The Role of Cold Gas in Massive Galaxy Evolution

Transcription

1 The Role of Cold Gas in Massive Galaxy Evolution Jenna Jo Lemonias Submitted in partial fulfillment of the requirements for the degree of Doctor of Philosophy in the Graduate School of Arts and Sciences COLUMBIA UNIVERSITY 2014

2 c 2014 Jenna Jo Lemonias All rights reserved

3 ABSTRACT The Role of Cold Gas in Massive Galaxy Evolution Jenna Jo Lemonias The cold gas content of a galaxy reflects its past assembly history as well as its potential for future star formation. It has been shown to be tied to a galaxy s morphology, current star formation rate, and environment. In combination with large surveys at optical and ultraviolet wavelengths, measurements of the cold gas in galaxies provide new ways of understanding and examining the complex relationship between cold gas and derived quantities related to structural and star-forming properties. In particular, measurements of the cold gas content of galaxies can help inform the interpretation of global scaling relations in the local population of galaxies that cannot be fully understood without knowledge of the gas content of galaxies. However, the long integration times required to detect neutral hydrogen gas (HI) and CO make it difficult to detect low levels of cold gas in large numbers of galaxies. Where the presence of cold gas is assumed to be important but observations are not available, we can sometimes make assumptions to estimate the precise role of cold gas. With the advent of large surveys measuring cold gas in representative samples of galaxies, we have been able to study the cold gas in galaxies in a statistical way that rivals the methods by which we can study other properties of galaxies. In this thesis we use measurements from GALEX, SDSS, and the GALEX Arecibo

4 SDSS Survey (GASS; Catinella et al. 2010) to quantitatively describe the distribution of cold gas in massive galaxies using sophisticated techinques that had previously only been applied to quantities derived from optical and ultraviolet observations. We also show how we can use distribution functions derived from large surveys to identify galaxies in distinct evolutionary phases that can shed light on the processes of galaxy evolution in general, and more specifically, about the crucial role HI plays in driving the evolution of massive galaxies. In Chapter 2 we design a classification scheme to identify galaxies with unexpected star formation in their outer disks (extended ultraviolet, or XUV, disks) and to extend the known sample of such objects out to moderate (z 0.05) redshifts. We find that 20% of galaxies in the most nearby portion of the sample exhibit XUV-disks and that XUV-disks are surprisingly common in massive, bulge-dominated galaxies. From our large, unbiased sample of galaxies we derive the space density of XUV-disks in the local universe. With this derived space density, and based on the assumption that XUV-disks must form in extended cold gas disks, we estimate the cold gas accretion rate onto XUV-disks in the local universe. In Chapter 3 we derive the bivarate HI-stellar mass function for massive galaxies, which is a crucial tool for constraining simulations. We test six different parameterizations of the distribution function and we also examine how the shape of the distribution function depends on star formation rate. We find that the location of the peak in the distribution function does not depend strongly on stellar mass or star formation rate but that the slope of the distribution function at low masses does. We also discuss how physical processes

5 drive the shape of the bivariate HI-stellar mass function. Finally, in Chapter 4 we demonstrate the utility of scaling relations derived from large datasets by using the gas fraction scaling relation to select an anomalous sample of massive HI-rich galaxies with surprisingly low levels of star formation. We obtain HI imaging of these galaxies to ascertain why so much of their cold gas content is not participating in star formation. All of the galaxies we observe exhibit extended HI disks whose gas surface densities are below the threshold required for star formation. Since this type of galaxy is most prevalent at stellar masses above the transition mass noted in Kauffmann et al. (2003c), it is possible that the processes inhibiting star formation in these galaxies contribute to the change in star-forming properties above the transition mass.

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7 Contents List of Figures List of Tables Acknowledgments v ix xi 1 Introduction Galaxy Evolution in the 21st Century Galaxy Evolution Results from SDSS Galaxy Evolution Results from GALEX What s Missing? Cold Gas The Link Between Gas and Star Formation This Thesis Science Goals Approach Summary XUV-Disks Introduction Sample GALEX Imaging and Data SDSS Imaging and Data i

8 2.3 XUV-Disk Identification Methodology Examples Results and Data Analysis Redshift Distribution of XUV-disk Galaxies Morphology of XUV-disk Galaxies Colors and Stellar Masses of XUV-disk Galaxies The XUV Emission Discussion The Space Density of XUV-disk Galaxies The Origin of the XUV Emission XUV-disks and Their Relation to Disk-Building Conclusions The Bivariate HIMF Introduction Data Methodology The Models Continuous Fits Implementation Model Fitting The Bivariate HI Mass Function for Massive Galaxies Model Comparison Covariance of Parameters Model fit at high HI masses and comparison with ALFALFA Model Selection and Validation Discussion The Shape of the HIMF ii

9 3.5.2 The Dependence of the HI Mass Function on Stellar Mass and Star Formation Rate Physical Drivers of the HIMF Summary and Conclusions Appendix Appendix A - Applications of the HIMF: Comparing to Simulations and Photometric Gas Fractions Appendix B - Assumed stellar mass function Appendix C: Probabilities for Model Selection HI-Rich Galaxies Introduction Properties of Massive HI-Rich Galaxies Sample Selection Derived Quantities Results HI Imaging of Low-star-forming HI-Rich Galaxes Sample Observations and Data Reduction Derived Quantities Results The Suppression of Star Formation in Massive HI-Rich Galaxies AGN Feedback Morphological Quenching Below-Threshold Cold Gas Recent Gas Accretion The Emergence of Low-Star-Forming HI-Rich Galaxies at High Stellar Masses and the Role of H Summary and Conclusions Appendix Notes on Individual Galaxies iii

10 5 Conclusions Summary of Results Recent Developments XUV-Disks Future Prospects Bibliography 217 iv

11 List of Figures 1.1 From Catinella et al. (2010). HI scaling relations derived from GASS observations GALEX and SDSS color images of an XUV-disk galaxy GALEX and SDSS color images of an XUV-disk galaxy GALEX and SDSS color images of an XUV-disk galaxy GALEX and SDSS color images of an XUV-ambiguous galaxy GALEX and SDSS color images of the 24 XUV-disk galaxies in the sample GALEX and SDSS color images of the 24 XUV-disk galaxies in the sample GALEX and SDSS color images of the 24 XUV-disk galaxies in the sample The number and fraction of XUV-disk galaxies as a function of redshift The number and fraction of simulated XUV-disk galaxies as a function of redshift The maximum redshift at which an XUV-disk was detected around 35 artificially redshifted galaxies The number and fraction of XUV-disks as a function of concentration index (C=R 90 /R 50 ) NUV-r vs. log M /M for the sample NUV-r color vs. concentration index (C=R 90 /R 50 ) FUV-r color of each galaxy (FUV-r galaxy ) vs. FUV-r color of the XUV region (FUV-r XUV ) R 80 /R XUV vs. concentration index v

12 2.16 The FUV flux in the XUV region compared to the entire galaxy vs. the r-band flux in the XUV region compared to the entire galaxy The local space density of galaxies The volume-averaged XUV fraction (fraction of galaxies in our sample with XUV-disks), the local space density of galaxies, and the local space density of XUV-disk galaxies Same as Fig with XUV-ambiguous galaxies included Mass of gas accreted onto XUV-disks per bin Redshift-corrected space density of XUV-disks Redshift-corrected gas accretion rate onto XUV-disks Examples of the six models to the bivariate HI mass function The number of detections and upper limits per HI mass-stellar mass bin in the GASS sample Three variations of the Schechter function fit to the HISMF in six stellar mass bins Three variations of the log-normal function fit to the HISMF in six stellar mass bins Schechter parameters α, log M HI, f, and M HI,75 vs. stellar mass Log-normal parameters σ, µ, f, and M HI,75 vs. stellar mass Error contours for Schechter parameters α, M HI and f for the models in six stellar mass bins The broken Schechter fit to the GASS HISMF compared to the broken and bent Schechter fits to the HISMF that includes ALFALFA detections and upper limits The total HISMF for massive galaxies based on six different models compared to the ALFALFA HIMF The binned broken Schechter HISMF compared to the continuous bivariate fit, whose parameters depend on stellar mass, and the continuous trivariate fit An example of the continuous trivariate HI-M -SFR function for galaxies vi

13 3.12 The distribution of α vs. M HI as a function of stellar mass and SFR Same as Fig for α and f Predicted HI gas fraction vs. stellar mass in three bins of SFR based on the continuous trivariate fit Lines of constant α, M HI, f, and M HI,75, calculated from the trivariate fit, in the specific SFR-stellar mass plane The total HISMF divided by specific SFR and concentration (dashed and dotted lines) compared to the total HISMF (solid line). Left: The total HISMF for passively evolving (ssfr < -11.5) galaxies (dotted) and starforming (ssfr > -11.5) galaxies (dashed). Right: The total HISMF for bulge-dominated galaxies (R 90 /R 50 > 2.6; dotted line); the total HISMF for disk-cominated galaxies (R 90 /R 50 < 2.6; dashed line) Broken Schechter fits to the total HISMF derived from published photometric gas fractions calculated for galaxies in the GASS parent sample The broken continuous bivariate Schechter fit to the GASS HISMF compared to the broken Schechter fit to the HISMFs derived from photometric gas fraction relations Same as above for other photometric gas fraction relations The fractional difference in the total HISMF with other stellar mass functions Selection of HI-rich galaxies and their physical properties Selection of the VLA sample SDSS color images of the 20 galaxies in the VLA sample VLA instrument setup Velocity spectra from ALFALFA and this survey HI intensity and velocity maps for galaxies in the VLA sample See caption for Fig See caption for Fig R90 HI vs. R90 opt for galaxies in the VLA sample Histograms of the three measurements for HI surface density and SFR surface density vii

14 4.11 Predicted and measured values for Σ SFR vs. Σ HI Σ SFR vs. Σ HI with AGN classifications and concentration indices indicated viii

15 List of Tables 2.1 Properties of Sample Galaxies Properties of XUV-disks and XUV-ambiguous Galaxies Functional Forms of the Models Functional Forms of the Models Binned Data for Bivariate HISMF Number of Galaxies in Samples Schechter Function Fits to Bivariate HIMF a Log-normal Fits to Bivariate HIMF a Ω HI Continuous Fits a Model Probabilities a Probabilities for Total HISMF at log M HI > General Data Derived HI Quantities HI and SFR Surface Densities a ix

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17 ACKNOWLEDGMENTS Although this thesis has only one name on the front page, this work could not have been completed without the collaboration and support of many others. First, thank you to my advisor, David Schiminovich, for teaching me, supporting me, and encouraging me throughout my time here. I have learned more than I can imagine during my time at Columbia and I feel grateful to have been given the opportunity to do this type of work. The work presented here represents a true collaboration with David and has also benefited greatly, in concrete and abstract ways, from help from numerous others: Barbara Catinella, Tim Heckman, Sean Moran, Jacqueline van Gorkom, Greg Bryan. Thank you also to the numerous graduate students and postdocs who so generously shared their expertise on everything from VLA data reduction to plotting to installing code to graduate school in general, notably Ximena Fernández, Josh Peek, Adrian Price-Whelan, and Emily Rauscher. Stepping back a bit, I would like to thank the teachers who guided me towards this path - those who challenged me, inspired me, and made me excited about learning. I owe a special thank you to Ms. Claudia Leone for suggesting her students read Stephen Hawking s A Brief History of Time, which triggered my fascination with astronomy. Thanks are also due to Dr. Maynard Morin and Ms. Leda Eizenberg. At Vassar I had a number of professors without whom I would not have arrived at this achievement. Thanks to Jamie Lombardi, who questioned me when I did not register for the second semester of freshmen physics and then allowed me to fast-track my classes when I decided I wanted to study astronomy. To Fred Chromey, who was always xi

18 available for a talk and whose love for astronomy is obvious and infectious. And to Debra Elmegreen, a source of inspiration in so many ways and a true example of someone who can do everything and do it all at the highest level. Thank you to my friends at Columbia, in New York, and from home for supporting me through ups and downs, helping me with and distracting me from my work, and making my life so enjoyable these past six years. Finally, thank you to my family - Mom, Dad, and James - for supporting me in everything I choose to do. Thank you for encouraging me to flourish in all aspects of life and for giving me the opportunities and freedom to do so. And on an astronomical note, a special thanks to my Dad, who shared and nurtured my burgeoning interest in astronomy when I was in high school by giving me his old copy of Carl Sagan s Pale Blue Dot and watching NOVA with me. Thank you all for having such positive influences on my life. I hope to continue to make you proud. Jenna Lemonias April 2014 New York City xii

19 Chapter 1 Introduction 1.1 Galaxy Evolution in the 21st Century At the most fundamental level, galaxies are enormous gravitationally bound systems composed of four distinct elements: stars, gas, dust, and dark matter. Over the course of billions of years, these four elements interact in various ways and participate in competing processes such as inflow and outflow, accretion and star formation, to produce the population of galaxies we see today. A comprehensive model of how this process has proceeded - and will continue to do so - requires a precise understanding of each component, how it interacts with and affects the others, and how it can be inferred from observations. Although these parameters derived from observations - such as luminosity or HI mass - are seemingly simplistic quantities, they reflect the competition that has taken place over billions of years of evolution. It requires a tremendous observational and theoretical effort to disentangle the physical processes that yield these quantities as well as how and why 1

20 they vary among the local galaxy population. The past decade has witnessed a profound advancement in our ability to do just that. Beyond just categorizing galaxies by morphology as Hubble did in the first part of the 20th century (Hubble 1926), astronomers can now quantify galaxies in a myriad of ways to assess how their various components affect each other and drive galaxy evolution. Because this information is now available for large representative populations of galaxies, we can apply sophisticated analyses to enormous samples of galaxies to understand entire populations of galaxies in a complex, statistical way. This type of analysis marks a crucial step in developing a physically motivated model of galaxy evolution that can account for observations of the local universe and can be extended to higher redshifts. The most significant recent advances in the study of galaxy evolution can be attributed to the advent of large astronomical surveys, including the Sloan Digital Sky Survey (SDSS) and the Galaxy Evolution Explorer (GALEX). They have each yielded observations and measurements of unprecedentedly large numbers of galaxies, ushering in a new era of galaxy evolution research that enables us to study galaxies in ways that were previously not possible Galaxy Evolution Results from SDSS The Sloan Digital Sky Survey, begun in 2000, maps the sky in five bandpasses from 3500 to 9000 Angstroms with a 2.5-meter optical telescope at Apache Point Observatory in New Mexico. The main parts of the survey, SDSS I and SDSS II, imaged over one quarter of the sky. With 5-color ugriz images of almost a million galaxies and spectra for a sizable fraction 2

21 of those, SDSS revolutionized the ways in which galaxies are analyzed and understood. The enormous datasets provide new ways to quantify galaxies by their stellar mass, star formation rate, AGN properties, stellar mass surface densities, and spectral qualities, and revealed important correlations between these factors (Kauffmann et al. 2003b,c,a). In particular, they have revealed that the local galaxy population exhibits a bimodality based on a number of different properties. Strateva et al. (2001) and Baldry et al. (2004) showed that galaxies occupy two distinct regions of color-color and color-magnitude planes, which are roughly related to a division by morphology. Kauffmann et al. (2003c) showed that the star formation and structural properties of galaxies with stellar masses above and below a transition mass of M exhibit markedly different characteristics, with less massive galaxies exhibiting higher rates of recent star formation, lower stellar mass surface densities, and younger stellar ages. Since then, a substantial amount of work has focused on determining whether this is a strict bimodality or a smooth transition and what physical processes contribute to it Galaxy Evolution Results from GALEX GALEX is a NASA Small Explorer launched in 2003 to survey the sky at ultraviolet wavelengths. It was designed to be sensitive to the massive O and B stars with lifetimes up to 10 8 years that emit ultraviolet light. GALEX had two filters capable of detecting light at near-uv ( Angstroms) and far-uv ( Angstroms) wavelengths. Because of its sensitivity to UV light from massive stars, GALEX is ideal for probing the star formation history of the universe out to z 2 as well as the current star formation 3

22 properties of galaxies in the local universe. GALEX has revolutionized the way in which astronomers can measure star formation rates, using a direct measure of the UV light from massive stars rather than the detailed modeling necessary to derive star formation rates from SDSS data. A caveat is that SFRs derived from the UV must be corrected for UV light that is absorbed by dust and re-emitted in the infrared. Although GALEX is credited with many discoveries from extragalactic to stellar astrophysics, I will point out two advances relevant to this thesis that were made possible by GALEX observations. One is the UV-optical color-magnitude diagram, which expands upon the analysis of optical color-magnitude diagrams based on SDSS data in Strateva et al. (2001) and Baldry et al. (2004). Wyder et al. (2007) explores the NUV-r and FUV-r color-magnitude diagrams and finds that the UV-optical colors provide a better separation between galaxy populations compared to the color-magnitude diagrams based on only optical measurements because the GALEX passbands are more sensitive to recent star formation. Though the blue and red sequences are more distinct in the UV-optical colormagnitude diagram, this type of color-magnitude diagram reveals a minor population of green galaxies that are intermediate between the blue and red sequences. The socalled green valley contains galaxies that are transitioning between the two sequences; understanding galaxies in this regime could provide insight into the processes that turn star formation off and on in galaxies. Because of the small number of galaxies in the green valley, this transition could be rapid. It is worth noting that the UV-optical color can also be used as a proxy for the specific SFR, or the SFR normalized by the stellar mass of a galaxy (Brinchmann et al. 2004; Wyder et al. 2007; Schiminovich et al. 2007). 4

23 Another important discovery attributed to GALEX is the existence of low levels of recent star formation beyond stellar disks (Thilker et al. 2005; Gil de Paz et al. 2005). The ubiquity of these extended UV (XUV) disks highlights the utility of UV observations as a supplement to optical imaging of galaxies and underscores the significant role that extended star formation could play in the process of galaxy evolution (Thilker et al. 2007). It also challenged the notion that galaxies contain well-defined star formation thresholds beyond which star formation cannot occur (Martin & Kennicutt 2001). 1.2 What s Missing? Cold Gas Observations by GALEX and SDSS provide a comprehensive view of the stellar content of galaxies. One key component of galaxies that is missing from their analyses is an accounting of the cold gas in galaxies. The cold gas in galaxies can be a major component of galaxies (some galaxies, even massive ones, have more mass in cold gas than in stars (Catinella et al. 2010; Moran et al. 2010)) but even when it is not, it can inform the interpretation of trends that were uncovered by GALEX and SDSS. For example, as the fuel for star formation, measurements of massive galaxies cold gas content can aid in the understanding of why massive galaxies tend to form stars at lower rates, i.e. whether they contain gas that is not participating in star formation or whether they lack cold gas altogether. Likewise, the quantity, distribution, and the origin of the cold gas could shed light on the origin of XUV-disks. The cold gas in galaxies includes atomic hydrogen gas, which is referred to as HI, and molecular gas. The classic picture of star formation posits that when atomic hydrogen gas 5

24 cools and condenses it forms molecular hydrogen gas clouds, which collapse to form stars. Thus, one would expect the link between molecular gas and recent star formation to be more direct than that between atomic gas and star formation. But the ease with which one can detect atomic and molecular gas is very different. Since the rotational transitions of H 2 require high temperatures for excitation, the molecule is difficult to observe (Kennicutt & Evans 2012). Most observations of molecular gas must rely on carbon monoxide (CO) as a tracer for H 2, even though the exact link between the two (the X-factor ) is still a matter of debate (Pineda et al. 2010). Much of the work on cold gas in galaxies currently makes use of observations of the 21 cm line of HI, which is a direct measure of the atomic hydrogen gas in galaxies. Since it was first detected in 1951 (Ewen & Purcell 1951; Muller & Oort 1951), astronomers have observed HI via the spin-flip transition in the hydrogen atom, which emits electromagnetic radiation at a frequency of MHz, or a wavelength of approximately 21 cm. This spin-flip transition occurs when the spin of the electron spontaneously changes to that opposite the spin of the proton. Although this is a forbidden transition that occurs only once every several million years, it is easily detectable with large radio telescopes in galaxies with substantial reservoirs of HI and it has become an invaluable tool in radio astronomy. Following the advent of large surveys at optical and UV wavelengths at the turn of the millennium, several surveys at radio wavelengths have taken advantage of the ubiquity of the HI line to measure atomic hydrogen in large numbers of galaxies in order to understand its role in the process of galaxy evolution. I will briefly describe several 6

25 important HI surveys that play a role in this thesis, each of which has a different method and goal. We do not discuss older surveys such as HIPASS (Meyer et al. 2004) because the more recent surveys have superseded them in terms of survey depth and number of galaxies. The Arecibo Legacy Fast ALFA Survey (ALFALFA; Giovanelli et al. 2005) was designed to provide an inventory of the HI in low-redshift galaxies, but it has also yielded tremendous insight into the role that HI plays in galaxy evolution more generally. AL- FALFA scans the observable sky from Arecibo at a uniform depth sufficient to detect sources with HI fluxes 10 Jy km s 1 (though the exact sensitivity is dependent on the profile width) (Martin et al. 2010). As a blind survey it does not target individual galaxies. The α.40 sample, which includes 40% of the final survey area, contains over 15,000 extragalactic sources (Haynes et al. 2011). In Huang et al. (2012), they use a sample of over 9,000 galaxies observed by ALFALFA, SDSS, and GALEX to examine the relationships between cold gas, star formation, and stellar mass in local galaxies. They use this sample to confirm the existence of scaling relations noted above and to supplement these established trends with HI scaling relations that could explain the variation in optically derived quantities. However, they note that a sample defined by HI detection alone is biased towards galaxies with higher HI masses and lower SFEs. This translates into a bias in the UV-optical color magnitude diagram: over 95% of galaxies detected in all three surveys lie in the blue cloud. Though Huang et al. (2012) attempt to eliminate this bias by creating an additional sample that is optically selected, the sample still doesn t include many detections of galaxies with low levels of HI because the ALFALFA observations are 7

26 shallow. Because it can be time-consuming to detect HI in galaxies beyond the very nearby universe, a different approach is required to measure low levels of HI. The GALEX Arecibo SDSS Survey (GASS; Catinella et al. 2010) was designed to measure HI down to a low gas fraction in an unbiased sample of massive galaxies out to z=0.05. Almost 800 targets were randomly selected from a parent sample of all galaxies in the redshift range < z < 0.05 with stellar masses greater than log M /M = 10.0 that lie in the overlap of the GALEX, SDSS, and ALFALFA footprints. Instead of observing each galaxy with the same integration time, each galaxy was observed until a 1.5-5% HI gas fraction could be detected (this can require up to 90 minutes of integration time, compared to the 1 minute of integration time for ALFALFA). Galaxies that were previously observed and detected as part of ALFALFA were not observed again for GASS but were included in the sample in the appropriate proportions to ensure the sample was representative. GASS and ALFALFA differ by observing strategy and stellar mass range. GASS observes only massive galaxies with the goal of understanding the HI in a crucial stellar mass range that includes the transition mass at M (Kauffmann et al. 2003c). Importantly, the sample represents the true distribution of HI in massive galaxies in the local universe because the sample selection was not based on HI content. Scaling relations for massive galaxies based on GASS were first reported in Catinella et al. (2010) and Schiminovich et al. (2010) and the final scaling relations are listed in Catinella et al. (2013). Part of Fig. 8 from Catinella et al. (2010) is reproduced here in Fig. 1.1 to show the depth of GASS HI measurements compared to those from ALFALFA. 8

27 Figure 1.1 From Catinella et al. (2010). HI scaling relations derived from GASS observations (red circles and green triangles) extend to much lower gas fractions than ALFALFA data (gray circles) permit. Several other studies of moderately sized populations of galaxies include supplementary HI imaging or observations. The HI Nearby Galaxy Survey (THINGS; Walter et al. 2008) is one such survey that I refer to several times throughout this thesis. It includes resolved HI imaging of 36 nearby spiral galaxies (d<15 Mpc) to understand the relationship between gas and star formation on resolved scales. ATLAS3D (Cappellari et al. 2011) aims to combine theoretical modeling and multiwavelength observations to examine in detail 260 local early-type galaxies. They acquired HI imaging of a subset 9

28 of this sample from the Westerbork Synthesis Radio Telescope (WSRT) and describe it in Serra et al. (2012). 1.3 The Link Between Gas and Star Formation The gas content of a galaxy is a crucial driver of star formation as well as a repository for the by-products of star formation. A proper introduction to the relationship between gas and star formation in galaxies cannot begin without discussion of the Kennicutt-Schmidt law (Kennicutt 1998; Schmidt 1959). The Kennicutt-Schmidt law, which states that the surface density of star formation is a power-law function of the gas surface density, elegantly demonstrates the interconnectedness of these two quantities. Digging deeper, the details of the Kennicutt-Schmidt law reveal the complexity of the subject. In his classic paper, Kennicutt (1998) showed that the relationship between gas and star formation changes whether one considers atomic gas, molecular gas, or the sum of the two. In the 15 years since that paper was published, progress has been made by examining different chemical species of cold gas, various tracers of star formation, and varying scales within a galaxy (Bigiel et al. 2008; Leroy et al. 2008; Bigiel et al. 2010; Wyder et al. 2009; Schiminovich et al. 2010; Saintonge et al. 2011b; Schruba et al. 2011; Leroy et al. 2012). In addition to the complication that arises from using HI vs. CO as tracers of molecular gas (noted above), the scales on which many of the observations take place can be an obstacle to correctly interpreting the relationship between gas and star formation. Global star formation rates (SFR) and gas masses average over regions of high and low gas density and regions of high and low SFRs, losing information on smaller scales. Resolved 10

29 observations of gas and star formation on smaller scales have shown that the star formation law likely changes in regions of low gas density. In regions of low gas density where the gas is primarily atomic, such as the outer disks of galaxies, star formation rates are lower than would be expected based on the local gas density (Bigiel et al. 2010; Schruba et al. 2011). Low gas surface density is a common explanation for the low SFRs of low surface brightness galaxies and extended-uv (XUV) disks (Thilker et al. 2007; Wyder et al. 2009). A theoretical model for star formation developed by Krumholz et al. (2009), which depends on the interaction between self-shielding, the interstellar radiation field, turbulence, and metallicity, reproduces the star formation law observed by Bigiel et al. (2008). Simulations generally have not tried to reproduce the star formation law but instead use it as an input (e.g. Lagos et al. 2011b; Wang et al. 2012). They have not been able to test the precise relationship between gas and star formation without first understanding the bigger picture including the ways in which feedback processes affect cold gas reservoirs and subsequent star formation on both local and global scales. Moreover, it is not trivial to correctly partition the cold gas into HI and H 2 components, which is necessary to test observed star formation laws. Some progress on this front has been made, notably by Lagos et al. (2011a); Duffy et al. (2012); Kauffmann et al. (2012); Lu et al. (2012); Davé et al. (2013); Kim et al. (2013), who tested a range of feedback scenarios to examine the resulting distribution of HI masses. 11

30 1.4 This Thesis There are many questions pertaining to the role of cold gas in galaxy evolution that one can try to answer with large datasets such as the ones described above, and there are many ways in which one can attempt to answer these questions. In a broad sense, I use these datasets to accomplish two aims: 1) to quantitatively describe the distribution of cold gas among galaxy populations; and 2) to define subgroups of galaxies with unique characteristics that elucidate certain aspects of galaxy evolution. In Section I describe the scientific questions I attempt to answer throughout this thesis, and in Section I describe the techniques I use to do so. Finally, in Section I describe the three projects that comprise this thesis Science Goals Taking advantage of the large multiwavelength datasets described above, in this thesis I seek to address the following questions: How can subpopulations of galaxies in distinct evolutionary phases tell us about massive galaxy evolution in general? (Chapters 2, 4) How common is inefficient star formation and how is it related to HI content? (Chapters 2, 4) What drives massive galaxies to form stars at lower rates than less massive galaxies? (Chapters 3, 4) 12

31 What is the expected distribution of HI for populations of galaxies with a given stellar mass or star formation rate and what are the origins of the distribution? (Chapter 3) Approach My thesis combines several techniques to answer these questions. For one, it is multiwavelength and multi-scale in scope. The former means that I use data from a variety of space-based and ground-based telescopes to examine the relationship between gas content and SFR in galaxies in the local universe. I also approach these questions from a number of different scales. Some studies rely on moderately-sized (N several hundred) samples of galaxies to derive global distribution functions (Chapter 3) and estimates of the space density of galaxies with extended UV (Chapter 2). In these cases I base my results on quantities that represent global properties of galaxies, i.e. the total HI mass or SFR of a galaxy averaged over its entire extent. Distribution functions based on large numbers of galaxies allow us to statistically model well-defined samples and are useful in testing models of galaxy evolution. I complement this type of statistical analysis with observations of a small number of galaxies that deviate from typical trends. The study described in Chapter 4 relies on HI imaging of individual galaxies to understand how the distribution of HI, which is unknowable from single-dish observations with Arecibo, can affect their star-forming properties. The distribution functions are an asset to this type of work by providing valuable context for the interpretation of deep observations of individual galaxies. In 13

32 addition to the various astronomical methods I employ in this thesis, I also rely on modeling. In Chapter 3 I use Bayesian modeling to apply a Markov chain Monte Carlo (MCMC) method for quantifying the HI mass function Summary I this section I describe the three projects that comprise this thesis XUV-Disks Chapter 2 presents results of the first unbiased search for extended UV (XUV)-disk galaxies undertaken to determine the space density of such galaxies. Our sample contains 561 local (0.001 < z < 0.05) galaxies that lie in the intersection of available GALEX deep imaging (exposure time > s) and SDSS DR7 footprints. We explore modifications to the standard classification scheme for our sample that includes both disk- and bulgedominated galaxies. Visual classification of each galaxy in the sample reveals an XUV-disk frequency of up to 20% for the most nearby portion of our sample. On average over the entire sample (out to z=0.05) the frequency ranges from a hard limit of 4% to 14%. The GALEX imaging allows us to detect XUV-disks beyond 100 Mpc. The XUV regions around XUV-disk galaxies are consistently bluer than the main bodies. We find a surprisingly high frequency of XUV emission around luminous red (NUV-r > 5) and green valley (3 < NUV-r < 5) galaxies. Using the XUV emission as an indicator of recent gas accretion, we estimate the cold gas accretion rate onto these galaxies. The number of XUV-disks in the green valley and the estimated accretion rate onto such galaxies points to the intriguing 14

