 µm HIP43121 (50 Cnc, HD74873, HR3481) F ν (mjy) AU, amin = 2.2 µm Excess F ν (mjy) HIP57971 (HD103266, HR4553) F ν (mjy) Excess F ν (mjy) AU, amin = 2.6 µm HIP58220 (HD103703) F ν (mjy) Excess F ν (mjy) AU, amin = 2.7 µm λ (µm) λ (µm) Figure 3.1: Model spectra for the 13 targets that could be fit well by one belt. Targets marked with an asterisk have marginally detected features. IRS data are shown in black and the models are in solid green. The left panels show the total flux density, while the right panels show the excess flux density above the photosphere. Uncertainty in the data is shown in gray shading on the left panels, but is omitted from the right panels for clarity. Data between 13.5 and 15 µm were not included in the fitting procedure. The blackbody fits from Ballering et al. (2013) are shown in dashed green (warm component) and dashed blue (cold component). Cases where the blackbody fits do not match the data well are due to the differences between this work and Ballering et al. (2013) in how the stellar photosphere component was removed.

74 HIP58528 (HD104231) 15 F ν (mjy) Excess F ν (mjy) AU, amin = 1.8 µm HIP59394 (3 Crv, HD105850, HR4635) F ν (mjy) AU, amin = 2.6 µm Excess F ν (mjy) HIP61049 (HD108857) F ν (mjy) AU, amin = 2 µm Excess F ν (mjy) HIP66068 (HD117665) F ν (mjy) AU, amin = 2.8 µm Excess F ν (mjy) HIP78641 (HD143675) F ν (mjy) AU, amin = 1.8 µm λ (µm) Excess F ν (mjy) λ (µm) Figure 3.2: Continuation of Figure 3.1.

75 HIP79797 (HD145689, HR6037) 20 F ν (mjy) Excess F ν (mjy) AU, amin = 1.2 µm HIP86305 (π Ara, HD159492, HR6549) F ν (mjy) 10 3 Excess F ν (mjy) AU, amin = 2 µm HIP99742 (ρ Aql, HD192425, HR7724) F ν (mjy) 10 3 Excess F ν (mjy) AU, amin = 3.2 µm λ (µm) λ (µm) Figure 3.3: Continuation of Figure 3.1. possible pairing of inner and outer models 5 such that r out1 < r in2. The parameters of these best fits are presented in Table 3.3, and the fits are plotted in Figure 3.4. The fits were unable to constrain q; we generally found that we could fit the data nearly equally well while varying this parameter from 0 to 2 (although for the one-belt fits q tended to be closer to 0). For most targets, the 10 µm feature was fit almost entirely by the flux from the inner belt model; hence, the parameters of the inner belts were more constrained by our fitting than those of the outer belts, and we only report the parameters of the inner belts in Table 3.3. Virtually all the inner belts lie entirely within the terrestrial zones. In Tables 3.2 and 3.3 we give the total mass of dust (in grains from a min to 1000 µm) for the belts, computed from C M and C M. We also give 5 As a point of clarity, when using these models (specified in terms of dust location), we refer to inner and outer belts. This is in contrast to blackbody models (specified in terms of dust temperature), for which we refer to warm and cold components.

76 76 the fractional luminosity of each belt, L belt /L, where the belt s emitting luminosity was calculated from L belt = 4πD µm 1µm ( c λ 2 ) F ν,belt (λ) dλ. (3.7) The uncertainties in our model fits were likely dominated by systematic errors, rather than by the statistical errors in the IRS flux density measurements. Calibration errors in the data were one source of systematic error, although we mitigated this by allowing the normalization of stellar photosphere flux density to be a free parameter in the fitting. Any errors in the stellar properties (L, T, D, etc.) influenced the models, adding systematic error to the best fit parameters. By using Mie theory we implicitly assumed the dust grains are spherical, but real grains are not perfect spheres, which added uncertainty to our models via our computed Q abs values. The robustness of our fits was also limited by using only one dust composition, fixing the form of Σ(r) and n(a), fixing a max and p, and using a maximum of two belts in our models. Varying the grain composition can result in changes in the radial scale of the belt to fit the observations, but variations by more than a factor of two are unlikely based on the range of optical constants available via the DDS website. Some silicate compositions fail to reproduce the shapes of the observed features entirely. The validity of our assumptions depends in part on the source of feature-producing dust, which we discuss in 3.4. However, our best fit models generally reproduce the data well with physically reasonable parameters, so further increasing the model complexity and number of free parameters likely would have simply added degeneracies among the parameters. Furthermore, few if any of these additional free parameters could significantly undermine the detection of silicate features in the spectra. After inspecting the model fits, we segregated our targets into those with clear features and those with only marginally detected features. This designation is listed in Tables 3.2 and 3.3, and targets with marginal features are marked with asterisks in Figures 3.1 and 3.4. Some spectra with marginal features had only a very weak excess at 10 µm, although the shape of the excess resembled a silicate emission

77 HIP2578 (HD3003, HR136) 100 F (mjy) F (mjy) F (mjy) F (mjy) ν ν ν ν AU, amin = 3 µm AU, amin = 1 µm Total Model AU, amin = 2 µm AU, amin = 4 µm 10 0 Total Model AU, amin = 1.5 µm AU, amin = 2 µm Total Model AU, amin = 2.6 µm AU, amin = 5.3 µm Total Model λ (µm) Excess F ν (mjy) Excess F ν (mjy) Excess F ν (mjy) Excess F ν (mjy) HIP18437 (HD24966) HIP26395 (HD37306, HR1919) HIP26966 (HD38206, HR1975) λ (µm) Excess F ν Outer Belt (mjy) Excess F ν Outer Belt (mjy) Excess F ν Outer Belt (mjy) Excess F ν Outer Belt (mjy) λ (µm) Figure 3.4: Two-belt model fits for each target. Targets marked with an asterisk have marginally detected features. IRS data are shown in black, the inner belt models are in solid green, the outer belt models are in solid blue, and the total models are in solid red. The left panels show the total flux density, the center panels show the excess flux density above the photosphere, and the right panels show the remaining excess with the outer belt models removed. Uncertainty in the data is shown in gray shading on the left panels, but is omitted from the other panels for clarity. Data between 13.5 and 15 µm were not included in the fitting procedure. The blackbody fits from Ballering et al. (2013) are shown in the center panels in dashed green (warm component) and dashed blue (cold component). Cases where the blackbody fits do not match the data well are due to the differences between this work and Ballering et al. (2013) in how the stellar photosphere component was removed.

78 HIP27288 (ζ Lep, HD38678, HR1998) F ν (mjy) F ν (mjy) AU, amin = 3 µm AU, amin = 2 µm Total Model AU, amin = 2 µm AU, amin = 1 µm Total Model Excess F ν (mjy) Excess F ν (mjy) HIP41081 (HD71043, HR3300) HIP43121 (50 Cnc, HD74873, HR3481) 40 Excess F ν Outer Belt (mjy) Excess F ν Outer Belt (mjy) F ν (mjy) F ν (mjy) AU, amin = 1.7 µm AU, amin = 3 µm Total Model AU, amin = 3 µm AU, amin = 1 µm Total Model λ (µm) Excess F ν (mjy) Excess F ν (mjy) HIP57971 (HD103266, HR4553) λ (µm) Excess F ν Outer Belt (mjy) Excess F ν Outer Belt (mjy) λ (µm) Figure 3.5: Continuation of Figure 3.4.

79 HIP58220 (HD103703) 15 F ν (mjy) AU, amin = 2 µm 5 10 AU, amin = 5 µm 10 0 Total Model Excess F ν (mjy) HIP58528 (HD104231) Excess F ν Outer Belt (mjy) F ν (mjy) F ν (mjy) AU, amin = 2 µm 5 10 AU, amin = 2 µm 10 0 Total Model AU, amin = 2 µm AU, amin = 2 µm Total Model Excess F ν (mjy) Excess F ν (mjy) HIP59394 (3 Crv, HD105850, HR4635) HIP60561 (HD ) Excess F ν Outer Belt (mjy) Excess F ν Outer Belt (mjy) F ν (mjy) AU, amin = 3 µm AU, amin = 2 µm 10 0 Total Model λ (µm) Excess F ν (mjy) λ (µm) Excess F ν Outer Belt (mjy) λ (µm) Figure 3.6: Continuation of Figure 3.4.

80 HIP61049 (HD108857) 35 F ν (mjy) F ν (mjy) AU, amin = 2 µm AU, amin = 12 µm 10 0 Total Model AU, amin = 3 µm AU, amin = 1.5 µm Total Model Excess F ν (mjy) Excess F ν (mjy) HIP61558 (f Vir, HD109704, HR4799) HIP63439 (HD112810) Excess F ν Outer Belt (mjy) Excess F ν Outer Belt (mjy) F ν (mjy) AU, amin = 1.7 µm AU, amin = 6 µm 10 0 Total Model Excess F ν (mjy) HIP65965 (HD117484) Excess F ν Outer Belt (mjy) F ν (mjy) AU, amin = 2.5 µm AU, amin = 2.5 µm 10 0 Total Model λ (µm) Excess F ν (mjy) λ (µm) Excess F ν Outer Belt (mjy) λ (µm) Figure 3.7: Continuation of Figure 3.4.

81 HIP66068 (HD117665) 25 F ν (mjy) AU, amin = 2.5 µm AU, amin = 2 µm 10 0 Total Model Excess F ν (mjy) HIP71271 (HD127750) Excess F ν Outer Belt (mjy) F ν (mjy) 3 5 AU, amin = 2 µm AU, amin = 6 µm 10 0 Total Model Excess F ν (mjy) HIP78641 (HD143675) Excess F ν Outer Belt (mjy) F ν (mjy) 3 4 AU, amin = 1 µm AU, amin = 2 µm 10 0 Total Model Excess F ν (mjy) HIP79797 (HD145689, HR6037) Excess F ν Outer Belt (mjy) F ν (mjy) AU, amin = 0.6 µm 5 40 AU, amin = 1.5 µm Total Model λ (µm) Excess F ν (mjy) λ (µm) Excess F ν Outer Belt (mjy) λ (µm) Figure 3.8: Continuation of Figure 3.4.

82 HIP86305 (π Ara, HD159492, HR6549) F ν (mjy) AU, amin = 2 µm AU, amin = 10 µm Total Model Excess F ν (mjy) HIP99742 (ρ Aql, HD192425, HR7724) 80 Excess F ν Outer Belt (mjy) F ν (mjy) AU, amin = 2.5 µm AU, amin = 6 µm Total Model λ (µm) Excess F ν (mjy) λ (µm) Excess F ν Outer Belt (mjy) λ (µm) Figure 3.9: Continuation of Figure 3.4. feature. Others had a strong excess at 10 µm, but its shape only differed slightly from a featureless blackbody. The majority of targets presented here do have clearly detected features, and these features vary in strength and the degree to which their signal is potentially confused by flux density from the continuum. This suggests a natural variation in these features, predicting that there should be some low-level features that could be only marginally detected. Thus, it is likely that at least some of marginally-detected features here are true detections, and we include them in our target list for completeness. 3.3 Results A Window to Terrestrial Zones Are the inner belts of these systems located in the terrestrial zones? The terrestrial zone is most easily defined in terms of an equilibrium temperature of 300 K. In Figure 3.10 we plot the equilibrium temperatures of the dust in our best-fit models versus the temperatures of the warm components found by blackbody fitting from Ballering et al. (2013) for these systems. We calculated the equilibrium temperatures ( ) 1/4 L using T eq = (278.7 K) ( r 1/2. L 1 au) Note that Teq is not the temperature of

83 83 all dust grains in the belt at r, as the temperature varies significantly with grain size, and the smallest grains are significantly hotter than T eq. From the discussion in 3.2.3, the single belt models are not plausible, either because they do not produce satisfactory fits (9 cases) or because they require belts that are so wide that they are in fact indicating the need for two belts. We computed T eq at the midpoint of the inner belt, r = (r in1 + r out1 )/2. T eq values are listed in Table 3.3. We found that the inner belts are typically nearer to their stars than predicted by blackbody fitting. Within the errors, 18/22 of the inner belts lie within the terrestrial zones of their stars; there are two cases where the belts are too hot (HIP43121, HIP79797) and two where they are too cold (HIP61049, HIP86305). It might seem surprising that disk models using realistic grain properties would predict dust belts to be nearer their stars than derived from blackbody fitting. As discussed in the Introduction, blackbody models tend to place debris disks closer to their stars than they actually are due to the presence of small, superheated grains. However, blackbody models often miss the emission features entirely (see the dashed lines in the right panels of Figure 3.1 and the center panels of Figure 3.4). The signal of an emission feature (governed by Q abs ) is modulated by a blackbody function at the dust temperature (see Equation 3.1). Thus, disk spectra that show features are more likely to host an underlying population of dust at a temperature such that its blackbody peaks around 10 µm. The spectral shape of the emission from this population of dust differs enough from a blackbody that a blackbody fitting routine is likely to ignore, rather than attempt to reproduce, the feature. From our two-belt fits, we see that the flux density from the feature-producing inner belt falls off quickly towards longer wavelengths, requiring an additional outer belt to fit the data. Because the flux density from the inner belt is concentrated around the wavelength of the feature, the outer belt must account for more of the remaining flux density than a cold component typically will when fitting with blackbodies. Indeed, the best fitting outer belt models for our targets are typically radially very broad. There may actually be three components in these systems, with dust in the terrestrial, asteroid belt, and Kuiper belt zones. Our inner belt

84 84 Inner Belt Equilibrium Temperature (K) Clear Features, 2 Blackbody Belts Clear Features, 1 Blackbody Belt Marginal Features, 2 Blackbody Belts Marginal Features, 1 Blackbody Belt Warm Blackbody Temperature (K) from Ballering et al. (2013) Figure 3.10: The equilibrium temperatures of our best fitting models versus the temperatures of the warm component blackbody fits to these targets from Ballering et al. (2013). The equilibrium temperatures are calculated at the midpoint of the inner belt. Targets with clear features are stars and those with marginal features are squares. Green points are those that Ballering et al. (2013) fit with two blackbodies and cyan points are those that (Ballering et al., 2013) fit with only one blackbody. This figure illustrates that fitting models to emission features can detect exozodiacal dust in the terrestrial zones of these systems (or even hotter zones), while the blackbody fits would find only asteroid belt zone dust.

85 85 models fit to the terrestrial zone dust, while our outer belt models accounted for all of the asteroid belt and the Kuiper belt zone dust that contributed to the IRS data. Our one-belt fits lead to a similar result: dust must be located at a wide range of radial locations, with some dust at least as close to the star as the terrestrial zone. The exact number of individual belts and the radial width of each belt cannot be determined from these data. However, the models require dust in the terrestrial zones to reproduce the emission features. Thus, the presence of these features is a useful tracer of exozodiacal dust in terrestrial zones Notes on Specific Targets Most of the debris disks in our sample are not well studied in the literature. The presence of a warm component was reported for most of these targets, but only from IRAS, MIPS, or WISE photometry. The IRS data for many of these targets were not published prior to Ballering et al. (2013). Some targets, however, have been well-studied in the past. We discuss these here, and how our discovery of emission features in their spectra fits with what was known about these systems. We also discuss notable aspects of our model fits for certain targets. HIP2578 (HD3003, HR136) An infrared excess has been known to exist around HIP2578 for some time. The excess was detected with IRAS at 25 µm (Oudmaijer et al., 1992), with MIPS at 24 and 70 µm (Smith et al., 2006), and with AKARI at 18 µm but not at 9 µm (Fujiwara et al., 2013). Smith and Wyatt (2010) detected the excess at 18 µm with ground based observations, but could not confirm an excess at 10 or 12 µm. Schütz et al. (2009) also detected no excess in an 8-13 µm spectrum obtained from the ground. At 10 µm, these ground based measurements had uncertainties roughly as large or larger than the excess flux density level we found from the IRS data; thus, the ground based observations are consistent with our results. The IRS spectrum was previously published by Zuckerman et al. (2011) and by Donaldson et al. (2012). Donaldson et al. (2012) fit these data and Herschel PACS photometry for this target with a single broad belt extending from 7.8 to 120 au and a minimum grain size of 3.5 µm. This fit also required an unusually

86 86 steep grain size distribution with p=4.4. They noted no signs of emission features in the IRS spectrum. Ballering et al. (2013) fit the IRS and MIPS data with a single blackbody of temperature 194 K, while Chen et al. (2014) fit these data with two blackbodies at 472 and 173 K. Our inner belt location of au is consistent with the < 6.5 au constraint from (unresolved) images by Smith and Wyatt (2010), although both our fits require an outer population of cold dust as well. HIP2578 may be a binary system of two A stars separated by 0. 1 (4.6 au), measured in 1925 and 1964 (Dommanget and Nys, 1994; Mason et al., 2001). Eggleton and Tokovinin (2008) report that HIP2578 is part of a 6 component system consisting of a wide hierarchical triple of three close binaries. The binarity of this system could impact both the heating and orbital stability of the debris disk. A detailed consideration of these factors is beyond the scope of this chapter. HIP26966 (HD38206, HR1975) The mid-ir excess around HIP26966 was detected by both IRAS (Mannings and Barlow, 1998) and MIPS (Rieke et al., 2005; Su et al., 2006). The IRS data have been published several times (Morales et al., 2009, 2011; Zuckerman et al., 2011; Ballering et al., 2013; Chen et al., 2014), but the presence of a 10 µm emission feature has not been previously discussed. Smith and Wyatt (2010) did not detect an excess at 10 µm with ground based observations. Moerchen et al. (2010) also performed ground-based observations, detecting excess at 18.3 µm but not at 10.4 µm. Their results are consistent with our measurements, but their uncertainties at 10.4 µm were too large to claim a significant excess detection. The 18.3 µm images of Moerchen et al. (2010) were not spatially resolved, constraining the radius of the disk to <10.8 au, which is consistent with our inner belt extending to 4 au (nearly all of the excess flux density at 18.3 µm is emanating from the inner belt in our model). No circumstellar dust was detected around this target in scattered light with HST (Krist et al., 2010). HIP27288 (ζ Lep, HD38678, HR1998) HIP27288 has long been known to host a warm debris disk. The mid-ir excess was detected by IRAS (Cote, 1987; Aumann and Probst, 1991; Mannings and Barlow, 1998), ISO (Habing et al., 2001), MIPS (Rieke et al., 2005; Su et al., 2006), and a number of ground-based instruments

87 87 (Fajardo-Acosta et al., 1998; Chen and Jura, 2001; Jayawardhana et al., 2001; Schütz et al., 2005). Wyatt et al. (2007b) noted that this excess is unusually bright for a system of its age, suggesting that this dust may be transient. No evidence for a very hot dust component was seen from near-ir interferometric observations (Absil et al., 2013). Chen et al. (2006) fit the IRS excess with a single 190 K blackbody, and noted no signs of emission features. This disk was also spatially resolved by ground-based observations at 18.3 µm, locating the disk at 3 au with some emission extending out to 8 au (Moerchen et al., 2007). Our inner belt (5-6 au) is consistent with these results. Our models do differ significantly from the literature in that we include outer dust as well in the form of an outer belt in our two-belt model, or out to 40 au in our one-belt model. There is clearly some structure in the IRS data at 10 µm, but we classify the detection of a feature in this spectrum as marginal because this structure has a less peaked shape than features seen in other targets. If there is only one belt, then this structure must be the result of an emission feature. On the other hand, the structure could be the result of overlapping emission from multiple belts. A single blackbody model, however, is not a good fit to these data. HIP43121 (50 Cnc, HD74873, HR3481) The debris disk around HIP43121 has not been particularly well studied in the literature. However, the IRS data were published by Morales et al. (2009) and Morales et al. (2011). Both of these studies fit the excess with a single blackbody function at 190 K, but a footnote in Morales et al. (2009) remarked that there were hints of a 10 µm feature in the data. HIP58220 (HD103703) While fitting two-belt models to this target, we discovered a degeneracy in terms of which belt produced the majority of the 10 µm feature. Both local minima in parameter space produced fits with nearly identical χ 2. The model we present in Figure 3.4 relied on the inner belt to reproduce the feature while the outer belt resembled a nearly-smooth continuum, as was the case for most of our targets. In the alternative model, a broad outer belt with a small minimum grain size contributed significantly to the 10 µm feature while the inner belt with only larger grains provided primarily continuum. The parameters for this second case were: a min1 = 6 µm, r in1 = 0.8 au, r out1 = 1 au,

88 88 M dust1 = M, L belt1 /L = , a min2 = 1 µm, r in2 = 1 au, r out2 = 100 au, M dust2 = M, and L belt2 /L = HIP61049 (HD108857) Like HIP58220, this target also exhibited a degeneracy in terms of which belt produced the emission feature. In Figure 3.4 we show the fit where the inner belt could reproduce the entirety of the data with no need for an outer belt. In the other fit, the outer belt contributed significantly to the spectrum, including to the emission feature, due to having a smaller minimum grain size than the inner belt. The parameters of this fit were: a min1 = 5 µm, r in1 = 0.7 au, r out1 = 0.8 au, M dust1 = M, L belt1 /L = , a min2 = 1.7 µm, r in2 = 4 au, r out2 = 7 au, M dust2 = M, and L belt2 /L = HIP79797 (HD145689, HR6037) Zuckerman et al. (2011) fit the MIPS and IRS excess with a 220 K blackbody, but did not mention any emission feature. The noteworthy aspect of this system is that the primary star is orbited at a projected separation of 350 au by a binary system of brown dwarfs, separated from each other by 3 au (Huélamo et al., 2010; Nielsen et al., 2013). HIP86305 (π Ara, HD159492, HR6549) Excess emission was first detected around HIP86305 with IRAS (Cheng et al., 1992; Mannings and Barlow, 1998). No circumstellar dust was seen in scattered light with HST (Doering et al., 2007). Morales et al. (2009) and Morales et al. (2011) fit blackbodies to the IRS excess and found a warm component temperature of 160 K, well outside of the terrestrial zone, although Morales et al. (2009) noted that there may be signs of a faint spectral feature in the data. Morales et al. (2013) resolved the outer edge of the outer belt with Herschel (116 au) and reanalyzed the IRS data, incorporating the constraint from Herschel, and using physically-motivated belt models that could reproduce the structure in the IRS spectrum. They found an inner belt location of 9.1 or 9.8 au, depending on the grain composition, which falls between the inner and outer edges of our best fit inner belt model. The analysis of Morales et al. (2013) required grains three or four times smaller than the blowout size (requiring a min 1 µm), whereas we found a min1 consistent with the blowout size for this system (we found a larger minimum grain size and a slightly lower blowout size). Morales et al. (2013) used

89 Clear Features Marginal Features Inner Belt Minimum Grain Size (µm) Blowout Size (µm) Figure 3.11: This figure shows that a min is consistent with a BOS for our targets. Stars are targets with clear features and squares are those with marginal features. The bounding trend lines show the effect of varying a BOS by a factor of two (e.g., due to more complex grain structure). Low-level silicate emission features can arise in debris disk spectra, even when grains are not below the blowout size.

90 90 a lower value for the stellar luminosity ( 10 L ) and different grain compositions, which may have contributed to the discrepancy with our results. Furthermore, neither we nor Morales et al. (2013) could reproduce all of the structure seen in the IRS data, which may arise from crystalline grains. 3.4 Discussion Our analysis shows that a significant number of debris disks with excesses in the mid- IR exhibit low-level silicate emission features, indicating the presence of exozodiacal dust in their terrestrial zones. In this section we compare properties of these systems with others that host featureless warm debris disks, and we discuss potential sources for this exozodiacal dust. Dust produced by a steady state collisional cascade of planetesimals is expected to have a minimum grain size set by the blowout size of the system. Dust smaller than this size will be removed from the system by the star s radiation pressure. The presence of grains smaller than the blowout size could indicate that a large amount of dust was produced recently, such as in a massive collision. If the smallest grains were found to be significantly larger than the blowout size, then there might be other forces acting to remove small grains such as interactions with the ISM. We calculated the blowout size for each of our targets using Equation 5 of Donaldson et al. (2012): ( ) ( ) 1 ( ) 1 L M ρ a BOS = (1.15 µm) L M 1 g cm 3, (3.8) where ρ is the density of the grain material (we assumed ρ = 3.71 g cm 3 ). The results for our targets are given in Tables 3.2 and 3.3. In Figure 3.11 we plot the minimum grain size of the inner belt of the two-belt models versus the blowout size for the targets. We see that the minimum grain size does track the blowout size, suggesting that these systems are not being influenced by rare or extreme circumstances. Equation 3.8 assumes grains are solid spherical particles. Real grains may have more complex structures, so a BOS is likely only accurate to within a factor of 2.

91 91 B5 A0 Clear Features Marginal Features Without Features A5 Stellar Type F0 F5 G0 G5 K0 K Age (Myr) Figure 3.12: The stellar type and age for targets with clear features (green stars), marginal features (green squares), and no features (gray circles). The properties of the targets with no features are from Ballering et al. (2013). This illustrates that features can be used to probe the terrestrial regions of young planetary systems over a range of stellar types, and also for older planetary systems of early type stars. Note that there are actually three 30 Myr-old A0 targets with clear features and two 20 Myr-old A0 targets with marginal features in our sample.

92 92 We next investigated the age and stellar type of targets that exhibited features, as shown in Figure The gray points are systems with warm disks from the sample of Ballering et al. (2013) that did not show any features. For targets with no age determination in Ballering et al. (2013), we found age values from Nielsen et al. (2013), Zorec and Royer (2012), and Chen et al. (2014), as we did for the targets with features (see 3.2.1). In Figures 3.13 and 3.14 we show the fraction of warm debris disks that exhibit features, binned by stellar type and by age. We find that many of the disks with features are young ( Myr), but that there is a significant number of older disks (hundreds of Myr) that also have features. Young disks with features have stellar types spanning the range of the parent sample (late B through F), while the only older disks that show features are the early to mid A types. While the presence of features does not appear uniform across all stellar types and ages, it is clear that analyzing features in debris disks can provide a means to study the terrestrial zones of planetary systems with a large range of stellar types and ages. Disks with clear features and with marginal features are distributed in approximately the same way by stellar type and age, lending further evidence to the notion that there is natural variation in feature strengths for systems with dust in their terrestrial zones. Are features preferentially found in bright debris disks? In Figure 3.15 we plot the fractional luminosity of the mid-ir excess of these systems versus age. The gray points are again warm disks from Ballering et al. (2013) that do not show signs of features. The fractional luminosity values in this plot are not the same values as given in Tables 3.2 and 3.3. As discussed in and illustrated in Figures 3.1 and 3.4, the models we used in this chapter fit the IRS data differently than did the one or two blackbody functions used by Ballering et al. (2013). We did not have acceptable one-belt fits for all targets in this chapter, nor is it appropriate to compare the brightness of just our inner (outer) belt with the warm (cold) component from blackbody fitting, since the two fits in the two studies are constrained by different wavelength ranges. Comparing the total fractional luminosities of all components would also not be a valid comparison, as Ballering et al. (2013) included MIPS 70

93 93 Fraction of Warm Belts with Features Clear Features Marginal Features Total 0 B5 A0 A5 F0 F5 G0 G5 K0 K5 Stellar Type Figure 3.13: The fraction of warm debris disks showing features in bins of stellar type. The fraction with clear features is in green, the fraction with marginal features is in magenta, and the total (the sum of green and magenta) is in black. Note that the fractions with clear and with marginal features are consistent with each other in their variation with stellar type.