33 possibility that 7-18% of galaxies in this population are transitioning away from the red sequence The Bivariate HI Mass Function In Chapter 3 we present the bivariate neutral atomic hydrogen (HI) stellar mass function (HISMF) φ(m HI, M ) for massive (log M /M > 10) galaxies derived from a sample of 480 local (0.025 < z < 0.050) galaxies observed in HI at Arecibo as part of the GALEX Arecibo SDSS Survey (GASS). We fit six different models to the HISMF and find that a Schechter function that extends down to a 1% HI gas fraction, with an additional fractional contribution below that limit, is the best parametrization of the HISMF. We calculate Ω HI,M >10 10 and find that massive galaxies contribute 41% of the HI density in the local universe. In addition to the binned HISMF we derive a continuous bivariate fit, which reveals that the Schechter parameters only vary weakly with stellar mass. The dependence of f, the fraction of galaxies with HI gas fraction greater than 1%, on stellar mass should be a strong constraint for numerical simulations. To understand the physical mechanisms that produce the shape of the HISMF we redefine the parameters of the Schechter function as explicit functions of stellar mass and star formation rate to produce a trivariate fit. This analysis reveals strong trends with SFR. The HISMF is a crucial tool that can be used to constrain cosmological galaxy simulations, test observational predictions of the HI content of populations of galaxies, and identify galaxies whose properties deviate from average trends. 15

34 HI-Rich Galaxies In Chapter 4 we systematically assess the link between HI and star formation within a sample of galaxies with extremely high HI masses (log M HI /M > 10). We uncover a population of galaxies with an unexpected combination of high HI masses and low specific star formation rates that exists only at stellar masses greater than log M /M We obtained HI maps of 20 galaxies in this population to understand the distribution of the HI and the physical conditions in the galaxies that could be suppressing star formation in the presence of large quantities of HI. We find that all of the galaxies we observed have low HI surface densities in the range in which inefficient star formation is common. The low HI surface densities are likely the main cause of the low specific star formation rates, but there is also some evidence that AGN or bulges contribute to the suppression of star formation. The sample s agreement with the global star formation law highlights its usefulness as a tool for understanding galaxies that do not always follow expected relationships. 16

35 Chapter 2 The Space Density of Extended Ultraviolet (XUV) disks in the Local Universe and Implications for Gas Accretion onto Galaxies Introduction Ultraviolet observations of galaxies acquired by GALEX have recently challenged the notion of a well-defined star formation threshold by showing that outer star formation can exist at radii that are four times beyond the optical extent of the galaxy (Gil de Paz 1 This chapter is a reformatted version of an article by the same name by J. J. Lemonias et al.that can be found in The Astrophysical Journal, Volume 733, Issue 2, p. 74. An edited version of the abstract for this paper is reproduced in Section

36 et al. 2005; Thilker et al. 2005, 2010). Following the discovery of extended ultraviolet (XUV) emission in the outer disks of NGC 4625 and M 83 (Gil de Paz et al. 2005; Thilker et al. 2005), Thilker et al. (2007; hereafter T07) conducted the first survey of extended UV emission in a sample of 189 nearby (d < 40 Mpc) disk galaxies and concluded that 29% of disk galaxies exhibit XUV emission. They developed a classification system in which Type 1 XUV-disks show a number of UV-bright, optically-faint, structured complexes beyond the star formation threshold and Type 2 XUV-disks have a large, blue, low surface brightness (LSB) zone beyond the limit within which optical light dominates. Perhaps more surprising than the existence of star formation in the outer regions of disks is the existence of XUV-disks around early-type galaxies. In a survey of 31 E/S0 galaxies, Moffett et al. (2010a) identified 13 as XUV-disks. NGC 404 (Thilker et al. 2010) and ESO (Donovan et al. 2009) are both early-type galaxies considered Type 1 XUV-disks because of a ring of star formation discernible in the UV. Salim & Rich (2010) revealed a population of massive early-type galaxies with UV excess that contain extended UV structures. XUV-disks around early-type galaxies are especially puzzling because they suggest that extended star formation does not require the presence of an inner star-forming disk. A distinct but related phenomenon presented in Werk et al. (2010) is the presence of outlying HII regions around gas-rich galaxies, some of which are associated with Type 1 XUV-disks. Out of the seven galaxies they found to be supporting outer HII regions, six of them are undergoing interactions or have nearby companions, providing evidence for interactions as a cause of extended star formation. They estimate that 6-10% of gas-rich 18

37 galaxies contain recent star formation in their outer disks. The existence and frequency of galaxies with XUV emission has implications regarding not just the expected radial extent of star formation but also the viability of star formation in regions of low gas density, the process of disk-building, and the causes of star formation in the outer regions of galaxies of all types. Interactions, perturbations, gas accretion, and the outward propagation of spiral density waves have all been proposed as triggers of extended star formation (T07; Bush et al. 2008, 2010). Recent cosmological simulations done by Roškar et al. (2010) established a possible link between XUV-disks and cold gas accretion. A systematic analysis of the types of galaxies in which XUV-disks predominate could provide crucial information about the origin of XUV-disks and their context in the overall framework of galaxy evolution. In this chapter we extend the sample of XUV-disks to higher redshifts by conducting an unbiased survey of over 500 local galaxies with redshifts up to z=0.05. Such a large and volume-limited sample allows us to determine the space density of XUV-disk galaxies. We analyze the properties of the XUV-disk galaxies in relation to the rest of the sample in order to determine the types of galaxies that tend to exhibit XUV emission, the nature of the XUV emission itself, and the causes of XUV emission. We pursue the connection between XUV-disks and gas accretion posited by Roškar et al. (2010) by assuming that the XUV emission in our sample of galaxies is indicative of recent gas accretion and then calculating the expected gas accretion rate onto XUV-disks. As part of this analysis, we build on a large, homogeneous dataset of galaxies observed by SDSS and GALEX that includes measurements of the bivariate luminosity distribution (Wyder et al. 2007). 19

38 In Section 2.2 we describe the sample and the observations used for the survey. Section 2.3 describes the method we employed to identify XUV-disk galaxies and includes several examples of the application of our method. In Section 2.4 we analyze the properties of the XUV-disk galaxies in relation to the rest of the sample. Section 2.5 presents a discussion of our findings, including our estimate of the XUV-disk space density and a calculation of the inferred gas accretion rates onto XUV-disk galaxies. Throughout the paper, we use the standard cosmological parameters with H o = 70 km s 1 Mpc Sample We created our sample by compiling all the GALEX images of known galaxies in the redshift range < z < 0.05 that lie within the intersection of available GALEX deep imaging and the SDSS DR7 footprint. The redshift range was chosen to overlap with the redshift range of the galaxies in the low-redshift portion of the NYU Value-Added Galaxy Catalog (Blanton et al. 2005a,b) containing galaxies in the range 14.3 < d < Mpc. Each galaxy was matched to the nearest primary object in the SDSS DR7 photometric sample using a 5 search radius. We began with 907 GALEX images. Only 771 of these images were centered on unique galaxies; some galaxies had been imaged by GALEX more than once or as part of different surveys. We eliminated all images from the sample in which the target galaxy was within 2 of the edge or off the edge of the GALEX detector (N=246) and all images with a bright star or GALEX artifact close enough to the galaxy (within 30 ) such that UV photometry would be compromised (N=6). We also removed from the sample one image in which 20

39 Table 2.1. Properties of Sample Galaxies SDSS ID RA DEC z t exp (NUV) a t exp (FUV) b NUV-r FUV-r r log(m /M ) R 90 /R 50 (1) (2) (3) (4) (5) (6) (7) (8) (9) (10) (11) SDSS J SDSS J SDSS J SDSS J SDSS J SDSS J SDSS J SDSS J SDSS J SDSS J Note. This table is available in its entirety in a machine-readable form in the online journal. A portion is shown here for guidance regarding its form and content. a NUV exposure time in kiloseconds. b FUV exposure time in kiloseconds. the galaxy was off-center in the image (N=1). We removed galaxies with no matches to the MPA-JHU SDSS catalogs (N=8), from which we obtained optical photometry. We restricted our sample to galaxies with 0 < NUV-r < 7 and 8 < log(m /M ) < 12 to match the sample of galaxies in Wyder et al. (2007); galaxies with values beyond these limits were removed from the sample (N=30). We note that such extreme colors are probably not real. After removing galaxies from the sample for the reasons mentioned above, there were still some cases in which there was more than one GALEX image of the same galaxy (N=55); we kept only the image with the longest GALEX exposure time. Our final sample consists of 561 galaxies. We present the sample in Table GALEX Imaging and Data Observations of each object were obtained from GALEX deep imaging collected as part of primary mission surveys. All objects were imaged by GALEX in the near-uv (NUV; 21

40 Å) and far-uv (FUV; Å) bands for a minimum of s. The median exposure time for galaxies in the sample is s. The GALEX full-width at half-maximum (FWHM) of the point-spread function (PSF) is 5.3 in the NUV and 4.2 in the FUV (Morrissey et al. 2007). NUV and FUV Petrosian magnitudes (as described in Blanton et al. 2001; Yasuda et al. 2001) were computed using a custom code in which nearby objects are masked. We used the NUV image to determine the Petrosian radius, which we then used to define the photometric aperture for the NUV and FUV images. A standard circular aperture 15 in diameter was used for small LSB galaxies. All magnitudes cited in this chapter are corrected for Galactic extinction due to dust according to Wyder et al. (2007). Colors of the extended UV emission within the XUV region were computed by obtaining photometry outside of a surface brightness threshold defined by µ FUV =27.25 ABmag arcsec 2 and inside the contour at which µ FUV =29.0 ABmag arcsec 2. See section for an explanation of the XUV region SDSS Imaging and Data Cutouts of the SDSS r-band FITS images and SDSS gri color composite images of each GALEX-SDSS matched object were generated using smosaic, a tool developed for use with the NYU Value-Added Galaxy Catalog (Blanton et al. 2005a). We used the r-band FITS images to measure the optical magnitude of the extended UV emission, the limits of which are given above and explained in section Optical measurements (Petrosian magnitudes, R 50, R 90, and Galactic reddening) as well as stellar mass for each object were 22

41 obtained from the MPA-JHU SDSS catalogs 2. Isophotal measurements that quantify the ellipticity of the galaxy (major axis, minor axis, and position angle) were obtained for purposes of photometry from the SDSS SkyServer XUV-Disk Identification Methodology Previous Classification Schemes Used To date, there has been only one other systematic search for XUV-disk galaxies, done by T07. They identified two distinct populations of XUV-disk galaxies in a nearby (d < 40 Mpc) sample of late S0s through Sm galaxies with inclination 80. In their classification system, Type 1 XUV-disks contain structured UV-bright emission complexes beyond the expected extent of star formation. The UV image of each galaxy was checked against an r-band image to verify that the UV structures are not obvious at optical wavelengths. Type 2 XUV-disks were quantitatively identified based on the color and size of a LSB region within the star formation threshold but beyond a contour enclosing 80% of the K-band luminosity of the galaxy. Thus, the identification of Type 2 XUV-disks was based not on an assumed star formation threshold but on a significant level of recent widespread star formation compared to the underlying disk. Galaxies which satisfy the requirements of both XUV-disk definitions are called mixed-type XUV-disks. In their study of XUV-disks around 30 E/S0s, Moffett et al. (2010b) apply the classi

42 fication scheme of T07 to a fraction of their sample but find that the locations of the two contours used to classify Type 2 XUV-disks were often interchanged, making it impossible to adhere to the classification scheme as it was designed. We address this point in section Our Classification Scheme We adopted the criterion most central to T07 s Type 1 classification scheme, namely that there be UV emission beyond a putative star formation threshold given by Σ SFR = M yr 1 kpc 2, which corresponds to µ FUV =27.25 ABmag arcsec 2 using the star formation rate (SFR) calibration of Kennicutt (1998) and correcting for Galactic extinction. Although we use UV flux beyond this isophote as our main initial criterion, we emphasize that we do not make any attempt to classify the galaxies in our sample as Type 1 or Type 2 XUV-disks and that the galaxies we do identify as XUV-disks do not necessarily belong in either of T07 s categories. The theoretical and observational motivation behind the chosen star formation threshold is described in detail in T07. We note that the primary reason for the choice of the specific UV threshold given above stems from Boissier et al. (2007) which showed that the threshold given above coincides with the Hα break found in Martin & Kennicutt (2001) galaxies. More recent work has provided further evidence of the existence of a star formation threshold by comparing the star formation rate surface density to the gas surface density and demonstrating that there is a downturn in star formation at low gas surface densities (Wyder et al. 2009; Bigiel et al. 2010). 24

43 We proceeded by overlaying the contour representing the FUV surface brightness limit, given above, on a 4 4 GALEX FUV and NUV composite image of each galaxy. We visually inspected each image to identify UV emission beyond that contour. The exposure times in our survey allow us to detect LSB features down to a limiting magnitude of ABmag arcsec 2 with a signal to noise ratio equal to 5 on small scales comparable to the GALEX PSF. Each galaxy with detected UV flux - structured or diffuse, clearly connected to the target galaxy or not - beyond the threshold was identified as an XUV-disk galaxy. We also identified a number of galaxies as XUV-ambiguous. (All XUV-disk and XUV-ambiguous galaxy identifications were agreed upon by J.J.L. and D.S.) The XUV-ambiguous galaxies have UV emission just beyond the expected star formation contour that may be residual flux associated with the main star-forming disk as opposed to real extended star formation independent of the central disk. In some cases, the UV emission that qualified a galaxy for XUV-ambiguous status may actually be a background source or part of a broad wing of the GALEX PSF. Nevertheless, some of the XUV-ambiguous galaxies could very well turn out to be XUV-disks when deeper or more highly resolved images are obtained. In the following analysis, we include both the definite XUV-disks and the XUV-ambiguous galaxies to provide some measure of the uncertainty in our classification procedure though we treat them separately at times to point out the differences between the two populations. Here, we do not impose any restrictions on the optical brightness of the XUV-disk or its component structures. In section and the Appendix we examine how such a restriction may change our sample and conclusions. 25

44 Limits of our Classification Scheme We recognize that our classification scheme is less quantitative and therefore more ambiguous than previous XUV-disk classification schemes. The ambiguity inherent in our visual classification scheme may cause us to identify XUV-disks where others may not have seen XUV-disks, and it is quite likely that the limits imposed on our study by the resolution of GALEX causes us to underestimate the frequency of XUV-disks. At the highest redshifts represented in our sample, the image resolution is 2.4 kpc 2 per pixel (see discussion in section 2.4.1). Our goal is to use a complete sample of galaxies in the local universe to derive global properties of XUV-disk galaxies based on an estimate of the frequency of such galaxies in our sample. Our classification scheme is sufficient to meet these goals. In contrast to the classification scheme of T07, which distinguishes XUV-disks based on the morphology of the extended star formation and thus is potentially linked to various formation scenarios, ours consists of one umbrella term for all galaxies with star formation beyond the previously expected radial limits. This system does not allow us to characterize different types of XUV-disks, but it does allow us to identify XUV-disks at moderate redshifts. Indeed, it is only with such a volume-limited sample extending to moderate redshifts that we can attempt to estimate the global properties of galaxies with XUV-disks. This work also serves as a way of determining the feasibility of detecting XUV-disks at larger distances and assessing the incompleteness of such detections. 26

45 SDSS J Figure 2.1 GALEX and SDSS color imagery of an XUV-disk galaxy. On the left is the GALEX image of a 4 by 4 field of view centered on the galaxy (FUV is blue; NUV is yellow). The white contour indicates the position at which the FUV surface brightness is µ FUV =27.25 ABmag arcsec 2. The white scale bar represents 10 kpc. On the right is the SDSS DR7 gri color composite image of the same field of view Examples Figures show a representative sample of galaxies we identified as XUV-disk galaxies, chosen to showcase the diversity of galaxies with extended star formation. In each figure the 4 4 GALEX color composite image centered on the galaxy in question is shown on the left. The contour corresponding to µ FUV =27.25 ABmag arcsec 2 is indicated in white. On the right is the SDSS gri color composite image on the same scale. The optical image of the object in Fig. 2.1 shows a red (NUV-r = 4.89) centrallyconcentrated (R 90 /R 50 = 3.0) galaxy (characteristic of a morphologically early-type galaxy) with a very bright center whose surface brightness falls off quickly. The GALEX image on the left shows that the UV flux drops off much more rapidly than the optical light. Beyond 27

46 SDSS J Figure 2.2 GALEX and SDSS color imagery of an XUV-disk galaxy. See caption of Fig. 2.1 for an explanation of images. the optical extent of the object is at least one prominent spiral arm as well as a number of bright UV complexes that constitute the XUV emission. The XUV emission around this galaxy is similar to the XUV-bright complexes of prototypical XUV-disks (Gil de Paz et al. 2005; Thilker et al. 2005); this is one of the more obvious cases of an XUV-disk. Fig. 2.2 shows an edge-on disk galaxy with color NUV-r = 3.89 and a prominent red center presumably due to dust extinction. The faint UV emission apparent at both ends of the galaxy in the GALEX image is indicative of a region of XUV emission beyond the expected extent of star formation in the disk. This galaxy also appears to have a slight warp in its XUV-disk. Unlike other samples studied for the presence of XUV-disks, our sample is blind to inclination angle. Because the critical isophote we use is not dustcorrected, our method is less effective for edge-on galaxies because the precise location of the star formation threshold is not obvious. On the other hand, projection effects observed 28

47 SDSS J Figure 2.3 GALEX and SDSS color imagery of an XUV-disk galaxy. See caption of Fig. 2.1 for an explanation of images. in edge-on galaxies might make the XUV emission more apparent than it would be in a face-on galaxy. Fig. 2.3 shows a blue (NUV-r = 1.14) disk + bulge galaxy with R 90 /R 50 = 2.8. Within the contour defining the star formation threshold is bright UV emission that mirrors the optical image. Outside of the contour is an expansive LSB zone of UV emission. In Fig. 2.4 we present an example of an XUV-ambiguous galaxy. This red (NUV-r = 5.5) early-type (R 90 /R 50 =3.3) galaxy has a faint ring-like feature in the optical image which could be suggestive of an XUV-disk. In the GALEX image we see UV flux extending just beyond the star formation contour in all directions. Although this could be indicative of an XUV-disk, we classified this galaxy as XUV-ambiguous because the symmetry of the UV emission suggests that it might be a product of the GALEX PSF. We have not definitively determined that the GALEX PSF is the issue here because we have not deconvolved the 29

48 SDSS J Figure 2.4 GALEX and SDSS color imagery of an XUV-ambiguous galaxy. See caption of Fig. 2.1 for an explanation of images. images. We also note here that the XUV emission associated with definite XUV-disks generally extends further beyond the star formation threshold than XUV emission around what we consider to be XUV-ambiguous galaxies. 2.4 Results and Data Analysis We identified 24 galaxies out of our sample of 561 as XUV-disk galaxies; that is, more than 4% of our sample shows prominent UV emission in the outer extents of the galaxy. We identified another 56 galaxies as XUV-ambiguous. Thus, we report a total XUV frequency of up to 14%. The first frequency is a hard lower limit because of redshift effects that lessen our ability to identify XUV-disks at higher redshifts (see section 2.4.1) and because of the non-inclusion of XUV-ambiguous galaxies. See Fig. 2.5 for UV and optical images of XUV-disks and Table 2 for properties of all XUV-disks and XUV-ambiguous galaxies. As the examples in the previous section demonstrate, XUV-disks are a heterogeneous 30

49 Table 2.2. Properties of XUV-disks and XUV-ambiguous Galaxies SDSS ID FUV-r XUV R 80 /R XUV Type a Reject? b (1) (2) (3) (4) (5) SDSS J D N SDSS J D N SDSS J A N SDSS J D N SDSS J D N SDSS J A Y SDSS J A Y SDSS J D N SDSS J D Y SDSS J D Y Note. This table is available in its entirety in a machine-readable form in the online journal. A portion is shown here for guidance regarding its form and content. a D indicates XUV-disk. A indicates XUV-ambiguous disk. b Y indicates rejects with FUV-r XUV > 5.0. N indicates galaxies with FUV-r XUV < 5.0. group of galaxies. There are however, some features that are common to a number of galaxies that exhibit below-threshold star formation in their outer extents. Among these are rings and spirals arms beyond the central star-forming region of a galaxy. In our sample 4 XUV-disk galaxies have UV rings and 6 have spiral arms or fragments of spiral arms beyond the expected star formation threshold. One XUV-disk galaxy is clearly undergoing an interaction. Such features could be useful in identifying other XUV-disks and determining the origin of XUV-disks Redshift Distribution of XUV-disk Galaxies Fig. 2.8 shows the distribution of XUV-disk galaxies in terms of redshift. Our volumelimited sample is heavily weighted towards objects with z > Not surprisingly, the 31

50 absolute number of XUV-disk galaxies in our sample is also weighted towards objects with z > 0.02, but the proportion of sample galaxies with XUV-disks is higher at low redshifts. The data for our lowest and middle redshift bins show that almost 7% of galaxies at z < 0.01 have detected XUV-disks. The fraction of XUV-disk galaxies drops to less than 3% for galaxies with 0.03 < z < This trend with redshift is even more pronounced when we include XUV-ambiguous cases. Note that when both XUV-disks and XUV-ambiguous galaxies are included, the XUV fraction at low redshifts approaches 20%; taking into account the size of the error bars, this almost matches the frequency of XUV-disks, 29%, found in T07 s sample. That the XUV fraction drops with redshift is an indication of the incompleteness of our XUV-disk sample beyond z=0.025 (d 107 Mpc). In the following analysis we do not adjust our results to account for this dependency on redshift; in our discussion we emphasize that all numbers should be considered lower limits. In Section we explore how a redshift correction would change our results. Almost certainly, this trend with redshift is not a real trend but simply a result of the fact that the classification was done visually and our ability to visually classify galaxies is dependent on the spatial resolution of the images and thus the redshift of each galaxy. In order to test the conjecture that the observed XUV-disk redshift distribution is due to a selection effect, we used GALFIT (Peng et al. 2002) to generate a test sample of GALEX FUV-band images of artificial galaxies. Each test galaxy is the sum of an inner disk component and an outer spiral disk component with varying parameters. Each component has an apparent FUV magnitude between 16.0 and 18.0 at z=0.01. The inner disk has a half-light radius ranging from 3.5 to 17.5 kpc; the outer disk has a half-light 32

51 radius ranging from 10.5 to 52.5 kpc. The Sersic index for the inner disk is set to 1.0 while the Sersic index for the outer disk component ranges from 0.1 to 0.5. All test galaxies are face-on. We applied the GALEX PSF and noise to each image to mimic the actual images used for the survey. We then placed each test galaxy at five redshifts from z=0.01 to z=0.05 and used the methodology described above to identify the XUV-disk galaxies in a random selection of the test sample. Fig. 2.9 shows that we recovered the redshift trend reported above, supporting the hypothesis that the redshift trend of XUV-disk galaxies is not real but a function of the image resolution. Despite the incompleteness with respect to redshift, our results appear to show that deep GALEX imaging can detect a significant number of XUV-disks out to z=0.025 (d 107 Mpc). We note that this test is limited because such simple models lack the complexity of XUV-disks found in nature. To further test our ability to identify XUV-disk galaxies at moderate redshifts we artificially redshifted 35 (out of 54) of the galaxies selected in T07 to be Type 1 and Type 2 XUV-disks. The 35 galaxies were chosen because they had readily available NIR photometry. We used FUV intensity maps of these galaxies compiled as part of the GALEX Nearby Galaxies Atlas (Gil de Paz et al. 2007) as a model intensity distribution and then generated maps for a galaxy of equivalent luminosity at redshifts 0.01, 0.02, 0.03, 0.04 and Simulated intensity maps were generated assuming a s total exposure time, with photon contribution from both model and sky background. Images were convolved to produce an appropriate GALEX PSF (Morrissey et al. 2007) and then analyzed using the same methods described above for identifying XUV-disks. For each galaxy we determined the maximum redshift out to which we would iden- 33

52 tify it as an XUV-disk. In Fig we show the results of this analysis, with the maximum redshift indicated as a function of the galaxy s color, NUV-H, and H-band absolute magnitude, as a proxy for stellar mass. We find, not surprisingly, that the more luminous galaxies are easier to detect out to higher redshift. Additionally our methods appear to be more effective at identifying Type 1 vs. Type 2 XUV disks, as discussed above. We found that we could identify XUV-disks out to a median redshift of z=0.02 (z=0.03 for Type 1), consistent with our observational findings and GALFIT simulated results discussed above. There are only 2 (out of 23, or < 9%) Type 1 XUV-disks in the subset of T07 s sample that we studied which would not be considered XUV-disks according to our criteria at redshifts as nearby as However, our classification scheme would allow us to classify the galaxies appropriately as XUV-disks using their actual UV images at their actual distances. This emphasizes that our classification scheme is generally consistent with that of T07 s Type 1 classification scheme but is limited by redshift. We do not classify as XUV-disks a much higher fraction of T07 s Type 2 XUV-disk galaxies. In fact we only classified 2 out of 9 of T07 s Type 2 XUV-disks in the subset that we studied as XUV-disks according to our classification scheme. This inconsistency is expected because our classification scheme is dependent on UV flux beyond the star formation threshold whereas T07 s Type 2 classification criterion is a blue LSB region within the FUV star formation threshold. Although our methodology does recover many of T07 s identifications of XUV-disks, we emphasize that our goal is not to reproduce T07 s study at larger distances, which distinguished between different morphologies of 34

53 XUV emission, but to develop an alternative, complementary method for identifying and characterizing extended UV emission around galaxies at moderate redshifts in order to estimate global properties of the population Morphology of XUV-disk Galaxies In order to assess the origin and frequency of XUV-disk galaxies, we first investigated the properties of galaxies with and without XUV-disks. Fig 2.11 shows the distribution of our sample in terms of morphology. We used the SDSS R 90 and R 50 r-band values to compute the concentration index C=R 90 /R 50 and used C as a proxy for the morphology of each galaxy. According to Strateva et al. (2001), the division between early-type and late-type galaxies occurs at C=2.6; objects with C > 2.6 are considered early-type galaxies and objects with C < 2.6 are considered late-type galaxies. Our full sample is slightly biased towards late-type objects, median C=2.44. The population of XUV-disk galaxies in our sample has a median concentration (C=2.68) which is suggestive of more-evolved galaxies. The median does not change if we include XUV-ambiguous galaxies. Note that this figure shows that the fraction of XUV-disks increases with concentration index. This trend suggests that the XUV-disk phenomenon is more common among early-type galaxies with a high concentration index. An analysis of the colors and masses of the galaxies in our sample provides further evidence that this is the case. 35

54 2.4.3 Colors and Stellar Masses of XUV-disk Galaxies Fig 2.12 shows NUV-r vs. log M /M for the sample and confirms that a large population of XUV-disk galaxies are massive red early-types. A first glance at the plot shows that XUVdisks and XUV-ambiguous galaxies (represented by closed blue squares and closed red circles, respectively) are scattered fairly evenly throughout the plot. A closer look shows that a much higher fraction of the red, massive galaxies (NUV-r > 3 and log M /M > 10.0) in the sample are identified as either XUV-disk galaxies or XUV-ambiguous galaxies. This finding strongly suggests that XUV-disks are more likely to be detected around early-type galaxies. The recent finding of Kannappan et al. (2009) of a population of blue E/S0 galaxies led us to investigate whether the early-type galaxies we classified as XUV-disks are members of this population. Fig shows that most of the early-type XUV-disk galaxies have red colors with NUV-r > 3 and thus are too red to be members of this category of galaxies. There are, however, a small number of XUV-disks and XUV-ambiguous galaxies with C > 2.6 and NUV-r < 3 that occupy a region of Fig distinct from the regions occupied by blue late-types and red early-types. Thus, there is some evidence that a fraction of our XUV-classified galaxies may be part of this new population of early-type galaxies whose properties (e.g. color, visual evidence of star formation) are more akin to those of late-type galaxies. 36

55 2.4.4 The XUV Emission Definition of the XUV Region In order to characterize the extended star formation around XUV-disk galaxies, we computed the FUV and r-band magnitudes within the XUV region. We defined the XUV region as the region between the expected star formation threshold at which µ FUV =27.25 ABmag arcsec 2 and the contour at which µ FUV drops to 29.0 ABmag arcsec 2. The outer limit of the XUV region was chosen to maximize the amount of XUV flux contained within the contour and to minimize the number of neighboring sources that mistakenly fall within the XUV region. In many cases, the XUV region does not completely encompass each UV complex or the entirety of the UV-bright region that led us to visually classify the galaxy as an XUV-disk or XUV-ambiguous galaxy. But a rigorous definition of the XUV region allows us to comment further on the characteristics of the XUV emission. We obtained photometry of the XUV region for all galaxies in the sample to allow us to compare these regions of the galaxies and perhaps clarify our visual classification scheme. We note that a fraction of the galaxies with no XUV emission do not have XUV regions because they have peak FUV surface brightnesses fainter than ABmag arcsec Color of the XUV Region Fig shows the global FUV-r color of each galaxy plotted against the FUV-r color of each galaxy s XUV region (FUV-r XUV ). Our goal in picking out galaxies with extended UV emission was to characterize the types of galaxies with recent star formation beyond the expected limits; a color cut based on FUV-r distinguishes between those XUV-disk 37

56 galaxies with recent star formation in their XUV regions and those XUV-disk galaxies that contain more evolved stellar populations in their XUV regions. The vertical dashed line in Fig indicates FUV-r XUV = 5.0. Wyder et al. (2007) show that the blue starforming sequence of galaxies extends to FUV-r 5.0. Additionally, Johnson et al. (2007) show that galaxies with FUV-r 5.0 have a 4000 Å break strength (D n (4000); a standard stellar age index) of 1.7. Assuming an instantaneous burst of star formation, D n (4000) = 1.7 corresponds to star formation within the past 1.5 Gyr (Kauffmann et al. 2003b). Thus, removing from consideration galaxies with FUV-r XUV > 5.0 restricts our sample to galaxies whose XUV regions had some star formation at most 1.5 Gyr ago. If we were to include a color cut in our classification scheme, how would our sample of XUV-disks change? Clearly, the sample would no longer contain many red, massive early-types. This raises the question of what are the red, massive early-types that we identified as XUV-disks and XUV-ambiguous galaxies whose XUV regions are not very blue at all. Although the XUV regions are surprisingly red, if we look at galaxies with continually redder XUV regions we uncover galaxies that are redder than their XUV regions. That the XUV regions around these galaxies are slightly bluer than the colors of the overall galaxies suggests that star formation in the outer regions has proceeded more recently than would be expected given the global colors which suggest that galaxy-wide star formation has ceased. In order to assess why a fraction of XUV-disks and XUV-ambiguous galaxies have remarkably red XUV regions, we found the contour that includes 80% of the r-band light, R 80. We define R 80 as the mean of the projected major and minor axes of this contour. R 80 38

57 should be comparable to K 80, which defined the inner contour of the LSB region for Type 2 XUV-disks in T07. In Fig we show R 80 divided by the extent of the XUV threshold (R XUV ; also measured in projection) plotted against the concentration index (C=R 90 /R 50 ). The ratio R 80 /R XUV and the concentration index both measure how centrally concentrated the star formation is within a galaxy, but the former is directly related to our analysis in that it provides another indicator of the color of the XUV region. For high R 80 /R XUV, R 80 is well beyond the inner FUV threshold so we would expect a substantial amount of r-band light to contaminate the XUV region. In this figure XUV-disks and XUV-ambiguous galaxies with FUV-r XUV < 5.0 are shown as closed symbols and rejects, those with FUV-r XUV > 5.0, are shown as open symbols. Most of the rejects have high R 80 /R XUV and most of the galaxies with blue XUV regions have low R 80 /R XUV. This shows that excluding galaxies with high R 80 /R XUV is comparable to using a FUV-r cut on the color of the XUV region. Such galaxies have XUV region colors that may be redder than expected, but they still show evidence of recent and unexplained below-threshold star formation. For that reason, we do not exclude such galaxies in the following analysis, although we do explore how such a cut based on XUV region color would affect our conclusions in the Appendix. The left panel of Fig includes the entire sample of galaxies and shows that XUV-disks do not stand apart from the rest of the sample. This is possibly due to the fact that much of the UV flux seen beyond the threshold in general has a very low surface brightness. Similarly, T07 found that the star formation beyond the star formation threshold in XUV-disks contributed negligibly to the overall star formation in a galaxy. 39

58 Except for a few outliers, the rejects do occupy an extreme region of the plot. They tend to be highly-concentrated galaxies, and their R 80 /R XUV ratios show that their UV star formation threshold is well within the main part of the star-forming body, which R 80 approximates. Thus it is appropriate to discard them as true XUV-disks since their XUV emission is part of the main stellar disk. In extending the XUV-disk classification system of T07 to early-type galaxies, Moffett et al. (2010b) discovered that the XUV threshold at which µ FUV =27.25 ABmag arcsec 2, which defined the outer contour of the LSB region, often fell inside K 80, making it impossible to characterize these galaxies as Type 2 XUV-disks. They found that K 80 was within the star formation threshold for only the UV-bluest E/S0s, which also had the highest SFRs in their sample. For those galaxies that did have K 80 /R XUV < 1, the LSB region between K 80 and R XUV was not large enough for the galaxy to be considered a Type 2 XUV-disk according to T07 s rigorous definition. Moffett et al. (2010b) described such galaxies whose LSB regions were small but blue as modified Type 2 XUV-disks. Modified Type 2 XUV-disks may represent a class of galaxies that are fundamentally different from Type 2 XUV-disks. Although we did not search for Type 2 or modified Type 2 XUV-disks in our sample, it is likely that they would lie in the region of our plot where R 80 < R XUV. Rejects with R 80 /R XUV < 1.0 may in fact be Type 2 or modified Type 2 XUV-disks. Finally, we note that the colors of the XUV region provide support for our bimodal classification scheme in which XUV-disk galaxies and XUV-ambiguous galaxies are classified separately. Only 16% of the XUV-disk galaxies have FUV-r XUV > 5.0 but over 37% 40

59 of the XUV-ambiguous galaxies have FUV-r XUV > 5.0. Fig presents a variation of Fig in which we show the FUV flux in the XUV region compared to the global FUV flux (FUV XUV /FUV galaxy ) vs. the r-band flux in the XUV region compared to the global r-band flux (r XUV /r galaxy ). All XUV-disks appear to have an elevated FUV XUV /FUV galaxy and no galaxies with very low FUV XUV /FUV galaxy and r XUV /r galaxy, suggestive of a lack of star formation in the outer regions, are identified as XUV-disks or XUV-ambiguous galaxies. Although the XUV-disks do tend to have high FUV XUV /FUV galaxy, there are many sample galaxies with similar values, and there are a number of XUV-ambiguous galaxies with quite low FUV XUV /FUV galaxy. The sample galaxies with a high ratio of FUV flux in the XUV region compared to the entire galaxy tend to have UV thresholds that are well within the main body of the galaxy; this artificially enhances the FUV XUV /FUV galaxy ratio. XUV-ambiguous galaxies with low (< 10 1 ) ratios tend to have very diffuse, low surface brightness UV flux, which explains why the UV flux in the XUV region is so small compared to the UV flux emitted by the entire galaxy. Together, Figs show that XUV-disks do not occupy a single region of parameter space and thus may not represent a distinct population of galaxies. Their diversity, in terms of color, mass, and concentration, along with the diversity of the XUV regions themselves, supports previous suspicions based on the various morphologies of the extended star formation (see Section 2.3.2) that XUV-disks comprise a heterogeneous population of galaxies. Thus, galaxies hosting XUV flux are not a class of galaxies unto themselves; rather, they may represent an evolutionary phase during which the bulk of 41

60 star formation occurs beyond the main star forming disk. We discuss this idea further in Section Discussion The Space Density of XUV-disk Galaxies One of the primary goals of this survey was to determine the space density of XUV-disk galaxies in the local universe. The size of the sample and the unbiased nature of the survey allow us to do this. In order to compute the space density of XUV-disks we first determined the XUV fraction, or the fraction of galaxies exhibiting XUV-disks in colorstellar mass bins, by volume-averaging the XUV fraction in three evenly-spaced redshift bins. The space density of XUV-disks is the product of this XUV fraction and the space density (Mpc 3 ) of all galaxies in the local universe, derived from the color-magnitude diagram in Wyder et al. (2007). We found the space density of galaxies in each color-stellar mass bin by first deriving a color-dependent mass-to-light ratio from the sample in Wyder et al. (2007). We then used stellar masses from the MPA-JHU catalog as references and a Chabrier (2003) initial mass function to convert from absolute magnitude to stellar mass. The resulting distribution is shown as a contour plot in Fig 2.17, with the bins used in the following analysis indicated. We show in Fig (a) the volume-averaged XUV fraction used to find the XUV-disk space density. The extended peak for galaxies with NUV-r > 4 suggests that XUV-disks are more common among transition galaxies in the green valley (3 < NUV-r < 5) and 42

61 red-sequence (NUV-r > 5) galaxies. The local space density of galaxies derived from Fig is shown in (b). The product of the XUV fraction and the local space density, in (c), shows that the space density of XUV-disks is fairly even across the sequence. Fig shows the same sequence of histograms, but also includes in the XUV fraction the number of XUV-ambiguous galaxies. The peak in the XUV fraction histogram is spread in stellar mass. The total space density of XUV-disk galaxies is > Mpc 3, with the range given by the space density computed for XUV-disks only and for both XUV-disk and XUV-ambiguous galaxies. We emphasize that this is a lower limit because of the redshift effects discussed above The Origin of the XUV Emission Formation Scenarios A number of physical mechanisms including interactions, perturbations, gas accretion, and the outward propagation of spiral density waves have been proposed as triggers of star formation in XUV-disks (see T07; Bush et al. 2008, 2010, for a more complete discussion of possible formation scenarios). As mentioned in Section , we leave open the possibility that the extended star formation in some XUV-ambiguous galaxies is not distinct from the main body of the galaxies and so does not have a distinct formation scenario. Much has been said about the role of interactions in XUV-disks because many of the known XUV-disks show evidence of a recent interaction. One of the first XUV-disks discovered is considered a direct result of a previously-confirmed interaction (NGC 4625; 43

62 Gil de Paz et al. 2005). Thilker et al. (2010) provides an example of an XUV-disk galaxy following a merger that is undergoing enough star formation to rejuvenate the disk and shift a red lenticular galaxy towards the green valley. T07 report that 75% of the galaxies they identified as Type 1 and about 50% of the galaxies they identified as Type 2 show evidence of an interaction based on the tidal perturbation parameter from Varela et al. (2004). We leave an analysis of interactions and their relationship to XUV-disks to a later study. In disk galaxies, it is plausible that the gas dynamics and structuring in the inner disk play a role in generating the star formation in the outer disk. Bush et al. (2008, 2010) completed models to determine how XUV emission could be created in disk galaxies. They showed that in disk galaxies with extended gas disks, the spiral density wave can propagate into the outer disk, producing gravitationally unstable regions that collapse and form stars. This appears to be a reasonable explanation for the XUV emission in many late-type galaxies even though it doesn t address the origin of the extended gas distribution itself. It is worth noting that Bush et al. (2010) were successful in reproducing Type 1 XUV-disks but were unable to recreate Type 2 XUV-disks. They suggest that recent gas accretion might be responsible for producing young, blue Type 2 XUV-disks. T07 also proposed that gas has an important role in the formation of XUV-disks. They showed that XUV-disks are twice as gas-rich as would be expected based on their Hubble type. An enhanced HI content has been linked to a strong color gradient in which the outer disk of a galaxy is much bluer than the inner disk (Wang et al. 2011). Such galaxies, which are likely undergoing inside-out disk growth, may have experienced a recent gas 44

63 accretion event which elevated the HI content. Similar color gradients for the XUV-disks in our sample (see Fig. 2.14) point to the possibility that XUV-disks are the result of gas accretion. Whether the stars in XUV-disks are formed from recently accreted gas or an older gas reservoir, it is important to consider the gas from which these stars form. Galaxies form and evolve by accreting gas from their surroundings. The physical processes by which galaxies accrete enough gas to match the measured star formation rate are a subject of active study. The classical view of gas accretion focused on hot-mode accretion in which infalling gas is shock-heated to the virial temperature and then radiatively cools to form dense clouds that eventually produce stars. Recently, Kereš et al. (2009) showed that it is not hot-mode accretion but rather cold-mode accretion that supplies galaxies with most of their fuel for star formation via filaments that are accreted directly from the intergalactic medium (IGM). Kereš & Hernquist (2009) showed that these filaments can condense into clouds that can then rain onto galaxies and provide gas for star formation. The newly accreted clouds will be distributed in a flattened disk around the galaxy. These clouds may be analogs of high-velocity clouds (HVCs) surrounding the Milky Way which are thought to provide much of the fuel for star formation in the Galaxy. Kereš & Hernquist (2009) estimate that, for a Milky Way-sized halo, gas can be supplied in this manner at a rate of 0.6 M yr 1. If gas recycled through the galactic fountain is included, the accretion rate may reach 1 M yr 1, providing enough gas to sustain the current star formation rate of 1 M yr 1. Attempts to detect accreting gas rely on observational signatures of gas accretion 45

64 that include HI tails and filaments, accompanying dwarfs, extended and warped HI morphologies, lopsided disks, and extraplanar HI in spiral galaxies (Sancisi et al. 2008). In studies done thus far, measured accretion rates based on such signatures do not account for total star formation rates around 1 M yr 1. Sancisi et al. (2008) find an observed accretion rate of 0.2 M yr 1. Fraternali (2010) cites a number of studies based on measurements of extraplanar neutral gas that report accretion rates accounting for 5-24% of the star formation rate in each galaxy. Recent cosmological simulations done by Roškar et al. (2010) focused on the role of gas accretion in the creation of warped galactic disks and the misalignment of the inner and outer disks that underlie the warp. They found that cold gas accretion accounts for 75% of the mass in the misaligned outer disk, and cold gas that is not shock-heated is responsible for much of the star formation in the misaligned outer disk. They also find that such warps created by the accretion of cold gas onto a misaligned outer disk will disappear in the absence of continuous accretion of cold gas. Some of the first XUV-disks that were discovered were characterized by warped HI disks (Thilker et al. 2005; T07). In our sample, at least one galaxy appears to have a slight warp in its XUV-disk (see Section 2.3.2). Thus, it is reasonable to assume that there is a strong connection between XUV-disks and cold gas accretion and that XUV-disks may be fueled by cold gas accretion. Roškar et al. (2010) suggest that observations of stellar populations beyond the central stellar disk, such as those that form in an XUV-disk, will be valuable in probing cold accretion. 46

65 Gas Accretion Rate for Our Sample Here we use the extended star formation in XUV-disk galaxies as evidence of recent or ongoing gas accretion. Although XUV-disks cannot be linked unequivocally to gas accretion, we explore the possibility here. Many of the defining features of XUV-disks, such as rings, are suggestive of recent gas accretion. We use the calculated XUV-disk space density and the UV properties of XUV-disks to constrain the rate of cold gas accretion onto these galaxies. The cold gas accretion rate we estimate may include low-redshift cold accretion and cold gas clouds acquired from minor mergers or interactions. As discussed above, this work is an exploratory analysis and we caution that all numbers reported here are coarse estimates and the result of several assumptions. Our main goal here is to set up a framework for future analysis of XUV-disks and observations of gas accretion. Because our ability to detect faint UV features at moderate redshifts with existing and future technology surpasses our ability to directly measure the HI content of galaxies beyond the very local universe, methods similar to that which we develop here, in which estimates of cold gas accretion are based on the UV properties of galaxies, will play a crucial role in the interpretation of future observations of galaxies. We use the following equation to determine the gas accretion rate onto XUV-disk galaxies in bins of NUV-r and M Ṁ gas,xuv = φ f xuv < M gas,xuv > T (2.1) where φ = φ(nuv r, M ) is the galaxy volume density (Mpc 3 ; derived from Wyder et al. 2007), f XUV = f XUV (NUV r, M ) is the volume-averaged XUV fraction calculated 47

66 above, M gas,xuv = M gas,xuv (NUV r, M ) is the average HI mass within the XUV regions, and T is the accretion timescale. Below we describe some of the assumptions that went into our calculation. To estimate M gas,xuv we adopt an average HI surface density of 3 M pc 2 over the deprojected surface area of the XUV regions. Although this value is somewhat arbitrary and is uncertain by about a factor of 2, we selected it to match that observed for the outer parts of XUV-disks M 83 (Thilker et al. 2005) and NGC 4625 (Gil de Paz et al. 2005). This value is also consistent with the HI detected in outer regions of galaxies by the THINGS survey (Bigiel et al. 2008). For our sample, the average HI mass associated with XUV regions around XUV-disks ranges from to M with a median value of M. A critical assumption in determining the gas accretion rate is selecting the timescale over which gas is accreted. In general, the gas consumption timescale in the outer parts of disks is longer than the likely timescale for inflow (Bigiel et al. 2010). Thus we use a dynamical timescale for the gas accretion timescale ( T), which we assume to be 1 Gyr across all bins. It is not clear that this is the best estimate for each galaxy in our sample, but this is a reasonable approximation based on recent work. Sancisi et al. (2008) show that recently accreted asymmetric features, such as tails, will be incorporated into the parent galaxy over a few dynamical times, or roughly 1 Gyr. Haan et al. (2009) estimate that gravitational torques in spiral galaxies will redistribute cold gas on a similar timescale. The accretion timescale for the early-type galaxies in our sample may be longer than these estimates, but we use 1 Gyr since it is based on calculations from the literature. 48

67 Here we summarize the key assumptions that were made in determining the gas accretion rate that follows: 1. The presence of an XUV-disk is indicative of recently accreted HI. 2. The XUV region traces the extent of the HI reservoir. 3. The HI surface density in the XUV region is consistent with the HI surface density in the outer regions of other well-studied XUV-disks: Σ HI = 3 M pc The timescale over which the cold gas is accreted is a few dynamical times: T = 1 Gyr. The total amount of cold gas accreting onto XUV-disk galaxies is > M Mpc 3, with the lower estimate derived using only XUV-disks and the upper estimate derived using both XUV-disks and XUV-ambiguous galaxies. The HI volume density of the local universe is M Mpc 3 (Zwaan et al. 2005). From this we can estimate that 3-8% of the HI gas in the universe might be associated with XUV-disks. Our result for the gas accretion rate onto XUV-disk galaxies, in terms of M Mpc 3 yr 1, is shown in Fig The infall rate onto XUV-disks is > M Mpc 3 yr 1 with the range given by the difference between the two panels. Galaxies throughout the sequence, including those in the red sequence and green valley, are undergoing gas accretion. The local star formation rate density is 0.02 M Mpc 3 yr 1 (Salim et al. 2007). If all of the gas in the XUV region eventually forms stars, our liberal estimate that includes XUV-ambiguous galaxies suggests that cold gas accretion onto XUV-disk galaxies could account for about 23% of the local star formation rate density. The calculation of the 49

68 cold gas accretion rate derived from our conservative estimate, which excludes XUVambiguous galaxies, only accounts for about 9% of the star formation in the local universe. This is consistent with other estimates of the gas accretion rate noted above. Although simulations (e.g. those of Kereš & Hernquist 2009) have shown that gas accretion provides most of the fuel for continued star formation in galaxies, observational estimates of gas accretion rates have consistently underestimated the gas accretion rate by a factor of 5 to 20. The above calculation provides an estimate of the HI associated with XUV emission in our sample, but of course it cannot speak to the amount of HI accreting onto galaxies that do not exhibit XUV flux. Although it is reasonable to assume that the galaxies in our sample with XUV-disks have extended HI disks beyond the optical radius, the existence of extended HI in galaxies without XUV-disks is less clear. Indeed, Sancisi et al. (2008) describe the tenuous correlation between gas accretion and star formation rate, as evidenced by the existence of gas-rich ellipticals with no signs of recent star formation. Thus, our estimate of the amount of gas associated with XUV-disks underestimates the total amount of gas associated with extended HI disks because our methods only allow us to measure the HI associated with disks that support extended star formation. 50

69 SDSS J SDSS J GALEX SDSS GALEX SDSS SDSS J SDSS J GALEX SDSS GALEX SDSS SDSS J SDSS J GALEX SDSS GALEX SDSS SDSS J SDSS J GALEX SDSS GALEX SDSS SDSS J SDSS J GALEX SDSS 51 GALEX SDSS Figure 2.5 The 24 XUV-disk galaxies in the sample. See caption of Fig. 2.1 for an explanation of images.

70 SDSS J SDSS J GALEX SDSS GALEX SDSS SDSS J SDSS J GALEX SDSS GALEX SDSS SDSS J SDSS J GALEX SDSS GALEX SDSS SDSS J SDSS J GALEX SDSS GALEX SDSS SDSS J SDSS J GALEX SDSS 52 GALEX SDSS Figure 2.6 Continued

71 SDSS J SDSS J GALEX SDSS GALEX SDSS SDSS J SDSS J Figure 2.7 Continued 53

72 XUV-disks XUV-disks + XUV-amb. Survey Sample Number of Galaxies XUV Fraction z Figure 2.8 The number and fraction of XUV-disk galaxies as a function of redshift. The thin blue histogram shows the distribution of the entire sample; the thick red histogram shows only the XUV-disk galaxies; the medium green histogram shows both XUV-disk galaxies and XUV-ambiguous galaxies. The thick red and medium green dashed lines show the fraction of galaxies with XUV emission for XUV-disks only and for XUV-disks in addition to XUV-ambiguous galaxies, respectively. 54

73 XUV-Disks XUV-Disks + XUV-amb. Survey Sample Number of Galaxies XUV Fraction Figure 2.9 Same as Fig. 2.8 but with test galaxies generated with GALFIT. 55

74 NUV-H Undetected Type 1 Type 2 Mixed Type H Figure 2.10 The maximum redshift at which an XUV-disk was detected around 35 artificially redshifted galaxies from the sample of T07. Galaxies labeled undetected did not exhibit obvious XUV-disks at any of the redshifts we considered. 56

75 XUV-Disks XUV-Disks + XUV-amb. Survey Sample Number of Galaxies XUV Fraction R 90 / R Figure 2.11 The number and fraction of XUV-disks as a function of concentration index (C=R 90 /R 50 ). The dotted vertical line indicates the division between early-type galaxies (C > 2.6) and late-type galaxies (C < 2.6). The labels are the same as in Fig

76 XUV-disks XUV-amb. Survey Sample 5.0 NUV-r /M log M Figure 2.12 NUV-r vs. log M /M for the sample. XUV-disks are represented by blue closed squares, XUV-ambiguous galaxies by red closed circles, and galaxies with no XUV emission by gray dots. 58

77 Figure 2.13 NUV-r color plotted against concentration index (C=R 90 /R 50 ). The dashed vertical line indicates the division between early-type galaxies (C > 2.6) and late-type galaxies (C < 2.6). Labels are the same as in Fig

78 XUV-disks XUV-amb. Survey Sample FUV-r galaxy FUV-r XUV Figure 2.14 FUV-r color of each galaxy (FUV-r galaxy ) plotted against FUV-r color of the XUV region (FUV-r XUV ). The vertical dashed line shows where FUV-r XUV = 5.0. The solid line has a slope of 1. Labels are the same as in Fig

79 10 2 XUV-disks XUV-amb. XUV-disk Rej. XUV-amb. Rej. Survey Sample a) 10 2 b) R 80 / R XUV R 90 / R R 90 / R 50 Figure 2.15 R 80 /R XUV vs. concentration index for all galaxies in the sample (a) and only galaxies with XUV flux (b). Gray points are sample galaxies with no XUV flux. Blue closed squares are XUV-disks and red closed circles are XUV-ambiguous galaxies. Blue open squares are XUV-disk rejects and red open circles are XUV-ambiguous rejects. The dotted vertical line indicates the division between early-type galaxies (C > 2.6) and late-type galaxies (C < 2.6). The dashed horizontal line shows where R 80 =R XUV. 61

80 XUV-disks XUV-amb. Survey Sample 10 0 FUV XUV / FUV galaxy r XUV / r galaxy Figure 2.16 The FUV flux in the XUV region compared to the entire galaxy vs. the r- band flux in the XUV region compared to the entire galaxy. The solid line shows where FUV XUV /FUV galaxy =r XUV /r galaxy. Labels are the same as in Fig

81 Figure 2.17 The local space density of galaxies, derived from Wyder et al. (2007). The bins used to determine the space density of XUV-disks are indicated. 63

82 a) XUV Fraction b) Local Space Density [10 3 Mpc 3 ] c) XUV Space Density [10 4 Mpc 3 ] NUV-r /M log M 1 NUV-r /M log M NUV-r /M log M Figure 2.18 The volume-averaged XUV fraction (fraction of galaxies in our sample with XUV-disks), the local space density of galaxies (derived from Wyder et al. 2007), and the local space density of XUV-disk galaxies. The numbers overlaid on the XUV fraction plot indicate the total number of sample galaxies in each bin. Note that the scales for the plots in the middle and on the right are off by an order of magnitude. a) XUV Fraction b) Local Space Density [10 3 Mpc 3 ] c) XUV Space Density [10 4 Mpc 3 ] NUV-r /M log M 1 NUV-r /M log M NUV-r /M log M Figure 2.19 Same as Fig with XUV-ambiguous galaxies included. 64

83 Figure 2.20 Histograms showing the mass of gas accreted onto XUV-disks per bin. XUVdisks only are included in the plot on the left and XUV-disks and XUV-ambiguous galaxies are included in the plot on the right. The numbers overlaid on the plots indicate the total number of XUV-disks and XUV-disks plus XUV-ambiguous galaxies in each bin. 65

84 Space Density [10 4 Mpc 3 ] Space Density [10 4 Mpc 3 ] NUV-r /M log M 1 NUV-r /M log M 1 Figure 2.21 Redshift-corrected space density of XUV-disks on the left and XUV-disks plus XUV-ambiguous galaxies on the right. The numbers overlaid on the plots indicate the total number of XUV-disks and XUV-disks plus XUV-ambiguous galaxies in each bin in the original sample Redshift Correction As stated in section 2.4.1, our ability to detect XUV-disks beyond 100 Mpc is limited by the resolution of GALEX. Here we correct for this limitation by increasing the XUV fractions in each redshift bin to 20% to match the XUV fraction in the lower redshift bins. Correcting for incompleteness with respect to redshift, our estimate of the XUV-disk space density is > Mpc 3 (see Fig. 2.21), a modest increase over the space density determined without the correction. The gas accretion rate onto such galaxies increases to > M Mpc 3 yr 1 (see Fig. 2.22). 66

85 Figure 2.22 Redshift-corrected gas accretion rate onto XUV-disks on the left and onto XUV-disks plus XUV-ambiguous galaxies on the right. The numbers overlaid on the plots indicate the total number of XUV-disks and XUV-disks plus XUV-ambiguous galaxies in each bin in the original sample XUV-disks and Their Relation to Disk-Building Given that the gas accretion rate is significant (> M Mpc 3 yr 3 ) even for XUV-disks around transition galaxies in the green valley, it is reasonable to consider that the infall of gas onto the XUV-disks lying in the green valley may lead to enough star formation to cause the galaxy to transition away from the red sequence. Our results show that the XUV-disk fraction in the green valley is 7-18%; thus, it is possible that a similar fraction of green valley galaxies might be moving away from the red sequence due to a new round of star formation in their outer regions. Previous studies of the green valley (e.g. Martin et al. 2007) focused on the quenching processes occurring in green valley galaxies that might drive galaxies from the blue sequence to the red sequence. More recently, work has been done to target transition 67

86 galaxies in the green valley in order to identify galaxies that are transitioning either to or from the red sequence (e.g. Catinella et al. 2010). For example, NGC 404 is a lenticular galaxy that may be transitioning away from the red sequence. Thilker et al. (2010) showed that if its HI ring is the result of a recent accretion event (as proposed by del Río et al. 2004), the star formation in the ring caused the galaxy to move from the red sequence into the green valley. More recently, Williams et al. (2010) used HST observations of the galaxy to show that its star formation rate has since decreased after a brief increase immediately following the accretion event. Thus, although the accretion of new material initially led to an increased level of star formation that caused the galaxy to transition to the green valley, NGC 404 will likely fall back to the red sequence instead of moving blueward. NGC 404 is not a lone case: the majority of the massive early-type galaxies in the sample studied by Salim & Rich (2010) appear to be similar to NGC 404. They, too, lie in the green valley and have rejuvenated disks that are probably the result of gas accretion from the IGM or minor mergers. The temporary detour to the green valley that was seen for NGC 404 provides support for our suggestion that XUV-disks represent a phase in the evolution of a galaxy. There are numerous examples in the literature of galaxies whose morphologies are indicative of XUV-disks and that appear to be undergoing a star formation event that is associated with gas accretion. Indeed, Cortese & Hughes (2009) discovered a population of transition galaxies with a normal amount of HI (most of the transition galaxies they studied were HI-deficient) that are moving away from the red sequence as the HI is consumed and 68

87 converted to stars. Many of those HI-normal transition galaxies with obvious recent star formation display prominent UV rings. The presence of the UV rings suggests that the population Cortese & Hughes (2009) describe includes XUV-disk galaxies that are in the process of disk-building. Moffett et al. (2010b) interpreted XUV-disks in E/S0s as evidence for disk-building following a merger and Kannappan et al. (2009) suggested that blue E/S0s, which may make up a fraction of our XUV-disks, are probably building disks as well. That diskbuilding can be a result of gas accretion is consistent with Kereš & Hernquist (2009) - they suggest that the cold gas accretion will form a disk around an evolved galaxy, providing fuel for extended star formation and a path away from the red sequence. At this point, it is not easy to distinguish between transition galaxies that are experiencing a new wave of gas accretion and subsequently moving away from the red sequence and transition galaxies whose gas accretion rate is slowly decreasing, causing them to move towards the red sequence. Ring-like features around early-type galaxies are often interpreted as signs of recent gas accretion, but it is possible that the phase of gas accretion represented by the ring is in fact ending. Analysis of a galaxy s potential for new and continued star formation (and subsequent movement within the color-magnitude diagram) is locked up in the amount of HI gas in the galaxy. Such a detailed analysis is beyond the scope of this chapter but crucial in determining exactly how much star formation can be expected in the XUV-disk and what effects it may have on galaxy morphology. Future studies should focus on trying to disentangle observations of gas accretion and quenching of star formation so that we are able to conclusively identify a population of galaxies that 69

88 are re-building disks and explore its connection to the population of XUV-disks. 2.6 Conclusions We report the XUV-disk space density in the local universe based on an unbiased survey of galaxies in the intersection of available GALEX deep imaging and SDSS footprints. Galaxies of all colors and masses exhibit XUV-disks, but a higher fraction of red massive early-type galaxies show evidence of star formation in their outer extents. We investigated the possibility that the extended star formation in many XUV-disk galaxies is due to cold mode accretion by estimating the gas accretion rate onto XUV-disks. There is a significant level of gas accretion onto all galaxy types, including transition galaxies in the green valley. Gas accretion onto galaxies in the green valley may represent evidence that these galaxies are rebuilding their disks. Some of our key results follow: 1. Based on our measurements and simulations, we find that deep GALEX imaging allows us to detect XUV-disks beyond 100 Mpc. 2. We have used our unbiased survey to establish the average frequency of XUV-disks out to z=0.05 as 4-14%, with 4% as a hard lower limit. The incidence rises to close to 20% for the nearby portion of our sample (somewhat consistent with, though lower than, previous findings; i.e. those of T The calculated XUV-disk fraction along with measurements of the local space density of galaxies allows us to estimate that the space density of XUV-disks is >

89 Mpc 3. We used an estimate of the gas content associated with XUV-disk galaxies to establish a gas accretion rate onto XUV-disk galaxies of > M 3 yr Under the assumption that XUV-disk galaxies in the green valley might be rebuilding their disks, we find that 7-18% of galaxies in the green valley could be transitioning away from the red sequence. The work presented here represents an attempt to expand the known sample of XUVdisk galaxies and to estimate global properties of such galaxies. We are limited by the resolution of GALEX and thus restricted in our ability to make firm conclusions about the prevalence of such galaxies in different mass ranges and at various redshifts. Future searches for XUV-disks will require data with greater sensitivity and finer resolution in order to detect small pockets of star formation in the outer reaches of galaxies. We thank the anonymous referee for valuable comments that substantially improved the quality of this chapter. This work has made extensive use of the MPA/JHU and the NYU SDSS value-added catalogs. 71

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91 Chapter 3 The Bivariate Neutral Hydrogen-Stellar Mass Function for Massive Galaxies Introduction The cold gas content of a galaxy provides insight into a galaxy s accretion history and its potential for future star formation activity. It reflects a complex interaction between gas accretion, gas consumption, and feedback processes that inhibit both. Recent simulations have sought to determine which processes dominate in different types of galaxies. They have experimented with various levels and types of inflow, outflow, and feedback (Hopkins et al. 2008; Kereš et al. 2009; Davé et al. 2011a,b; Leitner & Kravtsov 2011; Duffy et al. 2012; Kauffmann et al. 2012; Kim et al. 2013) and tested a range of star formation laws 1 This chapter is a reformatted version of an article by the same name by J. J. Lemonias et al.that can be found in The Astrophysical Journal, Volume 776, Issue 2, p. 74. An edited version of the abstract for this paper is reproduced in Section