94 94 Fraction of Warm Belts with Features Clear Features Marginal Features Total Figure 3.14: The fraction of warm debris disks showing features in bins of system age. The fraction with clear features is in green, the fraction with marginal features is in magenta, and the total (the sum of green and magenta) is in black. Features are found around both young and older systems. Note that the fractions with clear and with marginal features are consistent with each other in their variation with age. The sharp spike at Myr and minimum at Myr may be a result of small number statistics, as there are few total warm disks in this age range. Age

95 95 µm data in the fitting and so were sensitive to a significant amount of cold dust that was not measured in this study. To properly compare these two samples, we calculated the luminosity of the total model (inner + outer belts using our two-belt models; one or two blackbodies) using Equation 3.7, but only over the wavelength range from 1 to 30 µm. Figure 3.15 shows that targets with features (either clear or marginal) are not extraordinary in terms of the brightness of their mid-ir excess. This suggests that the detection of features is not a selection effect limited to very bright disks. Some planetary systems have a detectable population of dust in their terrestrial zones while others have significantly less dust in this region, but otherwise the systems with features and without features are quite similar. What is the source of exozodiacal dust? There could be a belt of parent body planetesimals in the terrestrial zone undergoing a collisional cascade and producing the dust. This model can explain most standard debris disks with dust in the asteroid belt or Kuiper belt zones, although debris disks on smaller orbits are expected to grind down and dissipate on much shorter timescales. Kennedy and Wyatt (2013) investigated the possibility of in situ dust production to explain the detection of excesses at 12 µm with WISE photometry, which they interpreted as emission from exozodiacal dust. As in this study, they found that most systems with exozodiacal dust were young, but that some older systems had 12 µm excess as well. They could reproduce this finding by assuming that all systems start with a population of parent bodies in this zone that steadily collide and decay with time (this explains the young systems), but additionally there are occasional random collisions between the remaining parent bodies, as required to explain the exozodiacal dust in the older systems. Another possibility is that the dust was produced farther out and migrated inwards via Poynting-Robertson (PR) drag or other drag forces. Theoretical studies find that the interaction of PR drag and dust sublimation can create a population of dust extending inwards from the parent body belt where the dust is created to the sublimation radius (Kobayashi et al., 2008; van Lieshout et al., 2014).

96 Clear Features Marginal Features Without Features Fractional Luminosity (1 30 microns) Age (Myr) Figure 3.15: The fractional luminosity (of the infrared excess from 1 to 30 µm) and age of targets with clear features (green stars), marginal features (green squares), and no features (gray circles). The properties of the targets with no features are from Ballering et al. (2013). The overall decrease in disk brightness is well-known from previous debris disk studies. We see that the fractional luminosities of disks with features (clear or marginal) are consistent with those of featureless disks.

97 97 Exozodiacal debris could also be delivered to terrestrial zones by planetesimals scattered inwards from an outer belt. Bonsor et al. (2012) modelled this scenario and found that a chain of closely packed planets is required to move material inwards effectively. Furthermore, for older systems the outer belt must be located at a large orbital radius such that it can be massive enough to deliver sufficient material inwards without quickly grinding itself down. The inward scattering of planetesimals can occur at a higher rate and be sustained for a longer time period if the outermost planet is actively migrating outwards into the planetesimal belt (Bonsor et al., 2014). The efficiency of this mechanism depends sensitively on the number, locations, and masses of the planets in the chain, and on the properties of the planetesimal belt. If this mechanism is the dominant source of the exozodiacal dust, the detection of silicate emission features also implies that these targets host rich planetary systems. A dynamical instability in a planetary system can also deliver planetesimals to the terrestrial region. In this case, planets scatter each other, destabilizing their orbits and scattering many planetesimals. Bonsor et al. (2013) simulated such events and found that their signals are short-lived ( Myr). Detecting a significant number of systems that recently underwent a dynamical instability is unlikely, and this mechanism cannot be the dominant source of exozodiacal dust. Exozodiacal dust may be the byproduct of collisions associated with the final, chaotic stage of terrestrial planet formation. Jackson and Wyatt (2012) modeled the dust production from such a collision (analogous to our Moon-forming impact) and found that, after an initial spike in infrared excess from vapor condensates, a low but detectable amount of debris can persist in the terrestrial regions for at least 1 Myr and often longer than 10 Myr. Each terrestrial planet undergoes multiple giant impacts during the chaotic phase of its formation. Terrestrial planet formation is expected to have finished once the system reaches an age of 100 Myr, so this explanation is plausible for the younger targets in our sample, but not for the older systems. Our targets potentially represent a different source of exozodiacal dust than the debris disks with previously studied features listed in 3.1. The excesses in those

98 98 systems tend to be anomalously bright, and the emission features are often very strong. Those systems may have very recently experienced massive collisions such that transient populations of dust (e.g. vapor condensates) are still present. These massive collisions may be part of the terrestrial planet formation process (for the younger systems) or from periods of dynamical instability. 3.5 Conclusions In summary, we found low-level silicate emission features in the IRS spectra of 22 warm debris disks that were previously studied by Ballering et al. (2013). 13 of these had clearly detected features, while 9 were only marginally detected. We fit these data with physically-motivated models, allowing us to constrain the radial locations and minimum grain sizes of the dust belts more precisely than was possible when fitting with blackbodies. Our fits place dust in the terrestrial zones of these targets, which was missed when these data were fit with only blackbody functions. An outer population of dust was also required to fit the data. The minimum grain sizes of the terrestrial zone dust were consistent with the blowout sizes of these systems, and the mid-ir fractional luminosities of debris disks with features were comparable to those of warm debris disks without features, implying that disks with features are normal. The properties of systems with marginally detected features were distributed almost identically as those of systems with clear features, suggesting that many of the marginal cases are likely true emission features. We found systems with features at a range of stellar types and ages (although no features were found around older, later type stars). The analysis of emission features in the spectra of unresolved debris disks provides a powerful method to probe the terrestrial zones of planetary systems at various stages of their evolution. These results will complement mid-ir interferometric studies of exozodiacal dust, allowing for the robust characterization of regions of planetary systems that have, until now, remained largely out of reach.

99 99 Table 3.1. Target Properties HIP Other Spectral D Age Age a Age T L R M V K Fν(24 µm) IRS Identifier Identifiers Type (pc) (Myr) Qual Refs (K) (L ) (R ) M (mag) (mag) (mjy) AOR HIP2578 HD3003, HR136 A0V , ± HIP18437 HD24966 A0V ± HIP26395 HD37306, HR1919 A2V ± HIP26966 HD38206, HR1975 A0V , ± HIP27288 ζ Lep, HD38678, HR1998 A2IV-Vn: ± HIP41081 HD71043, HR3300 A0V ± HIP Cnc, HD74873, HR3481 A1V ± HIP57971 HD103266, HR4553 A2V ± HIP58220 HD F3V ± HIP58528 HD F5V ± HIP Crv, HD105850, HR4635 A1V ± HIP60561 HD A0V ± HIP61049 HD F7V ± HIP61558 f Vir, HD109704, HR4799 A3V ± HIP63439 HD F4IV/V ± HIP65965 HD B9V ± HIP66068 HD A1/A2V ± HIP71271 HD A0V ± HIP78641 HD A5IV/V ± HIP79797 HD145689, HR6037 A4V ± HIP86305 π Ara, HD159492, HR6549 A5IV-V ± HIP99742 ρ Aql, HD192425, HR7724 A2V ± a 1 means there was a single age determination, 2 means there were two independent and consistent age determinations. References. (1) Vican (2012) isochrone ages; (2) Rhee et al. (2007b); (3) Su et al. (2006); (4) Tetzlaff et al. (2010); (5) Rizzuto et al. (2011); (6) Hoogerwerf (2000); (7) Zuckerman and Song (2004); (8) Nielsen et al. (2013); (9) Zorec and Royer (2012); (10) Chen et al. (2014).

100 100 Table 3.2. One Belt Fitting Results HIP Other a BOS a min r in r out M dust L belt /L Feature Identifier Identifiers (µm) (µm) (au) (au) ( 10 5 M ) ( 10 5 ) Detection HIP2578 HD3003, HR clear HIP27288 ζ Lep, HD38678, HR marginal HIP Cnc, HD74873, HR clear HIP57971 HD103266, HR marginal HIP58220 HD clear HIP58528 HD clear HIP Crv, HD105850, HR clear HIP61049 HD clear HIP66068 HD clear HIP78641 HD clear HIP79797 HD145689, HR clear HIP86305 π Ara, HD159492, HR clear HIP99742 ρ Aql, HD192425, HR marginal Note. a BOS is the blowout size for grains in the system, calculated from Equation 3.8. a min is the minimum grain size of our best-fit model. r in and r out are the inner and outer orbital radii of our best-fit model, respectively. M dust is the total mass of dust (in grains from a min to 1000 µm) of our best-fit model. L belt /L is the fractional luminosity of our best fit model, with L belt calculated from Equation 3.7. The final column notes whether the detection of features was clear or marginal, as discussed in

101 101 Table 3.3. Two Belt Fitting Results: Inner Belt Properties HIP Other abos amin1 rin1 rout1 Teq Mdust1 Lbelt1/L Feature Identifier Identifiers (µm) (µm) (au) (au) (K) ( 10 5 M ) ( 10 5 ) Detection HIP2578 HD3003, HR clear HIP18437 HD marginal HIP26395 HD37306, HR clear HIP26966 HD38206, HR clear HIP27288 ζ Lep, HD38678, HR marginal HIP41081 HD71043, HR clear HIP Cnc, HD74873, HR clear HIP57971 HD103266, HR marginal HIP58220 HD clear HIP58528 HD clear HIP Crv, HD105850, HR clear HIP60561 HD marginal HIP61049 HD clear HIP61558 f Vir, HD109704, HR marginal HIP63439 HD marginal HIP65965 HD marginal HIP66068 HD clear HIP71271 HD marginal HIP78641 HD clear HIP79797 HD145689, HR clear HIP86305 π Ara, HD159492, HR clear HIP99742 ρ Aql, HD192425, HR marginal Note. abos is the blowout size for grains in the system, calculated from Equation 3.8. amin1 is the minimum grain size of our best-fit model s inner belt. rin1 and rout1 are the inner and outer orbital radii of our best-fit model s inner belt, respectively. Teq is the equilibrium temperature at the midpoint of our best-fit model s inner belt. Mdust1 is the total mass of dust (in grains from amin to 1000 µm) of our best-fit model s inner belt. Lbelt1/L is the fractional luminosity of our best fit model s inner belt, with Lbelt calculated from Equation 3.7. The final column notes whether the detection of features was clear or marginal, as discussed in

102 102 CHAPTER 4 WHAT SETS THE RADIAL LOCATIONS OF WARM DEBRIS DISKS? The architectures of debris disks encode the history of planet formation in these systems. Studies of debris disks via their spectral energy distributions (SEDs) have found infrared excesses arising from cold dust, warm dust, or a combination of the two. The cold outer belts of many systems have been imaged, facilitating their study in great detail. Far less is known about the warm components, including the origin of the dust. If the dust is generated from collisions in an exo-asteroid belt, the dust is expected to trace the location of the water snow line in the primordial protoplanetary disk. If, instead, the dust arises from the inward transport of material from a reservoir of cold, icy material farther out in the system, the dust location is expected to be set by the current snow line. The snow line location vs. stellar mass relation differs between the primordial and current snow lines, providing a means to differentiate between the two. Here we analyze the SEDs of a large sample of debris disks with warm components. We find that warm components in single-component systems (those without cold components) follow the primordial snow line rather than the current snow line, so they likely arise from exo-asteroid belts. While many warm components in two-component systems also follow the primordial snow line, there is more diversity in their locations, suggesting additional effects also play a role in these systems. 4.1 Introduction A debris disk is the remnant population of circumstellar planetesimals and the dust generated by the collisional destruction of these planetesimals. While observations of protoplanetary disks show planetary systems in the early stages of formation, debris disks reveal the properties of more mature systems. The spatial structure of

103 103 a debris disk traces the architecture of the planetary system because planets remove planetesimals from their vicinity. However, dust grains, the observable component of a debris disk, can move from the location of their production by various processes. The interpretation of the observations involves connecting the properties of the dust to those of the unseen planetesimals and planets. For recent reviews of debris disk science, see Wyatt (2008); Matthews et al. (2014b). Hundreds of spatially unresolved debris disks have been characterized by the infrared excess evident in their systems SEDs the thermal emission from the debris disk dust. This excess typically takes the form of a cold component ( 130 K), a warm component ( 190 K), or both (Morales et al., 2011; Ballering et al., 2013; Chen et al., 2014). 1 Kennedy and Wyatt (2014) concluded that for most systems the warm and cold components arise from radially distinct distributions of dust (as opposed to being co-located and having different temperatures due to different grain properties). The cold components are the best-studied parts of debris disk systems. They reside far enough (i.e. > tens of au) from their host star that some have been imaged, revealing a belt where dust is produced by collisions of parent body planetesimals analogous to the Kuiper belt in the solar system. The nature of the warm components is less certain, as they are expected to reside closer to the star and cannot easily be spatially resolved. For example, the nearby (7.7 pc) star Fomalhaut hosts a well-studied cold belt that has been imaged at several wavelengths (Kalas et al., 2005; Acke et al., 2012; Boley et al., 2012). From an analysis of its SED, Fomalhaut also hosts a warm component (Stapelfeldt et al., 2004; Su et al., 2013), but obtaining resolved images of this warm component to confirm its properties remains difficult (Su et al., 2016). In this study, we aim to draw conclusions about warm 1 Su and Rieke (2014) identified five dust components that a debris disk can posses, which, in addition to the warm and cold components described here, also include: a blowout halo of small grains outside of the cold belt (Augereau et al., 2001; Su et al., 2005); exozodiacal dust that is hotter and nearer to the star than the warm dust and emits at 10 µm (Kennedy and Wyatt, 2013; Ballering et al., 2014); and very hot dust emitting in the near-ir (Absil et al., 2013; Ertel et al., 2014) likely composed of nanograins trapped in the star s magnetic field (Rieke et al., 2016).

104 104 components by analyzing the SEDs of a large sample of sources and examining how their properties vary with the properties of their host stars. The origin of the warm dust is not known, but there are two general hypotheses: 1) the dust is produced in-situ by the collisional processing of a belt of parent bodies analogous to the asteroid belt in the solar system, or 2) the dust is transported inwards from the outer reservoir of cold planetesimals. As we will describe below, both of these possibilities predict that the locations of warm components will be set by the snow line (i.e. where water ice condensation/sublimation occurs). However, these hypotheses differ as to whether it is the primordial snow line or the current snow line that sets the warm dust location. These two snow lines predict different relations between the location of the warm dust and the mass of the host star. By examining the observed relation between warm dust locations and stellar mass, we can determine which snow line (primordial or current) was responsible for setting the dust locations, and thus which theory for the origin of the dust is favored. If the warm dust is produced in-situ, it is expected to occur near the primordial snow line because planetesimals are expected to preferentially form there. This is due to a local gas pressure maximum in the primordial protoplanetary disk near the snow line. This acts to trap inward migrating solids and reduce their collisional velocities, thus promoting the growth of larger particles (Kretke and Lin, 2007; Brauer et al., 2008). If planetesimal formation is inefficient in the disk overall, then the planetesimals formed at the snow line may become the belt of parent bodies that give rise to the warm excess. If, however, planetesimal formation is generally efficient throughout the disk, the boost in planetesimal formation at the snow line may lead to the formation of a giant planet in this vicinity. This planet will then stir the residual planetesimals interior to its orbit, preventing them from coalescing into a planet. This is similar to how the gravitational influence of Jupiter stirs the asteroid belt in the solar system (e.g. Petit et al., 2001). The stirred population of residual planetesimals would then serve as the parent bodies for the warm dust. If, instead, the warm dust is transported inwards from an outer reservoir, it is expected to pile up at the current snow line. There are two plausible mechanisms

105 105 for the inward transport. The first mechanism is analogous to that described by Nesvorný et al. (2010), who found that most of the warm dust in the inner region of the solar system originates from the disruption of Jupiter family comets. planetesimals originating in the cold belt become trapped in roughly-circular orbits by planets located just outside of the snow line (the region between the snow line and the cold belt may be maintained by one or more planets (Su et al., 2013)). Perturbations to these planetesimals increase their eccentricity, causing their orbits to cross the snow line where they begin to sublimate and eventually disintegrate, releasing dust. For the second mechanism, dust generated by collisions in the outer parent body belt flows inwards due to Poyting-Robertson (P-R) drag or stellar wind drag. While Wyatt (2005) argued that most disks we can detect are collision-dominated rather than drag-dominated (that is, grains are destroyed by mutual collisions faster than they can move inwards), Kennedy and Piette (2015) noted that some inward transport is inevitable unless planets are present interior to the cold belt to remove the inflowing dust. Since these grains originate in the outer part of the system, they may contain a mixture of icy and refractory material. When the grains reach the snow line the ices sublimate, reducing the grain size and consequently increasing the ratio of the radiation force to the gravitational force on the grain (β). This halts the grain s inward motion and eventually causes it to be expelled outwards. The net result is a pile-up of grains at the location of the snow line (Kobayashi et al., 2008). The location of the current snow line is determined by the incident stellar flux, so its location scales as r SL L 1/2. Combining this with L M 4, the typical relation between stellar luminosity and mass, yields r SL M 2. The temperature in the midplane of a protoplanetary disk is set primarily by viscous heating, rather than stellar flux, so the relation between the primordial snow line location and stellar mass differs from the current snow line relation. Min et al. (2011) give the following relation for the location of the primordial snow line: r SL M 1/3 Ṁ 4/9 κ R 2/9 f 2/9 α 2/9 T ice 10/9, (4.1) Icy

106 106 where Ṁ is the mass accretion rate, κ R is the Rosseland mean opacity, f is the gas-to-dust ratio, α is the turbulent mixing strength, and T ice is the ice sublimation temperature. Of these parameters, only Ṁ is believed to vary significantly with stellar mass and thus is relevant for estimating the form of the r SL M relation. The mass accretion rate has been found to vary with stellar mass as Ṁ M 2 over a large range of stellar masses, including the masses of the stars in our sample (Calvet et al., 2004; Muzerolle et al., 2005; Natta et al., 2006). This implies that r SL M 1.2, so the primordial snow line relation is shallower than the current snow line relation. Other investigations into the location of the primordial snow line also find the r SL M relation to be significantly shallower than the current snow line relation (Kennedy and Kenyon, 2008; Martin and Livio, 2013). Some observational evidence points to the association between warm disks and snow lines. Morales et al. (2011) found that warm disks tend to have a similar temperature ( 190 K), independent of stellar type. This suggests that the locations of the warm components are not set randomly, but by a temperature-dependent effect such as the snow-line. Kennedy and Wyatt (2014), in contrast, found that warm components tend to have somewhat higher temperatures around higher mass stars than around lower mass stars. Nevertheless, these results compared the observed dust temperature with the stellar properties, whereas it is the dust location that must be compared against stellar mass in order to distinguish between the two possible snow lines (current or primordial). The dust temperature depends on both the grain size and location, so inferring the dust location from the observed SED requires accounting for the grain size, which is expected to vary systematically with stellar type. In this chapter we analyze the SEDs of a sample of debris disks with warm components. To infer the warm dust stellocentric location in each system, we fit the SED with a model of the dust belt emission that properly accounts for the variation in the minimum grain size with stellar properties. We then examine the r dust M relation to gain insight into which snow line likely sets the dust location, and thus what is the origin of the warm components.

107 Methods Target Selection For our sample, we used the systems with a warm component found by Ballering et al. (2013). We separated the systems with only a warm component from those that also possess a cold component. The systems without a cold component should provide less ambiguous results, since these warm components could not arise from inward flowing particles from the cold belt. Ballering et al. (2014) discovered silicate emission features in Spitzer Infrared Spectrograph (IRS; Houck et al., 2004) spectra of 22 of these systems. These features revealed the presence of exozodiacal dust, which is believed to arise from a different location than the typical warm component. Ballering et al. (2014) found that, besides the exozodiacal dust, an additional colder component was also required to fit the full IRS spectra of these sources. Whether this remaining excess consists of one or of multiple components is difficult to determine. Thus, to ensure a pure sample of warm components, we excluded these 22 targets. We also excluded HIP because the IRS data may have been contaminated by background galaxies (Donaldson et al., 2012). We removed additional targets in the course of our fitting procedure, as described in Section The remaining 83 targets used for our analysis are listed in Table D.1. The stellar temperature (T ), luminosity (L ) and distance from Earth (D) of most of our targets are taken from McDonald et al. (2012), who derived T and L by fitting the visible and near-ir photometry of these systems with stellar SED models. We then obtained the stellar mass (M ) from L using the (broken) power law relation by Eker et al. (2015). For the targets not listed in McDonald et al. (2012) (denoted with an a after the target name in Table D.1), we inferred their stellar properties from their V-K color using the tabulated values maintained online 2 by E. Mamajek as an expanded and updated version of Table 5 in Pecaut and Mamajek (2013). 2

108 108 We required a model spectrum of the stellar photosphere for each of our targets, both for modeling the photospheric contribution to the observed SED and for calculating the temperature of dust grains when generating model spectra of the dust emission. We used an ATLAS9 (Castelli and Kurucz, 2004) photosphere model with log g = 4.0, solar metallicity, and T closest to that for each target. These spectra were modeled only out to 160 µm, so we extended them to 10,000 µm by extrapolating with a Rayleigh-Jeans power-law. We normalized the integrated spectra to L for each target (although during the fitting process we allowed the amplitude of the model photosphere to vary, see Section 4.2.5) IRS Data While many infrared excesses have been identified from photometric measurements alone (Rieke et al., 2005; Su et al., 2006; Wyatt, 2008; Sierchio et al., 2014; Matthews et al., 2014b), accurately measuring the temperature/location of the emitting dust requires the denser spectral coverage offered by IRS. We obtained low-resolution IRS spectra for our targets from the LR7 release of the Cornell AtlaS of Spitzer/IRS Sources 3 (CASSIS; Lebouteiller et al., 2011). Both LL orders were available for all targets, with one or both of the SL orders also available for most of the targets. The IRS Astronomical Observation Requests numbers (AORs) for our targets are given in Table D.1. We removed outlying points more than 3σ away from a third-degree polynomial fit to each spectral order. To remove offsets between orders, we multiplied the LL1, SL1, and SL2 flux density values by correction factors (determined by eye) to align them with the LL2 order and to each other. The choice to pin the other orders to LL2 was arbitrary but had no effect on the results because, as described in Section 4.2.5, the amplitude of the whole IRS spectrum was varied as part of the fitting process. These correction factors (designated x LL1, x SL1, and x SL2 ) are listed in Table D.1. During this process we opted to remove HIP from our sample 3 The Cornell Atlas of Spitzer/IRS Sources (CASSIS) is a product of the Infrared Science Center at Cornell University, supported by NASA and JPL.

109 109 because the offsets between the orders were much greater than for any other target, suggesting the data may be unreliable IR and Sub-mm Photometry In addition to the IRS data, we included in our SEDs photometry from MIPS at 24 and 70 µm plus additional photometry at wavelengths 70 µm from the literature. These data are listed in Table D.2. Upper limits are at the 3σ level Modeling dust emission The radial distribution of dust in the disk was modeled as a power law in both location (stellocentric distance r) and grain size (grain radius of a) as n(r, a) r p a q, where n(r, a) is the volume number density. The dust radial distribution was bounded by r in and r out, and the grain size distribution was bounded by a min and a max. The only parameter of the dust model varied in the fitting was r in. We assumed the dust belt was a narrow ring with r out = r in + 2 au. p was fixed to 2, but this choice had little effect on the resulting SED for a narrow ring. We also assumed the dust distribution was wedge-shaped with a constant opening angle, meaning the surface number density varied as Σ(r) r 1. We also fixed q = 3.65, as suggested by Gáspár et al. (2012), and a max = 1000 µm; the flux emitted from grains larger than this size is negligible. The choice of a min can have a substantial effect on the derived dust location, with a smaller value of a min leading to a larger inferred r in. We fixed a min = a BOS, the predicted blowout size for each system. This choice is justified theoretically and also empirically, e.g. detailed fits to debris disk spectra exhibiting silicate emission features were able to constrain both the dust location and minimum grain size; these fits showed the minimum spherical grain size to be consistent with the blowout size (Ballering et al., 2014). a BOS is the largest grain size for which β > 0.5, where β is the ratio of the

110 110 radiation force to the gravitational force on a grain. β is given by β = 3L 16πGM acρ Q 0 pr (λ, a)f λ (λ) dλ, (4.2) F 0 λ (λ) dλ where ρ is the grain density and Q pr (λ, a) is the radiation pressure efficiency of the grain. a BOS for each target is given in Table D.1. For the composition of the dust, we used a mixture of 60% astronomical silicates and 40% organics refractory material (by volume), as found by fitting the brightness of the β Pictoris debris disk simultaneously in both thermal emission and scattered light (Ballering et al., 2016). This composition has a mean density of ρ = 2.34 g cm 3 (2.7 g cm 3 for the astronomical silicates and 1.8 g cm 3 for the organic refractory material). The optical constants of this mixture are given in Table 3 of Ballering et al. (2016). We computed Q pr (λ, a) and the absorption efficiency, Q abs (λ, a), from the optical constants using the Mie theory code miex (Wolf and Voshchinnikov, 2004). (We also repeated the entire analysis using a composition of 100% astronomical silicates and arrived at the same general conclusions, so the specific choice of optical constants did not have a large effect). To compute the model dust emission, we needed the temperature of the grains as a function of their radial location and size. We calculated this by computing r(t dust, a) = 1 Qabs (λ, a)l λ (λ) dλ (4.3) 4π Qabs (λ, a)b λ (λ, T dust ) dλ then inverting it to solve for T dust (r, a). Equation 4.3 is derived from balancing the heating and cooling power on the grain. Finally, we calculated the emission spectrum from each grain, ( a ) 2 F ν (λ, r, a) = Qabs (λ, a)πb ν (λ, T dust ), (4.4) D and combined these spectra into a single spectrum according to the model s n(r, a) Fitting Models to the Observed SEDs We fit the observed SED of each target (including photometric points at V, J, H, and K, the IRS spectrum, and the additional photometry listed in Table D.2) with

111 111 a model photosphere (see Section 4.2.1) plus three different models for the excess: a single modified blackbody (to double check for single-cold-component systems), a single dust belt, and a dust belt plus a modified blackbody to fit the cold component. One free parameter in all of the fits was the amplitude of the photosphere, which we allowed to vary from the amplitude determined by the star s luminosity and distance. Another free parameter was an amplitude adjustment to the IRS data (c IRS ), which we allowed to take values between 0.8 and 1.2. This effectively corrected any systematic calibration error of the IRS data in the fitting process. This procedure yielded good results with c IRS constrained at two points: first, the short end of the IRS data needed to match the photosphere model, which in turn had to match the visible/near-ir photometry; second, the IRS data needed to match the MIPS photometry point at 24 µm in order for the best fit model to pass through both the MIPS and IRS data at this wavelength. For the modified blackbody, we followed the formulation used by Kennedy and Wyatt (2014): F ν (λ) = c BB B ν (λ, T disk )X(λ) 1, (4.5) where c BB is a constant (amplitude), B ν is the blackbody function, and 1 λ < λ 0 X(λ) =. (4.6) (λ/λ 0 ) β λ > λ 0 The modification to the blackbody, X(λ), models the steeper than Rayleigh-Jeans fall off at long wavelengths due to grains not emitting efficiently at wavelengths longer than their size. The free parameters for the modified blackbody were c BB, T disk, λ 0, and β. In the fitting we required 50 µm < λ 0 < 500 µm and 0 < β < 2. When fitting with the excess modeled as a single warm belt, the free parameters of the fit were: c IRS, the amplitude of the photosphere, the location of the dust (r warm = r in ), and the amplitude of the dust belt (M warm ). When fitting with a dust belt plus a modified blackbody the fit included c BB, the blackbody temperature (called T cold in Table D.4), λ 0, and β as additional free parameters. In practice, we performed a grid search over r in (in steps of 0.1 au) and c IRS (in steps of 0.01). At