92 (Lagos et al. 2011a,b; Wang et al. 2012) to understand the roles that each may play in determining the gas and stellar masses of galaxies. Observations, meanwhile, have focused on constraining the global distribution of cold gas in the local universe and studying how the cold gas content of galaxies is related to their evolution and growth. Attempts to observationally describe the distribution of galaxies in terms of their atomic gas content include HI surveys of large samples of galaxies or large areas of the sky (Haynes & Roberts 1979; Fisher & Tully 1981; Giovanelli & Haynes 1985) and have often relied on the measurement of HI mass functions (Shostak 1977; Briggs & Rao 1993; Rao & Briggs 1993; Zwaan et al. 1997; Henning et al. 2000; Rosenberg & Schneider 2002; Zwaan et al. 2003, 2005; Martin et al. 2010). HI mass functions (HIMFs) estimate the space density of galaxies as a function of HI mass and are generally parametrized by a Schechter function (Schechter 1976). The HIMF can shed light on many aspects of galaxy evolution. Comparisons of HIMFs derived from galaxies in different environments and across morphological types provide insight into the processes of gas stripping and accretion (Solanes et al. 1996; Springob et al. 2005). The HIMF also provides a constraint for models of galaxy formation and evolution (e.g. Lagos et al. 2011a; Duffy et al. 2012; Kauffmann et al. 2012; Lu et al. 2012; Davé et al. 2013; Kim et al. 2013). Another motivation for constructing HIMFs was to examine the low-mass end of the HIMF for evidence of a population of dark galaxies with no optical counterparts, so-called missing satellites (Zwaan et al. 1997; Henning et al. 2000; Rosenberg & Schneider 2002). Early HIMFs were, by necessity, derived from relatively small samples of galaxies, sometimes as small as 60, observed as part of shallow surveys. Much larger and deeper 74

93 surveys have yielded samples of thousands of galaxies that better constrain the HIMF and can map the large-scale structure of the local universe (Zwaan et al. 2003, 2005; Martin et al. 2010). Remarkably, the shape of the HIMF has not changed significantly since the first HIMFs based on fewer galaxies. The large samples have, however, facilitated more complex analyses of the HI content of galaxies including the relation between HI and optical- and UV-derived properties such as stellar mass, color, and SFR (e.g. Toribio et al. 2011; Huang et al. 2012) and bivariate mass functions (Zwaan et al. 2003). Despite the utility of the HIMF, few studies have sought to explain the physical mechanisms that can shape the full distribution. The HIMF is also hard to interpret in an evolutionary context the origin of HI in galaxies and its evolution over time are presently quite challenging to model. Like the star formation rate (SFR) of a galaxy, HI content may increase or decrease as gas is accreted, converted to stars, cooled, ionized or heated. This contrasts with the monotonic growth history that generally characterizes the stellar mass of galaxies. In this respect it is natural to study the HI content of galaxies by adopting the same approach as has been used for studying the distribution and evolution of SFR vs. stellar mass in galaxies, using the bivariate distribution, as in the color-magnitude diagram and the specific SFR-stellar mass plane (e.g. Wyder et al. 2007; Schiminovich et al. 2007). Thus we construct the bivariate M HI -M HIMF, which we call the HISMF and which describes the space density of galaxies in terms of both HI mass and stellar mass. This type of HI study necessarily assumes that all HI-detected galaxies are optically detected and benefits from samples that are complete in stellar mass. This strategy is behind the GALEX Arecibo SDSS Survey (GASS; Catinella et al. 2010), which serves as the basis of 75

94 this work and is described in detail in the next section. In this chapter we use data from GASS to construct the HISMF for massive (log M /M > 10) galaxies, φ(m HI, M ). A key difference between this work and previous work is that we are working with a stellar mass-complete sample of galaxies, each of which has either an HI detection or upper limit. The detections and upper limits can be used to constrain the full HISMF. We conduct the analysis by using a Markov chain Monte Carlo (MCMC) routine to fit a Schechter (Schechter 1976) function and a log-normal function, and two variations of each, to the distribution of HI masses in six stellar mass bins from log M /M = 10 to log M /M = This allows us to examine for the first time how the HIMF varies with stellar mass in a large statistical and unbiased sample of local galaxies. In addition to the binned HISMF, we also derive continuous bivariate (M HI, M ) and trivariate (M HI, M, SFR) HIMFs. These functions drive our discussion of the processes shaping the distribution of HI masses with respect to stellar mass. To demonstrate the utility of the HISMF in testing simulations and observational prescriptions, we compare it to the HISMFs derived from published photometric gas fraction relations, which provide estimates of HI content based on photometrically derived quantities. The primary goal of this work is to develop a simple parametrization of the HISMF that provides an accurate and complete description for model comparison, and that also allows some physical interpretation of its form. Recent theoretical models have already begun to predict the HIMF and interpret the physical mechanisms behind it (Lagos et al. 2011a; Duffy et al. 2012; Kauffmann et al. 2012; Davé et al. 2013; Kim et al. 2013). Our HISMF should be an important constraint for future models and will complement other 76

95 recent studies seeking to build a global census of baryons in and around galaxies. This chapter is organized as follows. In Section 3.2 we describe the data and in Section 3.3 we describe our methodology for deriving the HISMF for massive galaxies. We present the HISMF in Section 3.4. In Section 3.5 we interpret the shape of the HISMF in light of the trivariate fit, and in Section 3.6 we summarize our findings. The Appendix contains a comparison of our derived HISMF to the HISMF based on photometric gas fractions and an analysis of the HISMF with different assumed stellar mass functions. 3.2 Data The GALEX Arecibo SDSS Survey (GASS; Catinella et al. 2010) is an HI survey at Arecibo of 800 massive (log M /M > 10) local (0.025 < z < 0.05) galaxies. GASS is unique for its sample selection and observing strategy. From a parent sample of galaxies, the Arecibo targets were selected to yield a relatively flat distribution across stellar mass, ensuring uniform statistics throughout the entire stellar mass range. Our final volume statistics are determined by adopting an assumed stellar mass function. Each galaxy was observed with Arecibo down to an HI gas fraction limit to efficiently detect low levels of cold gas. Because the survey is limited by gas fraction instead of HI flux, the M HI detection threshold varies with stellar mass. The imposed limits are M HI /M = 1.5% for galaxies with log M /M > 10.5 and a gas mass detection limit of log M HI /M = 8.7 for galaxies with log M /M < Since the targeted GASS sample is complete in each stellar mass bin (the sample was selected in an unbiased way, making it representative of the true distribution of galaxies in the local universe), non-detections provide an accurate 77

96 measure of the number of galaxies with gas fractions below the imposed limit. The sample we use is based on GASS Data Release 2 (DR2) and is identical to that described in Catinella et al. (2012). It contains 480 galaxies selected from the GASS parent sample, each of which is observed down to the specified limit. GASS DR2 includes 232 Arecibo HI detections, 184 non-detections, and 64 HI detections from ALFALFA (Giovanelli et al. 2005) and the Cornell HI archive (Springob et al. 2005) that are added to create a statistically representative sample (see Catinella et al. 2010). Each galaxy has been observed by GALEX and SDSS, which provide homogeneously measured stellar mass and star formation rates for the sample. Stellar masses and optical photometry are from the Max Planck Institute for Astrophysics (MPA)/Johns Hopkins University (JHU) value-added catalogs based on SDSS DR6 and DR7, respectively. SFRs are derived from near-uv (NUV) GALEX detections and are described in detail in Schiminovich et al. (2010). A correction for dust attenuation is applied to star-forming galaxies with D n (4000) < 1.7 (where D n (4000), the 4000 Å break strength, is a proxy for star formation history). HI masses for detections and HI upper limits for non-detections are calculated according to Catinella et al. (2010). This sample includes a small number of galaxies (N=22) whose HI masses may be contaminated by nearby gas-rich galaxies. We found that the distribution of HI masses is nearly identical if we remove these potentially confused galaxies from the sample so we choose to keep them in our analysis (see Catinella et al. 2010). We rely on several derived quantities including the gas fraction, specific SFR, and concentration index for GASS galaxies. We follow Catinella et al. (2010) and Schiminovich et al. (2010) in calculating these quantities. The HI gas fraction is the HI mass divided by 78

97 the stellar mass, M HI /M, such that the HI gas fraction can have values above one. We refer to this quantity alternately as the HI gas fraction or just the gas fraction, making no correction for molecular gas. The specific SFR is the SFR normalized by stellar mass, SFR/M. The concentration index, R 90 /R 50, in which R 90 and R 50 are the radii encompassing 90 and 50% of the Petrosian flux measured in the r-band, is used as a proxy for morphology. 3.3 Methodology The Models Astronomers have found success modeling distribution functions of galaxy properties with a Schechter (1976) function. The Schechter function has been applied to optical and near-infrared luminosity functions (Bell et al. 2003), UV luminosity functions (Martin et al. 2005), HI mass functions (Zwaan et al. 2005; Martin et al. 2010), and SFR functions (Bothwell et al. 2011). In this chapter we compare the success with which three variations of the Schechter and log-normal functions describe the HISMF. The log-normal function is not often used to describe HIMFs, but it has been used to model other galaxy properties, including the star formation rate function (Martin et al. 2005), the X-ray luminosity function (Norman et al. 2004) and the IR luminosity function (Chapman et al. 2003). Kauffmann et al. (2003c) found that the distribution of galactic size (in their case, R 50 ) in narrow stellar mass bins is well-fitted by a log-normal function. Their use of the log-normal function was motivated by models showing that the spin parameter, λ, directly proportional to disk size, is distributed according to a log-normal function (Fall & Efstathiou 1980; Mo et al. 79

98 Table 3.1. Functional Forms of the Models Schechter Functions Full Schechter φ(m HI ) dlogm HI = φ ( M HI M ) α exp( M HI M ) dlogm HI 0.01 M HI,break < M HI < (1) HI HI Broken Schechter φ(m HI ) dlogm HI = (1 f ) 2.0 φ 0.01 M HI,break < M HI < M HI,break (2) φ(m HI ) dlogm HI = f φ ( M HI M ) α exp( M HI M ) M HI > M HI,break HI HI Bent Schechter Log-normal Functions φ(m HI ) dm HI = φ ( M HI,break M HI φ(m HI ) dm HI = φ ( M HI M HI ) α exp( M HI,break M ) 0.01 M HI,break < M HI < M HI,break (3) HI ) M HI > M HI,break ) α exp( M HI M HI Full Log-normal φ(m HI ) dlogm HI = φ exp( (logm HI µ) 2 )dlogm 2σ 2 HI 0.01 M HI,break < M HI < (4) Broken Log-normal φ(m HI ) dlogm HI = (1 f ) 2.0 φ 0.01 M HI,break < M HI < M HI,break (5) φ(m HI ) dlogm HI = f φ exp( (logm HI µ) 2 ) 2σ 2 M HI > M HI,break Bent Log-normal φ(m HI ) dm HI = φ exp( (logm HI,break µ) 2 ) 2σ M HI,break < M HI < M HI,break (6) φ(m HI ) dm HI = φ exp( (logm HI µ) 2 ) 2σ 2 M HI > M HI,break 1998). If the cold gas surface density is approximately constant across the disk of a galaxy, then it follows that the total HI mass of a galaxy should also approximate a log-normal function. Cortese et al. (2011) also noted that HI gas fractions are distributed according to a log-normal function. Here we describe the functional forms of and motivation for each model we test for the binned HISMF. The functional forms are compiled in Table 3.1. The Schechter function (Eq. 1 in Table 3.1) is composed of a power law that describes the distribution of lowmass galaxies and an exponential that describes the distribution of high-mass galaxies. A schematic of the Schechter function is shown in the top panel of Fig. 3.1 in bold. The power law at low HI masses (α) characterizes an extended tail of galaxies with small amounts of HI; the exponential at high HI masses above M HI shows that the number of HI-rich galaxies drops off sharply above a given HI mass. The Schechter function nicely 80

99 fits the one-dimensional HIMF derived from surveys with high numbers of HI-poor galaxies (Martin et al. 2010). However it is not apparent that the HI distribution at a given stellar mass should also be characterized by a simple power law at the HI-poor end. In particular, for a survey such as GASS in which the tail of the distribution is dominated by non-detections below the gas fraction limit, the shape of the distribution of low-hi-mass galaxies is not well constrained. Though upper limits provide some information about the total number of galaxies with low HI masses, we do not want upper limits to strongly constrain the shape of the function below M HI. To account for this issue, we introduce two versions of a truncated Schechter function that do not extend to low HI masses. In both cases the function is a combination of a Schechter function at relatively high HI masses and a constant distribution at low HI masses. We do not necessarily expect the true distribution of HI-poor galaxies to be flat, but we choose a flat distribution for simplicity and because we have no way of determining from GASS what the true distribution is where the sample is dominated by upper limits. The flat distribution at low HI masses reflects the fact that while we choose not to use the GASS sample to put constraints on the shape of the HISMF in this range, we can use it to derive the total number of galaxies expected to have low HI masses. The choice of where to impose the break in the Schechter function is somewhat arbitrary (its precise location does not significantly affect the parameters of the fit). For simplicity we have elected to set it at a constant gas fraction with respect to stellar mass to match our observational limits. We set M HI,break equal to 1% of the central stellar mass in each mass bin: 81

100 logm HI,break = log(m,bin ) 2.0, (3.1) which is just below the gas fraction detection threshold for GASS. With this choice, most HI detections are above M HI,break and upper limits tend to cluster around M HI,break. Two variations of a Schechter function are shown in the bottom panels of Fig In the middle panel the function is parametrized according to Eq. 2 in Table 3.1. We call this a broken Schechter function. In addition to α and M HI, we fit another parameter, f, defined as the fraction of galaxies in a given stellar mass bin with HI masses above the cutoff: f = N M HI >M HI,break N tot. (3.2) Because of our treatment of upper limits (see below), all upper limits contribute to the estimate of the number of galaxies below M HI,break even if the value of the upper limit is greater than M HI,break. (1 f )φ is derived so that the balance of galaxies expected to reside below M HI,break are uniformly contained within a range of HI masses extending up to M HI,break. All functions are normalized to match the Borch et al. (2006) stellar mass function. We must be careful to properly define the HI mass range within which we derive the HISMF. The low HI mass cutoff impacts the probability for non-detections (see below) and the normalization of the HISMF. The chosen lower limit should reflect the minimum HI mass expected to be associated with a galaxy of a given stellar mass, whether or not it 82

101 is detectable by GASS. We adopt a lower limit of log M HI,low = log M,bin (an HI mass four dex smaller than the central stellar mass of each bin). This limit is suggested by Lyα absorber measurements in Thom et al. (2012) showing that early-type and spiral galaxies in a mass range similar to that for GASS are likely to have the same minimum amount of HI in their CGM, which they give as approximately log M HI /M 6.0 and scales with galactic surface area. This value is also generally consistent with upper limits for the least HI-rich galaxies in Serra et al. (2012). We set the high HI mass limit to be log M HI = 12.0; choosing a slightly higher or lower value would negligibly affect our results. The two main differences between the broken Schechter and the full Schechter are that the broken Schechter is discontinuous and potentially multipeaked. We will discuss whether a multipeaked distribution function makes sense physically in Section 5. Because the discontinuity at M HI,break is clearly unphysical, we introduce another function that requires the flat part of the function to connect smoothly to the Schechter part of the function. We label this the bent Schechter function (Eq. 3 in Table 3.1). An example of it is shown in the bottom panel of Fig Because the bent Schechter function is required to be continuous, α might be biased by f. We will show that this constraint tends to flatten the distribution. Though the Schechter function has been used successfully to describe HIMFs, we also test a log-normal fit to the HISMF. The space density of galaxies in a stellar mass bin as described by a log-normal distribution is shown as Eq. 4 in Table 3.1. µ is the mean and σ 2 is the variance of the distribution. A key difference between the Schechter and log-normal functions is that the log-normal function is symmetric about its mean. We also 83

102 Table 3.2. Functional Forms of the Models Fits Including Stellar Mass α = α m (logm 10.5) + α o M HI = M m (logm 10.5) + M o f = f m (logm 10.5) + f o Fits Including Stellar Mass and SFR α = α m (logm 10.5) + α s logsfr + α o M HI = M m (logm 10.5) + M s logsfr + M o f = f m (logm 10.5) + f s logsfr + f o test two variations of the log-normal function: the broken log-normal function, Eq. 5 in Table 3.1 and Fig. 3.1b, and the bent log-normal function, Eq. 6 in Table 3.1 and Fig. 3.1c Continuous Fits Parametrizations for Continuous Fits Ultimately our goal is not just to accurately model the HISMF but to understand the physical processes that shape it. If its shape is the result of processes linked to halo or stellar mass and SFR then one might conjecture that the parameters of the distribution function could be related to a continuous function of observable physical quantities. Later in this chapter, we examine the dependence of the HIMF on stellar mass and SFR by introducing a hierarchical model in which we redefine the distribution function parameters in terms of these physical quantities. First we define the Schechter parameters α, M HI and f as functions of stellar mass and then we add SFR as an additional parameter. The parametrizations for these hierarchical models are listed in Table 3.8. This fit is discussed in Section Determining the dependence of the HIMF on SFR can be difficult when using UV- 84

103 derived SFRs because such SFRs are considered upper limits for passively evolving galaxies (Schiminovich et al. 2007). To test that the SFRs for passively evolving galaxies do not significantly bias the fit, we implemented another version of the fit in which we treat galaxies with low specific SFRs differently. For galaxies with log SFR/M < -12, we redefined their SFRs as a function of stellar mass only: logsfr = logm 12.0 (3.3) and substituted this equation for log SFR in the parametrizations in Table 3.8. Thus, the resulting Schechter parameters depend only on stellar mass for low star-forming galaxies. We found that this parametrization yields results similar to the original parametrization. When we discuss this fit in Section we only refer to the results with the original parametrization Implementation We conduct this analysis in a Bayesian framework, deriving the best-fit parameters of the models described above by maximizing the posterior probability given our dataset D = { MHI, M HI,lim, M }. We describe the HI mass function φ(mhi ) using a vector of parameters Θ. For example, Θ = { { α, MHI} for the full and bent Schechter functions and Θ = α, M HI, f } for the broken Schechter function, where φ (HI) is not included as a free parameter because it is derived using φ (M ) as discussed further below. The total posterior probability for a given set of parameters is the product of the posterior probabilities calculated for each galaxy in D: 85

104 i=n P(Θ D) = P i (Θ D i ). (3.4) i=1 We define the posterior probability for each galaxy by rewriting Bayes theorem in accordance with our measurements and generalized model. The posterior probability P(Θ D) depends on the likelihood function of the data given the model, a prior, and a normalization factor. It can be written as: P i (Θ D i ) = P i (D i Θ)P i (Θ) (3.5) P i (Θ) is the prior on the model parameters. We impose a flat prior on α and σ and a flat prior in log space on M HI and µ. We constrain f to lie between 0 and 1. An important part of our analysis is the inclusion of upper limits for galaxies not detected in HI. This strategy allows us to model more accurately the mass function at low HI masses and high stellar masses, where many of the non-detections lie. We follow the method outlined in Gelman et al. (2003) for incorporation of censored data. In this method the likelihood P i (D i Θ) is defined separately for galaxies detected and not detected in HI and we define an inclusion vector I where I i = 1 if the galaxy is detected and I i = 0 if the galaxy is not detected in HI. The likelihood for galaxies with HI detections is: p(d i Θ, I i = 1) φ(m HI,i ; Θ), (3.6) where the proportionality is due to an extra normalization term. The likelihood for 86

105 undetected galaxies is the integral of the mass function from some lower limit to the calculated HI mass upper limit of each individual galaxy: MHIlim,j p(d i Θ, I i = 0) φ(m HI ; Θ)d log M HI (3.7) M HI,low Putting everything together, we can define the total posterior of a set of parameters as: p(θ D, I) = p(θ)p(d, I Θ) i=n det p(θ) φ(m HI,i ; Θ; I i = 1) i=1 j=n nondet MHIlim,j j=1 M HI,low φ(m HI ; Θ; I j = 0)dM HI (3.8) First we consider the form of the HISMF within a stellar mass bin: φ(m HI ) = M + M /2 M M /2 φ(m HI, M )dm where M is the width of the stellar mass bin and φ(m HI, M ) can take any of the six forms listed above. We use the space density of galaxies in each stellar mass bin to determine the normalization factor for the likelihoods. This space density is the integral of the stellar mass function φ(m ) within a given stellar mass bin: 87

106 M,bin + M,bin/2 Φ(M,bin ) = φ(m )d log M (3.9) M,bin M,bin /2 where the functional form for φ(m ) has been determined independently by a number of authors (see the Appendix). With this space density we can rewrite the likelihoods with an extra normalization term p(bin M,i) Φ(M,bin ) where p(bin M,i) is a step function and equals 1 when a galaxy s stellar mass is within the stellar mass bin under consideration. Including the normalization term in Eq. 3.8 yields the exact definition of the posterior, leaving out a constant combinatorial term: p(θ D, I) = p(θ)p(d, I Θ) i=n det = p(θ) j=n nondet j=1 φ(m HI,i ; Θ; I i = 1) p(bin M,i) Φ(M,bin ) i=1 MHIlim,j M HI,low φ(m HI ; Θ; I j = 0) p(bin M,i) Φ(M,bin ) dm HI (3.10) Model Fitting We determine the parameters of the HISMF and their errors by using a Python implementation of the Markov chain Monte Carlo (MCMC) method called emcee (Foreman-Mackey et al. 2013). One of the advantages of emcee is that it evolves an ensemble of walkers simultaneously, significantly shortening the autocorrelation time. We run emcee using 50 walkers, 100 burn-in steps, and then 100 steps per walker. emcee uses the value of the posterior probability calculated for each set of parameters Θ to determine how the 88

107 walkers will subsequently move in parameter space. The final output of emcee is a list of = 5000 sets of parameters that describe the locations of the walkers in parameter space. Because the most likely regions of parameter space are more densely occupied by the walkers, we simply take the median value of each parameter as the best-fit parameter. Choosing the best-fit parameters by selecting the iteration with the maximum probability yields virtually identical fits, though taking the median means the best-fit parameters are more robust to artificial spikes in the probability. We run emcee six times; the only difference between each run is the definition of the PDF for each of our six models. In practice, and in order to treat each model identically, we express each model PDF as a finely resolved histogram. The probability for a detection is defined as the value of the at the HI mass of the detection (Eq. 3.6). The probability for an upper limit is defined as the integral of the PDF from some lower limit (M HI,low ) to the HI upper limit of the non-detection (Eq. 3.7). The total PDF is the product of the probabilities of each detection or upper limit. In practice, we sum the logarithm of the probabilities. The only source of uncertainty that we include in our model is the uncertainty on the HI measurements. We convolve each HI measurement with its total error, which we define as the sum in quadrature of the error on the distance (which we assume to be 5%) and the error on the HI flux. For upper limits of GASS non-detections we set the total error to 0.3 dex. The probability for each convolved HI measurement is the final probability that contributes to the model. Cosmic variance could produce additional uncertainty in the normalization of the HISMF, but our sample is drawn from a region 3 Mpc 3 in volume 89

108 for which cosmic variance should be small (Somerville et al. 2004). We tested our methodology by applying the same analysis to a simulated sample of galaxies with stellar masses and redshifts assigned to mimic the observed GASS sample and with HI masses extracted from a known Schechter function. We observed the simulated dataset based on the GASS detection limits, producing sets of HI masses and HI upper limits. Checks show that the simulated sample matches the stellar mass distribution and detection fraction of the actual sample, as expected. Applying the methodology described above on the simulated sample recovered the original Schechter function that described the simulated sample, confirming the validity of our method. To test the effect of the imposed gas fraction limit on GASS, which becomes an HI mass limit at log M /M < 10.5, we also observed the simulated sample with the gas fraction limit extending to different stellar masses. This change can moderately affect α because it changes the proportion of detections to non-detections at low HI masses and low-to-moderate stellar masses. We also used the simulation to test the weighting of each stellar mass bin in the continuous fits. The relatively flat stellar mass distribution of the sample (except for a deficit of galaxies in the highest stellar mass bin) means that for the continuous fit, galaxies do not contribute to the fit in proportion to the z=0 stellar mass function. However, we found that weighting the continuous fit by the observed stellar mass function in order to account for the stellar mass distribution of the sample does not significantly change the results; the results are robust to different weighting schemes. 90

109 Table 3.3. Binned Data for Bivariate HISMF log M log MHI log φ(m HI, M ) all log φ(m HI, M ) det (1) (2) (3) (4) 10.0, , ± , ± ± , ± ± , ± ± , ± ± , ± ± , ± ± , , Note. This table is available in its entirety in a machinereadable form in the online journal. A portion is shown here for guidance regarding its form and content. Errors reported are Poisson errors. Table 3.4. Number of Galaxies in Samples GASS ALFALFA log M Total Detections Total Detections (1) (2) (3) (4) (5) 10.0, , , , , , Total The Bivariate HI Mass Function for Massive Galaxies Model Comparison 91

110 10-3 log M HI,lim log M 10-4 log M HI,break φ(m HI, M ) [Mpc 3 dex 1 ] Full Broken Schechter Log-normal Bent log M HI Figure 3.1 Examples of the six models described in Section From top to bottom, the panels show the full, broken, and bent variations of the Schechter function (bold black line) and log-normal function (thin red line). Each curve shown here is a fit to galaxies with stellar masses in the range 10.0 < log M < 10.25, as described in Section

111 N gal Detections 10.0, Detections + Upper Limits 10.25, , , , , log M HI Figure 3.2 The number of detections and upper limits per HI mass-stellar mass bin in the GASS sample. 93

112 φ(m HI, M ) [Mpc 3 dex 1 ] , Full Broken 10.0, Bent 10.0, , , , , , , , , , , , , , log M HI 11.25, log M HI 11.25, log M HI Figure 3.3 Three variations of the Schechter function fit to the HISMF in six stellar mass bins. The stellar mass bins are indicated in the upper right corners. Each panel presents the binned GASS data for detections (solid black circles) and detections plus upper limits (empty circles). Error bars on the show Poisson uncertainties. Shaded regions show the 1σ uncertainties determined from the MCMC fit. Vertical dotted lines indicate M HI,break = 0.01 M,bin in each stellar mass bin. 94

113 φ(m HI, M ) [Mpc 3 dex 1 ] , Full Broken 10.0, Bent 10.0, , , , , , , , , , , , , , log M HI 11.25, log M HI 11.25, log M HI Figure 3.4 Same as Fig. 3.3 but showing three variations of the log-normal function fit to the HISMF. 95

114 Table 3.5. Schechter Function Fits to Bivariate HIMF a log M log M α f log φ HI [M ] [M ] [Mpc 3 dex 1 ] (1) (2) (3) (4) (5) Full Schechter 10.0, ± ± , ± ± , ± ± , ± ± , ± ± , ± ± Broken Schechter 10.0, ± ± ± , ± ± ± , ± ± ± , ± ± ± , ± ± ± , ± ± ± Bent Schechter 10.0, ± ± , ± ± , ± ± , ± ± , ± ± , ± ± a The fits to the M HI distributions are in the form of a Schechter function M HI such that φ(m HI ) dm HI = φ ( M HI M ) α M e HI dm HI. Reported errors for the HI Schechter parameters α, M, and f are 1σ uncertainties determined from HI the MCMC parameters. Values for φ are based on the median Schechter 96

115 parameters. 97

116 Table 3.6. Log-normal Fits to Bivariate HIMF a log M µ σ f log φ [M ] [M ] [Mpc 3 dex 1 ] (1) (2) (3) (4) (5) Full Log-normal 10.0, ± ± , ± ± , ± ± , ± ± , ± ± , ± ± Broken Log-normal 10.0, ± ± ± , ± ± ± , ± ± ± , ± ± ± , ± ± ± , ± ± ± Bent Log-normal 10.0, ± ± , ± ± , ± ± , ± ± , ± ± , a The fits to the M HI distributions are log-normal such that φ(m HI, M ) = a exp( (logm HI µ) 2 2σ 2 ). In this section we present the results of the six models described above. We attempt to make some determination of which is the better fit, though we note that none of these simple parametrizations can precisely capture the true distribution of HI masses. In Fig. 3.3 we show φ(m HI, M ), the binned HISMF for three variations of the Schechter function, along with the data used in the fits. To display the data, we binned the detections and upper limits into HI mass bins 0.3 dex wide. In each panel of Fig. 3.3, detections are shown as black circles and the full sample including upper limits for HI non-detections is indicated by empty circles. As stellar mass increases, the open circles identifying upper limits appear at progressively higher HI masses because of the GASS detection threshold, 98

117 which is based on HI fraction. Error bars indicate Poisson uncertainties. The reported volume densities in each stellar mass bin have been corrected according to the effective volume of the GASS sample in each bin, which is the number of GASS galaxies in each bin divided by the expected space density of galaxies in that bin according to the Borch et al. (2006) stellar mass function. The binned data are given in Table 3.3 and the numbers of galaxies in each stellar mass bin are shown in Table 3.4. We also show a histogram of the detections and upper limits in each HI mass-stellar mass bin in Fig We present the binned data only to describe the sample and compare the data to the fits derived from the data. We emphasize that the fits are not derived from binned HI measurements; rather, each individual HI detection and upper limit contributes to the total probability of the fit independently. Each column in Fig. 3.3 represents one of the three Schechter functions: full on the left, broken in the middle, and bent on the right. Each row represents a stellar mass range from log M = 10.0 to log M = 11.5; the stellar mass interval is indicated in the upper right corner of each panel. The best-fit parameters and their 1σ uncertainties determined from the MCMC fit are listed in Table σ uncertainties on the fit for each HI mass bin are also reflected in the shaded regions surrounding each curve and were determined by computing φ(m HI, M ) using all 5000 emcee iterations. First we examine qualitatively how the HISMF varies with stellar mass and from model to model. Overall there is remarkable similarity between the HISMF at different stellar masses and for different parametrizations of the Schechter function. The main difference with respect to stellar mass is that the HISMF reflects the stellar mass function, 99

118 which decreases with stellar mass. Because fewer galaxies are used to fit the models at high stellar masses and the fraction of non-detections increases, the error bars generally widen with stellar mass. Though the shape of the functions is close to invariant with respect to stellar mass, galaxies in the range 10.5 < log M /M < 11.0 tend to have higher values of α, which makes the slope of the bivariate HIMF for moderate HI masses steeper, and slightly smaller values for M HI, so the function cuts off at lower HI masses. We also find that the shape of the HISMF is largely independent of the parametrization used. Though the two pieces of the broken Schechter function are not required to match as they are in the bent function, they almost do, such that the broken Schechter function closely resembles the bent Schechter function. In this case, the constraint on the bent Schechter function does not seem to bias the fit. (We will show an example later in which it does.) Moreover, the calculated space density for galaxies below M HI,break is very similar for the broken and bent cases, showing that the two parametrizations consistently identify a similar fraction of galaxies with a gas fraction above 1%. One of the main differences among the three parametrizations is that the error bars for the broken function in the region described by α are significantly larger. It is reasonable for the error bars to be larger here because there are few detections in this narrow range of HI masses contributing to the estimate of α. Thus the small error bars for the bent Schechter functions perhaps indicate that the constraint that the entire function be continuous does affect α for the bent Schechter function. Finally, in Fig. 3.4 we present the results of the three log-normal fits to the data. The best-fit parameters and associated uncertainties are listed in Table 3.6. Because the log- 100

119 normal function is symmetric, it predicts a much higher space density of galaxies at high HI masses than does the Schechter function. The three variations of the log-normal functions are similar to the three Schechter functions in that the fits are largely independent of stellar mass except for what was noted above for galaxies with intermediate stellar masses. A closer look at the fits for the highest stellar mass bin (11.25 < log M /M < 11.5) reveals that they do not exhibit the same shape as do the fits at lower stellar masses. Moreover, the size of the error regions indicates that these fits are not well constrained (see also reported errors in Tables 3.5 and 3.6 and plots below). These results can be attributed to the small number of galaxies in this stellar mass bin, a number that is less than a third of the number of galaxies in the other stellar mass bins (Table 3.4) despite attempts to maintain a flat stellar mass distribution for the GASS sample. We choose to keep this stellar mass bin in our analysis to show where our ability to accurately describe the shape of the HISMF breaks down. More observations at higher stellar masses (and the final GASS data release; Catinella et al. 2013) will be necessary to understand how the HISMF changes for the most massive galaxies in the local universe. In Figs. 3.5 and 3.6 we quantitatively examine how the best-fit Schechter and lognormal parameters vary with stellar mass. The top three panels show log M HI, α and f vs. stellar mass for the three parametrizations of the Schechter function. This plot quantitatively confirms the trends we discussed above. The full, broken and bent fits yield values for M HI that are close to constant with respect to stellar mass. We will discuss the relative constancy of M HI in Section The broken and bent Schechter models produce α s that range between 0.5 and 1.2 with no obvious trend with stellar mass. The 101

120 log M HI α log M HI,75 f Full Broken Bent log M Figure 3.5 Schechter parameters α, log M HI, f, and M HI,75 vs. stellar mass and the best-fit lines as a function of stellar mass from Section full Schechter function yields values for α that are slightly lower than the other α s ( 0.5). The third panel shows f vs. stellar mass for the broken and bent models. This value is a parameter in the broken model and can be derived from the results of the bent model. The effective f for the bent fit and f for the broken fit track each other nicely, confirming that the fits yield similar HISMFs. (As an additional check they are also comparable to the observed detection fractions reported in Catinella et al. (2010, 2012).) Both models show that the fraction of galaxies with gas fractions above 1% decreases with stellar mass. As another way of comparing the three Schechter functions, in the bottom panel we show M HI,75 for each of the three fits, where M HI,75 is the HI mass in each stellar mass bin below which lie 75% of the galaxies in that stellar mass bin. The broken and bent Schechter 102

121 µ Full Broken Bent σ log M HI,75 f log M Figure 3.6 Log-normal parameters σ, µ, f, and M HI,75 vs. stellar mass. functions yield values for M HI,75 that are nearly identical. The values for the full Schechter function are similar to those of the truncated Schechter functions but diverge slightly from them at high stellar masses. Fig. 3.6 shows a similar analysis of the parameters of the log-normal fits. The trends for M HI,75 and f vs. stellar mass are similar to those for the Schechter functions. µ, which is related to M HI for the Schechter fit, does not show an obvious correlation with stellar mass. σ, which measures the width of the distribution, decreases slightly with stellar mass from about 0.6 to

122 3.4.2 Covariance of Parameters Next we wish to examine the relationship between the model parameters to uncover any covariance. As an example, we do this for the broken and bent Schechter fits in Fig Each row shows a different stellar mass bin corresponding to the six rows in Fig In each panel we show the error contours associated with two parameters for both functions. The contours enclose 10, 25, 50, and 95% of the 5000 Schechter parameters (α, M HI, f ) representing the 5000 MCMC iterations for each stellar mass bin. In the left column the tilt in the contours for α vs. M HI shows that the two Schechter parameters for the broken and bent Schechter functions exhibit some covariance along the direction in which they are anti-correlated. A high α and a low M HI could describe the distribution just as well as a low α and a high M HI. We comment on the origin of this covariance in Section The narrower contours for the bent fit show that α is more tightly constrained by the model, likely because of the requirement that the Schechter function smoothly connect to the flat part of the function at M HI,break. Though there are some noticeable differences between the two fits at high stellar masses, the contours for the two fits generally overlap across the entire stellar mass range, indicating that any difference between the two model fits is small compared to the errors in the parameters. The middle column shows the relationship between M HI and f and the right column shows f vs. α. For the bent fit we only show the effective f. We find that the broken fit yields a tight constraint on f, which is not surprising since the GASS survey is designed to provide an accurate measure of this quantity. We also find that there is little obvious covariance between f and α. 104

123 3.4.3 Model fit at high HI masses and comparison with ALFALFA An important distinction between the two classes of models considered above (Schechter vs. log-normal) is the shape of the function at high HI masses. Here we explore two questions: 1) whether GASS includes sufficient numbers of HI-rich galaxies to provide a strong constraint on the function at the HI-rich end and 2) whether we can favor one class of model over the other based on the success of our fits. To test these questions we first conduct an analysis that makes use of an enlarged sample of HI-rich galaxies obtained using the ALFALFA survey. We then use the sum of each model across stellar masses to provide sufficient signal to allow us to distinguish between model classes. GASS was designed to sensitively detect HI in massive HI-poor galaxies but does not detect as many HI-rich galaxies as do other shallower blind surveys with significant sky coverage, such as ALFALFA (Giovanelli et al. 2005). When complete, ALFALFA will have scanned over 7000 square degrees of the sky, so the number of ALFALFA detections in the GASS stellar mass range exceeds the number of GASS detections. We refine the measurement of the HISMF at high HI masses by including in the fits detections and upper limits from the ALFALFA survey. The ALFALFA sample we use includes all galaxies in the GASS parent sample that lie in the regions of the sky already observed and cataloged by ALFALFA as of the α.40 release (Haynes et al. 2011). In this region 1102 galaxies were detected by ALFALFA and 3443 were not detected (see Table 3.4). We calculate upper limits for the non-detections by using the ALFALFA integrated flux limit, S lim in Jy km s 1, from Martin et al. (2010). S lim depends on the signal-to-noise ratio (S/N) and velocity width (W 50 ) of the HI line: 105

124 S lim = 0.15 S/N (W 50 /200) 1/2 if W 50 < 200kms 1 ; 0.15 S/N (W 50 /200) if W kms 1. (3.11) We let S/N = 5.0 and W 50 = 300 km s 1 to be consistent with the calculation of upper limits for GASS. Martin et al. (2010) calculate HI masses according to: M HI = D 2 Mpc S lim. (3.12) Thus, the upper limits we calculate for ALFALFA non-detections are simply a function of distance: M HIUL = D 2 Mpc (3.13) To derive the HISMF that accounts for the GASS and ALFALFA surveys together we simply add the log likelihoods for the galaxies in each sample. (We checked with our simulation that applying different weights to each sample does not significantly affect the result.) As we mentioned above, the log likelihoods include the error on each HI measurement. We derive errors for the ALFALFA detections in the same way we did for GASS. We also set the error for ALFALFA upper limits to 0.3 dex. In Fig. 3.8 we present the ALFALFA data and the results of the joint fit to GASS and ALFALFA. We show the ALFALFA data in the same way we show the GASS data: detections are shown as solid symbols and the full sample including upper limits is shown as open symbols. The ALFALFA data generally extend to higher HI masses (log M HI /M 10.5) than the GASS data, which end at log M HI /M in most stellar mass bins. 106

125 Though ALFALFA provides better coverage of the HI-rich end of the HIMF, the small number of galaxies detected by ALFALFA below log M HI /M 10.0 emphasizes the need for deeper surveys such as GASS that can provide HI measurements of massive galaxies with smaller amounts of HI. Fig. 3.8 compares the GASS broken Schechter fit to the bent and broken versions of the GASS + ALFALFA fit. First we will examine the HI-rich end of the HISMF. In general both variations of the GASS+ALFALFA fits predict slightly fewer HI-rich galaxies at low stellar masses and slightly more HI-rich galaxies at high stellar masses. The major difference between the two fits is in the range < log M /M < 11.0, where the GASS+ALFALFA fit extends to higher HI masses. We noted previously that the GASS fits in this mass range predicted surprisingly low space densities. The GASS+ALFALFA fits are more consistent with respect to stellar mass, perhaps making up for small anomalies in the GASS sample. Though the fits in this mass range argue that ALFALFA data are necessary to properly describe the HI-rich end of the HISMF, we see this mass range as an exception rather than the rule. We will show later that a continuous fit applied to only GASS data is able to account for the anomaly in the stellar mass bin < log M /M < 11.0 without including ALFALFA galaxies. Thus, the binned fit, rather than the use of only GASS data, is the cause of the discrepancy in this stellar mass bin. At lower HI masses, the broken and bent GASS+ALFALFA fits vary significantly. The broken Schechter fit exhibits a steep slope down to M HI,break while the constraints of the bent Schechter fit cause the slope to be much shallower. The significant difference between α for the bent and broken fits with ALFALFA contrasts with the relative similarity between 107

126 α for the bent and broken fits to GASS data only. It is likely that the lack of ALFALFA data at low HI masses had too much influence on the fit here, biasing the broken fit to predict low numbers of galaxies within this HI mass range. For ease of analysis and because we have shown the GASS sample to provide a sufficient estimate of the HISMF at high HI masses, we do not include ALFALFA in each of our subsequent fits. Future work may continue to explore the combined use of GASS and ALFALFA Model Selection and Validation We have produced six fits to the HISMF based on six different models and we wish to select which is the best match to the data. To distinguish between the models quantitatively we calculated several parameters that are commonly used to assess goodness-of-fit or for model selection. We list these numbers in the Appendix and briefly discuss them here. They include the probabilities calculated in the MCMC runs, the Bayesian Information Criterion (BIC; Schwarz 1978), the Poisson probabilities, and the χ 2 statistic. In Table 3.9 we list the MCMC probabilities and Bayesian Information Criterion for each model and each stellar mass bin. Both measures of the probabilities are in the same range for each stellar mass bin and do not strongly favor one model over the others. We can examine the qualitative differences among the six models in two ways: by comparing the integrated model HISMFs, which emphasize deviations from the data, and by considering the limitations of each model that are not quantifiable. We derive the total HISMF for massive galaxies (Fig. 3.9) by summing the HISMF across all stellar mass bins for each model. Because M HI,break varies with stellar mass and the total HISMF is a sum 108

127 over all stellar mass bins, the total HISMFs for the broken and bent fits do not have the same characteristic flat regions at low HI masses. At the lowest HI masses the shape of the HISMF is still poorly constrained by our data. First we examine the differences between the Schechter functions and log-normal functions, which are shown separately in the panels on the left and right. Though the Schechter and log-normal functions predict a similar number of galaxies at low HI masses, each of the three log-normal fits systematically predicts more galaxies at high HI masses than do the three Schechter fits. The space densities they predict are well above the data points and their error bars. Based on this discrepancy between the data and the log-normal fits to the data, we can safely conclude that the Schechter function s steeper dropoff at high HI masses makes it a better approximation of the true HISMF To test this conclusion we quantitatively compare the predictions of the six models to the data by calculating the χ 2 statistic and the Poisson probability for HI masses above log M HI /M = 10. These numbers (see Table 3.10) confirm that the Schechter function is a much better description of the data at high HI masses. Solanes et al. (1996) conducted a test similar to ours by comparing Schechter and Gaussian fits to the total HIMF derived from 934 giant spirals in an HI flux limited sample. They found that the Gaussian and Schechter fits describe the full sample and the sample divided by morphology equally well. They note that discrepancies between the two fits occur at low (log M HI /M < 9.0) and high (log M HI /M > 10.5) HI masses. It is in these HI mass ranges where we also find the greatest discrepancy between the two fits. We cannot favor one version of the Schechter fit over another based on their total 109

128 HISMFs because they are virtually identical, which Table 3.10 confirms. Instead it is important to consider the limitations inherent to each model. Upper limits can significantly affect the slopes of the full Schechter and log-normal models at moderate HI masses. The break in the broken and bent models allows us to use upper limits to estimate the space density of galaxies with low HI fractions while not allowing upper limits to dictate the shape of the function. A limitation of the bent model is that the two sections of the function are required to meet. This requirement seems reasonable because a true disconnect in a mass function (such as in the broken model) does not make physical sense. But this requirement is only reasonable if we are confident in the shape we impose on both sides of the break. A flat distribution at low HI masses is not the only choice and we discuss this in Section Because of the obvious limitations of the full and bent models, we choose to proceed with the broken Schechter function. We emphasize, though, that this parametrization is not necessarily the best or most precise way of describing the HISMF but reflects our desire to provide a model for the data that accurately describes the true distribution in an intuitive way with as few parameters as needed. In Fig. 3.9 we also compare our total HISMF for massive galaxies to the HIMF from ALFALFA (Martin et al. 2010). The GASS HISMF matches the ALFALFA curve at high HI masses but misses many of the HI-poor galaxies that are detected in ALFALFA because they are below the GASS stellar mass and redshift cutoffs (e.g. dwarf galaxies). The agreement between the two functions at high HI masses indicates that many of the most HI-rich galaxies in the local universe are in fact galaxies that are also massive in stars (any 110

129 contribution to the HI-rich end of the function from lower stellar mass galaxies would be small). This was also seen and discussed in Schiminovich et al. (2010). We return to this point below. We calculate Ω HI,M >1010, the ratio of the HI density contributed by massive galaxies to the critical density, and present our results for each stellar mass bin in Table 3.7. In each bin we compute Ω HI,M >1010 by integrating the broken Schechter fit to the HISMF. We do the same with the bivariate and trivariate fits (see Section 3.5.2) and we compare the results to a simple sum of the HI detections and upper limits. The total HI density in the GASS stellar mass range, obtained by summing Ω HI in each stellar mass bin for the broken Schechter function, is log Ω HI = -3.75, which is 41% of the total Ω HI in the local universe derived from ALFALFA (Martin et al. 2010). This HI density agrees with that reported in Schiminovich et al. (2010), which represents 42% of the Martin et al. (2010) value. The agreement between their calculation, which is based on a simple sum of the observed HI masses, and ours validates our model of the HISMF. A sum of the GASS detections and upper limits (see final column) overestimates Ω HI,M >1010 because the upper limits are included as true HI masses in the sum whereas our fitting method assumes the true HI masses can be less than the upper limits. As Schiminovich et al. (2010) noted, the comparison between Ω HI derived from ALFALFA with Ω HI,M >1010 derived from GASS emphasizes that massive galaxies contribute significantly to the total HI content in the local universe. This is not entirely surprising since Martin et al. (2010) show that galaxies with 9.0 < log M HI /M 10.0 contribute the most to Ω HI and this is the HI mass range that many of the GASS galaxies occupy. 111

130 Table 3.7. Ω HI log M log Ω HI,M a Ω HI,M / Ω HI b Broken Schechter Bivariate Trivariate Dets. All c 10.0, , , , , , Total a Typical errors are 0.1 assuming a 1σ error on the space density. b Ω HI,M as a fraction of Ω HI reported in Martin et al. (2010). c The sum of detections and non-detections where we have set the HI mass of non-detections equal to their upper limits. 3.5 Discussion The Shape of the HIMF In this chapter we explore the shape of the HISMF within six independent stellar mass bins (effectively resulting in 12 or 18 parameter fits) to assess what shapes the distribution of HI masses at different stellar masses. Later in this section we explore how this shape can be expressed as a function of stellar mass and also SFR, leading to a reduced parametrization, and providing some clues on how the processes that drive the shape of the mass function depend on these physical parameters. Without a detailed model predicting the shape we adopted a generalized approach, comparing the results of six different fits to the HISMF. We tested three variations of the Schechter and log-normal functions in order to account for the high fraction of HI nondetections at low HI masses. For two of these variations we imposed a flat distribution on the HI-poor end because we have very little a priori knowledge of the true shape of 112

131 Table 3.8. Continuous Fits a α m α s α o M m M s M o f m f s f o Bivariate Fit Trivariate Fit a Top row: best-fit parameters for broken Schechter fits where the parameters depend on stellar mass. Bottom row: best-fit parameters for broken Schechter fits where the parameters depend on stellar mass and SFR. the distribution. This form is also easy to interpret as representing the low gas fraction component of the distribution. We found that the broken Schechter function, in which we fit a Schechter function above a 1% HI gas fraction and a flat function below, describe the shape of the GASS HISMF better than the log-normal functions and is free of the potential bias of the other Schechter models. In the following sections we appeal to higher-dimensional fits to the HIMF, simulations that seek to reproduce the HIMF, and other HI observations to understand the physical processes that contribute to the shape of the HISMF The Dependence of the HI Mass Function on Stellar Mass and Star Formation Rate To gain insight into the physical mechanisms that shape the HISMF, we fit two additional models to the data, both of which are continuous fits across the range of stellar masses rather than binned fits within indepedent stellar mass bins. The first is a continuous bivariate fit whose Schechter parameters (α, M HI, f ) depend on stellar mass, which yields a variation on the HISMF, φ(m HI,M ). The second is a continuous trivariate fit in which the parameters are functions of stellar mass and SFR. From this fit we can derive φ(m HI, M, 113

132 SFR), the HI-M -SFR function. As stellar mass is related to the growth history of galaxies and SFR is linked to cold gas content, the variation of the HIMF with respect to these two quantities could provide insight into what shapes the distribution of HI masses at a given stellar mass. Although galaxies on the star-forming sequence have a well-defined link between SFR and stellar mass (e.g. Brinchmann et al. 2004; Salim et al. 2007; Schiminovich et al. 2007), at a given stellar mass galaxies exhibit a wide range of SFEs (Schiminovich et al. 2010, e.g.). The scatter between SFR and M HI, and the additional scatter between those two quantities and stellar mass, suggests that including SFR as a parameter in our model should uncover trends that are otherwise not apparent. First we assess the results of the continuous bivariate fit, which is shown in the left column of Fig The best-fit parameters are listed in Table 3.8 and the definitions of the parameters are in Table 3.2. The plot was constructed by calculating α, M HI, and f based on the central stellar mass of the previously defined stellar mass bins. The fits are similar to the original binned fits (with one exception, noted below). We examine these fits by considering each parameter individually. The line in Fig. 3.5 shows how each parameter changes with stellar mass according to this fit. The results of this higher-dimensional fit track the results of the broken Schechter function fit to the HISMF. The weak correlation between M HI and stellar mass (M HI M 0.07 ) confirms the relative invariance of the fits with respect to stellar mass, which was illustrated in Fig The inverse relationship between f and stellar mass reveals that more massive galaxies are less likely to have a high gas fraction, and in particular, one above 1%. This result verifies that HI gas fraction is inversely correlated with stellar mass 114

133 (e.g. Catinella et al. 2010). Next we discuss the trivariate fit, whose parameters are defined according to the equations in Table 3.2. This fit reveals the joint effect of stellar mass and SFR on the HIMF and shows that the shape of the HIMF is more strongly dependent on SFR. The best-fit parameters (see Table 3.8) reveal that α is much more dependent on both stellar mass (α M 0.47 ) and SFR (α SFR 0.95 ) than are M HI and f. α is higher ( 2-3) for galaxies with higher stellar masses and higher SFRs, implying that the distribution of HI masses is more sharply peaked. In the right column of Fig we show how this fit compares to the original fit. The curve for each stellar mass bin is constructed by dividing the galaxies in that stellar mass bin into bins of SFR and summing the mass functions derived using the central stellar mass of the bin and the central SFR for each SFR-M bin. The HIMF for each SFR-M bin is weighted by the number of galaxies in it. This fit generally approximates the original fit at high HI masses. At low HI masses and low stellar masses, the trivariate fit predicts slightly more galaxies. This is due to the combination of low stellar masses and low SFRs that produces a low value for α and a mass function that rises towards lower HI masses. We note that the main difference between the bivariate, trivariate and binned fits is in the stellar mass bin < log M /M < In this stellar mass range the bivariate and trivariate fits predict more HI-rich galaxies and their prediction matches that of the GASS+ALFALFA fit described in Section These fits appear to do a better job than the binned fits of averaging over anomalies in the GASS data and arriving at the true distribution of HI masses. Overall these fits match the broken Schechter function fit: 115

134 Ω HI,M >1010 derived from the bivariate and trivariate fits agree with that derived from the broken Schechter function (see Table 3.7). In Table 3.9 we compare these fits to the binned fits and we find that based on some measures they describe the data just as well as do the binned Schechter fits. To emphasize the variation in the HI-M -SFR function with SFR we present in Fig the HIMF for galaxies with 10.5 < log M /M < and log SFR ranging from -2.5 to 0.5. The overall shape of the HIMF, and in particular the slope at the HI-poor end, varies significantly with SFR. We discuss this in more detail in the following section. In Figs and 3.13 we show the relationship between the three Schechter parameters and how they vary with 9 combinations of stellar mass and SFR that probe the GASS stellar mass range and 3 dex in SFR. The contours are derived by using all 5000 iterations of the 9 MCMC parameters (α o, α m, α s, M o, M m, M s, f o, f m, f s ) to calculate the 5000 sets of associated Schechter parameters (α, M HI, f ) for each stellar mass-sfr bin. The contours enclose 10, 25, 50, and 90% of the 5000 calculated Schechter parameters. SFR increases across the rows and stellar mass increases down each column. Fig reveals how the relationship between α and M HI changes with stellar mass and SFR. As mentioned above, α increases with both stellar mass and SFR from a low of about 0.0 to a high of 2.5. M HI, on the other hand, shows less variation between 9.6 and 9.8. This figure emphasizes the covariance between α and M HI, also noted in Fig M HI denotes the transition point between the power law and the exponential regions of the Schechter function. We might ask how a fixed quantile of the distribution varies and how this relates to M HI. We explored the analytic form of the relationship between M HI 116

135 and M HI,75 for a broken Schechter distribution and we found that the difference between the two quantities is a function of α. The curves in each panel of Fig show lines of constant M HI,75, where the value of M HI,75 is calculated assuming the median α and M HI in each bin (denoted by the crosshairs). These lines follow the direction of covariance between α and M HI. Their covariance signifies the existence of a range of combinations of the two parameters that maintain a fixed M HI,75 quantile. While M HI varies by less than 0.3 dex across the range of stellar masses and SFRs represented here, M HI,75 increases with stellar mass by at least 0.3 dex, and more so at low SFRs. The variation in M HI,75 shows that the quantiles of the distribution vary even though the peak at the characteristic HI mass remains relatively constant. Fig shows the same analysis of α and f. f ranges from 0.4 to 1.0 with this combination of stellar masses and SFRs and generally decreases with stellar mass and increases with SFR. The negative correlation between f and stellar mass was noted above. Values for f cluster near 1.0 for galaxies with log SFR=1.0 because galaxies with moderateto-high SFRs are very likely to have gas fractions above 1%. We constrained f to not exeed 1.0 because that would be unphysical. We can also examine how the Schechter parameters vary with specific SFR, noted in each panel of Figs and As specific SFR decreases from the upper right corner to the lower left corner, the main difference is a strong decrease in f - stronger than the variation in f with respect to stellar mass or SFR alone. Since f is related to gas fraction, this means that specific SFR strongly depends on gas fraction. Again, this result agrees with previous analyses (e.g. Catinella et al. 2010; Schiminovich et al. 2010). 117

136 Finally in Fig we show the distribution of HI gas fractions for three bins of SFR based on the higher dimensional fits examined above. We used the bivariate and trivariate fits to calculate the distribution of HI masses in narrow bins of stellar mass and then divided by stellar mass to obtain the distribution of HI gas fraction. Solid lines show quantiles based on the trivariate fit while dotted lines show quantiles based on the bivariate fit (the latter quantiles are the same for each SFR bin). The trivariate fits show that the range of gas fractions varies significantly with SFR. At log SFR = -1.0, galaxies with gas fractions in the middle 80% of the distribution have a gas fraction range that spans 3 dex; at log SFR = 1.0, galaxies with gas fractions in the middle 80% have gas fractions spanning only 1 dex. Though the distribution of gas fractions changes with SFR, it doesn t change in proportion to SFR. As SFR increases by a factor of 100, the gas content of galaxies with gas fractions in the top 10% at a given SFR increases by less than a factor of 10. The gas fraction vs. stellar mass distribution based on the bivariate fit exhibits a wide range of gas fractions and is most similar to the range of gas fractions for low-sfr galaxies in the trivariate fit. Because the bivariate fit does not depend on SFR, it cannot capture the change in the gas fraction distribution with respect to SFR. We compare the gas fraction distribution based on these fits to two other measures of the gas fraction vs. stellar mass scaling relation. First, we show that M HI,75 calculated in each M -SFR bin tracks the trivariate fit s 75% quantile fairly well in each SFR bin. This fit matches M HI,75 better than does the bivariate fit. The better match to the trivariate fit confirms that SFR provides crucial additional information about HI content that is not already embedded in the relationship between HI mass and stellar mass. 118

137 To assess how our predicted gas fractions compare to median gas fractions calculated directly from the data, we show the median gas fraction scaling relation from Catinella et al. (2012), which is averaged over galaxies of all SFRs. The median gas fractions should agree well with the 50% quantile, and they do if we look at the bivariate fit. Turning to the trivariate fit, the Catinella et al. (2012) median gas fractions overestimate the gas fractions for galaxies with low SFRs and underestimate the gas fractions for galaxies with higher SFRs. To summarize, in Fig we explore how the Schechter parameters vary within the specific SFR-stellar mass plane. We find that α is high for galaxies with high stellar masses and high specific SFRs, which we also saw in Fig Lines of constant α are steeper than the star-forming sequence (Salim et al. 2007) and average specific SFR vs. stellar mass trend for GASS galaxies (Schiminovich et al. 2010), indicating that α does have a dependence on stellar mass in addition to the dependence on SFR one would expect. The upper right panel shows that M HI slowly increases with stellar mass and depends less on SFR. Lines of constant f confirm that galaxy populations with high specific SFR are likely to contain mostly galaxies with high gas fractions. The lines of constant f are almost parallel to the star-forming sequence, emphasizing the tight link between HI content and specific SFR. Finally, we show lines of constant M HI,75 in the last panel. As we showed before, M HI,75 exhibits a wider range of values than does M HI. Additionally, the lines for the two parameters are oriented almost perpendicular to each other. While the peak of the distribution, M HI, slowly increases with stellar mass, the shape of the distribution, indicated by the changing values of M HI,75, depends strongly on both stellar mass and 119

138 SFR. Finally, the spacing between the lines of constant M HI,75 change with SFR such that the value for M HI,75 changes more quickly among highly star-forming galaxy populations. To test the robustness of these trends, we used the 5000 iterations of the trivariate MCMC run to derive the standard deviation of α, M HI, f, and M HI,75 at the center of each panel. The standard deviations (0.26, 0.08, 0.04, and 0.03, respectively), which are smaller than the uncertainties on the individual parameters in the binned models and the continuous models (e.g. α m, α s, α o ), are also small compared to the contour spacing so these trends are robust Physical Drivers of the HIMF The fits presented above and in Section 3.4 reveal how the HISMF varies quantitatively with stellar mass and SFR. We can use these trends to better understand how the HISMF is shaped by various physical processes that act within different ranges of stellar mass and HI mass. To guide our discussion of the physical drivers of the HISMF, we consider four aspects of the HISMF: 1) the steep dropoff at high HI masses; 2) the invariance of M HI with respect to stellar mass; 3) the dependence of α on stellar mass and SFR; and 4) the shape of the HISMF at low HI masses Steep Slope at High Masses Our results show that it is very uncommon for galaxies to exist containing > M of HI. There exist several scenarios in which the buildup of HI may be stalled or halted. Since M HI is largely independent of stellar mass and SFR, we can conjecture that the 120

139 processes responsible for suppressing the buildup of HI are the same for most galaxies in the GASS stellar mass range. To determine how various processes affect the HI-rich end of the HISMF, we turn to recent simulations that have incorporated interstellar medium physics in an attempt to reproduce the observed HIMF and understand its origin (though the difficulty of doing so is emphasized in Fontanot et al. (2013)). Duffy et al. (2012), Davé et al. (2013) and Kim et al. (2013) derived HIMFs from cosmological simulations with varying types and levels of feedback and compared them to the observed HIMF. Duffy et al. (2012) found that their HIMF depended more strongly on their self-shielding prescriptions than a range of feedback prescriptions. Kim et al. (2013) and Davé et al. (2013) (who also included self-shielding in their simulations) found that the variations in their feedback models affected the stellar mass or luminosity functions more than the HIMF. In the Kim et al. (2013) models, strong supernovae feedback decreased the amplitude of the HIMF and luminosity function and steepened the slope of the HIMF at the HI-rich end. AGN feedback, often used to suppress the growth of massive galaxies, also steepened the slope at the HI-rich end. The outflow models in Davé et al. (2013) fit the HIMF better when their wind speed and mass-loading factor depended on galaxy velocity dispersion. But their models require a quenching prescription to match the massive end of the stellar mass function; a more physical model could change the properties of massive and HI-rich galaxies, so the present results are difficult to interpret. Is it possible that the steep slope at high HI masses results from high HI masses triggering the formation of H 2 or star formation and depleting HI? For this scenario to be true, recently acquired gas must be funneled to the center of the galaxy where it is 121

140 most likely to contribute to high HI surface densities that can fuel star formation. The universal neutral hydrogen profile uncovered by Bigiel & Blitz (2012) indicates that this might happen in non-interacting spiral galaxies. They found that the radial distribution of neutral gas (HI + H 2 ) surface density is remarkably similar across a sample of 33 nearby spirals. They suggest that continuous gas inflow is responsible for this result by providing a fresh supply of neutral gas to the centers of galaxies where star formation depletes the neutral gas content. Though recent simulations show that cold gas accreted via cosmological filaments tend to have high angular momentum and is deposited at large radii where the HI surface density is low (Kimm et al. 2011; Stewart et al. 2011), the resulting extended HI disks are likely short-lived as inflow will even out the distribution of cold gas The Peak at M HI and the Invariance of M HI The HISMF for massive galaxies has a feature that is not seen in the HIMF derived from surveys such as ALFALFA (Martin et al. 2010): the HISMF is peaked at M HI whereas the HIMF merely bends at M HI and has more galaxies with lower HI masses. Why does the HISMF exhibit a peaked distribution? To evaluate whether the peak at M HI is dominated by star-forming galaxies with high HI masses, we derive the fit to the HISMF for subsamples of the GASS sample defined by color and concentration index. In Fig we show how galaxies with various colors and concentrations contribute to the total HISMF for massive galaxies. based on NUV-r color and in the right panel we divide the sample into two categories based on concentration 122