112 112 each point in the grid we then found best values for the rest of the free parameters with a Levenberg-Marquardt algorithm (the Matlab function lsqcurvefit). The best fit was the model that minimized the standard χ 2 metric. When calculating χ 2, we enhanced the weights of the photometry points at 70 µm by a factor of 25 to balance their influence on the fit against the large number of points in the IRS spectra. Parameters λ 0 and β were often not well constrained by the fitting except for the targets with sufficiently-informing far-ir/sub-mm photometry. We calculated the luminosities of the best fit model components by integrating under the model spectra. We then found the fractional luminosity of each component: f warm = L warm /L and f cold = L cold /L. We inspected the results of our single blackbody fits to ensure that we only included genuine warm components in our sample. Ballering et al. (2013) made the distinction between warm and cold components at a dust temperature of 130 K, so targets that were fit well by a single blackbody with temperature <130 K were discarded from our sample. These included: HIPs 544, 2072, 9141, 16852, 17764, 24947, 46843, 51194, 59072, 59960, 61960, 65728, 66065, 90936, and Some of these targets had single warm components with temperatures just above the 130 K cutoff according to Ballering et al. (2013), but with the additional far- IR photometry and the new fitting procedure used here, they now fell below this cutoff. For others, Ballering et al. (2013) had found two components with the warm component being relatively weak, but here we found that the warm component was no longer necessary to fit the IRS data. We also excluded HIP 6276 because it has an extremely weak warm excess (and no evidence for a cold component) from which we could not place any meaningful constraints on the dust location. Finally, we excluded HIP and HIP because any model fit to the IRS data significantly over-predicted the far-ir photometry. A similar steep decline of the disk flux in the far-ir has been noted in a few other disks (Ertel et al., 2012), requiring a very unusual distribution of grain sizes to model. We examined the fits of the remaining targets to determine which were best fit

113 113 with a single warm belt and which required a cold component as well. In many cases, the requirement for a cold component came from the far-ir photometry, with the IRS data being fit well by a single warm belt. We included a cold component when the warm-only model under-predicted the far-ir data by more than 2σ (with the offset from multiple far-ir points combined in quadrature) and the addition of a cold component improved the fit. For most systems, the designations agreed with those of Ballering et al. (2013). Five systems that previously had been fit with a single warm component now were fit with two components (HIPs 1473, 1481, 77432, 78045, and 85922) and two systems that previously had been fit with two components were now fit best with a single warm belt (HIP and HIP ). The best fit cold component of HIP had T cold = 130 K (the upper bound allowed by the fit), suggesting this system has an unusually warm cold component. However, the model fit the data well, so a significantly higher value of T cold is likely not required. An unusually warm cold component does not, however, impact the need for a separate warm belt, as we found that a single component could not fit all the data. The results of the fitting are given in Tables D.3 and D.4. The best fit model SED for each target is shown in Figures C.1 and C.4. Our final sample had 29 systems with single warm components and 54 systems with two components. 4.3 Analysis and Results With the locations of the warm dust components for our targets found, we next turned our attention to the relationship between the dust location and the stellar mass. We expected the relation to follow a power law (r warm M ), b considering the predicted relation for both snow lines takes this form. Our goal was to measure the value of the exponent b and see if it aligned with the predicted value for the current or primordial snow line. We did not attempt to compare the absolute values of the measured dust locations to those predicted for the snow lines. The actual location of the primordial snow line is less certain than its predicted relation with stellar

114 114 mass, considering the uncertainty on the values of the all the factors in Equation 4.1. We first considered the systems with a single warm component. Figure 4.1 plots r warm vs. M and shows clear evidence for a positive trend. To quantify this trend, we fit the function log(r warm /au) = a + b log(m /M ) to these points. The best fit values of b and a were computed as b = log(m ) log(r warm ) log(m ) log(r warm ) log(m ) 2 log(m ) 2 (4.7) and a = log(r warm ) b log(m ). We found b = 1.08, a = 0.566, i.e. r warm /au = 3.68(M /M ) This best fit trend line is plotted with the data points in Figure 4.1. Considering the substantial amount of scatter evident in the data around the trend line, we used a bootstrap procedure to quantify the significance of our derived value of b. We used 10,000 trials for the bootstrap procedure. For each trial we randomly selected 29 points (with replacement) from our sample and recomputed the best fit b using Equation 4.7. Figure 4.2 shows the distribution of b values found by the bootstrap procedure. The distribution was fit by a normal distribution with mean = 1.08 and σ = 0.21 using the Matlab function fitdist. We found that b for the targets with a single warm component was consistent (within 0.6σ) of the value predicted by the primordial snow line (1.2) but was not consistent with (> 4.3σ from) the relation predicted by the current snow line (2.0). Thus, we conclude that these warm components were more likely to arise from dust produced by exo-asteroid belts than from dust dragged inwards from an outer belt or by disintegrating comets. Next we examined the r warm M relation for the two-component systems, shown in Figure 4.3. There was more scatter than for the single-component systems, and no simple relation was evident that represented all the points. For comparison, we added to this plot the best fit trend found for the single-component systems (green dashed line from Figure 4.1). We found that many of the warm components in the two component systems did follow this same trend, but there were also outliers both

115 115 above and below the trend. We subtracted the values of r warm predicted by the trend line for the singlecomponent systems from the measured r warm values in both samples. Fitting a normal distribution to residuals of the single-component systems (using fitdist) gave a mean = 0.0 and σ=0.16 dex in log(r warm /au). This provided a measure of the inherent scatter around this trend for systems that likely follow the primordial snow line relation. The 1σ region around the trend due to this scatter is depicted in Figures 4.1 and 4.3 with thin dotted green lines. Figure 4.4 shows the distribution of these residual warm dust locations from the trend (green for the single-component systems, magenta for the two-component systems). The distribution for the two-component systems peaks around the trend (no residual), again showing that many of the warm components in these systems also follow the primordial snow line. To quantify this, we note that 20/54 of these warm belts fell within 1σ of the trend, 32/54 fell within 2σ, and 41/54 fell within 3σ. (For comparison, in the single-component sample 18/29 fell within 1σ of the trend, 28/29 fell within 2σ, and all systems fell within 3σ.) The histogram shows for the two-component systems a decreasing tail of warm dust locations below the trend (negative residual), whereas the warm dust locations above the trend show signs of a separate population of systems. In Section 4.4 we discuss various possibilities for the nature of the outlier systems. 4.4 Discussion of Outlier Systems We have shown that all of the single-component systems and many of the twocomponent systems reside at locations consistent with being set by the primordial snow line and not by the current snow line, and thus are likely to originate from exo-asteroid belts. Here we turn our attention to the nature of the outlier systems that do not appear to be set by the primordial snow line. Perhaps these systems do have asteroid belts, but the belts are not associated with the snow line. These systems may have particular planetary system architec-

116 rwarm (au) Mstar (Msun) Figure 4.1: The location of the warm dust vs. stellar mass for the 29 targets with a single dust component. The dashed line shows the best fit trend log(r warm /au) = log(m /M ), equivalent to r warm /au = 3.68(M /M ) The thin dotted green lines show the measured 1σ scatter around the trend (± 0.16 dex).

117 Number of bootstrap trials Primordial snow line prediction Current snow line prediction b Figure 4.2: The distribution of the results from the bootstrap procedure to estimate the uncertainty on the power law index (b) of the observed r warm M relation for systems with a single component. The distribution has mean = 1.08 and σ = The warm components are thus consistent with being set by the primordial snow line and inconsistent with being set by the current snow line.

118 rwarm (au) Mstar (Msun) Figure 4.3: The location of the warm dust vs. stellar mass for the 54 targets with two dust components. The dashed green line is the best fit trend line derived for the single component systems (as in Figure 4.1), which we found likely arise from asteroid belts with locations set by the primordial snow line. The thin dotted green lines show the measured 1σ scatter around the trend (± 0.16 dex). We see that many targets are consistent with this trend (suggesting they also are set by the primordial snow line) but there are also many outliers away from the trend.

119 Relative Frequency Residual log(rwarm/au) (dex) Figure 4.4: The distributions of the warm dust residual locations for the singlecomponent (green) and two-component (magenta) systems around the trend line found for the single-component systems. The single-component systems show a symmetric distribution of residuals with mean = 0.0 and σ=0.16 dex. A normal distribution with this mean and σ is shown in the dotted green line. All three curves are unity normalized in order to better compare their shapes. The two-component systems show a peak centered on the trend, a tail of outliers below the trend, and separate population of outliers above the trend.

120 120 tures or dynamical histories that led to belts of planetesimals forming at locations other than the primordial snow line. This explanation is difficult to disprove and may naturally produce a large scatter in warm dust locations, as is seen in the outlier population. However, it is not clear from this scenario why more scatter would arise in systems with two-components than in systems with only a warm component. As discussed earlier, the inward transport of material from the cold outer belt is expected to result in warm dust at a preferential location the current snow line. However, the outliers span a large range of dust locations for a given stellar mass, so inward transport cannot explain all of the outliers. Furthermore, most of the outliers are located in the lower half of our sample s stellar mass distribution, preventing us from meaningfully measuring their r warm M behavior. The specific scenario of inward transport by drag forces predicts that the warm component of dragged in material should be much fainter than the cold reservoir from which it originates (Kennedy and Piette, 2015). We looked for this in our sample by plotting the fractional luminosities of the warm 4 and cold components and their ratio against the residual warm dust location from the trend (Figure 4.5). We found that the f warm /f cold ratio (bottom panel) is roughly the same across our entire sample (perhaps somewhat larger in systems below the trend). Thus, this provides no additional support for the drag scenario. Later-type stars can drag in a substantial amount of dust to generate a bright warm component if their luminosity is low enough such that no grains are blown out of the system by radiation pressure (there is no a BOS ). Drag is also enhanced in later type stars by stronger stellar winds. This situation has been invoked to explain the warm component of the K2 star ɛ Eridani (Reidemeister et al., 2011). With no significant radiation force on the grains, there would also be no pile-up of grains when the icy constituents sublimate, so the warm components would not trace any snow line location. The outlier systems 4 Note from the top panel of Figure 4.5 that the two component systems (magenta points) near the trend have a similar brightness distribution as the single component systems (green points), furthering the notion that these warm components arise from a common mechanism likely exoasteroid belts.

121 121 in our sample, however, have larger stellar luminosities than ɛ Eridani, and we were able to calculate a BOS for all stars in our sample, so we deem this situation unlikely. The outliers below the trend line may result from exozodiacal dust components, which are considered a separate component from the traditional warm components (Su and Rieke, 2014). We purposely discarded targets with exozodiacal dust from our sample (Section 4.2.1), so perhaps these outliers should be ignored for the same reason. Two of the four systems with warm dust located more than 3σ below the trend (HIP 1481 and HIP 77432) show clear silicate features in their best fit model spectra, and silicate features are a signature of exozodiacal dust (Ballering et al., 2014). Ballering et al. (2014) found that all systems with exozodiacal dust also had outer components, consistent with finding these outliers only in our two-component sample. For the outliers above the trend, it is possible that we are not seeing an inner distribution of dust at all. Instead we may be seeing emission from the spatially unresolved blowout halo of small grains beyond the cold parent body belt. These grains must be small potentially below the blowout size so are warm despite their large stellocentric distance. Detailed studies of disks with such halos seen in resolved images have found that the halo component s contribution to the SED often peaks at wavelengths shorter than the cold component but longer than a typical warm component (as is seen for the outlier systems above the trend in our sample), although this varies among specific systems. For example, the halo of γ Ophiuchi peaks at nearly the same wavelength as the cold belt (Figure 3 of Su et al., 2008), the halo of HR 8799 peaks at a shorter wavelength (Figure 9 of Su et al., 2009), and the halo of β Pictoris peaks at an even shorter wavelength (Figure 14 of Ballering et al., 2016). Many of the debris disks with prominent halos are A type stars (rather than the F and G type stars in our outlier sample), which is intuitive given their high L and large a BOS. However, the fact that these outliers are primarily around F and G stars does not rule out that the outliers are due to halos. The halos of A stars may simply tend to blend more with the cold belt in the SED and be fit as a single component. This may be especially true if there

122 122 is also a genuine warm component in the system. In fact, HR 8799 (HIP ) and γ Ophiuchi (HIP 87108) which are known to have halos are in our sample but their halo components are not detected in our fitting separately from their cold components. From the middle panel of Figure 4.5 we see that the outlier systems above the trend tend to have slightly higher than average cold component fractional luminosities, consistent with systems capable of generating large halos. We consulted the literature in hopes of finding information to explain the nature of the specific systems with warm components significantly above the trend (nine systems are >3σ from the trend). The cold component of HIP 7978 (q 1 Eri, HD 10647) was imaged with Herschel but does not appear to host a halo component (Liseau et al., 2010). The cold component was also imaged with HST in scattered light, showing a ring out to 120 au with no sign of a halo 5. Schüppler et al. (2016) modeled the warm disk to be located at 3 10 au, which is much smaller than the location we derived, although their model over-predicts the IRS flux density. They also note the presence of a Jupiter-mass radial velocity planet at 2 au, inside the warm belt location, further complicating this system. HIP (HD 15745) has a fan-shaped outer component detected in scattered light out to 450 au (Kalas et al., 2007; Schneider et al., 2014), which may be a halo component, but no detailed models have shown that this halo could give rise to the warm part of the SED. HIP (HD 30447) was seen in scattered light as an edge-on disk out to 200 au (Soummer et al., 2014), but a halo component separate from the cold belt has not been identified. HIP (HD 61005, The Moth ) is seen in scattered light to have an outer belt with wings of dust swept back due to interactions with the ISM (Hines et al., 2007; Buenzli et al., 2010; Schneider et al., 2014). Ricarte et al. (2013) 5 See

123 123 modeled the outer belt in detail but still required a separate warm component to fit the SED, suggesting the warm component does not arise from any part of the outer disk. HIP (HD ) was seen in scattered light to have an edge-on disk from au with a large brightness asymmetry between the two sides of the disk (Draper et al., 2016a), but the source of the warm component is not revealed. HIP (HD ) has a narrow cold belt component (Schneider et al., 2006) plus an extended asymmetric halo of dust (Schneider et al., 2014), possibly from a recent massive collision (Stark et al., 2014). Lebreton et al. (2012) fit the entire SED with dust from an outer belt, and Kennedy and Wyatt (2014) note that this is one of the few systems where the two-temperature SED could arise from a single spatial location. There are no images or other revealing observations of the disks around HIP (HD 84075), HIP (HD ), or HIP (HD ). In conclusion, we find no single answer to the nature of these outlier systems. The systems below the trend may be exozodiacal dust. One system (HIP 95270) was found not to require an inner warm dust population at all. The others may trace blowout halos, planetesimal belts set by mechanisms not linked to the snow line, or the inward transport of material by comets. We deem inward transport by drag forces to be unlikely for these systems. 4.5 Summary 1. Warm components of debris disks have been observed in the spatially unresolved SEDs of many stars, but the nature and origin of the dust is not known. There are two plausible scenarios for its origin: the in-situ production of dust via collisions in an asteroid belt-like population of parent body planetesimals, or the inward transport of material from an outer reservoir.

124 fwarm / fcold fcold fwarm Residual log(rwarm/au) (dex) Figure 4.5: The fractional luminosity (brightness) of the warm components (top panel) and the cold components (middle panel), and the ratio of the two (bottom panel) vs. the residual warm dust locations relative to the best fit trend. The single component systems are in green and the two component systems are in magenta. The outlier systems above the trend (on the right side of these plots) tend to have brighter than average warm and cold components, but the ratio of their brightnesses are in line with the sample as a whole. The two component systems that are not outliers have a similar distribution of warm component brightnesses as the single component systems, suggesting all of these systems are due to the same phenomenon.

125 The first scenario predicts the dust to be located at the primordial snow line, while the second scenario predicts the dust to be located at the current snow line. The location of the primordial snow line follows a shallower power law relation with stellar mass than does the current snow line, providing a means to distinguish between the two. 3. We located the warm dust in 83 debris disk systems observed with Spitzer/IRS (29 with a single warm component, 54 that also possess a cold component) by fitting model dust belt emission spectra to their SEDs. 4. We found that the r warm M relation for the single-component systems is consistent with the primordial snow line and not consistent with the current snow line. We thus favor the in-situ production of dust scenario for these systems. Many of the two-component systems also follow the primordial snow line relation. Hence we conclude that the collisional processing of exo-asteroid belts is a common mechanism to produce warm debris disk components. 5. We are not able to definitively explain the two-component systems with warm components that do not follow the primordial snow line. Those nearer the star than the snow line may be exozodiacal dust. For those farther than the snow line there are several possibilities: the inward transport of material, a planetesimal belt that formed at a location different from the snow line, or that we are actually detecting warm dust co-located with the cold dust or even beyond the cold dust in a blowout halo component.

126 126 CHAPTER 5 A COMPREHENSIVE DUST MODEL APPLIED TO THE RESOLVED BETA PICTORIS DEBRIS DISK FROM OPTICAL TO RADIO WAVELENGTHS We investigate whether varying the dust composition (described by the optical constants) can solve a persistent problem in debris disk modeling the inability to fit the thermal emission without over-predicting the scattered light. We model five images of the β Pictoris disk: two in scattered light from HST /STIS at 0.58 µm and HST /WFC3 at 1.16 µm, and three in thermal emission from Spitzer/MIPS at 24 µm, Herschel/PACS at 70 µm, and ALMA at 870 µm. The WFC3 and MIPS data are published here for the first time. We focus our modeling on the outer part of this disk, consisting of a parent body ring and a halo of small grains. First, we confirm that a model using astronomical silicates cannot simultaneously fit the thermal and scattered light data. Next, we use a simple, generic function for the optical constants to show that varying the dust composition can improve the fit substantially. Finally, we model the dust as a mixture of the most plausible debris constituents: astronomical silicates, water ice, organic refractory material, and vacuum. We achieve a good fit to all datasets with grains composed predominantly of silicates and organics, while ice and vacuum are, at most, present in small amounts. This composition is similar to one derived from previous work on the HR 4796A disk. Our model also fits the thermal SED, scattered light colors, and high-resolution mid-ir data from T-ReCS for this disk. Additionally, we show that sub-blowout grains are a necessary component of the halo. 5.1 Introduction Debris disks are the circumstellar material that remains in planetary systems after the giant planets have formed and protoplanetary disks have dispersed, and they

127 127 provide a unique opportunity to study planetary systems over a large range of orbital scales. The presence of a debris disk confirms that the planet formation process has progressed at least to the formation of planetesimals. The locations of debris disks reveal the architectures of planetary systems, as planets sculpt and clear the debris material (e.g. Wyatt et al., 1999; Moro-Martín and Malhotra, 2005; Quillen, 2006; Rodigas et al., 2014b). The frequency and brightness of debris disks versus stellar age informs our understanding of the evolution of planetary systems (e.g. Rieke et al., 2005; Su et al., 2006; Sierchio et al., 2014). Finally, the composition of debris disks the focus of this study provides insight into the composition of planetesimals, a critical parameter in understanding their roles in planet formation. For recent reviews of debris disks, see Wyatt (2008), Matthews et al. (2014b). The particles in a debris disk range in size from parent body planetesimals down to the dust created by the collisional processing of the parent bodies; it is the dust that is primarily observable. Fully characterizing a debris disk involves determining three properties about this dust: its spatial distribution, its size distribution, and its composition. While hundreds of debris disks have been studied, most have only been characterized by their spectral energy distributions (SEDs) that result from infrared thermal emission from the dust (e.g. Ballering et al., 2013; Chen et al., 2014). SEDs provide the temperature of the dust, but the temperature of a dust grain depends on its location, size, and composition; thus, temperature alone is not sufficient to characterize a debris disk fully. Resolved images at multiple wavelengths are much more powerful for characterizing debris disks. An image provides an independent measure of the spatial distribution of the dust, while the variation of its brightness with wavelength allows the size distribution and composition of the dust to be constrained (e.g. Debes et al., 2008; Rodigas et al., 2015). Visible and near-infrared images trace starlight that is scattered by the circumstellar dust grains, while midinfrared to mm-wave images trace the grains thermal emission. A complete debris disk model would match all of the available data, including scattered light images, thermal images, and the thermal SED. Many studies of debris disks to date have had difficulty successfully modeling

128 128 both the thermal emission and scattered starlight in a self-consistent manner. Krist et al. (2010) imaged the debris disk around HD in scattered light with the Hubble Space Telescope (HST ), then modeled the thermal SED of the disk while using the image to fix its location. Assuming the dust was composed of astronomical silicates, they obtained a good fit to the SED by varying the grain size parameters. However, their best fit model significantly over-predicted the brightness of the disk in scattered light compared to the HST image. In a very similar analysis, Golimowski et al. (2011) modeled the HD debris disk (also assuming astronomical silicates for the dust composition) and found that their model over-predicted the observed scattered light brightness by a factor of five. Lebreton et al. (2012) modeled the thermal SED of the HD debris disk by varying the grain sizes and composition and fixing the dust location from an HST scattered light image at 1.1 µm; their best fit model over-predicted the scattered light brightness by a factor of 4.5. For the HD debris disk, Rodigas et al. (2014a) found that the best fitting model to the SED by Donaldson et al. (2013) was inconsistent with the disk s scattered light brightness. Rodigas et al. (2015), in characterizing the debris disk around HR 4796A, showed that models fit only to the scattered light data matched the thermal emission data very poorly, and vice versa illustrating the importance of modeling both the scattered light and thermal emission data simultaneously. The nearby A6V star β Pictoris hosts a large, bright, edge-on debris disk that is amenable to imaging at many wavelengths. The disk was discovered with the Infrared Astronomical Satellite (IRAS) through its thermal emission (published by Aumann (1985)) and subsequently imaged in scattered light by Smith and Terrile (1984). Since then, the β Pic disk has been observed with numerous instruments and analyzed many times to investigate its various properties. However, no model of the disk has yet been assembled to match the latest high-quality images in scattered light and thermal emission. In this study we perform such an analysis, modeling images from the Hubble, Spitzer, and Herschel space telescopes, and the Atacama Large Millimeter/submillimeter Array (ALMA). The β Pic debris disk consists of multiple components at various stellocentric

129 129 distances. We focused on the outer two components that were spatially resolved in all the images we considered. These components include a belt of parent body planetesimals and a halo of small dust grains generated by the collisional processing of the parent bodies and pushed into eccentric or unbound orbits by the force from stellar radiation (Augereau et al., 2001). The parent body belt traced by sub-mm images that are sensitive to large grains extends from 40 au to 150 au (Dent et al., 2014), while the halo which dominates the scattered light signal extends to at least 1800 au (Larwood and Kalas, 2001). Nearer the star is a warm debris component detected in the mid-ir (e.g. Knacke et al., 1993; Telesco et al., 2005; Chen et al., 2007; Li et al., 2012) and scattered light (Milli et al., 2014; Millar- Blanchaer et al., 2015), and also a very hot dust component detected from near-ir interferometery (Defrère et al., 2012). These inner components were unresolved in many of our data sets, so we did not include them in our analysis. In addition to dust, the β Pic debris disk also contains a gas component. The spatial distribution of much of the gas coincides with the dust, and this gas is likely produced by collisional vaporization or photodesorption of the dust grains (Brandeker et al., 2004; Roberge et al., 2006; Cataldi et al., 2014; Dent et al., 2014). The morphology of this debris disk is complicated by several asymmetries and substructures (Kalas and Jewitt, 1995; Golimowski et al., 2006; Apai et al., 2015), which likely originate from perturbations by the giant planet located 8 au from the star (Mouillet et al., 1997; Augereau et al., 2001; Nesvold and Kuchner, 2015) that was detected by Lagrange et al. (2010). The goal of our study was to better understand the grain properties rather than the morphology of this disk, so we did not attempt to reproduce the observed detailed structure. We did, however, account for the overall brightness asymmetry between the NE and SW sides of the disk by modeling them separately. An outline of this chapter is as follows. In 5.2 we summarize the properties of the central star. In 5.3 we present the data we used in this study, including previously unpublished images from HST and Spitzer. In 5.4 we detail our procedure for generating model images. In 5.5 we show our derived spatial parameters for the two

130 130 outer disk components, which we then adopt when modeling the dust composition as we describe in 5.6. When modeling the composition we first try grains composed of astronomical silicates ( 5.6.2), then we use a generic function for the material optical constants ( 5.6.3), and finally we use a mixture of astronomical silicates, water ice, refractory organics, and vacuum ( 5.6.4). In we check our best fit model against the thermal SED, while comparisons with additional datasets can be found in E. In 5.7 we discuss the broader implications of our results, then we offer a summary and conclusions in Stellar Properties β Pic is a Myr-old (Binks and Jeffries, 2014, 2016) A6V star located at a distance of pc (van Leeuwen, 2007) with M = 1.75 M, T = 8200 K, and L = 8.7 L (Crifo et al., 1997). We required a model SED of the star s photosphere both for measuring the excess infrared flux emerging from the debris disk and for determining the incident flux on dust grains when generating models of the scattered light and thermal emission from the disk. We used an ATLAS9 (Castelli and Kurucz, 2004) photosphere model with T = 8000 K, log g = 4.0, and solar metallicity. The spectrum was modeled only out to 160 µm, so we extended it to 10,000 µm by extrapolating with a Rayleigh-Jeans power-law. The amplitude of the photosphere SED model was set so that integrating under it yielded a total luminosity of 8.7 L, which required R = 1.54 R. Our final SED model agreed well with photometric data of this star in the visible and near-ir. 5.3 Data We characterized the β Pic outer debris disk by modeling five images in different wavelength regimes. Two images were obtained with HST and probe scattered light; they were taken with the Space Telescope Imaging Spectrograph (STIS) and the Wide Field Camera 3 (WFC3). The other three images probed thermal emission and were taken with the Multiband Imaging Photometer for Spitzer (MIPS; Rieke

131 131 et al., 2004) at 24 µm, the Herschel Photodetector Array Camera and Spectrometer (PACS; Poglitsch et al., 2010) at 70 µm, and ALMA at 870 µm. In the following sections we describe each of our five datasets, providing extra detail for the HST /WFC3 and Spitzer/MIPS data that are published here for the first time. There were several basic data processing steps that we applied to all of the images. We cropped the images to place the star at the center. We rotated the images to align the mid-plane of the (edge-on) disk horizontally, using the WCS associated with each image and the disk s known position angle (29 ). We extracted radial profiles by selecting a strip of each image along the mid-plane of the disk and computed the mean value of the pixels at each point along the length of the strip. There is a known asymmetry between the brightness of the NE and SW sides of the disk, so we extracted the profiles of each side separately. The widths of the strips were 25 pixels (1. 27), 11 pixels (1. 32), 5 pixels (6. 225), 5 pixels (8 ), and 5 pixels (0. 5) for the STIS, WFC3, MIPS, PACS, and ALMA images, respectively. For details on how we chose these values, see 5.4. In Table 5.1 we present a collection of photometry data for the whole disk spanning the range of wavelengths where the thermal radiation is dominated by the outer disk components (λ 20 µm). The Spitzer Infrared Spectrograph (IRS; Houck et al., 2004) data on β Pic (Chen et al., 2007) provides a detailed characterization of dust emission features arising mostly from the inner warm component, which is not the focus of this study, so we do not include it in our SED. The contribution to the flux density for the central star is also listed in the table; it is from the model discussed in HST/STIS β Pic was imaged with the STIS CCD in coronagraphic (50CORON) mode under program GO (PI: Apai), and the results of these observations were published in Apai et al. (2015). The observing strategy used multiple roll angles, various coronagraphic wedge positions, and dedicated point-spread function (PSF) star observations to achieve very sensitive imaging of the disk in scattered light, following

132 132 the technique of Schneider et al. (2014). The instrument bandpass is set by the response of the CCD and centered at 0.58 µm. While these images achieve a small inner working angle, the field of view of the instrument limited the detection of the disk to r 11 (210 au), well inside of its full extent. We converted the star-subtracted disk image from counts s 1 per pixel to mjy arcsec 2 using a conversion factor of Jy counts 1 s and the pixel size of (Apai et al., 2015). An image of the uncertainty in each pixel was also provided, and we extracted the radial profile of the uncertainty using the same steps. We combined this in quadrature with a calibration uncertainty of 0.3% of the signal in the profile. The STIS radial profiles for the NE and SW sides of the disk are show in Figure HST/WFC3 To detect the full extent of the disk s halo component in scattered light, we needed an image from an instrument with a larger field of view than STIS. We searched the HST archive and found previously unpublished observations of β Pic with the WFC3 instrument in the IR channel (filter F110W at 1.16 µm) from program GO (PI: Graham). We used the pipeline data products that were processed by MultiDrizzle to correct for the geometric distortion inherent in the raw images. No dedicated PSF star observations were taken with this instrument in this program, but images at multiple telescope roll angles were obtained, which we subtracted from each other to remove the light from the central star. Four images were available, each separated by 8 of rotation. We converted the images from electron s 1 per pixel to mjy arcsec 2 using a conversion factor of Jy electron 1 s (from the FITS file header) and the pixel size of To minimize self-subtraction of the disk signal and extract accurate radial profiles, we opted to use only the two images with the largest difference in rotation angle (24 ). These were data files ia1s70031 drz.fits and ia1s73031 drz.fits. We put each image onto a grid of pixels 10 times smaller than the native pixel size by cubic interpolation with Matlab s interp2 function. Prominent PSF diffraction

133 133 NE mjy/arcsec SW mjy/arcsec arcseconds Figure 5.1: Radial profiles of the NE and SW sides of the disk at 0.58 µm from HST /STIS. The gray region is the uncertainty along the profiles. The outer edges of the profiles are truncated by the field of view of STIS.