141 index, R 90 /R 50. As before, we fit a broken Schechter function to each color or concentration subset in several stellar mass bins and sum the normalized fits to obtain the total HISMF across the GASS stellar mass range. To maintain a statistically significant number of galaxies in each stellar mass bin and in each subset, we define only two subsets with respect to color and concentration and we divide the sample into three evenly spaced stellar mass bins instead of six. In the left panel we divide the sample into two categories based on specific SFR: ssfr < and ssfr > Fig shows that non-star-forming galaxies with ssfr < represent a large fraction of the massive galaxies with low HI masses (log M HI /M 8.0) and their contribution to the total HISMF decreases towards higher HI masses. This is not surprising if one assumes that the reason for low SFRs is a lack of cold gas. Star-forming galaxies, on the other hand, contribute less to the HISMF at low HI masses and represent many of the HI-rich galaxies with log M HI /M The peak of the total HISMF for massive galaxies is largely created by star-forming galaxies. In the right panel we show the contribution to the HISMF from bulge-dominated (R 90 /R 50 > 2.6) and disk-dominated (R 90 /R 50 < 2.6) galaxies. (The dividing line is taken from Strateva et al. (2001).) Though bulge-dominated galaxies tend to have lower HI masses and disk-dominated galaxies tend to have higher HI masses, the difference between bulgedominated and disk-dominated galaxies is less pronounced than the difference between star-forming and non-star-forming galaxies, especially at high HI masses. This points to specific SFR as a better indicator of cold gas content than the presence of a bulge. Indeed, GASS has shown that NUV-r color, a proxy for specific SFR, is a much better predictor 123

142 of HI gas fraction than concentration index (Catinella et al. 2010; Fabello et al. 2011a; Catinella et al. 2012). Together, these two cuts can inform our interpretation of the shape of the HISMF and the invariance of M HI. Because star-forming and disk-dominated galaxies dominate the HI-rich end of the HISMF, they appear to drive the shape of the peak of the distribution. Passively evolving, centrally concentrated galaxies exhibit no such peak at M HI and tend to lie at the HI-poor end of the HISMF. They will have a more significant impact on α, the slope of this part of the HISMF. We will discuss this in more detail below. We can also refer to simulations to see if they reproduce a peaked HIMF. Lagos et al. (2011a) show that low halo mass bins exhibit peaked HIMFs, though it is not clear if the existence of a peak in our HISMF is dependent on galaxy mass in the same way. Kauffmann et al. (2012) recreate peaked HI gas fraction distribution functions in bins of stellar mass, stellar mass surface density and concentration with their semi-analytic models, but their models fail to reproduce other important observational trends. We find that M HI, the HI mass at the peak of the HISMF, is nearly constant with respect to stellar mass despite its dependence on SFR. (The near constant HI mass for galaxies in the GASS mass range was noted previously (Catinella et al. 2010).) Although SFR is known to increase with stellar mass within the population of star-forming galaxies (e.g. Salim et al. 2007), the average SFR for the GASS sample, which is representative of massive galaxies in the local universe, is constant with respect to stellar mass (see dotted lines in Fig. 3.15). M HI can be constant with respect to stellar mass because the average SFR and the star formation efficiency (SFE = SFR/M HI ) are nearly constant within this 124

143 mass range (Schiminovich et al. 2010). A possible explanation for the near constant M HI is that galaxies tend to maintain an equilibrium HI mass even as they form stars and their stellar masses increase. If one considers a galaxy s HI mass as a product of the competing processes of gas accretion and gas consumption, a constant HI mass suggests that these processes cancel each other out within individual galaxies, maintaining a similar HI mass distribution across a range of stellar masses. Indeed, simulations have shown that for star-forming galaxies, the mass inflow rate is generally balanced by the sum of the mass outflow rate and the SFR, which also removes gas from the ISM (Eq. 1 in Davé et al. 2012; Schaye et al. 2010; Lagos et al. 2011b). Hopkins et al. (2012) showed that star formation is regulated by stellar-driven winds whose mass-loading increases with SFR. Davé et al. (2012) explained that galaxies out of equilibrium tend to return to equilibrium, such as when a galaxy that receives an influx of gas in a large accretion event subsequently experiences a higher SFR triggered by the higher gas fraction. Thus the increased gas consumption in the form of star formation balances the increased accretion rate and the galaxy returns to equilibrium. An alternative explanation for the constant M HI - that HI masses of galaxies vary in unpredictable ways as they evolve but that the distribution of HI masses is somehow maintained - is unlikely. Thus, our results support a scenario in which the processes that contribute to and deplete the HI content of a galaxy conspire to maintain an equilibrium HI mass. Finally, we note that Prochaska & Wolfe (2009) also uncovered a universal distribution of HI content: they found that damped Lyα systems exhibit the same HI column density distributions between z=2.2 and z=5, and that the distributions at these high redshifts 125

144 matches the distribution function for HI disks in the local universe. Their explanation that various processes affecting the HI content of galaxies must affect the inner, highcolumn density regions and the outer, low-column density regions of galaxies similarly could also apply to our result The Dependence of α on Stellar Mass and SFR The parameter α measures the slope of the HISMF between M HI,break, which is a function of stellar mass, and M HI, which depends weakly on stellar mass. Thus, the range of HI masses that α describes becomes much narrower at higher stellar masses and the number of galaxies contributing to the estimate of α decreases. Our definition of α contrasts with standard treatments of α, in which there is no cutoff at low masses and α describes the low-mass end of mass functions. We do not compare our derived values of α to other published values since we use α to characterize the shape of the HIMF at more moderate HI masses. We also note that in our model α represents the entire exponent in the Schechter function, whereas other authors have used α + 1 as the exponent (e.g. Martin et al. 2010). We find that α s dependence on stellar mass and SFR is stronger than the other parameters dependencies. The wide range of values for α is illustrated in Fig and significantly impacts the shape of the HISMF. If α is close to zero, then the HISMF has a relatively flat distribution below M HI. For higher values of α, the distribution above M HI,break becomes strongly peaked about M HI. α increases with both stellar mass and SFR causing samples with massive galaxies and with highly star-forming galaxies to have peaked distributions of HI masses. Assuming 126

145 that high SFRs are in part driven by the presence of large amounts of cold gas, it makes sense that there would exist fewer galaxies with low HI masses within a population of star-forming galaxies. The HISMF is flat or has a slowly decreasing slope at moderate HI masses when galaxies with low stellar masses or low SFRs comprise the population. The different distributions of HI masses at various SFRs has implications for the relationship between HI and star formation. Galaxies with low SFRs can have a wide range of HI masses while highly star-forming galaxies are more likely to have a high HI mass. This was also evident in Fig Thus, galaxies with low SFRs do not have a well-defined relationship between HI and star formation while galaxies with high SFRs exhibit a much tighter relationship between HI and star formation. The positive correlation between α and stellar mass for the bivariate and trivariate fits shows that HI masses are more strongly peaked among samples of massive galaxies independent of their SFRs. This trend shows that at high stellar masses galaxies tend to have higher HI masses as well. Although there does not exist an observational HISMF for comparison, we can look to Springob et al. (2005), who found that the HIMF depends on morphology. In particular, they noted that the HI-poor end of the HIMF is close to flat (or α is close to zero using our convention) when only early-type spirals are considered. The HIMF for later-type spirals rises towards lower HI masses (α is smaller and negative). They explain this result by appealing to the lower average HI mass found in later type galaxies. It is possible that this trend contributes to the relationship we find between α and stellar mass. As stellar mass increases, later-type galaxies become less common so the population will be dominated 127

146 by galaxies with higher average HI masses The Distribution of the HIMF at Low HI Masses There are two aspects of the HI-poor end of the HISMF that must be examined: the number of galaxies (or fraction of galaxies with a given stellar mass) that have a low gas fraction and the distribution of these galaxies with respect to HI mass. We quantified the former with 1 f and found that the fraction of galaxies with HI gas fractions less than 1% increases with stellar mass. If we assume that all galaxies are undergoing infall proportional to their halo masses (e.g. Dekel et al. 2013) then we must identify the processes that remove gas from galaxies to understand what sets 1 f and why it changes with stellar mass. These processes likely include AGN feedback, which heats gas in the disk and surrounding halo (e.g. Croton et al. 2006; Hopkins et al. 2008; Gabor et al. 2011), environmental effects that deplete gas (e.g. Tonnesen et al. 2007), and stellar-driven winds that expel gas from galaxies (e.g. Oppenheimer & Davé 2008; Oppenheimer et al. 2010). The GASS sample does not include many galaxies in dense environments so we ignore the effect of environment here, though we note that the stripping of gas can have a significant effect on galaxies in clusters. Likewise, stellar-driven winds do not remove large amounts of gas from massive galaxies because the gas can be reaccreted in the form of a galactic fountain (Oppenheimer & Davé 2008; Oppenheimer et al. 2010). It is likely that these processes as well as star formation contribute to the HI-poor end of the HISMF by removing some cold gas from galaxies or preventing gas from cooling. Though simulations have shown that such processes can effectively remove cold gas from galaxies, they do not always predict the right number 128

147 of HI-poor galaxies. Davé et al. (2013) predict the distribution of HI gas fractions as a function of stellar mass and find a negligible number of massive galaxies with gas fractions below 1%, in contrast to our HISMF, which predicts that 20-50% of galaxies in this stellar mass range should have such low gas fractions. The precise distribution of massive galaxies with low gas fractions is unknown and we do not attempt to fit the distribution of HI masses below M HI,break, where the HI measurements are mostly upper limits. Instead, we show the predicted space density of galaxies below a 1% gas fraction as a constant distribution with respect to stellar mass. Here we discuss whether that decision makes sense physically. The distribution of galaxies at low HI masses depends, in part, on the ways in which galaxies with little or no HI reacquire small amounts of cold gas. If we assume that a given fraction of halo baryons cool onto the disk from the hot halo (Anderson & Bregman 2010; Anderson et al. 2013), then we might expect the distribution of HI masses to exhibit a peak at low HI masses that depends on halo mass. However, stochastic additions to the cold gas in the disk, such as from infalling satellites or stellar mass loss (Leitner & Kravtsov 2011) would likely smooth the distribution. There is some indication that galaxies are distributed uniformly at low HI masses. Serra et al. (2012) measure the HI masses and characterize the HI morphology of 166 early-type galaxies brighter than M K = They find that galaxies with HI that they describe as unsettled (i.e. HI in streams or tails rather than an ordered disk) can contain a wide range of HI masses from a few times 10 7 to M whereas galaxies with settled HI disks tend to have higher HI masses. Galaxies with unsettled HI might be accreting 129

148 small amounts of cold gas episodically, such as from the halo (Putman et al. 2012) or intergalactic medium (Kereš & Hernquist 2009), and might not have a preferred HI mass scale. Serra et al. (2012) derive an HIMF for early-type galaxies, which is relatively flat for 7 < log M HI /M < 9.5, and an HIMF for spirals, which is sharply peaked and falls off sharply on either side of M HI. If late-type galaxies are the main contributors to the peak of the HIMF, as the Serra et al. (2012) results and our Fig suggest, then it is possible that early-type galaxies, and others undergoing episodic gas acretion, contribute to a broad distribution of HI masses at the HI-poor end of the HIMF. But there is some evidence that the HISMF for massive galaxies instead rises at low HI masses, making the HISMF for massive galaxies bimodal. We already noted above that this trend is evident in the simulated HIMF for galaxies in bins of halo mass from Lagos et al. (2011a). It is also reasonable to conjecture that the HISMF might mimic the distribution of SFRs in bins of stellar mass. Observations reveal that the distribution of SFRs has a star-forming sequence plus a tail towards passively evolving galaxies at a wide range of stellar masses (Salim et al. 2007; Wyder et al. 2007; Schiminovich et al. 2007) and some simulations have begun to reproduce this distribution by varying star formation prescriptions (Lagos et al. 2011b). Though it is difficult to make strong conclusions about the HI-poor end of the HIMF from surveys that are flux-limited, the Serra et al. (2012) HIMF for early-type galaxies reveals that the HI-poor end could slope upward if the HI in undetected galaxies is included. Finally, the results from our trivariate fit show that at the lowest stellar masses and SFRs we probe, α could become negative, indicating a possible 130

149 peak at low-to-intermediate HI masses (see bold line in Fig. 3.11). 3.6 Summary and Conclusions We have used 480 galaxies from the GALEX Arecibo SDSS Survey (GASS; Catinella et al. 2010) Data Release 2 (Catinella et al. 2012) that were observed in HI at Arecibo to derive the bivariate HI mass-stellar mass function for massive galaxies with log M /M > 10. Below we summarize our key results: We use an MCMC routine to fit six different models, three variations of the Schechter function and three variations of the log-normal function, to the HISMF in six bins of stellar mass from log M /M = 10.0 to log M /M = The Schechter and log-normal parameters M HI, α, µ, and σ show little variation with stellar mass, though f, the fraction of galaxies with gas fractions above 1%, decreases from about 80% to 40%. The continuous bivariate fit shows that α varies as M 0.39, M HI varies as M 0.07 and f varies as M The continuous bivariate fit should be taken as our main result to compare to future observations and simulations. In particular, we believe that the change in f with stellar mass will provide a strong constraint for simulations. To test the accuracy of the models, we compare the total HISMF for massive galaxies, constructed by summing the HISMF across all stellar mass bins, to the data. This comparison shows that each variation of the log-normal function overestimates the number of HI-rich galaxies. The three Schechter functions match the data reasonably 131

150 well, though we choose to proceed only with the broken Schechter function, which extends to a 1% gas fraction with a fractional contribution below that limit. The total HISMF for massive galaxies is consistent with the ALFALFA HIMF (Martin et al. 2010) at high HI masses, indicating that the most HI-rich galaxies in the local universe are also massive in stars. We find that massive galaxies contribute 41% of the total HI density in the local universe. To understand the physical drivers of the shape of the HISMF, we derive the continuous trivariate HI-M -SFR function, for which we redefine the Schechter parameters as functions of stellar mass and SFR. Though the bivariate fit uncovers an HISMF that varies only weakly with stellar mass, the trivariate fit shows that the shape of the HIMF is a strong function of SFR. The trivariate fit shows that α varies as M 0.47 and SFR We show that the peak at M HI is likely dominated by star-forming galaxies and that its slow variation with stellar mass could be related to the ways in which star-forming galaxies maintain an equilibrium HI mass. The dependence of α on SFR shows that highly star-forming galaxies tend to have a narrow range of HI masses peaked about a high HI mass whereas passively evolving galaxies can have a wider range of HI masses. The bivariate HI mass-stellar mass function provides a two-dimensional description of the ways in which HI mass and stellar mass are distributed among massive galaxies. The trivariate HI-M -SFR function expands upon this by exploring its relationship to SFR. 132

151 These are important constraints for simulations; likewise, simulations can shed light on the shape of these distribution functions by testing how feedback and star formation prescriptions affect them. For example, work done by Davé et al. (2013) suggests that galactic outflows could play an important role in preventing the buildup of HI in massive galaxies. Future simulations should begin to explore these bivariate and trivariate functions now that they have begun to incorporate interstellar medium physics and have had success matching observed one-dimensional distribution functions. Future observations can expand this work by extending these trends to lower stellar masses, a goal that is achievable with current facilities, and to higher redshifts, which should be possible with the next generation of radio telescopes. 3.7 Appendix Appendix A - Applications of the HIMF: Comparing to Simulations and Photometric Gas Fractions The HISMF provides a crucial constraint for estimates of HI content for populations of observed or galaxies. Simulations are generally normalized and adjusted until their output matches the observed one-dimensional stellar mass function and/or HIMF (Lagos et al. 2011a; Duffy et al. 2012; Davé et al. 2013; Kim et al. 2013). The HISMF adds an additional constraint because it defines not only the stellar mass function or HIMF but the relation between the two. Indeed, a sophisticated comparison between observations and simulations necessitates the use of the HISMF. For example, Lagos et al. (2011a) 133

152 demonstrate that galaxies in their simulations occupy the same region of the HI gas fraction - stellar mass plane as the GASS galaxies do by comparing their distribution of simulated z=0 galaxies to individual GASS detections and non-detections. It would be more revealing to ascertain whether the simulations and the observations yield samples that not only lie in the correct range of parameter space but are distributed within that parameter space in a similar manner. The HISMF derived here makes that comparison a possibility. Though the most obvious application of the HISMF is to simulations, it can be applied to a range of problems including photometric gas fractions. The difficulty of measuring HI in large unbiased samples of galaxies has led to the development of photometric gas fraction relations, which provide estimates of gas fractions are based on established correlations between HI gas fraction and other physical parameters such as color, surface brightness, and stellar mass surface density. A comparison between the HIMFs derived from various photometric gas fraction estimates and the HISMF derived here is a useful test of their validity. We compile photometric gas fraction relations from the literature and compare their HISMFs to our HISMF. We select photometric gas fraction relations from Kannappan (2004, their Fig. 1b), Zhang et al. (2009, Eq. 4), Catinella et al. (2010, their Fig. 12), Cortese et al. (2011, Eq. 5), and Huang et al. (2012, Eqs. 2 and 5). We apply them to all galaxies in the GASS parent sample and derive corresponding HI masses to be used in the HISMF fit. Though photometric gas fraction relations can be applied to galaxies with a wide range of parameters, Cortese et al. (2011) suggested that they might be valid only for 134

153 star-forming galaxies. To account for this, we apply our standard treatment of detections and non-detections to the derived photometric gas masses where galaxies with NUV-r < 4 are treated as detections and photometric gas masses for galaxies with NUV-r > 4 are treated as upper limits of non-detections. For simplicity, we first compare the total HISMFs derived from photometric gas fractions to our total continuous bivariate HISMF in Fig We calculate the photometric HIMSFs with and without errors on the predicted gas fractions and show the results of both sets of fits. To include the errors on the photometric gas fractions, we add a value to the predicted gas fraction that is randomly selected from a Gaussian distribution whose width is equal to the reported error in each photometric gas fraction relation. (Huang et al. (2012) do not report the scatter in their relations so we use an error of 0.3 dex, consistent with the most recently published photometric gas fraction relations.) Li et al. (2012) show that the errors on the predicted gas fractions can significantly affect results when compared to observed HI gas fractions. In the left panel of Fig we compare the photometric HISMFs without errors to our total HISMF. The photometric gas fraction relations generally underestimate the number of HI-rich galaxies. Huang et al. (2012) presented two photometric gas fraction relations, both of which we present here. The first is based on color and stellar mass surface density (their Eq. 2.) and the second uses color and the stellar mass surface density of the disk only (their Eq. 5) because HI is likely linked to the galaxy disk. Huang et al. (2012) show that photometric gas fractions derived from this equation exhibit less scatter when compared to measured HI masses. The HISMF derived using the disk 135

154 photometric gas fraction is the only photometric HISMF that slightly overpredicts the number of HI-rich galaxies. Though this result suggests that taking into account the disk mass represents a possible way to improve photometric gas fractions, the HISMF derived from this photometric gas fraction relation underestimates the number of galaxies with moderate (log M HI /M 10) HI masses. Other photometric gas fraction relations are a better match to the distribution of HI-poor galaxies. When we include in the fits the scatter in the photometric gas fraction relations, the comparison between the photometric and observed HISMFs is quite different: most photometric gas fractions overestimate the number of HI-rich galaxies and all underestimate the number of galaxies with moderate HI masses. There are several possible reasons why photometric gas fractions do not capture the details of the total HISMF for massive galaxies. One explanation is that the small number of HI detections for HI-poor galaxies and the most massive galaxies hinders the ability to derive accurate photometric gas fraction relations across a wide range of HI masses. Another explanation is that photometric gas fraction relations do not apply to non starforming galaxies. Cortese et al. (2011) argue that a plane describing the relationship between gas fraction, color, and stellar mass surface density may not be appropriate for use with these galaxies because they do not exhibit the same linear trends between HI gas fraction and both color and stellar mass surface density as star-forming galaxies. This was also seen in Catinella et al. (2010). Zhang et al. (2009) found that their photometric gas fractions reproduce the observed HIMF from Zwaan et al. (2005) if they only consider starforming galaxies, but we showed in the previous section that bulge-dominated galaxies 136

155 and red galaxies do contribute significantly to the HISMF for massive galaxies at the HI-rich end. The binned photometric and observed HISMFs provide a more nuanced view of the discrepancy between the photometric and observed HISMFs. In Figs and 3.19 we present the binned HISMF derived for each of the six photometric gas fraction relations with errors. Instead of analyzing the differences between each mass function in each stellar mass bin, we take a global view and note that the photometric HISMFs tend to diverge from the GASS HISMFs at higher stellar masses. That the accuracy of photometric gas fractions varies with stellar mass is not surprising given the results of the trivariate fit in Section We showed that the shape of the HISMF changes with stellar mass and SFR. Thus, a single photometric gas fraction estimator that assumes a simple relationship between gas content and other physical quantities is not likely to be valid across a wide range of stellar masses. There is still work to be done in deriving photometric gas fraction relations that reproduce the true distribution of HI masses while also yielding accurate estimates of gas fractions for individual galaxies. It is possible that an approach that considers how estimates of gas fraction might change with stellar mass will yield more accurate results Appendix B - Assumed stellar mass function We normalized the GASS HISMF by assuming the space density of galaxies in each stellar mass bin is given by the stellar mass function in Borch et al. (2006). Here we show that using other stellar mass functions would have a negligible effect on our final results. 137

156 We compiled z=0 stellar mass functions from Bell et al. (2003), Panter et al. (2007), Li & White (2009) and Bernardi et al. (2010). (A comparison of these mass functions can be found in Bernardi et al. (2010).) They represent a range of approaches and techniques. For example, Li & White (2009) found that a triple Schechter function is a better match to the data than a single Schechter function. Bernardi et al. (2010) included the effect of measurement errors to obtain a fit that matches the observed distribution of stellar masses rather than the intrinsic distribution of stellar masses. In Fig we show how our derived total HISMF would change if we assumed different stellar mass functions. We first converted all stellar mass functions to a Chabrier (2003) IMF, upon which all GASS derived quantities are based. The stellar mass function from Bell et al. (2003) produces a total HIMF that agrees well with the HISMF we derived based on the Borch et al. (2006) stellar mass function. The stellar mass function from Bernardi et al. (2010) yields an HISMF within 10% of ours while Li & White (2009) and Panter et al. (2007) yield HISMFs that are generally within 20% of ours. The HISMFs agree well in part because the stellar mass functions agree well in the GASS stellar mass range and are more discrepant at low (log M /M < 9.5) and high (log M /M > 11.0) stellar masses Appendix C: Probabilities for Model Selection In Table 3.9 we list the probabilities discussed in Section for each of the six models and six stellar mass bins. The top half of the table lists the probability of the MCMC iteration with the highest probability, and the bottom half presents the Bayesian Information 138

157 Criterion (BIC; Schwarz 1978). The equation for the BIC is: BIC = 2 ln(p) + kln(n) (3.14) where P is the MCMC probability, k is the number of free parameters for each model (in our case, k=2 for the full and bent models and k=3 for the broken models), and n is the number of galaxies contributing to each fit. A lower BIC indicates a better fit. In Table 3.9 we also show the same sets of probabilities for the broken Schechter fits to our simulated data. These probabilities are comparable to those derived from the observed data and show that the magnitude of the probabilities is strongly dependent on the number of galaxies in each stellar mass bin (the < log M /M ) < 11.5 bin contains many fewer galaxies). In Table 3.10 we compare the total HISMF derived from each of the eight models to the data at log M HI /M > 10. We calculate the χ 2 statistic as a discrepancy measure. We also use the Poisson probability function to calculate the probability of the number of observed galaxies in each HI mass-stellar mass bin given the number of galaxies that each model predicts. 139

158 Table 3.9. Model Probabilities a Model log M = 10.0, , , , , , 11.5 Schechter Full Schechter Broken Schechter Bent Log-normal Full Log-normal Broken Log-normal Bent Schechter Broken (simulation) Schechter Full Schechter Broken Schechter Bent Log-normal Full Log-normal Broken Log-normal Bent Schechter Broken (simulation) a og probabilities from MCMC runs (top seven lines) and BIC (bottom seven lines). Table Probabilities for Total HISMF at log M HI > 10 (1) (2) log M χ 2 ln(poisson Probability) Schechter Full Schechter Broken Schechter Bent Log-normal Full Log-normal Broken Log-normal Bent Bivariate Trivariate

159 α M HI f α M HI f α M HI f α M HI f α M HI f α M HI f M HI f α Figure 3.7 Error contours for Schechter parameters α, M HI and f for the broken (grayscale contours; red crosses) and bent (black contours; cyan crosses) models in six stellar mass bins. Contours enclose 10, 25, 50, and 95% of the 5000 Schechter parameters representing the 5000 MCMC iterations. 141

160 φ(m HI, M ) [Mpc 3 dex 1 ] , GASS GASS + ALFALFA , , , , , log M HI Figure 3.8 The broken Schechter fit to the GASS HISMF (black solid line) compared to the broken (solid red) and bent (dotted red) Schechter fits to the HISMF that includes ALFALFA detections and upper limits. Black circles are as in Fig Solid red circles show ALFALFA detections; open red circles show ALFALFA upper limits. 142

161 φ(m HI, M ) [Mpc 3 dex 1 ] Full Broken Bent ALFALFA Schechter log M HI Log-normal Broken Schechter log M HI Figure 3.9 The total HISMF for massive galaxies based on six different models compared to the ALFALFA HIMF (blue Martin et al. 2010). Left: The sum of the full, broken, and bent Schechter fits to the HISMF. Right: The sum of the full, broken, and bent log-normal fits to the HISMF. 143

162 , , Bivariate Fit Trivariate Fit , , φ(m HI, M ) [Mpc 3 dex 1 ] 10.5, , , , , , , , log M HI log M HI Figure 3.10 The binned broken Schechter HISMF (solid line) compared to the continuous bivariate fit (left; blue dashed line), whose parameters depend on stellar mass, and the continuous trivariate fit (right; blue dotted line), whose parameters depend on stellar mass and SFR. α, M HI and f in each bin are144 calculated as described in the text.