134 134 spikes in the images allowed us to accurately align the centers of the images. We subtracted the images and interpolated the difference image back onto the native pixel scale. The result had both a positive and negative disk signal offset by 24, and is shown in Figure 5.2. We extracted radial profiles of both disk images by rotating the difference image to orient each disk horizontally. The final radial profile was the average of these two profiles, and the uncertainty on the final profile was the difference between them. To estimate the amount of flux missing along our radial profiles due to disk self-subtraction, we subtracted two model images (after convolving with the WFC3 PSF, see 5.4) from each other, rotated by 24. We then used the result to correct our observed radial profiles. Beyond r > 3, where we perform our fitting (see 5.6.1), this correction was relatively small smaller than our estimated uncertainties. The profiles are shown in Figure 5.3. Golimowski et al. (2006) presented scattered light profiles of this disk measured with the HST Advanced Camera for Surveys (ACS). The shape and brightness of our profiles were similar to their results. For a quantitative comparison with the shape of the ACS data, we fit a power law, S(r) r α, to the outer part (r > 10 ) of our radial profiles. We found α = -3.5 and -4.0 for the NE and SW sides, respectively, which agreed well with the power law fits to the outer part of the (not deconvolved) ACS data, as given in Table 3 of Golimowski et al. (2006). Our power law fits are shown in Figure Spitzer/MIPS The MIPS observations of β Pic were taken under the Spitzer Guaranteed Time Observing Program 90 (PI: M. Werner). The data at all three bands (24, 70, and 160 µm) are published here for the first time. PACS provided a higher spatial resolution image in the far-ir than MIPS (see 5.3.4), so we used the MIPS 70 and 160 µm data for SED photometry points only. The MIPS data were processed using the Data Analysis Tool (Gordon et al., 2005) for basic reduction. Additional reduction steps, outlined below, were performed on individual exposures which were then mosaicked into one combined image with pixels half the size of the physical

135 arcseconds mjy/arcsec arcseconds arcseconds mjy/arcsec arcseconds 0.01 Figure 5.2: The difference of two HST /WFC3 images with roll angles separated by 24 degrees. The top panel shows the positive image (ia1s70031 drz.fits ia1s73031 drz.fits), where the bottom panel shows the negative image. The black dotted lines locate the midplane of the disk from the two images, along which we generated the radial profiles shown in Figure 5.3. The color is the surface brightness in log scale. In both images the SW side of the disk is up and to the left and the NE side is down and to the right.

136 136 NE mjy/arcsec Average Profile Positive Image Profile Negative Image Profile Power Law mjy/arcsec SW Average Profile Positive Image Profile Negative Image Profile Power Law arcseconds Figure 5.3: The NE and SW radial profiles of the disk at 1.16 µm from the HST /WFC3 difference image shown in Figure 5.2. The final profiles (black lines) are the average of the two profiles from the positive and negative images of the disk (dotted red and blue lines). The gray regions are the uncertainty along the profiles. The green lines are the power law fits to the outer parts (r > 10 ) of the radial profiles, with indices -3.5 and -4.0 for the NE and SW sides, respectively.

137 137 pixel scale. Two sets of 24 µm observations were obtained. The first set was obtained on 2004 March 20 using 4 sub-pixel cluster positions with a 3 s exposure time and 1 cycle in the large-field photometry Astronomical Observation Template (AOT), resulting in a total of 120 s of integration per pixel. The second set of data was obtained on 2004 April 11 using two large cluster positions with 3 s and 3 cycles in the large-field photometry AOT, resulting in a total of 180 s of integration per pixel. At 24 µm, the bright star amplified the jailbar effect, resulting in a striping pattern on each exposure. This striping pattern was removed by subtracting median column offsets in individual exposures. Due to the fine dither pattern in the large-field mode at 24 µm, the bright source (near hard saturation) was exposed to a similar part of the array in sequential exposures, resulting in a potential accumulation of latent images. Since the image latent is flushed out after the bias boost (the onset of an exposure), the data using the first difference in an exposure has the least influence from image latency. To test whether the image latency affected the surface brightness distribution of the central data, we generated two mosaics: one with only the first two differences (short exposure) and the other with the entire data (long exposure), and compared. The difference between the long and short mosaics was within the errors of the observations. The final 24 µm combined image used only the data obtained at the first epoch due to a more uniform coverage in the mosaic. PSF subtraction was used to remove the stellar contribution to the image using the brightness of the star predicted by our model of the stellar photosphere, as described in 5.2. To model the MIPS 24 µm PSF, we used the STinyTim software with the default throughput curve and assumed a Rayleigh-Jeans source. Engelbracht et al. (2007) showed that an STinyTim-produced PSF model could be made more accurate by smoothing it with a boxcar function. We achieved this by generating an oversampled model with pixels and then smoothed it with an 18 pixel boxcar.

138 138 We converted the disk-only image from instrument units of MIPS24 to mjy arcsec 2 using a conversion factor of MJy sr 1 MIPS24 1 (Engelbracht et al., 2007). The pixel scale was subsampled to , half the physical pixel size. An image of the uncertainty was derived from the square root of the image in instrument units with the same conversion factor applied, and a radial profile of the uncertainty was generated from this image in the same manner as from the image of the signal. This uncertainty profile was combined in quadrature with 4% calibration uncertainty (Engelbracht et al., 2007). Figure 5.4 shows the MIPS 24 µm image (first panel), the model PSF (second panel), and the residuals after intentionally over-subtracting the PSF (scaled to the peak brightness of the image) to clearly demonstrate that the disk was resolved by these observations (third panel). In the fourth panel of Figure 5.4 we show the image of the disk with the signal from the star removed, from which we generated the profiles used for our analysis (these are shown in Figure 5.5). The first and fourth panels are quite similar because the disk accounts for more than 95% of the total 24 µm flux from the system. In addition to radial profiles, we also measured the total flux density at 24 µm. Before color correction, this was 7.45 Jy using a circular aperture with a radius of 81 (the maximum flux in the encircled energy method). We applied a color correction of (for a blackbody with temperature of 100 K) to only the disk flux density (7.13 Jy after subtracting the expected stellar photospheric contribution of 318 mjy), yielding 7.53 Jy for the color-corrected disk flux density and 7.85 Jy for the color-corrected total flux density. We assumed a 5% uncertainty on this measurement. Although the total 24 µm flux density exceeded the saturation limit ( 6 Jy for a point source at 3 s exposures), the data were not (although close to) saturated because of the extended structure. At this flux level, there was no significant ( 0.3%) flux nonlinearity (Engelbracht et al., 2007). Two sets of 70 µm observations were obtained. The first set was obtained on 2004 April 12. Unfortunately the disk orientation was along the column direction of the Ge:Ga detector, resulting in much lower sensitivity in the extended disk region.

139 139 The second set was obtained on 2005 April 4 using 3 cluster positions with 10 s exposure times and 1 cycle in the large-field photometry AOT (a total exposure of 600 s per pixel). The 160 µm observation was performed on 2004 February 21 using 7 cluster positions each with 3 s exposure times and 3 cycles in the large-field photometry AOT, resulting in a total of 45 s per pixel. The 70 µm data reduction followed the steps recommended by Gordon et al. (2007) using time filtering with the source region masked out to avoid filtering out the signal. Several region sizes were tried, and an ellipse with a semimajor radius of 116 and a semiminor radius of 74 along the disk midplane (roughly covering the area of the 1-σ detection boundary in the final mosaic) gave a minimum value in background variation. The final 70 µm mosaic used only the data obtained with 10 s exposures (second epoch). No special steps were performed for the 160 µm data, and all the exposures were combined based on the WCS information. No leak subtraction was required at 160 µm. It has been shown that the ghost image produced by the 160 µm filter leakage was less than 15 times of the photospheric value at 160 µm, whereas the disk was expected to be 500 times brighter than the expected photospheric value. The calibration factors we used to transfer the instrument units to physical units were 702 MJy sr 1 MIPS70 1 (Gordon et al., 2007) and 41.7 MJy sr 1 MIPS160 1 (Stansberry et al., 2007) for the 70 and 160 µm data, respectively. At 70 µm, nonlinearity begins to affect the data when a source is brighter than 1 Jy (Gordon et al., 2007), and this nonlinearity becomes apparent for a given pixel when its value is 0.2 MIPS70 (140.4 MJy sr 1 ). This effect had a significant impact on the observed 70 µm disk surface brightness distribution as the central 3 3 pixels had values greater than 0.2 MIPS70. We compared the imaging data with the integrated flux in the MIPS-SED data, which was presented by Su et al. (2015). Even though the MIPS-SED observations were obtained with the same detector, the data were unlikely to be in the nonlinear regime because each pixel received less flux due to the dispersive nature of the spectrograph. The MIPS-SED data were taken at three slit positions that covered the NE, center, and SW parts

140 140 of the disk. Using the non-aperture-corrected MIPS-SED spectra, the integrated flux density in each of the slit positions was 2.3, 7.0, 2.3 Jy for the NE, center, and SW positions, respectively. Using the 70 µm imaging data, the total flux density within rectangular apertures of was 2.1, 4.4 and 2.1 Jy for the NE, center, and SW positions, suggesting a 60% and 9% flux deficit in the central and side regions of the image. After applying a flux nonlinearity correction (K. Gordon et al. 2009, private communication), the corrected 70 µm image gave 2.5, 7.5, and 2.5 Jy for the NE, center, and SW positions. These values agree with the MIPS-SED data to within 10%. We measured the broadband 70 µm flux of β Pic on the flux-nonlinearitycorrected image using the encircled energy method. The total flux density in the 70 µm band was Jy using a circular aperture with radius of 125 before color correction. The expected stellar photosphere was 32 mjy at 70 µm, suggesting a total disk flux density of Jy after a color correction of (assuming a blackbody of 100 K) with an assumed 10% error. This value agreed well with the color-corrected IRAS 60 µm measurement, and was slightly higher than the PACS flux density at 70 µm. The total flux density in the 160 µm band was 3.6 Jy using an elliptical aperture with semimajor radius of 112 and semiminor radius of 79 (covering the area within the 1-σ detection level) before color correction. The ghost image due to the 160 µm filter leak was estimated to contribute <3% of the total flux (less than the calibration error); therefore, no correction was attempted. The total disk flux density in the 160 µm band was 3.65 Jy after a color correction of with an assumed 20% error. This agreed well with ISO point at 170 µm, but was somewhat lower than the PACS flux density at 160 µm (these three measurements agreed to within 3σ, however) Herschel/PACS at 70 µm PACS 70 µm scan map observations of β Pic (PI G. Olofsson, observation IDs and ) were published by Vandenbussche et al. (2010). We

141 141 MIPS 24 µm Image PSF Peak Subtraction Rotated Disk Image arcseconds SW NE arcseconds arcseconds arcseconds arcseconds Figure 5.4: The first panel shows the Spitzer/MIPS image of the β Pic system at 24 µm prior to subtracting the signal from the star. The image is clearly elongated in the NE-SW direction (N is up, E is left), which agrees with the known orientation of the disk. The extension of the observed morphology is clear when comparing the image with the instrument PSF (second panel), which does not exhibit any elongation. We intentionally over-subtracted the PSF model (scaled to match the peak brightness of the observed image) from the observed image, and the result (the third panel) shows residual structure along the orientation of the disk, further confirming that the disk is resolved. In the fourth panel we show the image of the disk with the signal from the star removed and rotated to orient the disk horizontally. The disk accounts for more than 95% of the total 24 µm flux from the system, so this disk-only image looks very similar to the image prior to star-subtraction. The color scale in all four images gives the surface brightness (mjy arcsec 2 ) on a log scale.

142 142 NE mjy/arcsec arcseconds SW mjy/arcsec arcseconds Figure 5.5: The radial profiles of the disk at 24 µm. The gray region is the uncertainty along the profiles. The dashed lines shown the profile of the instrument PSF, scaled to the same peak value as the data s profile.

143 143 used the Standard Product Generation (SPG) v12.1 level 2.5 corrected MadMap image (a combination of the scan and cross-scan observations) from the Herschel Science Archive. We subtracted a constant background value of 1.3 mjy pixel 1 from the image, which was taken to be the median of the pixel values for three regions of the image away from the disk. We converted the units from Jy pixel 1 to mjy arcsec 2 using the pixel size of 1.6 arcsec. The star contributes a negligible amount of flux compared to the disk, so we did not perform PSF subtraction on this image. The uncertainty on the radial profile was a sum in quadrature of three components: 0.23 mjy pixel 1 estimated from the error image supplied by the pipeline processing, 0.19 mjy pixel 1 from the median of the standard deviations of the three regions of the original image used to estimate the background, and a 10% calibration error on the disk profile signal (Poglitsch et al., 2010). The radial profiles are shown in Figure 5.6. Our profiles agreed with those presented in Vandenbussche et al. (2010) ALMA We used the ALMA 870 µm continuum image previously published by Dent et al. (2014). The image had pixels of size We converted the image from Jy per beam to mjy arcsec 2 using a beam area of b maj b min where b maj = and b min = are the FWHM of the Gaussian beam major and minor axes, respectively (Dent et al., 2014). The star contributes a negligible amount of flux compared to the disk at this wavelength. We created an uncertainty image by combining mjy rms uncertainty and 10% calibration uncertainty in quadrature and then extracted the uncertainty radial profile from this image. The profiles are shown in Figure Model Images In this section we describe how we generated model debris disk images. The specific sets of models are discussed in subsequent sections. As mentioned previously, we focused our modeling effort on the parent body belt and halo components of the

144 144 NE mjy/arcsec SW mjy/arcsec arcseconds Figure 5.6: The radial profiles of the disk from Herschel/PACS at 70 µm. The gray region is the uncertainty along the profiles.

145 145 NE mjy/arcsec SW mjy/arcsec arcseconds Figure 5.7: The radial profiles of the disk from ALMA at 870 µm. The gray region is the uncertainty along the profiles.

146 146 Table 5.1. Broadband SED Photometry Data λ (µm) Total F ν (Jy) Error F ν (Jy) Star F ν (Jy) Excess F ν (Jy) Instrument Ref TReCS MIPS TReCS ISO IRAS ISO IRAS PACS MIPS IRAS PACS MIPS PACS ISO SPIRE SPIRE SPIRE SCUBA APEX ALMA SIMBA 9 References. (1) This work (2) Telesco et al. (2005) (3) Heinrichsen et al. (1999) (4) IRAS Faint Source Catalog (color-corrected values) (5) Vandenbussche et al. (2010) (6) Holland et al. (1998) (7) Nilsson et al. (2009) (8) Dent et al. (2014) (9) Liseau et al. (2003)

147 147 disk. We generated model images of these two components separately, and because the disk is optically thin, we could simply sum them together during the fitting process. Each component was modeled as a wedge-shaped 1 disk extending between inner and outer radial boundaries r in and r out. The number density of grains in the disk varied as a power law with both stellocentric radius and grain size (radius of a) as n(r, a) r p a q, and the grain size distribution was bounded by a min and a max. We used the code dustmap v (Stark, 2011) to generate model disk images in both thermal emission and scattered light. The disk geometry was input into dustmap by specifying the Cartesian coordinates of the desired dust distribution. We setup our model space with the star at the origin, the x coordinate to the right, the y coordinate away from the viewer, and the z coordinate up. Our models were seen perfectly edge-on, i.e. i = 90 with the midplane of the disk in the xy plane. We populated each model disk with grains equally spaced in Cartesian space within the defined wedge-shaped disk. The desired pixel size of the model images was in order to be as small as the smallest pixels in our data images (STIS). The spacing of model particles in Cartesian space was set to be the same as the pixel size (0.97 au), with the particles arranged to be located at the center of each pixel in the image plane. We set the field of view of the model image to be a square extending just to the outer edge of the disk. As the number of pixels spanning the field of view must be an integer, the final size of the model pixels differed very slightly from Each model particle was assigned an intensity value, allowing the particle to represent this number of physical dust grains. We used intensity values to implement the radial variation in grain number density where r = x 2 + y 2. dustmap can create a series of model images each assuming the grains are all of a single size and then sum the images together with relative scaling values; we used this feature to implement the grain size distribution. For both halo and parent body models, 1 We set the half-opening angle of the wedge disk to 4, determined by comparing vertical cuts of the WFC3 images with vertical cuts of model images made with a range of opening angles. We assumed the parent body and halo components had that same half-opening angle.

148 148 the grain size distribution was sampled with 50 values distributed logarithmically between a min and a max. We scaled each model image to represent a disk with a mass of M ( M ). The dust composition entered the model via the optical constants of the material, which are the real and imaginary components of its index of refraction, given by n(λ) and k(λ). From the optical constants, dustmap used Mie theory to compute the absorption and scattering efficiency factors and the scattering phase function of the dust grains when generating model images. We did not calculate the thermal emission contribution to the models at 0.58 and 1.16 µm, nor did we include the scattered light contribution to the model images at 24, 70, and 870 µm; the omitted components contribute negligibly to the total outputs at these wavelengths. dustmap model images were produced in Jy/pixel, which we converted to mjy arcsec 2 using the size of the model pixels. In practice, we generated each model image in pieces to use computer resources more efficiently, taking advantage of symmetries afforded by assuming the disk was perfectly edge-on. We first modeled the region x > 0, y > 0, and z > 0, and also split the x range into two sub-models. Combining these two sub-model images yielded one octant of the disk (the back side of one quadrant of the disk). Thermal emission is radiated isotropically, so for thermal models we doubled this image to model one quadrant of the disk. For the scattered light models, the front side (y < 0) of that quadrant was modeled separately, then the back and front pieces were added together. Finally, the quadrant model was mirrored over the x and z axes to yield a model image of the full disk. To compare the model images with the observations, we convolved our models with a model PSF appropriate for each instrument. We used the TinyTim software (Krist et al., 2011) to generate model PSFs for the two HST images. For the STIS PSF, we used λ=0.58 µm, a model diameter of 10, 0 defocus, and no oversampling. For the WFC3 PSF we used the source spectrum of an A5 star, a model diameter of 10, and 0 defocus. We selected the undistorted model, as the data products we used were corrected for the distortion in this instrument. We kept the default

149 149 orientation of the HST model PSFs because our images from these instruments were a product of multiple disk orientations. The MIPS 24 µm PSF was made using STinyTim as described previously in 5.3.3, except now assuming the source was a 100 K blackbody. We used PSF models for PACS at 70 µm derived from observations of Vesta taken with the same scan speed (slow) as our image of β Pic. 2 The ALMA PSF was modeled as an elliptical 2D Gaussian function with FWHM major and minor axes of and Before convolving with the model images, the MIPS, PACS, and ALMA PSFs were rotated to the same relative orientation with the disk midplane as in the observed data sets. We placed the model image onto the same pixel grid as the PSF model by linear interpolation in log space using MATLAB s interp2 function, then we performed the convolution of the two images with MATLAB s conv2 function. Finally, the convolved model image was interpolated onto the pixel scale of the observed image, and a radial profile was extracted using the same method as was used for the data (described in 5.3). Because the models were axisymmetric and we fit to each side of the observed disk separately, we only used half of each model radial profile. The widths of the strips used to make the radial profiles were chosen to capture the majority of the flux along the midplane of the disk. The disk was unresolved in the vertical direction by MIPS and PACS, so the strip widths were set to the FWHM of these instruments PSFs. To be symmetric, the strip widths needed to be an odd number of pixels: 5 pixels (6. 225) for MIPS and also 5 pixels (8 ) for PACS. The HST images did resolve the vertical extent of the disk, and to guide our choice of strip width we examined the model images (which had a vertical extent set to match the observed disk in scattered light). The images were brightest along the midplane and became much fainter above and below the midplane. For the halo images, the full width of the bright region was 1. 3 at r = 10. Thus, we used strip widths of 25 pixels (1. 27) for STIS and 11 pixels (1. 32) for WFC3. As we will 2 Specifically, we used psf20 blu 10 vesta od160 ama+63.fits. Files and documentation for this PSF are found at

150 150 show, the ALMA data trace the parent body component. Our parent body models had a bright midplane region with a full width of 0. 5 (at r = 4 ). This is also approximately the resolution of these ALMA data, so we used a strip width of 5 pixels (0. 5). 5.5 The Dust Spatial Distribution The first step in our characterization of the β Pic debris disk was to model its spatial properties, specifically r in, r out, and p for both the halo and parent body components (recall that n(r, a) r p a q ). Because we possessed well-resolved images of the disk, we could determine these parameters independently of the grain properties. Once the spatial parameters were measured, we kept them fixed while modeling the grain properties, as described in the next section. At sub-mm wavelengths, the small dust grains that likely constitute the halo component emit very inefficiently and the large grains in the parent body component dominate the signal. Thus, we could constrain the spatial properties of the parent body component by modeling the ALMA image. We performed this fit with a grid search across the parameters of interest, and the results are shown in red in Figure 5.8. We generated models with r in ranging from 35 to 70 au, r out from 130 to 170 au, and p from 0 to 2.0. For the spatial fitting, the grain properties were fixed at a min = 5 µm, a max = 5000 µm, q = 3.65, and a composition of astronomical silicates (Draine, 2003). We also varied the amplitude of the model over a large range of values. For each set of model parameters, we calculated the χ 2 goodness of fit between the model and observed radial profile. For the NE side, the best fit model had r in = 45 au, r out = 150 au, and p = 0.5. The variable r out was fairly well constrained by these data, whereas r in and p were not as well constrained. For the SW side, we thus tried using the same r in and p as found for the NE side, but allowing r out to vary. This yielded a very good fit with r out = 155 au. We conclude that the parent body component does not show any prominent asymmetries in terms of these parameters. Our values of r in and r out agree well with the analysis by Dent

151 151 et al. (2014) who modeled these data with concentric dust annuli (see their Figure 3C). With the spatial properties of the parent body component fixed, we next addressed the halo. Because the grains in the halo are thought to be generated by collisions in the parent body belt, we used the same r in for both components. Unlike the ALMA data, the WFC3, MIPS, and PACS radial profiles showed no sharp truncation the flux from the disk was simply lost in the noise at the outer edge. The PACS data showed signal to the largest radius, so we used these data to constrain r out. We found r out 1800 au for both the NE and SE sides, which was consistent with the detection of the disk to 1835 au by Larwood and Kalas (2001). To measure p, we used the WFC3 data because the shape of the WFC3 profiles were not significantly influenced by the instrument PSF. To ensure that we modeled only the halo component, we fit to the portion of the radial profile for r > 8 (>155 au). We fixed the grain properties to a min = 0.1 µm, a max = 5 µm, q = 3.65, and a composition of astronomical silicates. We found best fit p values of 2.4 for the NE side and 3.1 for the SW (see the blue curves in Figure 5.8). As a check of our best fit halo p values, we used the relation from Strubbe and Chiang (2006) for an edge-on disk that α = γ η 1, where α is the observed surface brightness power law exponent, γ is the disk surface density power law exponent, and η describes the opening of the disk as h = r η. For our wedge-shaped models, η = 1. Also, γ = p + η, so α = p 1. Thus, our measured α values of -3.5 and -4.0 from predicted p values of 2.5 and 3.0 for the NE and SW sides, which agreed with what we found from model fitting. According to Strubbe and Chiang (2006), a collision-dominated halo has α = 3.5 while a drag-dominated halo has α = 4.5. β Pic s NE side agreed with the collision-dominated case, whereas the SW side fell between the two cases. In summary, we found the following spatial parameters. For the NE side of the disk r in = 45 au, the parent body r out = 150 au, the parent body p = 0.5, the halo r out = 1800 au, and the halo p = 2.4. For the SW side the spatial parameters were the same except that the parent body r out = 155 au and the halo p = 3.1.

152 NE Side SW Side 5 5 χ 2 / min(χ 2 ) PB r in (AU) PB r out (AU) NE Side SW Side 5 χ 2 / min(χ 2 ) PB p Halo p Figure 5.8: Constraints on the spatial parameters of the two disk components. The red curves show constraints on the parent body component from the ALMA data. All three spatial parameters were constrained for the NE side, while for the SW side we assumed the same r in and p as the NE side but independently constrained its r out. The blue curves show the constraints on the halo p parameter for the NE and SE sides from the WFC3 data.