163 < log M < φ(m HI, SFR) [Mpc 3 dex 1 ] < log SFR < < log SFR < < log SFR < < log SFR < log M HI Figure 3.11 An example of the continuous trivariate HI-M -SFR function for galaxies with stellar masses in the range 10.5 < log M /M < and log SFRs ranging from -2.5 to 0.5. There is no population of galaxies with M HI < M HI,break in the highest SFR bin in this stellar mass range because f is expected to be close to

164 α α α log SFR = -1.0 log SFR = 0.0 log SFR = 1.0 log ssfr = log M HI,75 = 8.9 log ssfr = log M HI,75 = 9.3 log ssfr = log M HI,75 = log M HI log ssfr = log M HI,75 = 9.8 log ssfr = log M HI,75 = 9.9 log ssfr = log M HI,75 = 10.1 log ssfr = log M HI,75 = 10.1 log ssfr = log M HI,75 = 10.2 log ssfr = log M HI,75 = log M log M HI HI log M = log M = log M = Figure 3.12 Each panel shows the distribution of α vs. M HI calculated for a given stellar mass (increases down each column) and SFR (increases across each row) from the fit in Section The black cross indicates the median values in each panel and the black dotted lines show the median values for log SFR = 0 and log M /M = Dashed lines are lines of constant M HI,

165 α α α log SFR = -1.0 log SFR = 0.0 log SFR = 1.0 log ssfr = log ssfr = log ssfr = log ssfr = log ssfr = log ssfr = log ssfr = log ssfr = log ssfr = f f f log M = log M = log M = Figure 3.13 Same as Fig for α and f. 147

166 1 log SFR = log SFR = log SFR = log M HI /M log M log M log M Figure 3.14 Predicted HI gas fraction vs. stellar mass in three bins of SFR based on the continuous trivariate fit. Solid curves indicate the fraction of galaxies with HI gas fractions below the lines. The dotted curves show the same for the continuous bivariate fit. Green triangles represent M HI,75 in each M -SFR bin. Blue circles show the median gas fraction (including upper limits) from Catinella et al. (2012). Empty blue circles are close to the gas fraction detection limit of GASS. 148

167 9 4.0 α log M HI log ssfr f 9 log M HI,75 log ssfr log M log M Figure 3.15 Lines of constant α, M HI, f, and M HI,75, calculated from the trivariate fit, in the specific SFR-stellar mass plane. Dashed lines show the star-forming sequence from Salim et al. (2007). Dotted lines show the average specific SFR vs. stellar mass trend for GASS galaxies (Schiminovich et al. 2010). 149

168 φ(m HI, M ) [Mpc 3 dex 1 ] ssfr < ssfr > log M HI R90/R50>2.6 R90/R50< log M HI Figure 3.16 The total HISMF divided by specific SFR and concentration (dashed and dotted lines) compared to the total HISMF (solid line). Left: The total HISMF for passively evolving (ssfr < -11.5) galaxies (dotted) and star-forming (ssfr > -11.5) galaxies (dashed). Right: The total HISMF for bulge-dominated galaxies (R 90 /R 50 > 2.6; dotted line); the total HISMF for disk-cominated galaxies (R 90 /R 50 < 2.6; dashed line). 150

169 Without Errors 10-1 With Errors 10-2 φ(m HI, M ) [Mpc 3 dex 1 ] Kannappan 2004 Zhang et al Catinella et al Cortese et al Huang et al Huang et al (b) GASS log M HI Kannappan 2004 Zhang et al Catinella et al Cortese et al Huang et al Huang et al (b) GASS log M HI Figure 3.17 Broken Schechter fits to the total HISMF derived from published photometric gas fractions calculated for galaxies in the GASS parent sample. The fits presented in the left panel do not include errors while the fits shown in the right panel do include errors. The black line shows the total GASS HISMF based on the continuous bivariate fit; the colored lines show the total HISMF for massive galaxies based on photometric gas fractions. Because the best-fit models to the distributions of photometric gas fractions are poor in the highest stellar mass bin (see Figs and 3.19 below), here we show the sum of the HISMF only up to log M /M =

170 φ(m HI, M ) [Mpc 3 dex 1 ] , Kannappan 2004 Zhang et al , Catinella et al , , , , , , , , , , , , , , log M HI 11.25, log M HI 11.25, log M HI Figure 3.18 The broken continuous bivariate Schechter fit to the GASS HISMF (solid lines) compared to the broken Schechter fit to the HISMFs derived from photometric gas fraction relations published in Kannappan (2004), Zhang et al. (2009), and Catinella et al. (2010) (dotted lines). 152

171 φ(m HI, M ) [Mpc 3 dex 1 ] , Cortese et al Huang et al , Huang et al (b) 10.0, , , , , , , , , , , , , , log M HI 11.25, log M HI 11.25, log M HI Figure 3.19 Same for Fig for the photometric gas fraction relations published in Cortese et al. (2011) and Huang et al. (2012). 153

172 0.2 (φ(m HI,other ) - φ(m HI,Borch )) / φ(m HI,Borch ) Bell 2003 Li & White 2009 Panter 2007 Bernardi log M HI Figure 3.20 The fractional difference in the total HISMF when stellar mass functions other than that in Borch et al. (2006) are used. 154

173 Chapter 4 Resolved HI Imaging of a Population of Massive HI-Rich Galaxies with Suppressed Star Formation Introduction Many theories of galaxy evolution assume that a galaxy s evolutionary stage and its cold gas content are tightly linked. For example, it is often assumed that a depleted cold gas reservoir can explain why massive galaxies are redder and exhibit less active star formation, but recent observations have challenged this picture by identifying populations of galaxies that contain significant amounts of cold gas despite their low or moderate star 1 This chapter is a reformatted version of an article by the same name by J. J. Lemonias et al.that has been submitted to the Astrophysical Journal. An edited version of the abstract for this paper is reproduced in Section

174 formation rates (Morganti et al. 2006; Serra et al. 2012; Young et al. 2013). Some attempts have been made to systematically search for these galaxies to understand them as a population. In this chapter we pursue this line of reasoning by studying a sample of massive galaxies with an unusual combination of high HI masses and low specific star formation rates. Galaxies that have more cold gas than expected can be placed into two broad categories: red, early-type galaxies with unexpected measurable HI and galaxies that have significantly more HI than their star formation rates (SFRs) would suggest. In the first category, early-type galaxies were expected to be devoid of cold gas because they lack the spiral arms that indicate recent star formation. The first systematic imaging search for HI in early-type galaxies, motivated in part by the evidence for HI in individual early-types, found that HI is common at low levels in early-type galaxies in the field and could play an important role in their evolution (Morganti et al. 2006). More recent surveys have revealed that at least 32% of such galaxies have detectable HI and that 20% of ETGs have regularly rotating disks of HI (Serra et al. 2012). Young et al. (2013) show that even red early-type galaxies have cold gas at detection rates of 10-34% and that the detection rates are highest among the most massive (log M /M > 10.5) red early-types. Galaxies in the Serra et al. (2012) sample contain up to solar masses of HI. Because galaxies with more than this amount of HI are rare, study of these galaxies has so far focused on individual galaxies rather than entire populations. Galaxies with low rates of star formation compared to their cold gas content comprise a diverse population of not just red early-type galaxies but also massive spirals that are 156

175 expected to contain cold gas but have a high gas content incommensurate with their relatively low SFRs. The reasons for their low SFRs are largely unknown and difficult to ascertain. Recent simulations and observations have attempted to determine which physical processes or conditions can prevent cold gas from collapsing and forming stars. In simulations the heating and disruption of gas by AGN feedback are frequently used to explain the low specific star formation rates (ssfr = SFR/M ) of massive galaxies (e.g. Croton et al. 2006; Hopkins et al. 2008; Gabor et al. 2011). Gabor et al. (2011) showed that feedback from radio-mode AGN can shut down star formation, but it is unclear how this would affect the cold gas reservoir (Ho et al. 2008; Fabello et al. 2011b). Martig et al. (2009) show that morphological quenching can quench star formation in bulge-dominated galaxies without removing or heating the cold gas. A high cold gas content may coexist with a low SFR in galaxies such as those with inefficient star formation in their outer disks. The outer disks could harbor large quantities of gas but observations have shown that their densities are low and typically dominated by HI over H 2 (e.g. Wyder et al. 2009; Bigiel et al. 2010). Inefficient star formation is frequently attributed to a low gas surface density below a threshold level of 3-10 M pc 2 that is required for H 2 to form and for star formation to proceed efficiently (Schaye 2004; Bigiel et al. 2008). Below this threshold level the SFR surface density decreases steeply; this downturn could be related to Hα-derived star formation thresholds in outer disks such as those discovered by Martin & Kennicutt (2001). Low gas surface densities below the threshold required for star formation can also yield inefficient star formation, defined as low levels of star formation for a given amount 157

176 of cold gas. Observations have shown that galaxies form stars inefficiently in their outer disks where the gas density is low and HI dominates over H 2 (Wyder et al. 2009; Bigiel et al. 2010). Extended UV (XUV) disks and giant low surface brightness galaxies (GLSBs) are both populations of galaxies characterized by inefficient star formation. XUV-disks are defined by the presence of low-level UV flux beyond the main stellar disk. The prevalence of XUV-disks suggests that inefficient star formation in the outer disks of galaxies may be common (Thilker et al. 2007), especially around massive, bulge-dominated galaxies (Chapter 2; Lemonias et al. 2011). GLSBs have a less stringent definition than XUV-disks, but are generally known to have low surface brightness disks at optical wavelengths and massive HI disks that extend well beyond the optical radius. Malin 1 (Pickering et al. 1997) is the prototypical GLSB, and several similar galaxies have been discovered (e.g. Morganti et al. 1997; Portas et al. 2010). Simulations have shown that extended low surface density gaseous disks may be common if the cold gas building up the gaseous disk has a high angular momentum (Kimm et al. 2011; Stewart et al. 2011; Lu et al. 2014). It has become clear that cold gas and star formation are not always linked in obvious ways. To gain a deeper understanding of the role HI plays in galaxy evolution, both within the general population and in populations that deviate from the general population, it is necessary to have large, well-defined samples of galaxies with known star formation and gas properties. Recent large HI surveys such as the GALEX Arecibo SDSS Survey (GASS; Catinella et al. 2010) and the Arecibo Legacy Fast ALFA Survey (ALFALFA; Giovanelli et al. 2005) complement GALEX (Galaxy Evolution Explorer) and SDSS (Sloan Digital Sky 158

177 Survey) data on star formation and galactic structure by providing key measurements of the cold gas in galaxies. The advent of large HI surveys such as these provides the first opportunity for us to select and study volume-limited populations of galaxies defined only by their gas content. In this chapter we take advantage of these recent HI surveys to assess the link between cold gas and star formation in a unique and systematic way. Although the term cold gas generally refers to both atomic and molecular gas, in this paper we only have information about HI so we refer to cold gas and HI interchangeably throughout the rest of the paper except when noted otherwise. We define a sample of massive (log M /M > 10.0) HI-rich galaxies to investigate the relationship between HI and star formation in this crucial stellar mass range in which galaxies become less actively star-forming. We uncover an intriguing population of galaxies at stellar masses log M /M > 10.5 that exhibit surprisingly low ssfrs despite their significant amounts of HI. Because the galaxies were selected based on single-dish HI observations with Arecibo, there existed no information about the morphology or spatial extent of the HI, which are crucial in determining why much of the HI is not participating in star formation. In this chapter we describe the sample and report on the results of an HI imaging survey at the Jansky Very Large Array (VLA) intended as an observational test of the mechanisms acting to suppress star formation in these massive HI-rich galaxies. This chapter is organized as follows. In Section 4.2 we select a sample of HI-rich galaxies and we compare their star-forming and structural parameters to two control samples. This section motivates the observational test described in Section 4.3, in which 159

178 we obtain HI imaging for massive HI-rich galaxies with suppressed star formation. In Section 4.4 we discuss the implications of our results in terms of star formation suppression mechanisms. We summarize our findings in Section 4.5. In the Appendix we list notes on individual galaxies. 4.2 Properties of Massive HI-Rich Galaxies Sample Selection GASS (Catinella et al. 2010) is a targeted HI survey at Arecibo of 800 galaxies with stellar masses in the range 10 < log M /M < 11.5 and redshifts in the range < z < Each galaxy observed for GASS also lies in the ALFALFA, SDSS, and GALEX footprints, which yield homogeneously measured star formation rates and stellar masses for the sample. Because GASS is unbiased and complete with respect to stellar mass, we can use it to define scaling relations and select samples based on those scaling relations that are representative of the galaxy population in the local universe. We use the GASS representative sample from Data Release 2 (N=480; Catinella et al. 2012) to define a sample of galaxies that are HI-rich for their stellar mass. (We defined the HI-rich sample and the subsample for follow-up observations before the final data release in Catinella et al. (2013) was available, though that could be used now and should yield the same trends.) Our simple selection criterion, based only on HI mass and stellar mass, defines the HI-rich sample to contain galaxies that have HI gas fractions in the top 5% of the GASS distribution. To determine where the top 5% lies, we sort the HI gas fractions, or upper limits on the gas fractions for 160

179 non-detected GASS galaxies, and select the gas fraction that divides the bottom 95% from the top 5% (Fig. 4.1a) in six evenly spaced stellar mass bins in the range 10.0 < log M /M < We fit a line to these points that is parametrized as logm HI /M = α(logm /M 10) + k (4.1) where α = and k = We consider all galaxies above the line to be HI-rich for their stellar mass. A similar sample could be constructed using results of the bivariate HI mass function (Chapter 3; Lemonias et al. 2013), but we chose this method for simplicity. Although we use GASS to establish the criterion for selecting HI-rich galaxies, we select the HI-rich sample from ALFALFA, an untargeted wide-field HI survey that contains many more HI detections than GASS and whose sky footprint overlaps with that of GASS. Whereas GASS provides a complete census of HI in massive galaxies and can be used to derive quantiles of the distribution, ALFALFA mainly detects HI-rich galaxies at the redshifts probed by GASS and so cannot be as easily used to quantify the full range of HI masses for massive galaxies. However, ALFALFA is complete over this volume to the HI-rich gas fraction limits considered here and so is useful for selecting a large, unbiased sample of HI-rich galaxies. We select the HI-rich sample from the α.40 subsample (Haynes et al. 2011). To ensure that the physical parameters for galaxies in the HI-rich and GASS samples are measured homogeneously, the HI-rich sample contains only ALFALFA galaxies that are also in the GASS parent sample (N=12006). There are 1102 unique matches (see Fig. 4.1b) between the two samples, of which 258 meet the HI-rich criterion and do not appear to be contaminated by neighboring galaxies. The final HI-rich sample 161

180 contains 258 galaxies with total HI masses in the range 10.0 < log M HI /M < and a median mass of log M HI /M The median gas fraction for the sample is 62±38%. To compare to the HI-rich sample, we select a separate sample of ALFALFA galaxies with gas fractions in the range -0.7 < log M HI /M < -0.4 across the full range of stellar mass. ALFALFA is also complete to these limits over the given redshift volume. We call this sample the constant gas fraction sample, which contains 285 galaxies. The median gas fraction for the sample is 29±6%. The lower scatter in the average gas fraction compared to the HI-rich sample is by design Derived Quantities The calculation of the SFRs used in this paper is described in detail in Schiminovich et al. (2010). We use their DC,D4NCUT SFRs, which are derived directly from near-uv luminosities. Star-forming galaxies, defined as having a 4000Åbreak strength D n (4000) < 1.7, are corrected for internal dust attenuation according to the method outlined in Johnson et al. (2007). Their method for determining dust corrections, based on UV and optical fluxes, was empirically calibrated using UV+IR measurements from GALEX and Spitzer. We calculate the HI gas fraction as the HI mass divided by the stellar mass, M HI /M, such that the HI gas fraction can be greater than one. Stellar masses and AGN classifications are from the MPA-JHU SDSS DR7 catalog 2. AGN classes are described in Kauffmann et al. (2003a). Galaxy sizes (e.g. R 90, R 50 ) and axis ratios are from the NASA- Sloan Atlas 3. We define edge-on galaxies as those with axis ratio b a < 0.3. In Section

181 we estimate the SFR and HI surface densities of GASS galaxies by assuming that the star formation is contained within R 90 and that half of the total HI is contained within R 90. The latter is consistent with Wang et al. (2013), who show that the radius enclosing half of the HI flux (their R50) for normal galaxies is comparable to or less than the optical radius (half of D 25 ) Results First we examine how the SFRs of galaxies in the HI-rich sample vary with stellar mass. One might naively expect HI-rich galaxies to have uniformly high SFRs. To test this, in Figs. 4.1c,e we plot the gas fractions and ssfrs of the HI-rich galaxies vs. stellar mass. Two distinct results are apparent: 1) The ssfrs of the HI-rich galaxies decrease with increasing stellar mass faster than their HI contents decrease; and 2) the scatter in their ssfrs increases with stellar mass, leaving many HI-rich galaxies well below the star-forming sequence (dashed line; from Schiminovich et al. (2007)) at log M /M > This population is the subject of our study in the next section. Our HI-rich sample contains galaxies that have extreme HI contents for their stellar mass so their HI fractions necessarily decrease with stellar mass. But the decreasing gas fraction cannot be the sole driver of the decreasing trend in ssfr because the ssfrs decline with a steeper slope (α -1.29). To emphasize that the decreasing ssfrs are characteristic of HI-rich galaxies in general and not just a sample of HI-rich galaxies whose HI gas fractions decrease with stellar mass, we compare the HI-rich sample to the constant gas fraction sample, whose galaxies have higher-than-average gas fractions within the same 163

182 log M HI /M (a) log M /M (b) log M /M log M HI /M GLSBs (c) log M /M (d) log SFR/M GLSBs (e) (f) -9.0 log M /M -9.0 log M /M log SFE (g) (h) NUV-r (i) log M /M (j) log M /M Figure 4.1 The top row shows the selection of the HI-rich galaxies. The top left panel shows HI gas fraction vs. stellar mass for GASS detections (gray points) and upper limits for GASS non-detections (gray triangles). The solid line shows the HI-rich selection, and the dotted line is the median of the GASS distribution. The top right panel shows the ALFALFA detections in the GASS parent sample. In the bottom four rows we compare the HI-rich sample (left column; blue points) to the constant gas fraction sample (right column; red circles) in terms of HI gas fraction, ssfr, star formation efficiency, and NUV-r color. Edge-on galaxies are highlighted as cyan points. Stars indicate the HI fractions and ssfrs of giant low surface brightness galaxies from Wyder et al. (2009). In panels e and f, blue and red lines show the running medians for the HI-selected samples. The cyan line shows the same for the HI-rich sample excluding 164 edge-on galaxies. The black dashed line in panels e and f shows the SF sequence from Schiminovich et al. (2007). The black dashed line in panels g and h shows the average SFE from Schiminovich et al. (2010). Contours enclose 5%, 10%, 25%, 50%, and 95% of the GASS parent sample.

183 narrow range with respect to stellar mass. Even though the gas fractions for galaxies in this sample remain constant with respect to stellar mass, their ssfrs decrease in the same way as for the HI-rich sample. This inconsistent relationship between gas and star formation runs counter to the simple assumption that star formation efficiency (SFE=SFR/M HI ) does not vary with stellar mass (Schiminovich et al. 2010) and hints that something other than the lower gas fractions in massive HI-rich galaxies contributes to their low ssfrs. Importantly, this result is not just a reflection of the generic trend of decreasing ssfrs vs. stellar mass (e.g. Schiminovich et al. 2007) because we selected HI-rich galaxies which, by definition, are not representative of the full galaxy population. Thus, the decreasing ssfrs within the HI-rich sample is an unexpected result rather than a confirmation of expectations. That ssfrs decrease with stellar mass even within a sample of galaxies that have extremely high HI contents indicates that gas loss alone cannot explain why ssfrs decrease with stellar mass within the larger population. By studying this extreme population of galaxies with high HI fractions and incommensurately low SFRs, we can gain insight into the star formation suppression mechanisms at work both in HI-rich galaxies and in less extreme form in normal galaxies. Fig. 4.1g,h we show the SFE vs. stellar mass for the two HI-selected samples. The average SFE for GASS galaxies is constant with respect to stellar mass (dashed line) but exhibits a large scatter (Schiminovich et al. 2010). Overall the HI-rich sample exhibits SFEs lower than the median. There is also a clear trend for the distribution of SFEs to become wider and extend to lower SFEs at higher stellar masses, which confirms the increasingly weak relationship between HI and star formation within the HI-rich sample. 165

184 Finally, in Fig. 4.1i,j we show the NUV-r color of the samples, which is generally considered a proxy for specific SFR. Indeed, the distributions of NUV-r and specific SFR tell a similar story: at low stellar masses, HI-rich galaxies exhibit a narrow range of colors and lie on the blue sequence, but as stellar mass increase, galaxies become redder and the scatter in color increases. Although the massive HI-rich galaxies have much lower ssfrs than would be expected based on their HI contents, the galaxies do not lie on the red sequence. They appear to have a low level of residual or recent star formation. Because the two HI-selected samples have different HI properties by definition but produce similar trends in ssfr, there is some ambiguity in the role of the HI. It is only clear that within this stellar mass and HI gas fraction range, stellar mass is a better predictor of ssfr than is HI content. A clearer understanding of these trends requires knowledge of the molecular gas as well, which does not exist for this sample, though we discuss the possible relationship between HI and H 2 in this sample below. We determined that our UV-based SFRs, which can be strongly affected by dust, are not artificially low due to dust attenuation by examining their infrared colors (Wright et al. 2010) and D n (4000), and removing from the sample edge-on galaxies whose UV fluxes are most likely to be attenuated by gas. The distribution of D n (4000), a stellar age indicator that correlates with star formation history and is expected to be insensitive to extinction, mimics the distribution of ssfr, confirming the existence of a weaker link between gas fraction and ssfr at higher stellar masses. Although ssfrs for some edge-on galaxies may be underestimated by a factor of 10, it is unlikely that the decreasing ssfrs with stellar mass are driven by a higher proportion of edge-on galaxies at high stellar masses. 166

185 To be sure, we show in Fig. 4.1 that our results hold if we exclude edge-on galaxies from the HI-rich sample. Finally, we note that there is generally more scatter in UV-derived SFR measurements for more massive galaxies (see Schiminovich et al. 2010), but it is unlikely to produce the strong trend we see. The ssfrs of galaxies in the HI-rich sample show that the relationship between HI and star formation varies with stellar mass: at high stellar masses, star formation is suppressed even within galaxies that are HI-rich for the stellar mass. In the next section we describe HI imaging of 20 HI-rich galaxies with low ssfrs. The resulting HI maps provide insight into the physical conditions that can suppress star formation while maintaining a significant HI reservoir at high stellar masses. 4.3 HI Imaging of Low-star-forming HI-Rich Galaxes The low ssfrs in some massive HI-rich galaxies suggests that star formation is being suppressed in some massive galaxies without the removal of HI. The high gas fractions and low ssfrs in the most massive galaxies could be a signature of internal suppression of star formation, extended HI disks with surface densities below that required for efficient star formation, or recently accreted gas that has not yet formed stars. The distribution and surface density of the HI can provide key insight into the physical conditions of the cold gas in the galaxy, which can help us understand why the cold gas is not forming stars. We obtained followup HI imaging with the Jansky Very Large Array (VLA) for a subset of the HI-rich galaxies to understand the star formation suppression mechanisms at work in these galaxies. Below we describe the galaxies selected for followup, the observations, 167

186 0.5 VLA Targets -9.0 HI-rich 0.0 GASS log M HI /M -1.0 GLSBs log SFR/M GLSBs (a) (b) log M /M log M /M Figure 4.2 Left: HI gas fraction vs. stellar mass for GASS detections (gray points), upper limits for GASS non-detections (gray triangles), and HI-rich sample (blue points). Solid line shows HI-rich selection. Dotted line is the median of the GASS distribution. Stars indicate giant low surface brightness galaxies from Wyder et al. (2009). VLA targets are highlighted with black circles. Right: ssfr vs. stellar mass for HI-rich sample. Blue line shows the running median. Black dashed line shows the star-forming sequence from Schiminovich et al. (2007). Contours enclose 5%, 10%, 25%, 50%, and 95% of the GASS parent sample. and the conclusions we can derive from the observations Sample Galaxies in our HI-rich sample are ideal for followup with the VLA because their high HI fluxes ( Jy km s 1 ), previously measured at Arecibo for the ALFALFA survey, ensure they can be easily detected in a short amount of time. From the final HI-rich sample of 258 galaxies we selected 20 galaxies for followup with the VLA from the population of 168

187 Figure kpc 50 kpc SDSS color images of the 20 galaxies in the VLA sample. 169

188 galaxies with high HI masses and low ssfrs, i.e. those that deviated from the star-forming sequence at high stellar mass. The final sample includes all HI-rich galaxies with high stellar masses (log M /M > 10.6), low ssfrs (log ssfr < ), and moderate-to-high axis ratios (b/a > 0.5) to avoid edge-on galaxies whose low ssfrs might be artificially low due to internal dust attenuation. We refer to this subset of HI-rich galaxies as the VLA sample. They are indicated in Fig. 4.2 and their properties are listed in Table 4.1. In Fig. 4.3 we display their SDSS color images. One galaxy, GASS 11390, was removed from the sample because the VLA observations revealed no HI signal above the level of the noise. In the Arecibo spectrum the galaxy is at the edge of the band, which possibly affected the calculation of the HI mass for ALFALFA. We report on the results of the final sample below, which contains 19 galaxies. We note that there exist several other ongoing studies of HI-rich galaxies and we wish to distinguish our sample and our goals from theirs. The Bluedisks project, as described in Wang et al. (2013) uses HI maps to understand the origin of the excess HI in galaxies that have high HI gas fractions compared to their predicted gas fractions. Their goal contrasts slightly with our goal, which is to understand why some galaxies with large HI reservoirs do not have high ssfrs. Huang et al. (2012) describe a study of HI-rich galaxies observed by ALFALFA, HIghMass, that will include a multiwavelength analysis of galaxies with log M HI /M > 10.0 and high HI fractions. Their goal is similar to ours: understanding why some galaxies maintain large gas reservoirs without forming stars at a high rate, but they also include less massive galaxies. 170

189 Table 4.1. General Data GASS ID RA DEC z log M log M HI SFR ssfr NUV-r R 90 /R 50 b/a AGN Class M M M yr 1 yr 1 mag Weak AGN Composite Weak AGN Low S/N AGN Low S/N AGN Low S/N AGN Low S/N AGN Low S/N AGN Low S/N AGN Low S/N AGN Weak AGN Weak AGN Low S/N AGN Low S/N AGN Lee et al. (2014) present CO observations of a sample of 28 HI-rich galaxies, including 8 LSB galaxies, all of which have relatively high stellar masses (log M /M > 9.6) and HI masses (log M HI /M > 10.2). We refer to this work in Section when we discuss the possible molecular gas content of galaxies in our sample Observations and Data Reduction 171

190 z Frequency [Ghz] Figure 4.4 Instrument Setup. Blue bands and black stripes denote the eight spectral windows designed for HI lines. Each x denotes the redshifted frequency of the HI line for each galaxy. Observations with the VLA were conducted in June-July 2013 in spectral-line mode at 21 cm in C configuration. We selected integration times of 2 or 4 hours, including time for calibration (with standard flux calibrators 3C48, 3C147, and 3C286), for each galaxy depending on the HI fluxes detected at Arecibo, optical sizes, and an assumed HI diameter, D HI =1.5D opt, where D opt = 2R 90 using r-band measurements. We defined eight spectral windows to cover the velocity range needed to detect HI emission at the systemic velocities of the galaxies (see Fig. 4.4). Each spectral window had 256 channels covering a frequency range of 8 MHz for a frequency resolution of KHz or a velocity resolution of about 7 km/s. The spectral windows were not evenly spaced in frequency 172

191 space but were defined so that HI emission from each galaxy would fall close to the middle of a spectral window. Some of the spectral windows overlapped significantly. For data reduction we used only the data from the spectral window within which the galaxy was closest to the center (except for GASS40245; see Appendix). Data were reduced with CASA (McMullin et al. 2007) following standard calibration procedures. Bad data points were selected and flagged based on the calibration solutions and by-eye inspection of the visibilities. We determined the continuum by fitting a line to the line-free channels and subtracted the result. We used the CASA task CLEAN to create data cubes from the calibrated data. Data cubes were built with 6 6 arcsecond pixels and a velocity resolution of about 28 km/s by averaging four adjacent channels. The median size of the synthesized beam is arcseconds. We used a weighting scheme with a robustness parameter of 1 (Briggs 1995) to emphasize low signal-to-noise emission. The typical noise is 0.54 mjy per beam per channel; we CLEANed down to two times the noise level. From the data cubes, we chose by eye which channels to include in the total HI intensity (moment-0) and velocity (moment-1) maps. We selected only those channels containing emission that appeared in more than one adjacent channel and seemed to be associated with the galaxy. For all galaxies, we first chose which pixels to include by adjusting the flux thresholds until we reached a compromise between including enough low surface brightness flux and not too much noise. In practice, we convolved the original data cube with a arcsecond kernel and selected the flux threshold based on this convolved image to avoid including noise in the final moment maps. This image was 173

192 used to define which 6 6 arcsecond pixels of the original cube should be included in the moment maps. Thus, the final moment maps have 6 6 arcsecond pixels based on the original, unsmoothed data cube. We masked any remaining noise in the moment maps to minimize its effect on the calculation of HI masses, radial profiles, and HI radii. For three galaxies with low surface brightness HI emission (15607, 19918, 47708) we generated moment maps using a method that is less likely to exclude low levels of emission. Instead of imposing a threshold, we selected regions of emission in the data cube that appeared in more than one adjacent channel and summed the flux in those regions to produce the HI intensity and velocity maps Derived Quantities Following Walter et al. (2008), we derived HI quantities directly from the moment maps that were constructed and masked to limit spurious HI. HI mass We calculated HI masses by summing the flux in the HI intensity maps and converting the flux to HI mass in solar masses according to the following equation: M HI M = d 2 L 1 + z S (4.2) where d L is the luminosity distance in Mpc and S is the flux in Jy km s 1. HI Radius We constructed radial profiles by summing the flux in concentric elliptical annuli defined by the axis ratio and position angle of the optical disk reported in the NASA-Sloan Atlas. The annuli were 6 arcseconds in width; an average of 15 independent data points contributed to the measurement of the HI radii. HI fluxes were converted to 174

193 surface brightness in solar masses per square parsec. We determined the radial profiles out to a radius determined by eye for each galaxy. We use the radial profiles to calculate R90 HI, the radius that contains 90% of the total HI flux. In the HI intensity maps we also display the contour at which the HI surface brightness drops to 1 M pc 2, which is equivalent to a column density of atoms cm 2. Other methods of calculating the extent of cold gas include measuring the maximum distance to a given isophote (Serra et al. 2012; Davis et al. 2013). HI surface density The surface density of gas can be measured locally, for individual regions within a galaxy (as in, e.g., Bigiel et al. 2008, 2010; Leroy et al. 2008), and globally, over the entire extent of a galaxy (as in Kennicutt 1998). To be consistent with the analysis of Kennicutt (1998), and because the distances to galaxies in this chapter are large enough that there are only a few resolution elements per galaxy, we only calculate global HI surface densities. The global surface density necessarily averages over important variations in the local surface densities; the HI intensity maps in Fig. 4.6 give some indication of these variations. There are several ways of calculating the global HI surface density. To provide a sense of the possible range of global HI surface densities in these galaxies, we report the HI surface density calculated in three ways. First we calculate the HI surface density averaged over the regions of the galaxy within the 1 M pc 2 isophote. This contour is shown on the HI intensity maps. A benefit to this method of calculating HI surface density is that it only includes regions of the galaxy that contain significant amounts of HI. Second, we use the HI radii derived from these observations, R90 HI, and the optical 175

194 radii reported in the NASA-Sloan Atlas, R90 opt, to compute the HI surface densities within these regions - the HI disk and the stellar disk. Kennicutt (1998) calculate the the global HI surface density within the stellar disk, but this measurement provides no information about the outer parts of the HI disk since HI disks tend to extend well beyond the optical disks of galaxies. SFR Surface Density We also calculate the SFR surface density in three ways, averaging over the same three regions we used for the HI surface density. To determine the SFR within each region, we scaled the SFR from GALEX by the fraction of far-uv light contained within the given region, which assumes that the dust correction is uniform across the galaxy. Velocity Spectra In Fig. 4.5 we compare the velocity spectra from this survey to the ALFALFA spectra. The velocity resolution for the VLA spectra is coarser because we smoothed the cubes as described above. There is general agreement between the spectra except in cases where we do not recover the total HI mass that ALFALFA detected (see next section). In some cases the spectra match at the peaks but the VLA is missing some flux close to the systemic velocities. This flux might be harder to detect because the HI in channels close to the systemic velocity could, in a given channel, cover a larger physical area and subsequently have lower surface brightness below the noise level. We are probably not missing any high surface brightness gas, but there might be lower surface brightness gas that we are unable to detect, the presence of which would only strengthen the conclusions of this chapter. 176

195 Figure 4.5 Velocity spectra from ALFALFA (solid lines) and this survey (dotted lines). 177

196 4.3.4 Results HI Morphology In Fig. 4.6 we display the total intensity and velocity maps and the intensity maps overlaid on SDSS and GALEX images. It is clear that while all of the galaxies in the VLA sample exhibit HI emission well beyond the optical disks, the precise morphology of the HI varies widely. However, all 19 of our galaxies have HI that extends beyond the stellar disk and exhibit regularly rotating disks, placing them in the D category of Serra et al. (2012). As pointed out in Serra et al. (2012), regularly rotating disks of HI have likely been in place for several gigayears, while less settled HI morphologies might be the result of recent accretion or interactions. We comment on the role of external events such as these below. We also calculated the concentration of the HI using the proxy R90 HI /R50 HI and found no clear trends with respect to ssfr or SFE. This could mean that the star formation suppression mechanisms acting on the gas are independent of the precise distribution of HI HI Radii and Masses The derived quantities described above are listed in Tables 4.2 and 4.3. We can compare the HI masses calculated from the VLA observations to the HI masses derived from the ALFALFA Arecibo observations as a check on the VLA observations. In general, the HI masses derived from the VLA are within 0.3 dex of the ALFALFA masses. There are four galaxies whose VLA mass deviates from the ALFALFA mass by more than 0.3 dex. These include 15607, 19918, and 47708, all of which have lower column density HI than most of 178

197 Table 4.2. Derived HI Quantities GASS ID AA ID log AA MHI log VLA MHI Flux R 90HI R 90opt Vhelio Frequency t int Noise M M Jy km s 1 kpc kpc km s 1 MHz hours mjy/beam/channel Table 4.3. HI and SFR Surface Densities a GASS ID Σ HI,RHI Σ HI,Ropt Σ HI,1Msun Σ SFR,RHI Σ SFR,Ropt Σ SFR,1Msun M pc 2 M pc 2 M pc 2 M kpc 2 M kpc 2 M kpc a All surface densities are shown in log base