153 153 After successfully modeling the dust composition with a mixture of common materials ( 5.6.4), we fit the spatial parameters again, this time using the grain composition and size parameters of that best fit model. The results agreed with spatial parameters we found here when assuming the dust consisted purely of astronomical silicates. 5.6 The Dust Composition With the spatial parameters of the halo and parent body components determined, we next constrained the grain sizes and compositions by fitting models to our five images of the outer disk simultaneously. We performed our fitting only on the NE side, then checked if the same dust composition could also fit the SW side data ( E.1). In Section we show that the data cannot be reproduced with grains consisting entirely of astronomical silicates. In Section we find that a relatively good fit to the data can be obtained with a simple parametrized model for the dust optical constants. Then, in Section we find a good fit to our data with grains consisting of a mixture of common materials and derive significant constraints on the allowed grain composition. We begin, however, in the next section with a description of our model-fitting procedure Fitting Procedure In principle, there were six parameters describing the grain sizes: a min, a max, and q for both disk components; however, before fitting we used physical arguments to narrow these to four free parameters. The largest particles in the parent body component were the planetesimals that resupply the dust through collisions. However, the total surface area in these large bodies was small, so their contribution to the observed signal was insignificant. Thus, we set a max of the parent body component to 5000 µm, an arbitrary but sufficiently large value so the emission from grains larger than this does not contribute significantly to the total. The dust in the halo consisted of the smallest grains generated by the parent body collisional cascade

154 154 the grains small enough to have their orbits perturbed by the stellar radiation force. To model this, we defined the transition grain size, a tran, as a free parameter and set a min of the parent body component and a max of the halo component to this value. Therefore, the halo and parent body components overlapped spatially (they had the same r in ) but were segregated by grain size. In addition to the grain size parameters (halo a min, a tran, halo q, and PB q), the dust masses of each component, M PB and M halo, were also free parameters. Because debris disks are optically thin at all wavelengths, the final radial profile model that we compared to the data was the linear combination of the parent body and halo model profiles. The amplitudes of the two model components were directly proportional to M PB and M halo. Although we fit to only one side of the disk, these masses refer to the total mass of the model disk components (both sides). Finally, there were the free parameters describing the dust composition, which were specific to the analyses described in the following sections. We performed our fitting with a grid search, populating a chi-squared matrix for each of the five images, with one dimension of the matrix for each free parameter. We then combined these matrices according to χ 2 = 1 5 I χ 2 I (5.1) min (χ 2 I ), with I representing each of the five images. We normalized the matrix from each image by the χ 2 value of the best fitting model to that image in an attempt to weight the contribution from each of the five images equally. To find the constraints on a given free parameter, we stepped that parameter over its range of values, and at each point we searched the χ 2 matrix for the minimum over every combination of the other parameters. For the fitting described in the following sections, we fit the radial profile outwards of 3 because in the WFC3 image the flux measured near the star was more likely to have been artificially reduced due to self-subtraction of the disk. This also minimized the influence of the r in spatial parameter on the fits, which was not well constrained. The outer edge of the fitting was specific to each band.

155 Results with 100% Astronomical Silicates Many previous studies of debris disks both analyses of images and SEDs simply assumed the dust was composed entirely of astronomical silicates (e.g. Krist et al., 2010; Golimowski et al., 2011; Ertel et al., 2011). Astronomical silicates, however, is not well-defined material, rather it is a set of optical constants resembling silicates that has been optimized to reproduce the ISM UV extinction curve. The latest version of these optical constants is given by Draine (2003). It was, nevertheless, useful to model the β Pic disk with these optical constants, as doing so allowed us to compare our results more directly with those from other studies. Furthermore, there may be no clear superior alternative to astronomical silicates. Debris disks almost certainly do have a significant silicate component to their composition, as shown by the detection of the distinctive emission feature at 10 µm in the Spitzer/IRS spectra of many debris disks (Ballering et al., 2014; Mittal et al., 2015), including the inner warm component of the β Pic disk (Knacke et al., 1993; Chen et al., 2007). However, a precise laboratory analog to the silicates in debris disk dust and a set of associated optical constants spanning the UV to the mm is not known. We performed the fitting while varying the grain size parameters over the following values: halo q = [3, 4], halo a min = [0.1, 0.5] µm, and a tran = [2, 5] µm. Theoretical examinations of collisional cascades show that q = 3.65 (Gáspár et al., 2012), so we adopted this for the parent body component. The best fit was obtained with a min = 0.1 µm, a tran = 5 µm, and halo q = 3. However, as shown in Figure 5.9, this model did not achieve a good fit to all of the images. Specifically, the halo component (which provided the link between the thermal and scattered data) was fit well to the WFC3 data, but the model was too faint for the MIPS and PACS thermal emission data (and also somewhat too bright at the shorter wavelength STIS scattered light data). This was consistent with the mismatch between the scattered light and thermal emission found in attempts to model other debris disks with astronomical silicates the model, when fit to the thermal data, was too bright compared to the scattered light observations.

156 156 mjy/arcsec 2 mjy/arcsec STIS 5 10 WFC MIPS mjy/arcsec mjy/arcsec 2 mjy/arcsec PACS 00 ALMA 5 10 arcseconds Figure 5.9: The best fit model compared with the five data sets for the NE side of the disk, assuming a composition of 100% astronomical silicates. This illustrates that models with this composition cannot simultaneously fit both the thermal and scattered light data. For example, the model prediction lies above the STIS profile but below those from MIPS and PACS. The black lines are the data, the green lines are the parent body model, the blue lines are the halo model, and the dashed red lines are the total model. The vertical dashed lines show the range of data to which the model was fit.

157 Results with Generic Optical Constants When modeling the dust composition, one is fundamentally manipulating the optical constants, and it is possible that there are degeneracies in this procedure different mixes of grain compositions might produce similar optical constants and thus similar fits to broad-band data. We therefore start the discussion of optimizing the fit to β Pic by considering the optical constants themselves. We generated generic optical constants with only a few free parameters roughly modeled after astronomical silicates. The imaginary component, k(λ), of astronomical silicates shows two broad maxima with a trough between, and goes to zero outside the maxima. We modeled this behavior with the piecewise step function 0 λ < 0.05µm k µm < λ < 0.2µm k(λ) = k 2 0.2µm < λ < 8µm. (5.2) k 3 8µm < λ < 1000µm 0 λ > 1000µm We derived n(λ) from k(λ) using the Kramers-Kronig relation n(ω) = π 0 Ωk(Ω) dω, (5.3) Ω 2 ω2 where ω = 2πc/λ. When evaluating Equation (5.3) numerically, we avoided the singularity by splitting the integral into two pieces, Ω < ω and Ω > ω, then summed the results. Negative values of n(λ) sometimes arose from this procedure at the wavelengths where k(λ) was discontinuous; we removed these negative values from the optical constants before passing them to the modeling code. We assumed both components had the same composition, as the grains in the halo are generated from collisions in the parent body belt. We again fit to the five radial profiles, using the grain size parameters of the best model from the previous section (halo a min = 0.1 µm, a tran = 5 µm, halo q = 3, and PB q = 3.65). We allowed k 1, k 2, and k 3 each to take the values [0.1, 0.6, 1.2]. We found that the best

158 158 fit model had k 1 = 0.6, k 2 = 0.1, and k 3 = 0.1. The best model is compared with the five data sets in Figure 5.10, showing that varying the optical constants can significantly improve the fits, even with a very simple prescription for their form Results with Mixtures of Common Materials We now model the disk by mixing the optical constants of known materials. In principle, a broad variety of mixtures of materials might be able to approximate the desired optical constants, so we must use other constraints to guide the assumed grain composition. We kept the number of constituent materials to a minimum while still accounting for the primary types of materials expected. Johnson et al. (2012b) simulated the formation of planetesimals in the outer parts of protoplanetary disks of various C/O ratios, redox conditions, and temperatures. While the exact compositions of the resulting planetesimals depended on these disk parameters, the most common materials were always refractory silicates and metals, water ice, and simple carbon-bearing compounds that existed as ices or were trapped in the water ice as clathrates. These carbon-bearing ices and clathrates can be transformed into refractory complex organic material (sometimes called ice-tholins ) by exposure to UV radiation or cosmic rays (Khare et al., 1993; McDonald et al., 1996; Materese et al., 2014). This processing makes the material darker (lower albedo) and redder. Refractory organics are invoked to explain the low albedo and red color of some objects in the outer solar system (Cruikshank et al., 2005). We therefore proceeded with four materials: astronomical silicates with optical constants from Draine (2003), water ice with optical constants from Li and Greenberg (1998), refractory organic material with optical constants from Li and Greenberg (1997), and vacuum (to model grain porosity) with n=1 and k=0 at all wavelengths. There are multiple sets of optical constants available for both water ice and organics (e.g. see Table 4 of Rodigas et al. (2015)). We selected these specific constants because they had been used previously by Li and Greenberg (1998) to model β Pic s mid-ir spectral features. The grain densities were 2.7 g/cm 3 for the astronomical silicates (as is commonly assumed), and 1.2 and 1.8 g/cm 3 for the ice

159 159 mjy/arcsec 2 mjy/arcsec STIS 5 10 WFC MIPS mjy/arcsec mjy/arcsec 2 mjy/arcsec PACS 00 ALMA 5 10 arcseconds Figure 5.10: The best fit model compared to the five data sets using generic optical constants. This shows a much better fit compared to Figure 5.9, illustrating the potential for improving the fitting by modifying the optical constants, even using a very simple model to do so. The black lines are the data, the green lines are the parent body model, the blue lines are the halo model, and the dashed red lines are the total model. The vertical dashed lines show the range of data to which the model was fit.

160 χ 2 / min(χ 2 ) f sil f ice f org f vac χ 2 / min(χ 2 ) halo a min a tran halo q PB q Dust Mass (M ) Figure 5.11: The χ 2 curves (normalized to the value of the best model) for fitting the dust composition with a mixture of common materials. The thick lines give the best χ 2 values allowing all other parameters to vary. In the dust mass plot, the blue and green curves represent the halo and parent body models, respectively. The 24 thin lines in the top four plots are the curves with each combination of values of the grain size parameters (a min, a tran, halo q, PB q) fixed. This shows that the conclusions about grain composition do not depend strongly on the grain size parameters; that is, a mixture of astronomical silicates and organic refractory material with little to no ice or vacuum is favored regardless of the choice of a min, a tran, halo q, or PB q.

161 161 and organics, respectively (Li and Greenberg, 1998). The mixing of these component materials was parametrized by the volume fraction of each material, f sil, f ice, f org, and f vac with the sum of these fractions equal to unity. We derived the composite optical constants using the Bruggeman mixing rule, j f j ɛ j ɛ av ɛ j + 2ɛ av = 0, (5.4) where ɛ = ɛ 1 + iɛ 2 is the complex dielectric constant, ɛ av is the dielectric constant of the combined material, and j represents the materials to be combined. dielectric constant is related to the optical constants by The ɛ 1 = n 2 k 2, (5.5) ɛ 2 = 2nk, (5.6) n = 1 2 ɛ ɛ ɛ 1, (5.7) and k = 1 2 ɛ ɛ 2 2 ɛ 1. (5.8) Note that ɛ 1, ɛ 2, n, and k are functions of wavelength. Fitting the grain properties with these optical constants involved 10 freeparameters: the halo s a min, a tran, the halo q, the PB q, f sil, f ice, f org, f vac, M PB, and M halo. Figure 5.11 summarizes the results of this fitting with a subplot for each free parameter. The x axis of each subplot shows the range of values we modeled. The y axis shows the projection of the combined χ 2 matrix onto this parameter that is, the minimum χ 2 value found in the matrix while holding this parameter to the given value. This was then normalized to the χ 2 value of the overall best fit. We found that a mixture of silicates and organics was preferred, while water ice and vacuum were not favored. The parameters of the best fit model are summarized

162 162 Table 5.2. Properties of the Best Fit Model (of the NE side) Parameter Value for Best Model r in 45 au halo r out 1800 au PB r out 150 au halo p 2.4 PB p 0.5 halo a min 0.1 µm a tran 5 µm PB a max 5000 µm a halo q 3 PB q 3.65 f sil 0.6 f ice 0 f org 0.4 f vac 0 M halo M PB M M a This value was fixed prior to fitting. in Table 5.2. Figure 5.12 shows that the best fit model radial profiles match all five data sets well. The optical constants for the best fitting model are shown in Figure 5.13, along with the constants of the three constituent materials and the best fitting generic optical constants model we derived in We also provide the optical constants for our best fit composition in Table F.1. Although we only used two or three values for each of the grain size parameters, our best fit model agreed well with the data, so trying additional values of the grain size parameters was not justified considering our aim was to constrain the composition. Furthermore, as shown by the thin colored curves in the top panels in Figure 5.11, the general result for the grain composition a mixture of astronomical silicates and organic refractory material with little to no ice did not depend on the specific choice of grain size parameters.

163 163 mjy/arcsec 2 mjy/arcsec STIS 5 10 WFC MIPS mjy/arcsec mjy/arcsec 2 mjy/arcsec PACS 00 ALMA 5 10 arcseconds Figure 5.12: The best fit model with a dust composition of 60% astronomical silicates and 40% refractory organics provides a good fit to all five data sets (NE side of the disk). The black lines are the data, the green lines are the parent body model, the blue lines are the halo model, and the dashed red lines are the total model. The vertical dashed lines show the range of data to which the model was fit.

164 Best Fit Best Fit Generic Astro Silicates Ice Organics k Wavelength (µm) n Wavelength (µm) Figure 5.13: The optical constants for our best fit model (60% astronomical silicates and 40% refractory organics), in addition to the optical constants of the three constituent materials we used and the best fitting generic constants.

165 SED For an important check on our best fit model, we compared it to the full-disk thermal SED of the disk at λ 20 µm where the flux density from the outer components was dominant over the flux density from the inner components. To generate SED models, we first computed the dust temperature as a function of grain size and location from a min to a max and from r in to r out by equating the energy absorbed from stellar radiation (given by the model in 5.2) with the emitted thermal energy. We computed the absorption efficiency, Q abs (λ, a), with the code miex (Wolf and Voshchinnikov, 2004) using the given optical constants. The final SED was found by summing the contribution from grains of each size at each location, according to the model disk geometry and n(r, a). The results of our procedure to generate SEDs agreed very well with the total flux density in the thermal emission model images generated by dustmap. The best fit model SED is shown in Figure Although our model slightly under-predicted the data at λ 70 µm, overall our model fit the data very well, supporting the application of the model at additional wavelengths. The sub-mm slope of the SED is sensitive to the grain sizes of the parent body component. Vandenbussche et al. (2010) examined the sub-mm slope of the β Pic SED and concluded that the grain size distribution was shallower than predicted by a steady state collisional cascade. However, our best fit model has q = 3.65 for the parent body component, as predicted for a collisional cascade. In addition to the SED, we present three more comparisons with other data sets in E. These include the SW side of the disk (our fitting was only to the NE side), T-ReCS disk profiles in the mid-ir, and measurements of the disk s scattered light color. In all three cases, our model agrees satisfactorily with the additional data set.

166 166 Excess Flux Density (Jy) PB Model Halo Model Total Model TReCS IRAS MIPS ISO Herschel SCUBA APEX ALMA SIMBA Wavelength (um) Figure 5.14: The thermal SED of our best fit model, compared with the data given in Table 5.1. The fit is good and provides a valuable confirmation of the model.

167 Discussion Sub-blowout Grains To find the blowout size predicted for the best fit model we found in 5.6.4, we calculated the ratio of the radiation force to the gravitational force on a grain, β = 3L 16πGM acρ Q 0 pr (λ, a)f λ (λ) dλ, (5.9) F 0 λ (λ) dλ where ρ is the grain density and Q pr (λ, a) is the radiation pressure efficiency for a grain of radius a computed from the optical constants using the code miex (Wolf and Voshchinnikov, 2004). The blowout size occurs where β=0.5, with smaller grains (having larger β) being blown out. For the composition of our best fit model, the blowout size was 2.7 µm, which was between our best fit a min and a tran values. That is, our best fit halo model consisted of a mixture of sub-blowout grains in the process of leaving the system plus barely bound grains on elliptical orbits. One might expect that grains smaller than the blowout size would be depleted because they leave the system on short timescales. To test whether such a depletion was favored, we re-ran our fitting procedure (using the same mixture of common materials as in 5.6.4) but with three dust components: a halo of sub-blowout grains, a halo of barely bound grains, and a parent body component. The spatial distributions of the two halo components were identical to each other and to the halo component used previously; the spatial distribution of the parent body component was also unchanged. The division between the sub-blowout and barely bound components was at the grain size where β=0.5 and the division between the barely bound halo and the parent body component was at the grain size where β=0.2. That is, a max,sub = a min,barely = a(β=0.5), and a max,barely = a min,pb = a(β=0.2). We used a min,sub = 0.1 µm, a max,pb = 5000 µm, q = 3.65 for the parent body component, and q = 3.0 for both halo components. The masses of the three components were free parameters in the fitting. The composition parameters were varied as before (from 0 to 1 in steps of 0.2). The grain sizes where β=0.5 and β=0.2 varied with the composition because different compositions have different Q pr (λ, a) values. The

168 168 results were nearly the same as what we found in with the best fit composition again f sil = 0.6, f org = 0.4. The grain size corresponding to β=0.2 was 6.4 µm. Flux from the sub-blowout component was dominant in the scattered light bands and in thermal emission at 24 µm; all three components contributed significantly at 70 µm. The mass in sub-blowout grains was approximately the same as that in the original fitting where the halo component spanned both barely bound and sub-blowout grains in a single grain size distribution. Next we tried forcing the model to be depleted in sub-blowout grains. Simulations by van Lieshout et al. (2014) predicted that the dust surface area per decade of grain size would be reduced by three orders of magnitude in sub-blowout grains compared to barely bound grains. 3 We reran our three component fitting with this relative scaling between the sub-blowout and barely bound components imposed. We could not achieve a good fit to the data with any grain composition, confirming that sub-blowout grains were a necessary part of our model. Additional evidence exists for sub-blowout grains in the β Pic system: detailed fits to the mid-ir spectral features used grains as small as 0.1 µm in size (Li and Greenberg, 1998; Okamoto et al., 2004; Li et al., 2012). The data of Okamoto et al. (2004) are particularly significant since they see spatially distributed spectral features from sub-blowout crystalline and amorphous silicates to 30 au, where it appears the features become lost in the noise. de Vries et al. (2012) fit olivine features at 34 and 69 µm with a model emphasizing grain sizes of 1 3 µm and with the grain placement consistent with the inner part of the parent body disk, again showing the importance of sub-blowout grains in the overall SED. Finally, the SED of β Pic (Figure 5.14) shows its 24 µm flux density to be within a factor of two of the peak, whereas it is more typical of debris disks to have a difference of an order of magni- 3 These simulations included grain sublimation, so the magnitude of the depletion and the precise β value above which the depletion occurred depended on the orbital location of the dust. At 30 au (the location of the outer parent body belt in their model), the dust is unaffected by sublimation, and a depletion of three orders of magnitude in surface area per decade of grain size occurred at β 0.5 (see their Figure 5). This orbital location is most applicable to our situation, so we adopted these results.

169 169 tude. That is, the warm spectrum arising from small grains is unusually prominent compared with typical disks. Taken together with our models that showed no significant discontinuity could be tolerated in the grain size distribution at the blowout size, these observations support our assumption that small grains in the halo many of them below the blowout size are dominant in the output at wavelengths shorter than 50 µm. The emission at longer wavelengths is then contributed primarily by the larger grains in the parent body ring (created in the collisional cascade therein), as required to fit the well-resolved image with ALMA. Sub-blowout grains have been inferred from the modeling of other young, bright debris disks. For example, when modeling the debris disk around Fomalhaut, Acke et al. (2012) found that a significant contribution to the observed flux came from sub-blowout grains. Rodigas et al. (2015) used a min = 0.1 to fit the thermal and scattered light of the HR 4796A disk The Dust Composition Here we compare the composition/optical constants of our best fit model with those found in other studies. We reiterate that many models of debris disks simply assumed the dust was composed of astronomical silicates (e.g. Krist et al., 2010; Golimowski et al., 2011; Ertel et al., 2011). Other studies that did constrain the optical constants relied on fitting the thermal SED only and did not match the brightness of the disk in scattered light (e.g. Lebreton et al., 2012; Donaldson et al., 2013). Li and Greenberg (1998) modeled the SED of β Pic with a focus on fitting the detailed shape of the 10 µm feature, so their constraints were strongest for the inner dust component. They found that two grain populations were needed: silicate grains with organic refractory mantles and crystalline silicate grains. The silicate grains with organic refractory mantles were roughly consistent with the composition we found for the dust in the outer disk. Okamoto et al. (2004) and Li et al. (2012) found that the crystalline component detected near 10 µm was concentrated in the inner disk, while de Vries et al. (2012) detected crystalline grains via their 34 and

170 µm features in the outer disk. In both cases, the crystalline materials account for only a few percent of the dust mass, but are readily detectable in these small amounts because of their sharp spectral features. Both because of their small concentration and because the broad spectral character of the crystalline material is similar to that of the amorphous material assumed in our model (e.g. Fabian et al., 2000), basing the model on the amorphous material is acceptable given our emphasis on providing as simple a fit as possible. Min et al. (2011) derived expected dust compositions based on the solar elemental abundances, yielding four species with the following range of mass fractions: silicates (24 47%), FeS (7 14%), carbonaceous dust (0-20%), and water ice (39 49%). The range is due to the unknown fraction of carbon that ended up in dust versus CO gas. This mix of compositions was used to successfully fit the Herschel thermal images of the Fomalhaut disk (Acke et al., 2012), but was not quantitatively compared to the scattered light observations. Dust particles in the Uranus ring system are very dark in scattered light and lack water ice features (Karkoschka, 2001), making them potential analogs for the dust in the β Pic disk. Other solar system particles, like those in the rings of Saturn, do not share these properties, however. The most direct comparison with our work is the characterization of the composition of the HR 4796A debris disk using both scattered light and thermal emission by Rodigas et al. (2015). One of their best fitting models was an isolated case involving a large fraction of metallic iron. We did not include iron in our fitting of β Pic, but we consider it unlikely that the dust grains contain much metallic iron unless they have been exposed to very high temperatures. This fit illustrates our argument that multiple types of material are in principle capable of producing the optical constants needed to fit debris disk behavior. Excluding this case, Rodigas et al. (2015) found that silicates and organics were generally preferred and water ice was not. This agrees with our findings for β Pic and suggests that there may be some commonality to the composition of different debris disks.

171 Summary Matching the thermal emission and scattered light data simultaneously has been a persistent problem for debris disk modeling. Here we investigated whether this problem could be solved by varying the optical constants (and thus composition) of the debris disk dust. We tested this on the β Pic disk, for which there are highquality well-resolved images at many wavelengths, including in both scattered light and thermal emission. We fit our models to data from five instruments: HST /STIS, HST /WFC3, Spitzer/MIPS, Herschel/PACS, and ALMA. The main results of our modeling were as follows: When assuming the dust was composed entirely of astronomical silicates, we could not achieve a successful fit. This resulted in a model that was too bright in scattered light relative to its thermal emission the same offset found by studies that attempted to model other debris disks using only astronomical silicates. We found that a generic model for the optical constants with only a few free parameters could achieve a much-improved fit. This demonstrated that varying the optical constants was capable of solving the problem. Since a variety of materials might be capable of yielding the necessary optical constants, other constraints must be used to narrow the selection of grain compositions. We modeled the dust as a combination of plausible materials astronomical silicates, water ice, refractory organics, and vacuum. We found that a good fit could be achieved with a mix of silicates and organics, and that ice and vacuum were not favored. This model also reproduced well the observed thermal SED, the scattered light colors, and the images from T-ReCS at two mid-ir bands.

172 172 The resulting best fit composition was similar to candidates for the composition of the HR 4796A debris disk found also by simultaneously fitting the thermal and scattered light observations (Rodigas et al., 2015). With continued observations from HST and ALMA and future observations from JWST, the number of debris disks with high-quality data across the electromagnetic spectrum will grow. The composition of these disks can be measured by the method described here. This will allow compositions to be determined and compared for many debris disks.

173 173 CHAPTER 6 SUMMARY AND FUTURE PROSPECTS In Sections I summarize the conclusions of the four studies presented in this dissertation. I also discuss how future observations could further expand our knowledge in each of these areas. Then, in Sections I discuss various areas of promising future work in the field of debris disks more broadly. 6.1 Cold Belts In Chapter 2 I investigated the temperatures of cold debris belts and found them to correlate with the temperature of their host stars. This indicates that, in most cases, they are unlikely to be set by the location of an outer snow line. Instead, I suggest they are set by the stellocentric distance of the outermost planet in the system. My statistical study relied on analyzing the SEDs of a large number of spatially unresolved disks. However, the number of spatially resolved cold belts will continue to grow thanks to ALMA, high-contrast ground-based instruments, further observations with HST, and upcoming observations with JWST. The sample of resolved cold belts may soon be large enough to perform an investigation into the statistical properties of cold disk locations, analogous to what I present here, but without the uncertainties inherent in unresolved data. Detections of additional planets on wide orbits in debris disk systems will also clarify the role of planets is setting the architectures of the disks. High-contrast imaging surveys are currently underway with state-of-the-art extreme adaptive optics systems on eight-meter class ground based telescopes. Upcoming thirty-meter class telescopes will be sensitive to fainter companions (thus lower mass planets or planets in older systems). JWST will also be able to directly image planets, includ-

174 174 ing ice-giants in the process of formation. Finally, future space-based coronagraphic telescopes (e.g. the Wide Field Infrared Survey Telescope) will be highly optimized for planet imaging. 6.2 Exozodi In Chapter 3 I fit the spectra of 22 debris disks exhibiting spectral emission features. In doing so, I found that the emission arose from exozodiacal dust in the terrestrial regions of these systems. The minimum grain sizes of this dust were consistent with the predicted blowout sizes, and the features were found in disks of typical brightness for their age. This suggests this exozodi component is not the result of a transient spike in dust production. Thus, silicate features are a useful signpost for exozodi dust. The emission features in these spectra were weak, suggesting lower levels of exozodi could be identified with a more sensitive instrument. JWST /MIRI spectra will potentially detect exozodi in many systems, and, combined with results from nulling interferometry, will reveal the exozodi mid-ir brightness distribution. 6.3 Warm Disks In Chapter 4 I addressed the uncertain origin of warm debris components. The key to this investigation was that production of dust from an exo-asteroid belt should be located at the primordial snow line, whereas debris originating from an outer reservoir would be located at the current snow line. By showing that the relation between the warm dust location and stellar mass followed that of the primordial snow line for many systems, I concluded that warm components often originate from exo-asteroid belts. While no exo-asteroid belts have yet been definitively imaged, such observations for nearby stars are not unreasonable with current and near-future instruments like JWST. An exo-asteroid belt detection with ALMA would confirm the presence of parent-body planetesimals in the warm belt. Also, locating the primordial snow line

175 175 in observations of protoplanetary disks would allow for a more direct comparison with the location of warm debris. 6.4 Dust Composition In Chapter 5 I simultaneously fit images of the β Pic debris disk in both scattered light and thermal emission solving a persistent problem in debris disk modeling. In doing so, I better constrained the composition of the dust. The best fit was a mixture of astronomical silicates and organic refractory material. I measured the composition of a single debris disk. Observations with JWST will provide the high-quality images in the visible and infrared necessary to apply this technique to a larger sample, revealing the diversity in disk compositions. JWST /MIRI will also provide the sensitivity and spectral resolution required to measure the dust composition by analyzing mid-ir dust spectral features in great detail. The composition can also be measured with scattered light observations of disks at 3 µm where both organic compounds and water ice have an absorption feature (Inoue et al., 2008). Differentiating between the two materials requires spectra, which can be obtained with the near-ir integral field unit capabilities of JWST or with the Arizona Lenslets for Exoplanet Spectroscopy (ALES) integral field spectrograph on the LBT (Skemer et al., 2015). 6.5 Gas in Debris Disks ALMA will continue to discover trace amounts of gas in debris disk systems via submm emission lines. As discussed in Section 1.6.6, the gas is believed to be secondgeneration, meaning it is generated from the planetesimals and dust. Measuring the composition of gas in debris disks provides an additional method to constrain the composition of the debris material and, thus, the composition of terrestrial planets and giant planet cores which formed from the same initial population of planetesimals. For example, Roberge et al. (2006) found that the gas in the β Pic

176 176 disk is highly overabundant in carbon compared to other metals (relative to solar system abundances) and speculated that the dust may be as well. Modeling the production, evolution, and destruction of both dust and gas in debris disks will be crucial to properly interpret gas observations. For example, with a measurement of the abundance of a molecular gas species (like CO) in a disk and an estimate of the photo-dissociating radiation field, the destruction rate of the gas can be estimated. Assuming a steady-state scenario, this rate must also equal the gas production rate. At the same time, a model of the collisions in the disk can be established to fit observations of the dust. Relating the collisional model to the inferred gas production rate can then constrain the composition of the gas-producing solid material in the disk. 6.6 Modeling with Non-Spherical Grains Many studies which model debris disk observations, including the studies I presented in this dissertation, assume the dust grains are spherical when computing their optical properties with Mie theory. As discussed in Section 1.4, there are various techniques to model the optical properties of non-spherical grains, but such techniques have not been generally applied when fitting observations. As shown throughout this dissertation, assumptions must be made when modeling debris disks to limit the number of free parameters and avoid degeneracies. Including non-spherical grains requires additional free parameters, which is difficult to justify in many cases. The way forward is to focus on well-studied debris disks with a variety of highquality observations (well-resolved images at a range of wavelengths, a well-sampled SED, and polarization measurements). These systems may have enough data to meaningfully constrain the grain shapes. If similar results hold for a few such systems, then conclusions about the grain shapes could be extrapolated to disks with less-complete data.