198 the other galaxies in the sample. It is likely that the rest of the HI exists in an extended disk at even lower column densities that the VLA, with our several-hour integration times, was not sensitive to. If this is the case, then the HI radii should be considered lower limits and the HI surface densities upper limits. We found no evidence of radio continuum sources that could be absorbing the HI, artificially lowering the HI masses. Another galaxy with a low HI mass is Half of the data for this observation were corrupted and unusable so we didn t achieve the sensitivity we wanted. The HI measurements for should also be considered lower limits. We take the systematic and statistical errors on the HI masses as the lower and upper bounds on the errors. We take the systematic error to be 0.18 dex, the mean discrepancy between the ALFALFA and VLA masses. We calculate the statistical error on the HI mass to be 0.04 dex based on the average noise per channel of 0.5 mjy/beam. The error on the HI radius will scale with this error since our ability to calculate accurately the HI radius depends on our ability to detect HI. In Fig. 4.9 we compare R90 HI to R90 opt. All of the galaxies in our sample have HI disks that extend beyond the optical disks and almost all of the HI disks have radii that are twice as large as the optical radii. The median ratio of R90 HI /R90 opt is 2.6. There exists no obvious comparison sample since galaxies in the VLA sample span a wide range of morphologies and a narrow range of stellar masses and HI masses. The HI-to-optical ratio for our sample is higher than that for a sample of 68 early-type disk galaxies (S0-Sab) in Noordermeer et al. (2005), who report ratios of 1.72 for Sa/Sab galaxies and 2.11 for S0/S0a galaxies. While only 2 out of 68 galaxies in their sample have R HI > 40 kpc, almost all of 180

199 the galaxies in our sample have R HI >40 kpc. A noticeable difference between their sample and ours is that 18% of the galaxies in their sample have HI disks that lie within the stellar disks. They ascribe the smaller HI disks to ram-pressure stripping and other types of interactions because most of the galaxies with R HI < R opt show signs of interactions. Our results here are consistent with that found in Wang et al. (2013) for a sample of HI-rich galaxies, though their sample includes some galaxies with lower stellar masses and lower HI masses The Star Formation Law To understand the origin of the low ssfrs for galaxies in the VLA sample, it is crucial to determine not just the extent of their HI disks but also the surface density of HI within the HI disks. The HI surface density provides information about which types of suppression mechanisms are at work in these galaxies. Based on work showing that star formation is inefficient at low gas surface densities, low HI surface densities alone could explain low ssfrs. If galaxies in the VLA sample have high HI surface densities, then something else must be preventing the gas from forming stars. In combination with the SFR surface density, the HI surface density can tell us if these galaxies follow wellestablished relationships between cold gas and star formation, with both low gas and SFR surface densities as in the lower part of the star formation law, or if there is something unique about these galaxies. We compare the three calculations of HI surface densities in the left panel of Fig The HI surface density calculated within the 1 M pc 2 isophote and within R90 HI have 181

200 similar distributions. Since Fig. 4.6 shows that R90 HI and the 1 M pc 2 isophote map out similar regions, this is expected. Σ HI within the optical disk also has a similar distribution, with one exception at low surface densities that we will point out later. The similarities among the Σ HI ranges demonstrates that the HI is distributed close to uniformly within the galaxies. It is significant that all of the HI surface densities are below the critical surface density defined in Bigiel et al. (2008), above which most of the cold gas is in molecular form. We elaborate on this point below. We compare the three calculations of SFR surface densities in the right panel of Fig Σ SFR within the stellar disk is higher than the other measures of SFR surface density because most of the star formation is contained within the stellar disk. Σ SFR within the HI disk is lower since a similar amount of star formation is being averaged over a much larger surface area. A direct comparison between SFR and HI surface densities is in Fig Since GASS galaxies have single-dish HI measurements from Arecibo, which does not provide spatial information, we cannot compare the HI surface densities for the VLA galaxies directly to the HI surface densities for more typical galaxies. Instead, we first examine how well GASS and VLA galaxies follow theoretical predictions for the relationship between SFR and HI surface densities by assuming that their HI extents are typical, e.g. that half of the HI lies within the optical disk. We display these predicted surface densities for starforming and non-star-forming galaxies from GASS and for the VLA galaxies separately in the left panel of Fig We compare them to curves for Σ gas = Σ HI + Σ H2 from Krumholz et al. (2009), which match the observations in Bigiel et al. (2008). The GASS 182

201 galaxies lie close to the theoretical curve for galaxies with solar metallicities. The gasphase metallicities for these galaxies should be close to solar, although Moran et al. (2012) showed that HI-rich galaxies tend to have lower metalliticies beyond R 90. The theoretical curves include HI and H 2 and we only have HI measurements. Any measurable H 2 would shift the galaxies to the right in the plot. We highlight the surface density predictions for galaxies in the VLA sample, which overlap somewhat with the non-star forming galaxies but are further from the theoretical curves than the average galaxy. At this location, they lie below the star formation law with low SFR surface densities compared to their high HI surface densities. If this were their true location in this plane, then we would need to appeal to factors other than low HI surface densities that can prevent gas from forming stars. In the right panel of Fig we show the true locations of the HI-rich galaxies based on the VLA observations. It is significant that the HI-rich galaxies in the VLA sample lie remarkably close to the theoretical curve for solar metallicities and in the region of the plot in which the SFR surface density drops steeply as HI surface density also decreases. The location of the galaxies in the Σ SFR - Σ HI plane suggests that the relationship between cold gas and SFR surface densities in these galaxies conforms to theoretical expectations and that the discrepancy between their low ssfrs and high HI masses is simply due to the distribution of HI, which yields low gas surface densities. The outlier in this plot and the only galaxy with log Σ SFR < -5 is GASS 13340, which has the most extended HI disk and very little star formation. Although it appears that low HI surface densities could be a major reason for the low 183

202 total ssfrs in the VLA galaxies, other mechanisms likely contribute. As seen in Bigiel et al. (2008) and Leroy et al. (2008), at low gas surface densities a narrow range of gas surface densities can yield a wide range of SFR surface densities, which we also see in our sample. To explain this phenomenon, there must exist factors other than the gas surface density that regulate the relationship between cold gas and star formation. We consider factors related to the internal structure of the galaxy - concentration index and AGN classification. In Fig we show the Σ SFR -Σ HI plane again, indicating the concentration index and AGN classification for each galaxy. Some interesting trends are apparent, which point to the structure of the galaxy possibly playing a role in the suppression of star formation. In the left panel we indicate whether each galaxy has no AGN, a low signal-to-noise AGN, a weak AGN (with OIII luminosity < 10 7 ), or a spectrum indicating the presence of an AGN and star formation. Except for GASS 13340, evidence for the presence of an AGN becomes more common towards lower SFR surface densities. There exists a similar trend with respect to concentration, with more bulge-dominated galaxies exhibiting lower SFR surface densities. We discuss the implications of these trends below. 4.4 The Suppression of Star Formation in Massive HI-Rich Galaxies A number of factors regulate the relationship between cold gas and star formation, and although the HI maps move us closer to understanding the relationship between these 184

203 quantities in galaxies in the VLA sample, it is still difficult to draw firm conclusions. In the previous section we showed that low HI surface densities and the presence of a bulge might prevent HI-rich galaxies from forming stars at high rates. These situations are commonly invoked to explain low SFRs in quenched galaxies, but we emphasize that our galaxies are not quenched in the traditional sense: they have a surplus of cold gas and they are still forming stars, albeit at a low rate. In this section we delve into the observational and theoretical evidence for these star formation suppression mechanisms to understand not just if these mechanisms are acting in these galaxies but how we might be able to use additional data to draw firmer conclusions. We discuss in detail how AGN feedback and the presence of a bulge can suppress star formation and we describe why galaxies in the VLA sample might harbor long-lived low-surface-density HI disks. We also explain why recent gas accretion probably cannot account for the extreme HI masses in these galaxies. Finally, we discuss why galaxies with an unexpected combination of high HI masses and low ssfrs become common only at high stellar masses. We do not consider here environmental quenching mechanisms, such as ram-pressure stripping (e.g. Tonnesen et al. 2007), which remove substantial amounts of gas from galaxies, though it would be interesting to see if galaxies in the VLA sample are preferentially in extremely isolated environments, such as voids, where gas-rich galaxies are found with a higher frequency (Kreckel et al. 2012). We do know that the HI-rich galaxies are not cluster galaxies, but a thorough examination of their environments and a possible link between their environments and their gas and star-forming properties is beyond the scope of this work. 185

204 4.4.1 AGN Feedback AGN can inhibit star formation in at least three distinct ways, which can occur simultaneously but in different proportions within a given galaxy. AGN can remove potentially star-forming gas from galaxies via outflows; the energy released by AGN can contribute to the existence of a hot halo, preventing future gas accretion; and AGN can inject energy into the gas reservoir such that it is unable to collapse and form stars but stays within the galaxy. Most observational studies of star formation suppression via AGN focus on the detection of outflows as evidence that AGN can remove enough gas to significantly affect a galaxy s SFR (e.g. Cano-Díaz et al. 2012; Yuma et al. 2013; Förster Schreiber et al. 2014), but this type of suppression via AGN cannot explain the large cold gas contents in the HI-rich galaxies. The buildup of a hot halo that prevents future star gas accretion cannot explain why the cold gas already within the galaxy is stable against star formation, so is not helpful in explaining our results. The third scenario, in which AGN feedback disrupts the cold gas enough to prevent it from forming stars, could explain our results and is the scenario we discuss below. Because simulations have only just begun to include a multiphase ISM (e.g. Davé et al. 2013), to our knowledge none exist that specifically address how the HI that remains in a galaxy is affected by AGN feedback (though Gabor & Bournaud (2013) note that in gas-rich z 2 galaxies AGN feedback is not strong enough to disrupt dense clouds of star-forming gas). Observational studies of AGN hosts with measured HI masses show that HI can remain at high levels in galaxies with AGN: Ho et al. (2008) and Fabello et al. (2011b) show that AGN hosts contain just as much HI as do their counterparts without 186

205 AGN. If massive galaxies can simultaneously contain AGN and large HI reservoirs, how, if at all, is the AGN affecting the HI reservoir? Direct observational evidence of this is lacking, but Nesvadba et al. (2010) show how AGN feedback prevents the molecular gas from forming stars in the H 2 -luminous radio galaxy 3C 326 N. Like the HI-rich galaxies in this chapter, 3C 326 N contains a substantial amount of cold gas (M H2 = 10 9 ) but a surprisingly low SFR. They found that mechanical energy from the AGN that was injected into the ISM heated the molecular gas enough to make it stable against star formation but still detectable as H 2. It is possible that a similar mechanism that heats the HI is at work in some of the massive HI-rich galaxies discussed here. If this is so, HI-rich galaxies with AGN should have a lower SFR surface density than comparison galaxies with the same HI surface density. In Fig we show that this is indeed the case: galaxies with lower SFR surface densities tend to have evidence of an AGN. However, the only true AGN in the VLA sample are weak, with OIII luminosities less than 10 7 L, so it is unclear if they are powerful enough to affect the large quantities of gas in galaxies in the VLA sample Morphological Quenching One way in which star formation can be suppressed without removing or heating the cold gas is via morphological quenching, in which a galaxy s bulge stabilizes its gas disk against star formation. Martig et al. (2009) explain that gas disks embedded in bulge-dominated galaxies may exhibit SFRs a factor of 10 lower than similarly massive gas disks in spiral 187

206 galaxies for two reasons: bulge-dominated galaxies lack a stellar disk that contributes to the self-gravity of a gas disk and naturally have higher epicyclic frequencies, which can increase the Toomre Q parameter above the critical value for star formation. This scenario is also seen in simulations at redshift z 2 (Agertz et al. 2009; Ceverino et al. 2010) and is supported by observations at z 2 in which star-forming galaxies have higher values of Q at their centers where a bulge dominates (Genzel et al. 2014). In the local universe, lower HI and H 2 SFEs in bulge-dominated galaxies compared to late-type galaxies provide some evidence for morphological quenching (Saintonge et al. 2012). Martig et al. (2013) find that the effectiveness of morphological quenching depends on the precise gas content of the galaxy. Early-type galaxies with low cold gas fractions (1.3% in their simulation) contain gas disks that are stable against star formation and do not fragment. Early-type galaxies with higher gas fractions (4.5% in their simulation) have gas disks that do fragment but form stars less efficiently than similar gas disks embedded in a spiral galaxy because a smaller fraction of their cold gas is in a very dense (> 10 4 ) phase. The reduced fragmentation due to morphological quenching effectively lowers the fraction of cold gas in dense phases, which in turn lowers the global efficiency of star formation. Taking into account the range of possible gas fractions, Martig et al. (2013) report that gas disks embedded in bulge-dominated galaxies form stars 2-5 times less efficiently than do gas disks with a similar gas surface density embedded in spirals. While a direct comparison between the Martig et al. (2013) simulations and our HIrich galaxies is impossible because the HI-rich galaxies in this chapter have much higher gas fractions, ranging from 15% to over 60%, their results suggest that bulges could play 188

207 a role in lowering the SFE in some of our HI-rich galaxies. Martig et al. (2013) emphasize that morphological quenching is not strong enough to drive the evolution of all galaxies onto the red sequence, but could be a contributing factor alongside other quenching mechanisms. Martig et al. (2013) show in the radial profiles of their simulated galaxies that the gas surface density increases to greater than 10 2 M pc 2 at the centers of the galaxies. The gas in this density regime is likely molecular, which would create a central hole in a map of the HI flux. Some galaxies in the VLA sample do exhibit an HI depression in the center. If galaxies with little HI in their centers do have central H 2 and no sign of central star formation, this could be evidence of morphological quenching. If the center lacks cold gas altogether, it is unclear if morphological quenching is at work. H 2 observations of galaxies in the VLA sample could bring clarity to this scenario. Since all of the HI-rich galaxies described here have high gas fractions, which Martig et al. (2013) find lower the effect of morphological quenching, and most have low gas surface densities, which according to Martig et al. (2013) heighten the effect of morphological quenching, we cannot draw any definitive conclusions about the effect of morphological quenching in our sample except to say that it could be playing a role in the more highlyconcentrated galaxies based on the recent simulations and observations demonstrating its effects. In Figure 4.12 we identify the HI-rich galaxies based on their concentration index; there is some evidence that the more bulge-dominated galaxies have lower SFR surface densities at a given HI surface density, though it is unlikely that morphological quenching can affect the very extended gas disks in the VLA sample. Morphological quenching is 189

208 unlikely to play a role in less bulge-dominated galaxies Below-Threshold Cold Gas Inefficient star formation can result from low cold gas surface densities, which can be present in HI-rich galaxies if the HI extends over a large surface area. As noted above, HI disks generally extend well beyond stellar disks, and this is something we see in the VLA sample as well. Galaxies selected by HI tend to be more extended than those that are selected optically (Huang et al. 2012). Extended HI disks will form stars inefficiently only if the disks do not contain substantial amounts of H 2, the immediate precursor to star formation. Observations confirm that the outskirts of gaseous disks tend to be HI-dominated. Bigiel et al. (2008) show that in local spirals, HI extends well beyond the radius at which SFR and H 2 become negligible. In Leroy et al. (2008) the molecular fraction, Σ H2 /Σ HI, decreases steadily with radius, and in Martin & Kennicutt (2001) the total (HI + H 2 ) gas surface density profile decreases more quickly than the HI surface density profile. Schaye (2004) shows that extended gas disks tend to be HI-dominated because the transition from the neutral to the molecular phase proceeds efficiently only above a critical gas surface density of 3-10 M pc 2. A critical surface density of 9 M pc 2 is confirmed observationally by Bigiel et al. (2008), above which cold gas is mostly molecular. Our observed galaxies have HI surface densities that fall below the critical gas surface density, indicating that the gas disks in the VLA sample are likely HI-dominated. Where HI dominates over H 2, star formation necessarily proceeds at a slower rate. Observations 190

209 show that in the outskirts of galaxies where HI dominates, and in dwarfs that are HIdominated throughout, the local SFE decreases with radius (Bigiel et al. 2008; Leroy et al. 2008). Integrated and local measurements show that there is a break in the star formation law such that at gas surface densities below the critical density, galaxies exhibit SFR surface densities a factor of 5 below the extrapolation of the star formation law at higher gas surface densities (Wyder et al. 2009; Bigiel et al. 2008). Wyder et al. (2009) show that this downturn, which is equivalent to a lowering of the SFE at low gas surface densities, agrees with work by Krumholz & McKee (2005) and Blitz & Rosolowsky (2006) predicting lower H 2 fractions in low surface density gas. The galaxies in the VLA sample lie in the part of the star formation law in which star formation is least efficient. Thus, the low ssfrs in the galaxies in the VLA sample are reasonable given their HI surface densities. For the phenomenon of extended, low surface density HI disks to be common, the extended HI disks must be long-lived. Simulations have shown that extended low surface density gaseous disks may result when galaxies accrete from the IGM cold, dense filaments, which have higher angular momenta than the dark matter halo and prevents efficient gas transport to the disk (Kimm et al. 2011; Stewart et al. 2011). A more likely scenario for the massive galaxies in the VLA sample, which might not accrete gas directly from cold filaments in the IGM, is described in Lu et al. (2014). They show that extended gas disks with HI surface densities below the critical density for star formation can result when the gas disks are built up by gas cooling from large radii within the hot halo. Populations of galaxies in the local universe that are defined by inefficient outer star formation include GLSBs and XUV-disks. Galaxies in the VLA sample might be 191

210 analogs of GLSBs: in Fig. 1 we show that GLSBs and the VLA sample lie in the same region of the HI gas fraction - stellar mass plane. The prevalence of XUV-disks (Chapter 2; Lemonias et al. 2011; Thilker et al. 2007) confirms that inefficient star formation in extended disks is common. Galaxies in the VLA sample are probably not XUV-disks (except for 45664) because their UV images do not show evidence of recent star formation within the extended HI, but galaxies in the VLA sample and XUV-disks might represent different stages of the life of an extended HI disk Recent Gas Accretion If galaxies in our sample recently accreted cold gas, it is possible that the gas simply hasn t been in the galaxy long enough to collapse and form stars. Kereš et al. (2005) show that it generally takes 0.5 Gyr for the cosmic SFR to react to new gas accretion. To determine whether this scenario could account for the high HI masses and low SFRs of galaxies in our sample, we must consider, first, whether we expect galaxies at this mass scale to be accreting gas and at what rate, and, second, whether we see any evidence of recent accretion in the optical images and HI maps. Simulations have shown that the ways in which galaxies accrete gas depend on their mass, environment, and redshift. At z 0, gas that is accreted onto galaxies above a critical halo mass is shock heated to the virial temperature and likely stays warm (Birnboim & Dekel 2003; Dekel & Birnboim 2006; Kereš et al. 2005). Gas that is accreted onto galaxies below the critical halo mass tends to enter a galaxy in the form of cold streams from the IGM. Depending on the precise way in which one relates halo mass to baryonic mass, this 192

211 critical mass could lie just below the stellar mass at which many HI-rich galaxies with low SFRs are found. Thus, galaxies like those in our sample are probably accreting gas that is shock-heated and it is unclear whether that will ultimately cool into HI. For recent accretion to account for the large amount of excess HI in our HI-rich galaxies, we would expect to see large tidal features indicative of major accretion events in the HI maps or optical imaging. We do not see any obvious signatures of accretion events in the VLA sample and the HI maps suggest that galaxies in the VLA sample have regularly rotating, settled disks. GASS is the possible exception, with an HI distribution whose peak is offset from the stellar disk. The regions with the strongest HI emission exhibit prominent spiral arms, but other regions with significant HI do not have signs of star formation. This combination of UV-bright features embedded in an extended HI disk that does not show signs of star formation elsewhere suggests that we are seeing this galaxy in the process of re-building its stellar disk after a major accretion event. In this initial study of HI morphologies, we cannot assess the distribution and kinematics of the HI at the level done by Sancisi et al. (2008) because our observations do not have the required depth. That type of analysis could reveal lesser accretion events based on the presence of gas at anomalous velocities, but such lesser accretion events are unlikely to yield the high HI masses in the VLA sample. It appears that much of the cold gas in galaxies in the VLA sample has been retained as the galaxies evolved since there is no evidence that major episodes of accretion brought in large amounts of cold gas. 193

212 4.4.5 The Emergence of Low-Star-Forming HI-Rich Galaxies at High Stellar Masses and the Role of H 2 The results of our analysis of HI-rich galaxies in Section 2 are twofold: 1) that a population of HI-rich galaxies with surprisingly low ssfrs exists, and 2) that this population primarily exists above a stellar mass of log M = HI imaging allows us to understand the suppression of star formation in these galaxies. A separate question is why galaxies with an excess of HI compared to their SFRs become common above a threshold stellar mass. Some evidence exists to show that as stellar mass increases, not only do ssfrs decrease, but so does the efficiency with which galaxies convert their cold gas into stars. Young et al. (2013) show that cold gas (HI or H 2 ) content up to 10 9 solar masses does not measurably affect the UV-optical colors of massive (log M > 10.7) galaxies. They also find that less massive early-type galaxies with cold gas are blue while more massive early-type galaxies with measurable cold gas are red. Even when massive galaxies have significant amounts of H 2, which is one step closer to forming stars than HI, they are unlikely to form stars at a high rate. Although the HI-based SFE is constant with respect to stellar mass (Schiminovich et al. 2010), the H 2 -based SFE decreases as stellar mass increases (Saintonge et al. 2011b). Young et al. (2013) show that massive galaxies have older single stellar population ages than less massive galaxies with the same H 2 fraction. Together, these findings present a picture in which the most massive galaxies do not form stars even if they have the cold gas necessary to do so. A significant HI mass compared to SFR could be a sign that a galaxy is lacking H 2 and is suffering from inefficient conversion from HI to H 2. Huang et al. (2012) suggest 194

213 this is why their HI-selected sample has lower SFEs than an optically selected sample. An abundance of HI compared to H 2 might be more common in more massive bulgedominated galaxies. Saintonge et al. (2011a) find that the detection rate of HI and H 2 drops significantly among more bulge-dominated galaxies and that above these detection thresholds, galaxies have mostly HI if they have any cold gas at all. Similarly, red galaxies are more likely to be detected in HI than H 2 (Young et al. 2013). Lee et al. (2014) measure the H 2 in 28 HI-rich galaxies with stellar masses and HI masses similar to those for our sample. 15 out of 20 normal galaxies and 4 out of 8 LSB galaxies were detected. Their high H 2 contents place them at the high end of the H 2 gas fraction distribution shown in Saintonge et al. (2011a), but their cold gas reservoirs are still dominated by HI over H 2 by a factor of 2 to 3. Although our sample was selected differently from theirs to include only HI-rich galaxies with low ssfrs, there is still no evidence that HI-rich galaxies in general are molecular-dominated. Although we do not have H 2 measurements for the VLA sample, we assume based on the results of Saintonge et al. (2011a); Young et al. (2013); Lee et al. (2014) and on the low ssfrs in these galaxies that they do not contain significant quantities of H 2. What, then, is hindering the conversion from HI to H 2 in massive galaxies? Fu et al. (2010) predict that a high spin parameter λ (usually associated with more massive galaxies) is related to less efficient HI-to-H 2 conversion. Huang et al. (2012) show that at a given stellar mass, galaxies with higher HI fractions are in dark matter halos with higher spin parameters, which probably means that they are more extended since their halos have higher angular momenta. Although this phenomenon is no longer obvious at stellar 195

214 masses above M 10.5, Huang et al. (2012) generally find that HI-selected galaxies reside in halos with high spin parameters and are more extended. If massive HI-rich galaxies tend to have more extended HI disks than is typical, then the conversion from HI to H 2 must be weak because much of the gas lies beyond the radius at which the conversion proceeds efficiently (Schaye 2004). 4.5 Summary and Conclusions We used two recent large HI surveys, GASS and ALFALFA, to define and select a sample of massive galaxies (log M /M > 10) that are extremely HI-rich for their stellar mass. The HI-rich galaxies have HI fractions in the top 5% for their stellar mass and have HI masses greater than M. Within the HI-rich sample, we examined the relationship between HI and star formation as a function of stellar mass. We found that even though the HI fractions of the HI-rich galaxies decrease with stellar mass, their ssfrs decrease at a stronger rate. This trend of decreasing ssfrs revealed a sample of HI-rich galaxies with surprisingly low ssfrs at the high end of the stellar mass range (log M /M > 10.5). To understand the physical conditions producing this unexpected combination of very high HI masses and lower ssfrs, we obtained HI maps at the VLA of 20 of these galaxies. The HI maps yield the distribution of the HI along with the extent and surface density of the HI within the HI disk. We found that the HI surface densities are low enough that the galaxies fall in the region of the Σ SFR -Σ HI plane in which inefficient star formation is common. In this regime, a narrow range of HI surface densities can yield a wide range of SFR surface densities. 196

215 Because the HI surface densities for the galaxies in the VLA sample are low, their low ssfrs are not unexpected. But other conditions, including the internal structure of the galaxies, could also contribute to their low ssfrs. We found that galaxies with the lowest SFR surface densities are more likely to be bulge-dominated and exhibit stronger evidence of AGN. However, because bulge-dominated galaxies are generally more likely to host AGN, it is unclear whether the AGN or the structure of the galaxy (in the form of morphological quenching) is contributing to the suppression of star formation. Future observations of the molecular gas in these galaxies could provide some insight. A more detailed morphological analysis of the HI akin to that in Holwerda et al. (2011) could also provide some clues, but the distances to these galaxies coupled with the short integration times of the observations described here make that type of work less robust. It is not obvious that the same star formation suppression mechanisms must operate in other types of galaxies with less HI, but it is worth considering how these results might apply to other populations of galaxies with low ssfrs. Since all of the galaxies in the VLA sample have low HI surface densities, there is no strong evidence that high concentration index or AGN are driving the low ssfrs, but they seem to be contributing. As we have shown, ascertaining the driving factor behind suppressed star formation is not straightforward even when maps of the cold gas are available. Nevertheless, it could be worth examining in further detail how the HI distributions and HI surface densities vary with stellar mass within populations of galaxies with less cold gas to see if the same conditions apply in less extreme galaxies. Of course some massive galaxies have low ssfrs because they lack the cold gas necessary for star formation to proceed, but we have 197

216 shown that star formation drops with stellar mass even among populations of galaxies that have extremely high quantities of HI, so other conditions must be at work in the broader population. Although galaxies in the VLA sample appeared to challenge the star formation law with their unexpected combination of high HI masses and low ssfrs, the sample actually conforms to the global star formation law. We have shown that the star formation law is an important tool for understanding the relationship between gas and star formation in galaxies that appear to be outliers. Placing other atypical galaxies, such as XUV-disks, GLSBs, or galaxies transitioning between the red and blue sequences, on the Σ SFR -Σ HI plane could improve our understanding of these important populations. 4.6 Appendix Notes on Individual Galaxies Red galaxy with faint extended features. Double-horned profile in ALFALFA. Very faint signal in the UV Inclined, possible S0. Blue, edge-on galaxy less than 1 arcminute away with no redshift. Double-horned profile in ALFALFA Face-on spiral with possible ring and faint blue outer structure. This galaxy is at z=0.035; reddish spiral 2 arcminutes away at z= Very narrow, highly peaked double-horn profile in ALFALFA Broad ALFALFA spectrum with one narrow peak on one side Tightly wound spiral. Lopsided double-horned profile in ALFALFA. Strong UV flux extends to edge of faint optical disk. 198

217 25285 Tightly wound spiral with blue arms. Double-horned profile in ALFALFA. Two lobes of HI on each side of galaxy. Half of VLA data were corrupted Tightly wound spiral with at least one faint, blue, extended arm. Very strong double-horn structure in ALFALFA spectrum. Strong UV flux extends beyond main stellar body Reddish main body with faint blue outer arms. Double-horned spectrum in ALFALFA Reddish featureless galaxy with faint extended structure and one prominent blue tail/arm. Wide double-horned spectrum in ALFALFA. UV flux coincides only with main stellar body Reddish tightly wound spiral. UV flux coincides only with main stellar body Inclined spiral. Wide ALFALFA spectrum with peak only at low-velocity end Reddish center with blue flocculent spiral arms in outskirts of galaxy. Doublehorned profile in ALFALFA Inclined spiral. Broad and faint ALFALFA spectrum. Strong UV flux through main stellar body. Two HI lobess on each side of galaxy, maybe indicative of an HI ring Ring-like galaxy with very extended diffuse light. Blue arm of star formation 20 arcsec away from galaxy and unattached (in optical). Double-horned profile in ALFALFA. Best spectral window had bad data; very close to edge of spectral window used here Featureless elliptical with two very long blue arms that are strong in the UV but appear unattached to main galaxy at optical wavelengths. More bright, patchy UV surrounds galaxy. This galaxy is at z=0.0364; red barred spiral 1 arcmin to the north at 199

218 z= Another at 2 arcminutes at z= Broad, uneven ALFALFA spectrum, sloping upwards at higher velocities. Several bright patches of HI, many of which coincide with bright patches in UV Featureless elliptical at optical wavelengths. Very little UV flux. Blue edge-on galaxy 3 arcminutes away at same redshift. Red edge-on galaxy 2.5 arcminutes away at similar redshift. Reddish inclined galaxy 1 arcmin away at similar redshift. Faint blue spiral very nearby at same redshift. Is this a group or overdensity? Lopsided ALFALFA spectrum with more flux at low velocities Edge-on galaxy with strong dust lane. Very little UV flux. Broad and faint ALFALFA spectrum. Prominent HI structure offset from but in line with galaxy Early-type barred spiral. UV flux extends beyond main stellar body. Triplepeaked spectrum in ALFALFA Spiral with tightly wound blue arms and knot of star formation at the tip of an arm. UV flux coincides with optical flux. Double-horned profile in ALFALFA, with much stronger peak at higher velocities. 200

219 Figure 4.6 HI intensity and velocity maps for galaxies in the VLA sample, 5 arcminutes on a side. The column on the far left shows the HI intensity maps with lines of constant surface brightness indicated (red, green, and blue contours indicate 0.2, 1.0, and 5.0 M pc 2 ). The scalebar indicates 20 kpc. The next column shows the velocity maps; the velocity range for each map roughly corresponds to the velocity ranges in Fig The third and fourth columns show the surface brightness contours overlaid on the SDSS r-band and GALEX NUV images. Blue dashed ellipses indicate R90 HI and red dashed ellipses indicate R90 opt. 201 The beam size is shown in the lower left corner. SDSS and GALEX images were scaled to the same resolution as the HI maps and were obtained from the NASA-Sloan Atlas and MAST.

220 Figure 4.7 See caption for Fig

221 Figure 4.8 See caption for Fig