177 Global Debris Disk Simulations In this dissertation, I dissected debris disks into their constituent components (cold dust, warm dust, exozodi dust, blowout halos) and studied the properties of these components separately. Future studies of debris disks should focus on the connections among these components. Such studies could answer some unresolved questions, such as: what is the dominant source of exozodi? and, what is the nature of blowout halos? Global simulations of debris disks are a promising means to study these connections. These simulations include prescriptions for the collisions and dynamics of the planetesimals and dust (including gravitational, radiative, and other forces). Such simulations are now possible due to advances in computation power, especially GPU-based clusters for highly-parallel computing. In additional to providing insights into the working of debris disks, global models may also reduce the number of free parameters required to fit observations, because some of the properties of the model (e.g. the grain size distribution) will arise naturally from the simulation.

178 178 APPENDIX A DERIVING PHOTOSPHERE [24] Here we describe how we used photometry to derive a model photosphere magnitude at 24 µm. The relation among V, K s, and [IRAC] used to predict [24] is Equation A.7, but a number of other relations were used beforehand to improve the accuracy of the result. First, we preprocessed K s, H, and J photometry to remove small nonlinearities in the relations. These small corrections to the 2MASS photometry were derived by comparison with our all-sky warm mission measurements in IRAC Band 1. The preprocessing replaced K s with K s according to K s = K s K 3 s K 2 s K s , (A.1) H with H according to H = H K 3 s K 2 s K s , (A.2) and J with J according to J = J K s (A.3) Equation A.7 utilizes K s SUPER, a combination of measured and derived K s magnitudes. One of these, K s 1, was derived by solving the relation among V, K s 1, and J, given by J K s 1 = x x x x , (A.4) where x 1 = V K s 1. This relation is a fit to the behavior of more than 1000 mainsequence stars, as are the other relations that are given below. K s 2 was derived (if H was measured) by solving the relation among V, K s 2, and H, given by H K s 2 = x x x x , (A.5)

179 179 where x 2 = V K s 2. K s SUPER was then calculated by averaging K s, K s 1, and K s 2 with relative weights of 1, 0.75, and 0.47, respectively. The weights were determined from typical 2MASS errors and by minimizing the residuals in comparing the projected photospheric levels with the 24 µm measurements. Equation A.7 also uses [IRAC] SUPER, a combination of measured and derived IRAC magnitudes. The derived IRAC magnitude, [IRAC] 1, was calculated by solving [IRAC] 1 = K s SUPER x x x x , (A.6) where x = V K s SUPER. The measured [IRAC] and derived [IRAC] 1 were averaged together with relative weights of 1 and 0.5, respectively, yielding [IRAC] SUPER. Finally, [24] was calculated with [24] = [IRAC] SUPER x x x x x , (A.7) where, again, x = V K s SUPER. This process required V and at least one of J, H, or K s to proceed. Targets that did not have this minimum photometry available were not included in our sample, although nearly all targets in our sample had a complete suite of V, J, H, and K s photometry available (Table B.2). The accuracy and precision of this method is illustrated in Figure A.1, which shows the distribution of the difference between the observed and predicted [24] for over 1000 stars. A Gaussian fit to this distribution (the blue curve) has a mean of and a standard deviation of

180 Number Observed [24] Predicted [24] Figure A.1: The distribution of the difference between the observed and predicted 24 µm photosphere magnitude for a sample of 1037 stars. The blue curve shows the Gaussian fit to the distribution with µ = and σ =

181 181 APPENDIX B TARGET PROPERTIES AND RESULTS FROM CHAPTER 2

182 182 Table B.1: Target Properties HIP HD HR Spectral Distance Age Age Age IRS Excess Type (pc) (Gyr) Quality References AOR Verdict HIP110 HD G , Not Included HIP345 HD HR9102 A0V Warm + Cold HIP394 HD HR9107 G2V Not Included HIP490 HD105 G0V ,3,4,5,6,9, Cold HIP522 HD142 HR6 F7V ,17, Not Included HIP544 HD166 HR8 K0Ve ,2,6,15, Warm + Cold HIP560 HD203 HR9 F3Vn Cold HIP682 HD377 G2V ,4,9,12,20, Warm + Cold HIP910 HD693 HR33 F8Vfe-08H ,4,23, Not Included HIP919 HD691 K0V ,9,12,14,18,20, Not Included HIP1031 HD870 K0V , Cold HIP1134 HD984 F ,4,9, Not Included HIP1292 HD1237 G8.5Vk: ,3,4,5, Not Included HIP1368 K ,2, Cold HIP1473 HD1404 HR68 A2V Warm HIP1481 HD1466 F9V , Warm HIP1499 HD1461 HR72 G0V ,12,15,24, Cold HIP1599 HD1581 HR77 F9.5V ,5,6, Not Included HIP2072 HD2262 HR100 A5IVn Warm + Cold HIP2472 HD2834 HR125 A0V Warm + Cold HIP2484 B9V , Not Included HIP2578 HD3003 HR136 A0V , Warm HIP2710 HD3126 F Warm + Cold HIP2843 HD3296 F Cold HIP3093 HD3651 HR166 K0V ,2,5,10,13,14, Not Included HIP3185 HD3795 HR173 K0Vfe-15H ,5,9,12,17,24,27, Not Included

183 183 Table B.1 (cont d) HIP HD HR Spectral Distance Age Age Age IRS Excess Type (pc) (Gyr) Quality References AOR Verdict HIP3497 HD4308 G6VFe ,3,5,12,15,23, Not Included HIP3765 HD4628 HR222 K2.5V ,3,4,5,6,12,13,14, Not Included HIP3909 HD4813 HR235 F7IV-V ,4,12,15,23, Not Included HIP4148 HD5133 K2.5Vk: ,3, Cold HIP5054 HD6434 G2/G3V , Not Included HIP5521 HD6963 K0V ,9,12,14,15, Cold HIP5799 HD7439 HR366 F5V , Not Included HIP5862 HD7570 HR370 F9Vfe ,3,5, Not Included HIP5938 HD7661 G9Vk: ,4,9,14, Not Included HIP5944 HD7590 G ,9,11,12, Cold HIP6276 G9Vk: ,9, Warm HIP6643 HD8574 F ,10,12, Not Included HIP6869 HD8941 F8IV-V , Not Included HIP6878 HD8907 F ,9, Cold HIP6917 HD8997 K2V ,14, Cold HIP7244 HD9472 G ,9,12, Not Included HIP7513 HD9826 HR458 F8V ,2,5,10,12,23, Not Included HIP7576 HD10008 G5V ,12,14, Cold HIP7601 HD10800 HR512 G0+v ,3, Not Included HIP7805 HD10472 F2IV/V Warm + Cold HIP7978 HD10647 HR506 F9V ,4,17, Warm + Cold HIP7981 HD10476 HR493 K1V ,5,9,10,11,12,13,14, Not Included HIP8102 HD10700 HR509 G8V ,4,5,9,10,12,17,23,27, Not Included HIP8159 HD10697 HR508 G5IV ,10,12,24, Not Included HIP8241 HD10939 HR520 A1V Warm + Cold HIP9073 HD11850 G ,9,12, Not Included HIP9141 HD12039 G4V ,5,12,20, Warm

184 184 Table B.1 (cont d) HIP HD HR Spectral Distance Age Age Age IRS Excess Type (pc) (Gyr) Quality References AOR Verdict HIP9683 HD12661 K0V ,10,12, Not Included HIP9902 HD13246 F8V ,27, Warm HIP10138 HD13445 HR637 K1V ,3,4,5,14, Not Included HIP10218 HD13382 G5V ,18,20, Not Included HIP10321 HD13507 G0V ,9,12,14,15,20, Not Included HIP10339 HD13531 G0V ,9,12,14,15, Not Included HIP10644 HD13974 HR660 G0.5V ,9,10, Not Included HIP10680 HD14082 F5V , Not Included HIP10798 HD14412 HR683 G8V ,5,9,10, Not Included HIP11029 HD14691 HR692 F3Vn: Not Included HIP11160 HD15060 F5V Cold HIP11360 HD15115 F Warm + Cold HIP11437 K , Cold HIP11477 HD15427 HR724 A2V Warm + Cold HIP11847 HD15745 F2V Warm + Cold HIP11964 HD16157 K8Vkee ,3, Not Included HIP12048 HD16141 G5IV ,9,10,12, Not Included HIP12444 HD16673 HR784 F6V ,3,5,13,14, Not Included HIP12545 M , Not Included HIP12653 HD17051 HR810 F9Vfe ,3,4,5,14,17, Not Included HIP12777 HD16895 HR799 F7V ,5,23, Not Included HIP12964 HD17390 HR826 F3IV/V Cold HIP12990 HD17240 HR820 A9V Cold HIP13141 HD17848 HR852 A2V Warm + Cold HIP14230 HD18940 G ,9, Not Included HIP14258 HD19019 F ,9,12, Not Included

185 185 Table B.1 (cont d) HIP HD HR Spectral Distance Age Age Age IRS Excess Type (pc) (Gyr) Quality References AOR Verdict HIP14576 HD19356 HR936 B8V Not Included HIP14684 HD19668 G0V ,12,14, Warm HIP14954 HD19994 HR962 F8V ,9,10,12,15, Not Included HIP15323 HD20367 G ,9,10, Not Included HIP15338 HD20315 HR982 B8V Not Included HIP15371 HD20807 HR1010 G0V ,3,5,6,17, Not Included HIP15919 HD21197 K5V ,11, Not Included HIP16012 HD21411 G8V ,4,5, Not Included HIP16852 HD22484 HR1101 F9IV-V ,6,9, Warm + Cold HIP17096 HD23079 F9.5V ,5,17,24, Not Included HIP17420 HD23356 K2.5V , Cold HIP17439 HD23484 K2Vk: ,3, Cold HIP17549 HD23267 A Warm HIP17764 HD24636 F3IV/V Warm + Cold HIP17791 HD23763 A1V Cold HIP17851 HD23862 HR1180 B8IVev Not Included HIP18217 HD24141 HR1192 A5m Warm HIP18437 HD24966 A0V Warm + Cold HIP18481 HD24817 HR1224 A2Vn Warm HIP18859 HD25457 HR1249 F5V ,4,9,10,11,15, Warm + Cold HIP18975 HD25570 HR1254 F2V , Cold HIP19183 HD25953 F , Not Included HIP19335 HD25998 HR1278 F7V ,4,12,14, Cold HIP19893 HD27290 HR1338 F1V Cold HIP19911 HD26990 G ,4,12, Not Included HIP19990 HD27045 HR1329 A3m , Cold HIP20723 HD28185 G6.5IV-V ,12, Not Included

186 186 Table B.1 (cont d) HIP HD HR Spectral Distance Age Age Age IRS Excess Type (pc) (Gyr) Quality References AOR Verdict HIP20901 HD28355 HR1414 A7V Warm + Cold HIP20917 HD28343 K7V ,2, Not Included HIP21276 HD28495 G0Ve ,9,12,17,27, Not Included HIP21327 HD29231 G9V ,4,5, Not Included HIP22122 HD30501 K2V ,3,17,27, Not Included HIP22192 HD30422 HR1525 A3IV Warm + Cold HIP22226 HD30447 F3V Warm + Cold HIP22263 HD30495 HR1532 G1.5VH ,2,3,4,5,9,10,12,13,23, Cold HIP22439 HD30743 HR1545 F3-5V Not Included HIP22449 HD30652 HR1543 F6V ,4,9,10, Not Included HIP22602 HD31143 K0V , Not Included HIP22787 HD31392 G9V ,5,12, Cold HIP22845 HD31295 HR1570 A0V Not Included HIP23311 HD32147 HR1614 K3V ,2,10, Not Included HIP23451 HD32297 A , Warm + Cold HIP23786 HD32850 K0V ,9,15, Not Included HIP23816 HD33081 F7V , Cold HIP23871 HD32977 HR1658 A5V Warm HIP24205 HD33636 G0VH ,9, Cold HIP24947 HD35114 F5/F6V , Warm HIP25486 HD35850 HR1817 F8Vn:k: ,3,4,9, Cold HIP25878 HD36395 M1.5V Not Included HIP26373 HD37572 K1.5Vk ,4,5,9,38, Not Included HIP26394 HD39091 HR2022 G0V ,3,5, Not Included HIP26395 HD37306 HR1919 A2V Warm + Cold HIP26453 HD37484 F3V , Warm + Cold

187 187 Table B.1 (cont d) HIP HD HR Spectral Distance Age Age Age IRS Excess Type (pc) (Gyr) Quality References AOR Verdict HIP26653 HD37216 G ,9,12, Not Included HIP26737 HD37962 G2V ,4,5,12, Not Included HIP26796 HD38056 HR1966 A0V Warm + Cold HIP26966 HD38206 HR1975 A0V , Warm + Cold HIP27225 HD37006 G ,9,12, Not Included HIP27253 HD38529 HR1988 G4V ,4,9,10,12,20, Cold HIP27288 HD38678 HR1998 A2IV-Vn: Warm HIP27417 HD38949 G1V ,4,9,12, Not Included HIP27435 HD38858 HR2007 G4V ,9,10,12, Cold HIP28103 HD40136 HR2085 F2V ,23, Warm HIP28764 HD41700 HR2157 F9VFe ,5,9,10, Not Included HIP28767 HD40979 F ,10, Not Included HIP28902 HD40647 G ,12,20, Not Included HIP30030 HD43989 G ,12, Cold HIP30104 HD44594 HR2290 G1.5V ,4,10, Not Included HIP30314 HD45270 G0VpH ,3,34,38, Not Included HIP30503 HD45184 HR2318 G1.5V ,5,9, Cold HIP32366 HD49095 HR2500 F6.5V , Not Included HIP32435 HD53842 F5V Warm HIP32439 HD46588 HR2401 F8V ,2,6,15, Not Included HIP32775 HD50571 HR2562 F5VFe , Cold HIP32984 HD50281 K3V , Not Included HIP33212 HD50554 F8V ,10, Cold HIP33277 HD50692 HR2569 G0V ,6,9,12,15, Not Included HIP33719 HD52265 HR2622 G0III-IV , Cold HIP34017 HD52711 HR2643 G4V ,4,6,9,12, Not Included HIP34065 HD53705 HR2667 G0V ,15,24, Not Included HIP34276 HD54341 A0V Warm + Cold

188 188 Table B.1 (cont d) HIP HD HR Spectral Distance Age Age Age IRS Excess Type (pc) (Gyr) Quality References AOR Verdict HIP34834 HD55892 HR2740 F3Vfe , Not Included HIP35136 HD55575 HR2721 G0V ,12,15, Not Included HIP35350 HD56537 HR2763 A3V Not Included HIP35803 HD57703 F Cold HIP36188 HD58715 HR2845 B8Ve Not Included HIP36439 HD58855 HR2849 F6V , Not Included HIP36515 HD59967 HR2882 G2V ,3,4,5, Cold HIP36948 HD61005 G8Vk+? ,4,5,12, Warm + Cold HIP37068 HD61518 F5V Not Included HIP37170 HD60737 G ,12, Cold HIP37606 HD62644 HR2998 G8IV-V , Not Included HIP38018 HD61994 G ,2,9,12,20, Not Included HIP38647 HD64324 G ,12, Not Included HIP38784 HD62613 HR2997 G8V ,2,6,9,10, Not Included HIP39157 HD65583 G8V ,6,9,12,15, Not Included HIP40015 HD66751 F ,12, Not Included HIP40035 HD68146 HR3202 F6.5V Not Included HIP40093 HD67827 HR3193 G Not Included HIP40118 HD68017 G4V ,6,9,12,15, Not Included HIP40419 HD69076 G ,12,20, Not Included HIP40693 HD69830 HR3259 G8+v ,3,4,9,10, Not Included

189 189 Table B.1 (cont d) HIP HD HR Spectral Distance Age Age Age IRS Excess Type (pc) (Gyr) Quality References AOR Verdict HIP40843 HD69897 HR3262 F6V ,9,12,15, Not Included HIP41081 HD71043 HR3300 A0V Warm + Cold HIP41152 HD70313 HR3277 A3V Warm + Cold HIP41184 HD70516 G ,12, Not Included HIP41373 HD71722 HR3341 A0V Warm + Cold HIP41484 HD71148 HR3309 G5V ,6,9,12,15, Not Included HIP41820 HD71974 G , Not Included HIP41926 HD72673 HR3384 G9V ,4,5,9,12, Not Included HIP41967 HD72687 G5V ,5, Warm HIP42074 HD72760 G ,9,10,11,12, Not Included HIP42327 HD73210 A5V Cold HIP42333 HD73350 G ,9,11,12, Cold HIP42438 HD72905 HR3391 G1.5Vb ,6,9,10,11,12,13,14, Cold HIP42488 HD73668 G1V ,9,12, Not Included HIP42491 HD73668B G , Not Included HIP43121 HD74873 HR3481 A1V Warm HIP43297 HD75302 G ,4,9, Not Included HIP43299 HD75393 F7V ,9, Not Included HIP43587 HD75732 HR3522 G8V ,9,10,12, Not Included HIP43625 HD75616 F Cold HIP43726 HD76151 HR3538 G3V ,2,3,5,12,13, Cold HIP43797 HD76653 HR3570 F6V , Cold HIP43852 HD76218 G ,9,12,15, Not Included HIP44458 HD77407 G ,12,18,20, Not Included HIP44897 HD78366 HR3625 F9V ,2,10,12,13,14,15,23, Not Included HIP45167 HD79108 HR3651 A0V Warm + Cold HIP45585 HD80950 HR3721 A0V Not Included

190 190 Table B.1 (cont d) HIP HD HR Spectral Distance Age Age Age IRS Excess Type (pc) (Gyr) Quality References AOR Verdict HIP45982 HD80606 G ,10,12,20, Cold HIP46580 HD82106 K3V ,2,6,14, Not Included HIP46843 HD82443 K1Vk: ,3,14, Warm + Cold HIP47007 HD82943 F9Vfe ,10, Cold HIP47135 HD84075 G2V ,17,27, Warm + Cold HIP48113 HD84737 HR3881 G0.5Va ,12,15, Not Included HIP48331 HD85512 K6Vk: ,4,17, Not Included HIP48423 HD85301 G ,9, Warm + Cold HIP48833 HD86146 HR3928 F6Vs , Not Included HIP49081 HD86728 HR3951 G3Va ,9,12,15, Not Included HIP49593 HD87696 HR3974 A7V Warm HIP49767 HD88201 G0IV ,4,5,17,20, Not Included HIP49908 HD88230 K5V ,2, Not Included HIP50075 HD88742 HR4013 G0V ,3,4,5, Not Included HIP50786 HD89744 HR4067 F7V ,4,9,10,15,23,24, Not Included HIP50921 HD90156 G5V ,5,9,12, Not Included HIP51194 HD90874 HR4115 A2V Warm HIP51228 HD90712 G0VH ,3,4,5,17,20, Not Included HIP51386 HD90905 F ,9,12, Not Included HIP51523 HD91324 HR4134 F9Vfe-08H ,23, Not Included HIP51955 HD91782 G , Not Included HIP51966 HD91962 G ,4, Not Included HIP52409 HD92788 G ,9,10,12,20,24, Not Included HIP52462 HD92945 K1.5Vk: ,9,12,14, Cold HIP52498 HD92855 F9V ,9,12, Not Included HIP53721 HD95128 HR4277 G1V ,9,10, Not Included HIP53747 HD95188 G8V ,12,14, Not Included

191 191 Table B.1 (cont d) HIP HD HR Spectral Distance Age Age Age IRS Excess Type (pc) (Gyr) Quality References AOR Verdict HIP53910 HD95418 HR4295 A1V Cold HIP53954 HD95608 HR4300 A1m Warm HIP53985 HD95650 M Not Included HIP54035 HD95735 M2V , Not Included HIP54646 HD97101 K8V Not Included HIP54879 HD97633 HR4359 A2V Warm HIP55210 HD98281 G8V ,10, Not Included HIP55363 HD98553 G2/G3V ,9,12,20, Not Included HIP55485 HD98673 HR4388 A7Vn Warm + Cold HIP55848 HD99492 K2V ,10, Not Included HIP56242 HD HR4437 G0V ,9,10,12,13,14, Not Included HIP56257 HD F ,12, Not Included HIP56452 HD HR4458 K0V ,3,4,5,9,10, Not Included HIP56673 HD F5IV Not Included HIP56830 HD HR4489 G7V ,12, Not Included HIP56960 HD G ,9, Not Included HIP56997 HD HR4496 G8V ,6,9,10,12,13,14, Not Included HIP57087 M3.5V Not Included HIP57217 HD F9V ,5,9,12, Not Included HIP57271 HD K0.5V ,9,12, Not Included HIP57507 HD HR4525 G6V , Not Included HIP57524 HD G4Vp ,34, Warm HIP57589 K ,34, Not Included HIP57632 HD HR4534 A3V Cold HIP57950 HD F2IV/V Warm HIP57971 HD HR4553 A2V Warm HIP58067 HD G ,9,12, Not Included

192 192 Table B.1 (cont d) HIP HD HR Spectral Distance Age Age Age IRS Excess Type (pc) (Gyr) Quality References AOR Verdict HIP58220 HD F3V Warm HIP58345 HD K5V , Not Included HIP58451 HD K2V Cold HIP58528 HD F5V Warm HIP58720 HD HR4597 B9V Warm + Cold HIP58722 HD G ,12,17,20,27, Not Included HIP58803 HD HR4600 F5V , Not Included HIP58876 HD F ,9,12, Cold HIP59072 HD HR4616 F2V Warm + Cold HIP59280 HD K0V ,9,11,12,15, Not Included HIP59394 HD HR4635 A1V Warm HIP59422 HD F Cold HIP59481 HD F3V Not Included HIP59572 HD G8V ,20, Not Included HIP59610 HD G0V ,10,12, Not Included HIP59750 HD HR4657 F5V ,2,3,14, Not Included HIP59774 HD HR4660 A3V Not Included HIP59960 HD F5V Warm + Cold HIP60074 HD G2V ,9,12, Warm + Cold HIP60348 HD F5V Warm HIP60561 HD A0V Warm + Cold HIP60582 HD F Not Included HIP61049 HD F7V Warm HIP61053 HD HR4767 F9V , Not Included HIP61072 HD F Not Included HIP61087 HD F6V Not Included

193 193 Table B.1 (cont d) HIP HD HR Spectral Distance Age Age Age IRS Excess Type (pc) (Gyr) Quality References AOR Verdict HIP61498 HD HR4796 A0V ,35, Cold HIP61558 HD HR4799 A3V Warm HIP61622 HD HR4802 A2V Not Included HIP61684 HD A9V Warm + Cold HIP61960 HD HR4828 A0V Warm + Cold HIP62134 HD F2V Warm HIP62207 HD HR4845 G0V ,12,15, Cold HIP62523 HD HR4864 G5V ,9,10,11,12, Not Included HIP62657 HD F5/F6V Warm + Cold HIP63005 HD HR4899 B5Vne , Not Included HIP63008 HD F8V ,18, Not Included HIP63076 HD HR4916 F0IV-V Cold HIP63439 HD F4IV/V Warm + Cold HIP63584 HD HR4934 F6V , Cold HIP63836 HD F Warm + Cold HIP64053 HD HR4951 B8V Warm HIP64184 HD F3V Cold HIP64394 HD HR4983 G0V ,2,9,10,11,12,13, Not Included HIP64426 HD F9V Not Included HIP64457 HD K , Not Included HIP64532 HD G1Va ,2,6, Not Included

194 194 Table B.1 (cont d) HIP HD HR Spectral Distance Age Age Age IRS Excess Type (pc) (Gyr) Quality References AOR Verdict HIP64877 HD F5V Warm HIP64924 HD HR5019 G7V ,4,5,9,12,13, Cold HIP64995 HD F2IV/V Cold HIP65109 HD HR5028 A3V Warm HIP65515 HD G9V ,11,12,15, Not Included HIP65721 HD HR5072 G5V ,4,6,9,10,12,23, Not Included HIP65728 HD HR5085 A1Vn Warm + Cold HIP65875 HD F6V Cold HIP65965 HD B9V Warm + Cold HIP66065 HD HR5097 A0/A1V Warm HIP66068 HD A1/A2V Warm HIP66121 HD HR5082 F8VFe Not Included HIP66234 HD HR5112 A5V Cold HIP66447 HD A3IV/V Cold HIP66704 HD HR5148 F7.7V , Cold HIP66765 HD K0Vk: ,3,5,17,27, Cold HIP67068 HD F3V Warm HIP67230 HD F5V Warm HIP67275 HD HR5185 F6IV ,2,4,9,10,13, Not Included HIP67472 HD HR5193 B2Vnpe Not Included HIP67497 HD F0V Cold HIP67620 HD HR5209 G5+v ,3,5,9, Not Included HIP67904 HD G ,15, Not Included HIP68162 HD G2V , Not Included HIP68184 HD HR5256 K3V , Not Included HIP68380 HD HR5258 F8V , Not Included

195 195 Table B.1 (cont d) HIP HD HR Spectral Distance Age Age Age IRS Excess Type (pc) (Gyr) Quality References AOR Verdict HIP68593 HD F ,9, Cold HIP69562 HD K5.5Vkee , Not Included HIP69618 HD HR5316 B4Vne , Not Included HIP69989 HD HR5365 F5IV , Cold HIP69995 HD HR5357 A2Vn Not Included HIP70319 HD HR5384 G1V ,5,9,12,15, Not Included HIP70455 HD B8V Warm HIP70952 HD HR5436 F4IV Cold HIP71181 HD K3V , Cold HIP71271 HD A0V Warm + Cold HIP71395 HD K0V ,10,14, Cold HIP71631 HD G0V ,2,9,12,15,18,20, Not Included HIP71743 HD G8Vk: ,11,12, Not Included HIP71855 HD G5V ,3, Not Included HIP71957 HD HR5487 F2V , Not Included HIP72033 HD F7IV/V Not Included HIP72070 HD G3V Cold HIP72339 HD K0V , Cold HIP72573 HD HR5596 F9V , Not Included HIP73100 HD HR5581 F7V ,4,15, Not Included HIP73145 HD A2IV Warm + Cold HIP73184 HD HR5568 K4V ,3,5, Not Included HIP73269 HD G0V ,9, Not Included HIP73754 HD F9VH ,3,5,9,20, Not Included HIP73869 HD G ,6,9,12, Not Included HIP73996 HD HR5634 F5V ,2,16, Not Included HIP74045 HD G ,18,20,34, Not Included

196 196 Table B.1 (cont d) HIP HD HR Spectral Distance Age Age Age IRS Excess Type (pc) (Gyr) Quality References AOR Verdict HIP74499 HD F4V Warm + Cold HIP74500 HD HR5657 G6IV-V ,9,10,12,17,24, Not Included HIP74702 HD K ,9, Cold HIP74824 HD HR5670 A3Va Warm HIP74948 HD F , Not Included HIP74959 HD F5V Cold HIP75077 HD A1V Warm + Cold HIP75151 HD HR5697 A0sp Not Included HIP75210 HD B8/B9V Warm + Cold HIP75277 HD K ,12,15, Not Included HIP75829 HD G ,9,12,15,20, Not Included HIP76267 HD HR5793 A0V Not Included HIP76568 HD HR5830 F2V Not Included HIP76629 HD K0Vk ,3,4,18,34, Not Included HIP76736 HD HR5792 A1V Warm + Cold HIP77315 HD A0V Warm HIP77432 HD F5V Warm HIP77464 HD HR5875 A5IV Warm + Cold HIP77520 HD F3V Not Included HIP77740 HD G1V ,9,10,12, Not Included HIP77760 HD HR5914 F8Ve ,12, Not Included HIP77810 HD G ,4,9, Not Included HIP77986 HD HR5938 B9pe Not Included HIP78043 HD F3V Warm + Cold HIP78045 HD HR5905 A3V Warm HIP78072 HD HR5933 F6IV ,4,9,10,23, Not Included HIP78459 HD HR5968 G0Va ,9,10,12,15,23, Not Included HIP78641 HD A5IV/V Warm

197 197 Table B.1 (cont d) HIP HD HR Spectral Distance Age Age Age IRS Excess Type (pc) (Gyr) Quality References AOR Verdict HIP78663 HD F5V Cold HIP78775 HD G8V ,6,9,10,12,15, Not Included HIP79054 HD F0V Not Included HIP79165 HD G ,9,12, Cold HIP79248 HD K0V ,6,9,10, Not Included HIP79516 HD F5V Warm + Cold HIP79631 HD B9.5V Warm + Cold HIP79672 HD HR6060 G2Va ,9,12,15,17,27, Not Included HIP79710 HD F0V Warm HIP79742 HD F Warm + Cold HIP79797 HD HR6037 A4V Warm + Cold HIP79881 HD HR6070 A0V Warm HIP80337 HD HR6094 G1VH ,3,4,5,11, Not Included HIP80902 HD G ,6,9,10,12, Cold HIP81300 HD HR6171 K0Vk: ,2,3,9,10,12,14,15, Not Included HIP81662 HD F ,9,12, Not Included HIP81800 HD F8V , Cold HIP82003 HD K ,12,15, Not Included HIP82388 HD G3V ,4, Not Included HIP82587 HD HR6279 F0V , Cold HIP82688 HD G ,12,20, Not Included HIP83159 HD F5V Not Included HIP83181 HD G ,4,9, Not Included HIP83187 HD HR6297 A5IV-V Warm + Cold HIP83541 HD K0IV-V ,5,9, Not Included HIP83591 HD K5V Not Included HIP83601 HD HR6349 F8.5IV-V ,4,10,11,12,14,15, Not Included HIP84478 HD K5Vk: ,2,3,5,10,14,23,32, Not Included

198 198 Table B.1 (cont d) HIP HD HR Spectral Distance Age Age Age IRS Excess Type (pc) (Gyr) Quality References AOR Verdict HIP84586 HD G5IV+K0IV ,23,34,38, Not Included HIP84714 HD G , Not Included HIP84862 HD HR6458 G0V ,9,12, Not Included HIP85235 HD HR6518 K0V , Cold HIP85295 HD K ,2, Not Included HIP85523 M2+v Not Included HIP85537 HD HR6507 A8V Warm + Cold HIP85810 HD HR6538 G5V ,6,9,10,11,12,15, Not Included HIP85922 HD HR6534 A5V Warm HIP86162 M3.5V Not Included HIP86305 HD HR6549 A5IV-V Warm + Cold HIP86486 HD HR6569 F4V Not Included HIP86540 HD K ,20, Not Included HIP86796 HD HR6585 G3IV-V ,5, Not Included HIP87108 HD HR6629 A0V , Warm + Cold HIP87937 M4Ve Not Included HIP88175 HD HR6710 F2IV , Not Included HIP88348 HD K0V ,9,10,12,15,20, Not Included HIP88972 HD HR6806 K2V ,2,5,6,10,13,14, Not Included HIP89282 HD F ,9,12, Not Included HIP89348 HD HR6850 F5V ,2, Not Included HIP89474 HD HR6847 G2V ,6,9,12,15, Not Included HIP89770 HD F Warm HIP89844 HD G6V ,9,10,12, Not Included HIP89937 HD HR6927 F7V , Not Included

199 199 Table B.1 (cont d) HIP HD HR Spectral Distance Age Age Age IRS Excess Type (pc) (Gyr) Quality References AOR Verdict HIP90586 HD G ,9,12, Not Included HIP90936 HD HR6948 F5V , Warm + Cold HIP91438 HD HR6998 G6V ,4,5,9,10,12, Not Included HIP91507 HD F ,9, Not Included HIP92043 HD HR7061 F6V ,2,4,5,16, Not Included HIP92680 HD K0Vp ,5,34,38, Not Included HIP93746 HD K , Not Included HIP93815 HD HR7213 F7V ,23, Not Included HIP94114 HD HR7254 A2Va Warm + Cold HIP94645 HD HR7291 F8.5V ,3,4,9,10,12,17,20, Not Included HIP94858 HD HR7297 F7V Cold HIP95149 HD HR7330 G1V ,3,5,6, Not Included HIP95270 HD F5/F6V Warm + Cold HIP95319 HD HR7368 G8V ,9,12,15,23, Not Included HIP95560 HD HR7390 A0V Warm HIP95793 HD HR7400 A0V Cold HIP95849 HD F8.5VFe ,3,4,5,12, Cold HIP96100 HD HR7462 K0V ,2,9,10,12,14,15, Not Included HIP96901 HD HR7504 G3V ,3,9,10,12,15,23,24, Not Included HIP97779 HD G ,9,12,20,32, Cold HIP98470 HD HR7631 F8.5Vfe-06H ,3,4, Not Included HIP98495 HD HR7590 A0Va Not Included HIP98714 HD G5IV ,12,20,21, Not Included HIP98767 HD HR7670 G7IV-V ,9,10,12,15,24, Not Included HIP98819 HD HR7672 G0V ,3,5,6,9,10,12,14, Not Included

200 200 Table B.1 (cont d) HIP HD HR Spectral Distance Age Age Age IRS Excess Type (pc) (Gyr) Quality References AOR Verdict HIP98959 HD HR7644 G2V ,5, Not Included HIP99461 HD HR7703 K2.5V ,3,5,12,14,17, Not Included HIP99701 HD K , Not Included HIP99711 HD K2V ,10,14, Cold HIP99742 HD HR7724 A2V Warm + Cold HIP99825 HD HR7722 K2+v ,3,12, Not Included HIP HD F ,4,9,12, Not Included HIP HD HR7779 A0V Cold HIP HD G ,12, Not Included HIP HD HR7848 F0V Warm + Cold HIP HD HR7883 A2V Warm + Cold HIP HD G3V , Not Included HIP HD HR7875 G0Vfe-08H Not Included HIP HD HR7914 G5V ,9,12,15, Not Included HIP HD HR7936 F5V ,3,4,16, Not Included HIP HD K0V , Cold HIP HD G ,9,12, Not Included HIP HD F8V ,4,20,23,34, Not Included HIP HD HR8013 F6V ,3,12, Cold HIP HD G0V ,9,12, Not Included HIP HD G ,9, Not Included HIP HD G ,9,12, Cold HIP HD G ,9,12,15, Not Included HIP HD G5V ,3,5,9,12, Not Included HIP HD G8V ,9,12,14, Not Included HIP HD G5V ,5,9, Cold HIP HD HR8181 F9Vfe-14H Not Included

201 201 Table B.1 (cont d) HIP HD HR Spectral Distance Age Age Age IRS Excess Type (pc) (Gyr) Quality References AOR Verdict HIP HD F8V ,9, Cold HIP HD K1.5V ,3,5, Not Included HIP HD F4IV Warm + Cold HIP HD HR8265 A2V Warm HIP HD G1V ,3,5,9,12, Not Included HIP HD G9V ,5,17, Not Included HIP HD G8V ,9,12,15, Cold HIP HD HR8314 G0VH ,2,3,5,12,13,14,15,16, Not Included HIP HD F5V , Cold HIP HD HR8323 G0Vfe ,3,5,17, Warm + Cold HIP HD G5V ,9,12, Not Included HIP HD F6.5V ,3,9, Cold HIP HD G1V ,3,9,14,20, Not Included HIP HD G0V ,9,10,12,15, Not Included HIP M Not Included HIP HD HR8447 F6V ,9,16, Not Included HIP HD HR8477 G2V ,5, Not Included HIP HD G ,12, Not Included HIP HD HR8531 G2IV-V ,5,17,24, Not Included HIP HD HR8526 G0V ,5,17,24, Not Included HIP HD F Cold HIP HD K5V ,17, Not Included HIP HD G0/G1V ,24, Not Included HIP HD HR8585 A1V Not Included HIP HD HR8581 F7V Not Included HIP HD HR8586 F1V Cold HIP HD HR8592 F5V ,3,4, Not Included

202 202 Table B.1 (cont d) HIP HD HR Spectral Distance Age Age Age IRS Excess Type (pc) (Gyr) Quality References AOR Verdict HIP HD HR8673 B9V Warm + Cold HIP M Not Included HIP HD HR8701 G1Vfe ,17,24, Not Included HIP HD HR8729 G2V ,3,5,9,10,12,13,15,23,24,32, Not Included HIP HD HR8734 G8IV ,10,12, Not Included HIP HD G1.5Vk: ,3,5, Not Included HIP HD G5V ,9,12, Not Included HIP HD HR8799 A5V , Warm + Cold HIP HD G3V Cold HIP HD K5.5Vk: , Not Included HIP HD HR8853 F7V Cold HIP HD HR8843 F6V , Cold HIP HD HR8911 A0p Warm HIP HD F Cold HIP HD HR8974 K1IV , Not Included HIP HD K3+v ,3, Not Included HIP HD G9.5V ,5,6,12, Not Included HIP HD HR8969 F7V , Not Included HIP HD G , Not Included HIP HD HR9016 A0V Warm + Cold HIP HD HR9062 A1V , Not Included References. (1) Duncan et al. (1991); (2) Rosat All Sky Survey (Voges et al., 1999, 2000); (3) Gray et al. (2006); (4) Schröder et al. (2009); (5) Henry et al. (1996); (6) Rocha-Pinto and Maciel (1998); (7) Vican (2012) isochrone ages; (8) Schmitt and Liefke (2004); (9) Wright et al. (2004); (10) Katsova and Livshits (2011); (11) Martínez-Arnáiz et al. (2010); (12) Isaacson and Fischer (2010); (13) Vican (2012) gyro ages; (14) Barnes (2007); (15) Gray et al. (2003); (16) v sin(i);

203 203 (17) Jenkins et al. (2006); (18) Montes et al. (2001); (19) Vican (2012) X-ray; (20) White et al. (2007); (21) log(g); (22) Lachaume et al. (1999); (23) Buccino and Mauas (2008); (24) Sierchio et al. (2014) HR diagram position; (25) Paunzen (1997); (26) Nakajima and Morino (2012); (27) Jenkins et al. (2011); (28) Mamajek and Hillenbrand (2008); (29) Barrado y Navascues (1998); (30) Rhee et al. (2007b); (31) Su et al. (2006); (32) Pace (2013); (33) Feltzing et al. (2001); (34) Tetzlaff et al. (2010); (35) Rizzuto et al. (2011); (36) Hoogerwerf (2000); (37) Plavchan et al. (2009); (38) Zuckerman and Song (2004); (39) Herrero et al. (2012); (40) Murgas et al. (2013); (41) Karataş et al. (2005); (42) Mishenina et al. (2012); (43) Takeda et al. (2007); (44) Ng and Bertelli (1998); (45) Baines et al. (2012).

204 204 Table B.2: Photometry and IR Excess Properties HIP V J H Ks Phot. T IRAC MIPS24 MIPS70 RJ MIPS70 Excess T cold Twarm f cold fwarm ID (mag) (mag) (mag) (mag) Refs. (K) (Jy) (mjy) (mjy) (Jy µm 2 ) (mjy) (K) (K) ( 10 5 ) ( 10 5 ) ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± 10.6 < ± ± ± ± ± ± ± ± 5.15 < ± ± ± ± ± ± ± ± ± ± ± ± ± 4.47 < ± ± ± ± ± ± ± ± ± ± 6.5 < ± ± ± ± ± ± ± ± 5.39 < ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± 52.1 < ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± 7.58 < ± ± ± ±

205 205 Table B.2 (cont d) HIP V J H Ks Phot. T IRAC MIPS24 MIPS70 RJ MIPS70 Excess T cold Twarm f cold fwarm ID (mag) (mag) (mag) (mag) Refs. (K) (Jy) (mjy) (mjy) (Jy µm 2 ) (mjy) (K) (K) ( 10 5 ) ( 10 5 ) ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ±

206 206 Table B.2 (cont d) HIP V J H Ks Phot. T IRAC MIPS24 MIPS70 RJ MIPS70 Excess T cold Twarm f cold fwarm ID (mag) (mag) (mag) (mag) Refs. (K) (Jy) (mjy) (mjy) (Jy µm 2 ) (mjy) (K) (K) ( 10 5 ) ( 10 5 ) ,4, ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± 3.1 < ± ± ± ± 4.18 < ± ± ± ± ± ± ± 3.27 < ± ± ± 4.36 < ± ± ± ± ± ± ± ± ± ± 16.9 < ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± 5.57 < ± ± ± ± ± ± ± ± ± 10.2 < ± ± ± ± ± ± ± ± ± ±

207 207 Table B.2 (cont d) HIP V J H Ks Phot. T IRAC MIPS24 MIPS70 RJ MIPS70 Excess T cold Twarm f cold fwarm ID (mag) (mag) (mag) (mag) Refs. (K) (Jy) (mjy) (mjy) (Jy µm 2 ) (mjy) (K) (K) ( 10 5 ) ( 10 5 ) ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± 3.85 < ± ± ± 13.4 < ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± 18.2 < ± ± ± ± 4.99 <45 4.1

208 208 Table B.2 (cont d) HIP V J H Ks Phot. T IRAC MIPS24 MIPS70 RJ MIPS70 Excess T cold Twarm f cold fwarm ID (mag) (mag) (mag) (mag) Refs. (K) (Jy) (mjy) (mjy) (Jy µm 2 ) (mjy) (K) (K) ( 10 5 ) ( 10 5 ) ± ± ± ± ± ± ± 2.16 < ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ,2, ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± 7.13 < ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± 11.5 < ± ± ± ± ± ± ± ± ± ± 41.5 < ± ± ± ± ± ± ±

209 209 Table B.2 (cont d) HIP V J H Ks Phot. T IRAC MIPS24 MIPS70 RJ MIPS70 Excess T cold Twarm f cold fwarm ID (mag) (mag) (mag) (mag) Refs. (K) (Jy) (mjy) (mjy) (Jy µm 2 ) (mjy) (K) (K) ( 10 5 ) ( 10 5 ) ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± 4.38 < ± ± ± ± ± ± ± 21.1 < ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± 31 < ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± References for heritage photometry used in addition to 2MASS. (1) Obtained from SAAO (unpublished); (2) ESO (Bouchet et al., 1991; van der Bliek et al., 1996); (3) Johnson et al. (1966); (4) Carter (1990); (5) Glass (1974); (6) Aumann and Probst (1991); (7) Allen and Cragg (1983); (8) Groote and Kaufmann (1983); (9) Kidger and Martín-Luis (2003); (10) Alonso et al. (1998).

210 210 APPENDIX C PLOTS OF WARM BELT FITS FROM CHAPTER 4

211 F 8 (mjy) F 8 (mjy) F 8 (mjy) F 8 (mjy) HIP 9902 HIP HIP HIP HIP HIP HIP HIP HIP HIP HIP HIP ( 7m) ( 7m) ( 7m) Figure C.1: The best fits to the 29 single component systems. Small black points are the IRS data (with grey error bars), large black circles are photometry data, and the black triangles are photometric upper limits. The stellar photosphere is cyan, the warm dust belt model is green, and the total model is red.

212 F 8 (mjy) F 8 (mjy) F 8 (mjy) F 8 (mjy) 212 HIP HIP HIP HIP HIP HIP HIP HIP HIP HIP HIP HIP ( 7m) ( 7m) ( 7m) Figure C.2: Continuation of Figure C.1

213 F 8 (mjy) F 8 (mjy) 213 HIP HIP HIP HIP HIP Figure C.3: Continuation of Figure C.1

214 214 HIP 345 F8 (mjy) 10 HIP HIP F8 (mjy) HIP HIP HIP HIP HIP HIP F8 (mjy) HIP HIP HIP F8 (mjy) ( 7m) ( 7m) ( 7m) Figure C.4: The best fits to the 54 two component systems. Small black points are the IRS data (with grey error bars), large black circles are photometry data, and the black triangles are photometric upper limits. The stellar photosphere is cyan, the warm dust belt model is green, the cold component is blue, and the total model is red.

215 215 HIP HIP F8 (mjy) HIP HIP HIP F8 (mjy) HIP HIP HIP HIP F8 (mjy) HIP HIP HIP F8 (mjy) ( 7m) ( 7m) Figure C.5: Continuation of Figure C.4 6 ( 7m)

216 216 HIP HIP HIP F8 (mjy) HIP HIP HIP F8 (mjy) HIP HIP HIP F8 (mjy) HIP HIP F8 (mjy) HIP ( 7m) ( 7m) Figure C.6: Continuation of Figure C.4 6 ( 7m)

217 217 HIP HIP HIP F8 (mjy) HIP HIP HIP F8 (mjy) HIP HIP F8 (mjy) 10 0 HIP HIP HIP HIP F8 (mjy) ( 7m) ( 7m) Figure C.7: Continuation of Figure C.4 6 ( 7m)

218 F 8 (mjy) F 8 (mjy) HIP HIP HIP HIP HIP HIP Figure C.8: Continuation of Figure C.4

219 219 APPENDIX D TARGETS PROPERTIES AND FITTING RESULTS FROM CHAPTER 4

220 220 Table D.1: Target Properties HIP Spectral V J H K T L M abos D IRS xll1 xsl1 xsl2 Identifier Type (mag) (mag) (mag) (mag) (K) (L ) M (µm) (pc) AOR Single-Component Targets HIP 9902 F8V HIP G0V HIP A HIP A5m HIP A2Vn HIP A5V HIP a F2V HIP G5V HIP A7V HIP A2V HIP G4Vp HIP F2IV/V HIP F5V HIP F2V HIP F HIP B8V HIP F5V HIP F3V HIP F5V HIP B8V HIP A3Va HIP A0V HIP F0V HIP A0V HIP F HIP A0V

221 221 Table D.1 (cont d) HIP Spectral V J H K T L M abos D IRS xll1 xsl1 xsl2 Identifier Type (mag) (mag) (mag) (mag) (K) (L ) M (µm) (pc) AOR HIP A2V HIP B9V HIP a A0p Two-Component Targets HIP 345 A0V HIP 682 G2V HIP 1473 A2V HIP 1481 F9V HIP 2472 a A0V HIP 2710 F HIP 7805 F2IV/V HIP 7978 F9V HIP 8241 A1V HIP F HIP A2V HIP F2V HIP a A2V HIP a F5V HIP A7V HIP A3IV HIP F3V HIP A HIP F3V HIP A0V HIP A0V HIP G8Vk+? HIP A3V HIP A0V

222 222 Table D.1 (cont d) HIP Spectral V J H K T L M abos D IRS xll1 xsl1 xsl2 Identifier Type (mag) (mag) (mag) (mag) (K) (L ) M (µm) (pc) AOR HIP A0V HIP G2V HIP G HIP A7Vn HIP B9V HIP a G2V HIP A9V HIP F5/F6V HIP A2IV HIP F4V HIP A1V HIP B8/B9V HIP A1V HIP F5V HIP A5IV HIP F3V HIP A3V HIP F5V HIP F HIP A5IV-V HIP A8V HIP A5V HIP A0V HIP A2Va HIP F5/F6V HIP a F0V HIP A2V HIP F4IV

223 223 Table D.1 (cont d) HIP Spectral V J H K T L M abos D IRS xll1 xsl1 xsl2 Identifier Type (mag) (mag) (mag) (mag) (K) (L ) M (µm) (pc) AOR HIP A5V HIP a A0V

224 224 Table D.2: Target Photometry HIP λ F ν Instrument Ref. Identifier (µm) (mjy) Single-Component Targets HIP ± 0.47 Spitzer/MIPS Ballering et al. (2013) HIP <12.56 Spitzer/MIPS Ballering et al. (2013) HIP <60.60 Spitzer/MIPS Moór et al. (2009) HIP ± 0.22 Spitzer/MIPS Ballering et al. (2013) HIP <16.38 Spitzer/MIPS Ballering et al. (2013) HIP <12.00 SEST Carpenter et al. (2005) HIP <2.30 OVRO Carpenter et al. (2005) HIP ± 0.40 Spitzer/MIPS Ballering et al. (2013) HIP ± 3.20 Spitzer/MIPS Ballering et al. (2013) HIP ± 0.68 Spitzer/MIPS Ballering et al. (2013) HIP <34.44 Spitzer/MIPS Ballering et al. (2013) HIP ± 0.49 Spitzer/MIPS Ballering et al. (2013) HIP <37.02 Spitzer/MIPS Ballering et al. (2013) HIP ± 0.98 Spitzer/MIPS Ballering et al. (2013) HIP <36.90 Spitzer/MIPS Ballering et al. (2013) HIP ± 5.67 Spitzer/MIPS Ballering et al. (2013) HIP ± 6.16 Spitzer/MIPS Ballering et al. (2013) HIP ± 1.42 Herschel/PACS Eiroa et al. (2013) HIP ± 1.84 Herschel/PACS Eiroa et al. (2013) HIP ± 0.22 Spitzer/MIPS Ballering et al. (2013) HIP <14.16 Spitzer/MIPS Ballering et al. (2013) HIP <54.00 CSO Roccatagliata et al. (2009) HIP ± 2.14 Spitzer/MIPS Ballering et al. (2013) HIP ± 5.99 Spitzer/MIPS Ballering et al. (2013) HIP ± 2.36 Herschel/PACS Thureau et al. (2014) HIP ± 3.40 Herschel/PACS Thureau et al. (2014) HIP ± 4.00 Spitzer/MIPS Ballering et al. (2013) HIP ± 6.28 Spitzer/MIPS Ballering et al. (2013) HIP ± 0.17 Spitzer/MIPS Ballering et al. (2013) HIP <14.80 Spitzer/MIPS Ballering et al. (2013) HIP ± 0.22 Spitzer/MIPS Ballering et al. (2013) HIP <30.51 Spitzer/MIPS Ballering et al. (2013) HIP ± 0.18 Spitzer/MIPS Ballering et al. (2013) HIP <22.70 Spitzer/MIPS Ballering et al. (2013) HIP ± 0.16 Spitzer/MIPS Ballering et al. (2013) HIP <23.62 Spitzer/MIPS Ballering et al. (2013) HIP ± 0.16 Spitzer/MIPS Ballering et al. (2013) HIP <25.19 Spitzer/MIPS Ballering et al. (2013) HIP ± 0.69 Spitzer/MIPS Ballering et al. (2013) HIP <19.81 Spitzer/MIPS Ballering et al. (2013)

225 225 Table D.2 (cont d) HIP λ F ν Instrument Ref. Identifier (µm) (mjy) HIP ± 0.99 Spitzer/MIPS Ballering et al. (2013) HIP < Spitzer/MIPS Ballering et al. (2013) HIP ± 0.17 Spitzer/MIPS Ballering et al. (2013) HIP <33.48 Spitzer/MIPS Ballering et al. (2013) HIP ± 1.24 Spitzer/MIPS Ballering et al. (2013) HIP < Spitzer/MIPS Ballering et al. (2013) HIP ± 0.33 Spitzer/MIPS Ballering et al. (2013) HIP <11.27 Spitzer/MIPS Ballering et al. (2013) HIP ± 3.46 Spitzer/MIPS Ballering et al. (2013) HIP < Spitzer/MIPS Ballering et al. (2013) HIP ± 0.60 Spitzer/MIPS Ballering et al. (2013) HIP ± 7.22 Spitzer/MIPS Ballering et al. (2013) HIP ± 1.07 Spitzer/MIPS Ballering et al. (2013) HIP < Spitzer/MIPS Ballering et al. (2013) HIP ± 1.09 Spitzer/MIPS Ballering et al. (2013) HIP <47.88 Spitzer/MIPS Ballering et al. (2013) HIP ± 2.00 Herschel/PACS Riviere-Marichalar et al. (2014) HIP <7.00 Herschel/PACS Riviere-Marichalar et al. (2014) HIP <13.00 Herschel/PACS Riviere-Marichalar et al. (2014) HIP ± 0.90 Spitzer/MIPS Ballering et al. (2013) HIP ± 5.08 Spitzer/MIPS Ballering et al. (2013) HIP ± 0.65 Spitzer/MIPS Ballering et al. (2013) HIP <34.77 Spitzer/MIPS Ballering et al. (2013) HIP ± 0.37 Spitzer/MIPS Ballering et al. (2013) HIP <21.42 Spitzer/MIPS Ballering et al. (2013) HIP ± 0.66 Spitzer/MIPS Ballering et al. (2013) HIP ± 7.65 Spitzer/MIPS Ballering et al. (2013) HIP ± 1.12 Spitzer/MIPS Ballering et al. (2013) HIP ± 8.38 Spitzer/MIPS Ballering et al. (2013) Two-Component Targets HIP ± 0.38 Spitzer/MIPS Ballering et al. (2013) HIP ± 5.35 Spitzer/MIPS Ballering et al. (2013) HIP ± 0.39 Spitzer/MIPS Ballering et al. (2013) HIP ± Spitzer/MIPS Ballering et al. (2013) HIP ± Spitzer/MIPS Hillenbrand et al. (2008) HIP <66.00 JCMT/SCUBA-2 Panić et al. (2013) HIP ± 1.20 JCMT/SCUBA-2 Panić et al. (2013) HIP ± 1.40 SMA Steele et al. (2016) HIP ± 1.00 IRAM Roccatagliata et al. (2009) HIP <2.40 OVRO Carpenter et al. (2005) HIP <1.83 OVRO Carpenter et al. (2005)

226 226 Table D.2 (cont d) HIP λ F ν Instrument Ref. Identifier (µm) (mjy) HIP <0.01 VLA MacGregor et al. (2016) HIP <0.04 GBT Greaves et al. (2012) HIP ± 1.56 Spitzer/MIPS Ballering et al. (2013) HIP ± 6.50 Spitzer/MIPS Ballering et al. (2013) HIP ± 2.65 Herschel/PACS Thureau et al. (2014) HIP ± 4.10 Herschel/PACS Thureau et al. (2014) HIP ± 0.36 Spitzer/MIPS Ballering et al. (2013) HIP < Spitzer/MIPS Ballering et al. (2013) HIP ± 0.90 Herschel/PACS Donaldson et al. (2012) HIP <10.60 Herschel/PACS Donaldson et al. (2012) HIP ± 1.12 Spitzer/MIPS Ballering et al. (2013) HIP ± 6.54 Spitzer/MIPS Ballering et al. (2013) HIP ± 0.44 Spitzer/MIPS Ballering et al. (2013) HIP ± 6.50 Spitzer/MIPS Ballering et al. (2013) HIP ± 0.31 Spitzer/MIPS Ballering et al. (2013) HIP ± 9.30 Spitzer/MIPS Ballering et al. (2013) HIP ± 1.96 Spitzer/MIPS Ballering et al. (2013) HIP ± Spitzer/MIPS Ballering et al. (2013) HIP ± Herschel/PACS Eiroa et al. (2013) HIP ± Herschel/PACS Eiroa et al. (2013) HIP ± Herschel/PACS Eiroa et al. (2013) HIP ± Spitzer/MIPS Tanner et al. (2009) HIP ± Herschel/SPIRE Eiroa et al. (2013) HIP ± Herschel/SPIRE Eiroa et al. (2013) HIP ± 9.80 Herschel/SPIRE Eiroa et al. (2013) HIP ± 4.10 APEX/LABOCA Liseau et al. (2008) HIP <17.00 SEST/SIMBA Schütz et al. (2005) HIP ± 0.02 ATCA Ricci et al. (2015b) HIP ± 1.09 Spitzer/MIPS Ballering et al. (2013) HIP ± Spitzer/MIPS Ballering et al. (2013) HIP ± Herschel/PACS Moór et al. (2015b) HIP ± Herschel/PACS Moór et al. (2015b) HIP ± Herschel/PACS Moór et al. (2015b) HIP ± 7.00 Herschel/SPIRE Moór et al. (2015b) HIP ± 6.00 Herschel/SPIRE Moór et al. (2015b) HIP ± 6.00 Herschel/SPIRE Moór et al. (2015b) HIP ± 0.64 Spitzer/MIPS Ballering et al. (2013) HIP ± Spitzer/MIPS Ballering et al. (2013) HIP ± ISO Moór et al. (2006) HIP ± Spitzer/MIPS Moór et al. (2011b) HIP < JCMT/SCUBA-2 Panić et al. (2013)

227 227 Table D.2 (cont d) HIP λ F ν Instrument Ref. Identifier (µm) (mjy) HIP ± 1.20 JCMT/SCUBA-2 Panić et al. (2013) HIP ± 1.60 JCMT/SCUBA Williams and Andrews (2006) HIP <15.30 APEX/LABOCA Nilsson et al. (2009) HIP ± 0.80 SMA MacGregor et al. (2015) HIP ± 0.00 VLA MacGregor et al. (2016) HIP ± 1.06 Spitzer/MIPS Ballering et al. (2013) HIP ± 8.81 Spitzer/MIPS Ballering et al. (2013) HIP ± 1.71 Spitzer/MIPS Ballering et al. (2013) HIP ± Spitzer/MIPS Ballering et al. (2013) HIP ± ISO Moór et al. (2006) HIP ± Spitzer/MIPS Moór et al. (2011b) HIP ± 0.88 Spitzer/MIPS Ballering et al. (2013) HIP ± Spitzer/MIPS Ballering et al. (2013) HIP ± Herschel/PACS Moór et al. (2015b) HIP ± Herschel/PACS Moór et al. (2015b) HIP ± Herschel/PACS Moór et al. (2015b) HIP ± 5.00 Herschel/SPIRE Moór et al. (2015b) HIP ± 6.00 Herschel/SPIRE Moór et al. (2015b) HIP <30.00 Herschel/SPIRE Moór et al. (2015b) HIP ± 2.02 Spitzer/MIPS Ballering et al. (2013) HIP ± Spitzer/MIPS Ballering et al. (2013) HIP ± ISO Moór et al. (2006) HIP ± Spitzer/MIPS Hillenbrand et al. (2008) HIP <9.90 APEX/LABOCA Nilsson et al. (2010) HIP <34.00 SEST Carpenter et al. (2005) HIP <2.20 IRAM Roccatagliata et al. (2009) HIP <2.48 OVRO Carpenter et al. (2005) HIP <2.23 OVRO Carpenter et al. (2005) HIP ± 1.40 Spitzer/MIPS Ballering et al. (2013) HIP ± Spitzer/MIPS Ballering et al. (2013) HIP ± 0.47 Spitzer/MIPS Ballering et al. (2013) HIP ± 3.92 Spitzer/MIPS Ballering et al. (2013) HIP ± 3.80 Herschel/PACS Draper et al. (2016b) HIP ± 1.50 Herschel/PACS Draper et al. (2016b) HIP ± 0.30 Spitzer/MIPS Ballering et al. (2013) HIP ± Spitzer/MIPS Ballering et al. (2013) HIP ± ISO Moór et al. (2006) HIP ± Spitzer/MIPS Moór et al. (2011b) HIP <15.00 APEX/LABOCA Nilsson et al. (2010) HIP ± 2.26 Spitzer/MIPS Ballering et al. (2013) HIP ± Spitzer/MIPS Ballering et al. (2013)

228 228 Table D.2 (cont d) HIP λ F ν Instrument Ref. Identifier (µm) (mjy) HIP ± Herschel/PACS Donaldson et al. (2013) HIP ± Herschel/PACS Donaldson et al. (2013) HIP ± Herschel/PACS Donaldson et al. (2013) HIP < Spitzer/MIPS Maness et al. (2008) HIP ± Herschel/SPIRE Donaldson et al. (2013) HIP ± 8.00 Herschel/SPIRE Donaldson et al. (2013) HIP ± 7.00 Herschel/SPIRE Donaldson et al. (2013) HIP <19.50 APEX/LABOCA Nilsson et al. (2010) HIP ± 0.82 IRAM/MAMBO2 Meeus et al. (2012) HIP ± 0.74 SMA Meeus et al. (2012) HIP ± 1.10 CARMA Maness et al. (2008) HIP ± 0.54 Spitzer/MIPS Ballering et al. (2013) HIP ± 7.80 Spitzer/MIPS Ballering et al. (2013) HIP <42.00 Spitzer/MIPS Hillenbrand et al. (2008) HIP <45.00 SEST Carpenter et al. (2005) HIP ± 0.39 Spitzer/MIPS Ballering et al. (2013) HIP ± 4.19 Spitzer/MIPS Ballering et al. (2013) HIP ± 0.37 Spitzer/MIPS Ballering et al. (2013) HIP ± Spitzer/MIPS Ballering et al. (2013) HIP ± 8.90 Herschel/PACS Vican et al. (2016) HIP ± Herschel/PACS Vican et al. (2016) HIP ± 0.47 Spitzer/MIPS Ballering et al. (2013) HIP ± Spitzer/MIPS Ballering et al. (2013) HIP ± Spitzer/MIPS Hillenbrand et al. (2008) HIP ± CSO Roccatagliata et al. (2009) HIP <18.00 APEX/LABOCA Nilsson et al. (2010) HIP < SEST Carpenter et al. (2005) HIP ± 0.80 SMA Steele et al. (2016) HIP ± 0.30 SMA Ricarte et al. (2013) HIP ± 0.01 VLA MacGregor et al. (2016) HIP ± 0.82 Spitzer/MIPS Ballering et al. (2013) HIP ± Spitzer/MIPS Ballering et al. (2013) HIP ± 4.80 Herschel/PACS Morales et al. (2013) HIP ± 3.90 Herschel/PACS Morales et al. (2013) HIP ± 0.59 Spitzer/MIPS Ballering et al. (2013) HIP ± Spitzer/MIPS Ballering et al. (2013) HIP ± 4.10 Herschel/PACS Morales et al. (2013) HIP ± 8.70 Herschel/PACS Morales et al. (2013) HIP ± 0.49 Spitzer/MIPS Ballering et al. (2013) HIP ± 5.37 Spitzer/MIPS Ballering et al. (2013) HIP ± 0.13 Spitzer/MIPS Ballering et al. (2013)

229 229 Table D.2 (cont d) HIP λ F ν Instrument Ref. Identifier (µm) (mjy) HIP ± 3.27 Spitzer/MIPS Ballering et al. (2013) HIP ± 0.38 Spitzer/MIPS Ballering et al. (2013) HIP ± 4.36 Spitzer/MIPS Ballering et al. (2013) HIP <44.80 Spitzer/MIPS Hillenbrand et al. (2008) HIP <17.40 CSO Roccatagliata et al. (2009) HIP <2.70 IRAM Roccatagliata et al. (2009) HIP ± 0.45 Spitzer/MIPS Ballering et al. (2013) HIP ± 6.17 Spitzer/MIPS Ballering et al. (2013) HIP ± 1.10 Spitzer/MIPS Ballering et al. (2013) HIP ± 6.32 Spitzer/MIPS Ballering et al. (2013) HIP ± 0.64 Spitzer/MIPS Ballering et al. (2013) HIP ± Spitzer/MIPS Ballering et al. (2013) HIP ± CSO Corder et al. (2009) HIP ± JCMT/SCUBA Williams et al. (2004) HIP ± 4.00 JCMT/SCUBA Williams et al. (2004) HIP ± 1.00 SMA Hughes et al. (2011) HIP ± 1.30 ALMA Ricci et al. (2015a) HIP ± 1.40 CARMA Corder et al. (2009) HIP ± 0.23 OVRO Carpenter et al. (2005) HIP ± 0.03 ATCA Ricci et al. (2015b) HIP ± 0.42 Spitzer/MIPS Ballering et al. (2013) HIP ± 6.09 Spitzer/MIPS Ballering et al. (2013) HIP ± 0.43 Spitzer/MIPS Ballering et al. (2013) HIP ± Spitzer/MIPS Ballering et al. (2013) HIP ± 4.00 Herschel/PACS Draper et al. (2016a) HIP ± 6.00 Herschel/PACS Draper et al. (2016a) HIP ± 0.11 ALMA Lieman-Sifry et al. (2016) HIP ± 1.67 Spitzer/MIPS Ballering et al. (2013) HIP ± Spitzer/MIPS Ballering et al. (2013) HIP ± Herschel/PACS Moór et al. (2015a) HIP ± Herschel/PACS Moór et al. (2015a) HIP ± Herschel/PACS Moór et al. (2015a) HIP ± Herschel/SPIRE Moór et al. (2015a) HIP ± 8.30 Herschel/SPIRE Moór et al. (2015a) HIP ± 8.90 Herschel/SPIRE Moór et al. (2015a) HIP <13.20 APEX/LABOCA Nilsson et al. (2010) HIP ± 0.15 ALMA Lieman-Sifry et al. (2016) HIP ± 0.27 Spitzer/MIPS Ballering et al. (2013) HIP ± Spitzer/MIPS Ballering et al. (2013) HIP ± 0.24 Spitzer/MIPS Ballering et al. (2013) HIP ± 4.64 Spitzer/MIPS Ballering et al. (2013)

230 230 Table D.2 (cont d) HIP λ F ν Instrument Ref. Identifier (µm) (mjy) HIP ± 0.46 Spitzer/MIPS Ballering et al. (2013) HIP ± 3.74 Spitzer/MIPS Ballering et al. (2013) HIP ± 0.82 Spitzer/MIPS Ballering et al. (2013) HIP ± Spitzer/MIPS Ballering et al. (2013) HIP ± 0.19 Spitzer/MIPS Ballering et al. (2013) HIP <27.93 Spitzer/MIPS Ballering et al. (2013) HIP ± 0.81 Spitzer/MIPS Ballering et al. (2013) HIP ± Spitzer/MIPS Ballering et al. (2013) HIP ± 0.16 Spitzer/MIPS Ballering et al. (2013) HIP ± 6.32 Spitzer/MIPS Ballering et al. (2013) HIP ± 0.07 ALMA Lieman-Sifry et al. (2016) HIP ± 0.63 Spitzer/MIPS Ballering et al. (2013) HIP ± Spitzer/MIPS Ballering et al. (2013) HIP ± 0.57 Spitzer/MIPS Ballering et al. (2013) HIP ± Spitzer/MIPS Ballering et al. (2013) HIP ± 0.12 ALMA Lieman-Sifry et al. (2016) HIP ± 0.34 Spitzer/MIPS Ballering et al. (2013) HIP ± Spitzer/MIPS Ballering et al. (2013) HIP ± 0.09 ALMA Lieman-Sifry et al. (2016) HIP ± 0.80 Spitzer/MIPS Ballering et al. (2013) HIP ± Spitzer/MIPS Ballering et al. (2013) HIP ± 1.03 Spitzer/MIPS Ballering et al. (2013) HIP ± Spitzer/MIPS Ballering et al. (2013) HIP ± Herschel/PACS Pascual et al. (2016) HIP ± Herschel/PACS Pascual et al. (2016) HIP <0.75 SMA Meeus et al. (2012) HIP ± 0.88 Spitzer/MIPS Ballering et al. (2013) HIP ± 9.07 Spitzer/MIPS Ballering et al. (2013) HIP ± 4.34 Spitzer/MIPS Ballering et al. (2013) HIP ± Spitzer/MIPS Ballering et al. (2013) HIP ± Herschel/PACS Moór et al. (2015b) HIP ± Herschel/PACS Moór et al. (2015b) HIP ± Herschel/PACS Moór et al. (2015b) HIP ± Herschel/SPIRE Moór et al. (2015b) HIP ± Herschel/SPIRE Moór et al. (2015b) HIP <69.00 JCMT/SCUBA-2 Panić et al. (2013) HIP ± Herschel/SPIRE Moór et al. (2015b) HIP ± 1.00 JCMT/SCUBA-2 Panić et al. (2013) HIP <15.60 APEX/LABOCA Nilsson et al. (2010) HIP ± 2.40 Spitzer/MIPS Ballering et al. (2013) HIP ± 5.92 Spitzer/MIPS Ballering et al. (2013)

231 231 Table D.2 (cont d) HIP λ F ν Instrument Ref. Identifier (µm) (mjy) HIP ± 2.31 Spitzer/MIPS Ballering et al. (2013) HIP ± Spitzer/MIPS Ballering et al. (2013) HIP ± Herschel/PACS Lebreton et al. (2012) HIP ± ISO Moór et al. (2006) HIP ± Herschel/PACS Lebreton et al. (2012) HIP ± Herschel/PACS Lebreton et al. (2012) HIP ± Spitzer/MIPS Schneider et al. (2006) HIP ± ISO Moór et al. (2006) HIP ± 6.20 APEX/LABOCA Nilsson et al. (2009) HIP ± 0.20 ALMA Marino et al. (2016) HIP ± 0.25 ATCA Lebreton et al. (2012) HIP ± 0.02 ATCA Ricci et al. (2015b) HIP ± 2.05 Spitzer/MIPS Ballering et al. (2013) HIP ± Spitzer/MIPS Ballering et al. (2013) HIP ± Herschel/PACS Moór et al. (2015b) HIP ± Herschel/PACS Moór et al. (2015b) HIP ± Herschel/PACS Moór et al. (2015b) HIP ± Herschel/SPIRE Moór et al. (2015b) HIP ± 7.00 Herschel/SPIRE Moór et al. (2015b) HIP ± 7.00 Herschel/SPIRE Moór et al. (2015b) HIP <21.30 APEX/LABOCA Nilsson et al. (2010) HIP ± 0.77 Spitzer/MIPS Ballering et al. (2013) HIP ± 7.64 Spitzer/MIPS Ballering et al. (2013) HIP ± 0.34 Spitzer/MIPS Ballering et al. (2013) HIP ± Spitzer/MIPS Ballering et al. (2013) HIP ± Spitzer/MIPS Moór et al. (2011b) HIP < JCMT/SCUBA-2 Panić et al. (2013) HIP ± 1.40 JCMT/SCUBA-2 Panić et al. (2013) HIP ± 0.87 Spitzer/MIPS Ballering et al. (2013) HIP ± Spitzer/MIPS Ballering et al. (2013) HIP ± Herschel/PACS Matthews et al. (2014a) HIP ± ISO Moór et al. (2006) HIP ± Herschel/PACS Matthews et al. (2014a) HIP ± Spitzer/MIPS Su et al. (2009) HIP ± Herschel/PACS Matthews et al. (2014a) HIP ± Herschel/SPIRE Matthews et al. (2014a) HIP ± Herschel/SPIRE Matthews et al. (2014a) HIP <90.00 Herschel/SPIRE Matthews et al. (2014a) HIP ± 1.80 JCMT/SCUBA Williams and Andrews (2006) HIP ± 0.50 ALMA Booth et al. (2016) HIP ± 1.61 Spitzer/MIPS Ballering et al. (2013)

232 232 Table D.2 (cont d) HIP λ F ν Instrument Ref. Identifier (µm) (mjy) HIP ± 7.16 Spitzer/MIPS Ballering et al. (2013) HIP ± 2.85 Herschel/PACS Thureau et al. (2014) HIP <9.70 Herschel/PACS Thureau et al. (2014)

233 233 Table D.3. Single-Component Fit Results HIP r warm M warm f warm c IRS Identifier (au) ( 10 5 M ) ( 10 5 ) HIP HIP HIP HIP HIP HIP HIP HIP HIP HIP HIP HIP HIP HIP HIP HIP HIP HIP HIP HIP HIP HIP HIP HIP HIP HIP HIP HIP HIP

234 234 Table D.4: Two-Component Fit Results HIP r warm M warm f warm T cold f cold λ 0 β cirs Identifier (au) ( 10 5 M ) ( 10 5 ) (K) ( 10 5 ) HIP HIP HIP HIP HIP HIP HIP HIP HIP HIP HIP HIP HIP HIP HIP HIP HIP HIP HIP HIP HIP HIP HIP HIP HIP HIP HIP HIP HIP HIP HIP HIP HIP HIP HIP HIP HIP HIP HIP HIP HIP

235 235 Table D.4 (cont d) HIP r warm M warm f warm T cold f cold λ 0 β cirs Identifier (au) ( 10 5 M ) ( 10 5 ) (K) ( 10 5 ) HIP HIP HIP HIP HIP HIP HIP HIP HIP HIP HIP HIP HIP

236 236 APPENDIX E β PIC MODEL COMPARED WITH ADDITIONAL DATA E.1 The SW Side Our constraints on the dust composition used data only from the NE side of the disk. Here we use the data from the SW side of the disk as a check on our results. We generated model images using the same grain size and composition parameters as our best fit model to the NE side, but with the spatial parameters found in 5.5 for the SW side (parent body r out = 155 au instead of 150 au, and more significantly the halo p = 3.1 instead of 2.4). The results are shown in Figure E.1. The models fit the STIS, WFC3, and MIPS data well, but the halo component under-predicts the observed flux density at 70 µm. The parent body model fits the ALMA data well, but is somewhat too bright in the MIPS and PACS bands. The masses of the model components found by this fitting were M halo = M and M PB = M. Compared to the NE side, the SW side had a less massive halo and a more massive parent body component. Our fitting to the the SW side implicitly assumed that the known asymmetry between the two sides was caused by differences in the spatial distribution of the dust, rather than differences in the grain properties. Perhaps the fit to the SW side could be improved by using different grain size parameters. The SW side also hosts a large clump seen in thermal emission at several wavelengths and in CO gas (Telesco et al., 2005; Dent et al., 2014), which may be the site of a recent massive collision and may contribute to the asymmetry. A detailed study of the differences between the NE and SW sides of the disk, however, is beyond the scope of this study.

237 237 mjy/arcsec 2 mjy/arcsec STIS 5 10 WFC MIPS mjy/arcsec mjy/arcsec 2 mjy/arcsec PACS 00 ALMA 5 10 arcseconds Figure E.1: Models generated with the grain properties derived from fits to the NE side but with the spatial parameters found for the SW side. The models were fit to the data from the SW side of the disk. The halo component matched the HST and MIPS bands well, but was too faint compared to the 70 µm PACS data. In addition, the parent body component fit the ALMA data well, but contributed too much at 24 and 70 µm. The black lines are the data, the green lines are the parent body model, the blue lines are the halo model, and the dashed red lines are the total model. The vertical dashed lines show the range of data to which the model was fit.

238 238 E.2 Gemini/T-ReCS β Pic was imaged with Gemini/T-ReCS in five bands: 8.7, 11.7, 12.3, 18.3, and 24.6 µm, and these data were published by Telesco et al. (2005). Here we used the images at 18.3 and 24.6 µm, wavelengths at which the outer disk components contributed significantly. We obtained the rotated, calibrated images with units of mjy/pixel. From each image we subtracted a constant background value, derived using the IDL program mmm.pro. These values were ± mjy/pixel at 18.3 µm and ± mjy/pixel at 24.6 µm. We converted the surface brightness to units of mjy arcsec 2 using a pixel size of for the 18.3 µm image and for the 24.6 µm image. We smoothed each image with a boxcar kernel roughly the size of the FWHM of the instrument PSF (5 5 and 7 7 pixels for the 18.3 and 24.6 µm images, respectively). We extracted radial profiles using a cut width of 9 pixels (0. 81 at 18.3 µm, at 24.6 µm). The profiles are shown in Figure E.2. The uncertainty on the profiles was the combination in quadrature of 10% calibration uncertainty and the mjy/pixel uncertainty of 0.13 and 0.7 for the 18.3 and 24.6 µm images, respectively, from Table 1 of Telesco et al. (2005). The profiles had a central, unresolved component arising from the star plus the warm inner disk component with the flux outside of this arising from the outer disk components. We included the photometry measurements of the whole disk as given by Telesco et al. (2005) for these data in our Table 5.1. The T-ReCS flux density at 24.6 µm was higher than the MIPS flux density and ISO flux density at similar wavelengths, which may be due to a calibration problem (this is supported by the relatively large background value we found for the 24.6 µm image). We compared our best fit model with the outer parts of the 18.3 and 24.6 µm T-ReCS profiles. We convolved model images at these wavelengths with PSFs that were modeled as symmetric 2D Gaussians with FWHM of 0. 54, and for the 18.3 and 24.6 µm images, respectively. The comparison is shown in Figure E.3. We find good agreement between our models and these data. The 18.3 µm image is the

239 239 T ReCS 18.3 µm 10 3 mjy/arcsec arcseconds T ReCS 24.6 µm 10 3 mjy/arcsec arcseconds Figure E.2: Profiles of the T-REcS images of the β Pic disk at 18.3 and 24.6 µm. The gray region is the uncertainty along the profiles. The NE side of the disk is to the right, the SW side is to the left. The central peak is the unresolved flux from the central star and the inner disk component. Outside of that, the broad shoulder is the flux from the outer disk components.

240 T ReCS 18.3 µm mjy/arcsec T ReCs 24.6 µm mjy/arcsec arcseconds Figure E.3: The best fit model compared with NE side profiles of the T-ReCS data at 18.3 and 24.6 µm. We achieved a good fit with the exception of the shape of the model at 18.3 µm at small r. shortest wavelength in the thermal regime at which our model was tested. E.3 Scattered Light Color Golimowski et al. (2006) imaged β Pic s disk with the HST /ACS High Resolution Channel in three scattered light bands: F435W, F606W, and F814W with central wavelengths , , and µm, respectively. They found that the disk was redder than the star, and that the disk became somewhat redder moving outwards along the midplane. Specifically, for their PSF-deconvolved images, the F435W F606W color ranged from 0.1 to 0.2, and the F435W F814W color ranged from 0.2 to 0.35 along the disk (see their Figure 18).

241 241 Golimowski et al. (2006) investigated whether they could constrain the dust composition and minimum grain size using their measured scattered light colors. They found that many combinations of parameters could fit their data, which supports the premise of our work that both scattered light and thermal data are required to constrain the composition. They did, however, exclude very porous grains (90%), which always resulted in scattered light colors bluer than the star. We generated model images at these ACS wavelengths to see if our best fit halo component (which dominated the scattered light signal) showed a similar behavior in its scattered light colors. Figure E.4 shows the F435W F606W and F435W F814W colors of our model. To make these images, we divided the model image at each wavelength by the flux density of the star at that wavelength (as discussed in 5.2) and then divided the two images by each other and converted the result to a magnitude scale. Because we were comparing with the deconvolved ACS data, we did not convolve our model images with any model PSF. Our results generally agreed with the ACS data the midplane of the disk was redder than the star by a couple of tenths of magnitude, and became redder farther from the star. Our model used the same grain sizes and composition at all locations in the disk, so the change in disk color across the image must result from the wavelength dependence of the scattering phase function. Interior to r in and also above the disk wedge locations dominated by forward- or back-scattering the dust was bluer (at some points even bluer than the star), whereas in the disk plane where scattering occurred at angles closer to 90, the dust was red. The increasing redness of the disk outwards along the midplane likely also arises due to an increasing proportion of the scattering happening at 90. In Figure E.5 we plot profiles of the color images along the midplane as well as the color profile measured by Golimowski et al. (2006). They smoothed their image with a 7 7 pixel boxcar before extracting a profile along the midplane, so we extracted a four pixel wide profile to capture approximately the same region of the image (the ACS pixels were half the size of our model pixels). This confirmed the general agreement of our model with these measurements. In the range of the

242 242 arcseconds F435W F606W arcseconds 5 0 F435W F814W arcseconds Figure E.4: Images of the F435W-F606W and F435W-F814W colors of our model disk. The disk is bluer in regions dominated by forward- and back-scattering radial profile where Golimowski et al. (2006) measured the disk colors (3 13 ), our model color profiles show a constant color. However, using a wider profile cut to generate the profiles would result in an increasing red color over this range of the profile, because less of the bluer flux from above the wedge would be included with increasing distance from the star. Next we looked into the color of the dust predicted by our model at wavelengths beyond those measured by ACS, STIS, and WFC3. We generated models of the halo component from µm, and normalized them by the brightness of the star at those wavelengths. In Figure E.6 we show the resulting scattered light SEDs extracted at the origin and at r = 10 on the disk midplane. The SED from the disk midplane showed the dust reddening across the visible, but the color became more neutral at longer wavelengths. At the origin, which probed only the forwardand back-scattered light, the dust was blue across this whole wavelength range, although the gradient of the color was shallower at longer wavelengths.

243 243 Saving as PDF only save what is in the boundary of the slide. Figure E.5: The F435W-F606W and F435W-F814W colors of the disk (relative to the star) along the disk s miplane. The black line is the measured color profile from Golimowski et al. (2006) (the dotted line is their measurement prior to deconvolution). The colored lines are our model with various dust compositions: red is f sil = 0.6 and f org = 0.4 (our best fit model), green is f org = 1, magenta is f sil = 1, blue is f ice = 1, cyan is f sil = 0.6 and f ice = 0.4, and yellow is f sil = 0.6 and f vac = 0.4. There is relatively good agreement between the data and our best fit model, especially for F435W-F814W. The data for both colors falls between the silicates and organics models (implying a mixture of the two materials) and is redder than mixtures with significant amounts of water ice or vacuum, which agrees with the results of our fitting. The bluer region of the disk inside r < 2.3 is from within r in of our model, so the flux is starlight that was highly forward- or back-scattered. Our model s color profile was fairly constant out to 15 shown here, but does get redder toward the outer edge.