ABSTRACT VARIABILITY OF HOT SUBDWARF STARS FROM THE PALOMAR-GREEN CATALOG OF ULTRAVIOLET EXCESS STELLAR OBJECTS

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2 ABSTRACT VARIABILITY OF HOT SUBDWARF STARS FROM THE PALOMAR-GREEN CATALOG OF ULTRAVIOLET EXCESS STELLAR OBJECTS This thesis presents a survey for variability in 985 objects identified as hot subdwarf stars by the Palomar-Green Catalog of Ultraviolet Excess Stellar Objects. Catalina Real-Time Transient Survey (CRTS) light curves are used to find the variability. Landolt standard stars that are also hot subdwarf stars in the Palomar-Green Catalog are used to calibrate CRTS photometry in the visual (V) band, and show it is accurate to within ΔV = 0.1 magnitudes between V = 12.0 and V = Eleven objects are found to have variability that exceeds four standard deviations above the means of their CRTS light curves. Two are objects already known to be variable. They are PG (Mrk 421), a BL Lac object, and PG , a short-period, pulsating sdb star. The other nine are new discoveries of variability: PG , PG , PG , PG , PG , PG , PG , PG , and PG PG is a spectrophotometric standard of Massey et al. (1988): this discovery of its variability shows that it should not be used as a standard. PG is identified as a BL Lac object. More tentative identifications include PG as an AM CVn star, PG and PG as dwarf novae, and PG as an eclipsing binary star system. Detailed follow-up observations are needed for the other variables, although they may be pulsating hot subdwarf stars. Melissa Blacketer December 2015

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4 VARIABILITY OF HOT SUBDWARF STARS FROM THE PALOMAR-GREEN CATALOG OF ULTRAVIOLET EXCESS STELLAR OBJECTS by Melissa Anne Blacketer A thesis submitted in partial fulfillment of the requirements for the degree of Master of Physics in the College of Science and Mathematics California State University, Fresno

5 APPROVED For the Department of Physics: We, the undersigned, certify that the thesis of the following student meets the required standards of scholarship, format, and style of the university and the student's graduate degree program for the awarding of the master's degree. Melissa Anne Blacketer Thesis Author Frederick A. Ringwald (Chair) Physics Gerardo Munoz Physics Douglas Singleton Physics For the University Graduate Committee: Dean, Division of Graduate Studies

6 AUTHORIZATION FOR REPRODUCTION OF MASTER S THESIS X I grant permission for the reproduction of this thesis in part or in its entirety without further authorization from me, on the condition that the person or agency requesting reproduction absorbs the cost and provides proper acknowledgment of authorship. Permission to reproduce this thesis in part or in its entirety must be obtained from me. Signature of thesis author:

7 ACKNOWLEDGMENTS I would like to thank the Department of Physics faculty at California State University, Fresno for their endless support and encouragement I received since day one. I thank the College of Science and Mathematics of California State University, Fresno for a Faculty Sponsored Student Research Award, which allowed me to share my research with the top scientists in the field of astronomy at the American Astronomical Society meeting in Boston. Also much thanks to the Department of Physics of California State University, Fresno for support through a teaching assistantship. Many thanks to the Catalina Real-Time Transient Survey (CRTS) for their photometry used in this research. The Catalina Sky Survey (CSS) is funded by the National Aeronautics and Space Administration under Grant No. NNG05GF22G issued through the Science Mission Directorate Near-Earth Objects Observations Program. The CRTS survey is supported by the U. S. National Science Foundation under grants AST and AST This research has made use of data obtained from, and software provided by, the US Virtual Astronomical Observatory, which is sponsored by the National Science Foundation and the National Aeronautics and Space Administration (NASA). This research has made use of the SIMBAD database, operated by CDS, Strasbourg, France. This research has also made use of NASA's Astrophysics Data System Bibliographic Services. Last but certainly not least, I would like to thank my family for their endless love and support. To Danny Guice, thank you for believing in me even when I didn t. I could not have done this without you.

8 TABLE OF CONTENTS Page LIST OF TABLES... ix LIST OF FIGURES... x INTRODUCTION... 1 What Are Hot Subdwarf Stars... 1 Formation Theories... 7 Hot Subdwarf Research RESEARCH PROGRAM Palomar-Green Catalog Catalina Real-Time Transient Survey Types of Variability Method OBSERVATIONS AND ANALYSIS Analysis Part I Analysis Part II Calibration List of Standard Stars List of PG Hot Subdwarf Stars Part I List of PG Hot Subdwarf Stars Part II RESULTS AND DISCUSSION PG PG PG PG

9 viii Page PG PG PG PG PG PG PG CONCLUSION... 82

10 LIST OF TABLES Page Table 1: PG highest stars on Figure Table 2: PG hot subdwarf stars and related objects significant variance Table 3: PG highest variable stars on Figure Table 4: PG hot subdwarf stars and related objects significant variance Table 5. PG Standard Stars from Figure Table 6. PG Standard Stars from Figure Table 7. PG Standard Stars from Figure Table 8: The candidates... 84

11 LIST OF FIGURES Page Figure 1. This Hertzsprung-Russell diagram shows the placement of the hot subdwarf stars sdb and sdo on the extreme horizontal branch (EHB). (Heber U. 2009, ARAA, 47, 211)... 4 Figure 2. Diagram of the stellar evolution of a typical 1 solar mass star. The evolution starts on the MS curve, and progresses to the red giant branch (RGB), to the horizontal branch, to the AGB, planetary nebula phase, and down to the last stage white dwarf stars. (Carrol, B., Ostlie, D., 2007, Introduction to Modern Astrophysics, 2 nd ed.)... 6 Figure 3. Roche lobe equipotential surface diagram of two masses M 1 and M 2. L 1, the inner Lagrangian point is pictured between the two masses, at the apex of the tear-drop shape. The arrows indicate direction of force a test mass would experience at that location. (Boehm-Vitense 1989)... 9 Figure 4. The theoretical formation channels for hot subdwarf stars: Roche lobe overflow, Common Envelope phase, and two white dwarf mergers. (Heber 2009) Figure 5. This figure shows the first half of each star's average magnitude against their standard deviation Figure 6: This figure shows the second half of each star's average magnitude against their standard deviation Figure 7. Average magnitude of the PG standard stars from Landolt (1992a, 1992b) plotted against each stars standard deviation Figure 8. Light curve of PG Figure 9. Light curve of PG Figure 10. Light curve of PG Figure 11. Light curve of PG Figure 12. Light curve of PG Figure 13. Light curve of PG Figure 14. Light curve of PG

12 xi Page Figure 15. Light curve of PG Figure 16. Light curve of PG Figure 17. Light curve of PG Figure 18. Light curve of PG

13 INTRODUCTION Stars are formed within clouds of gas and dust that collapsed upon themselves due to their own gravity. As a cloud condenses its center starts to heat up and if there is sufficient mass the core will eventually become hot enough to ignite nuclear fusion. The differences between stars, for example, mass, density, temperature, or surface gravity, can lead to extraordinarily different lives. This is especially evident in the variety of ways in which stars live out the end of their lives and eventually, their deaths. A star that is born with low mass and a star that is born with high mass will have dramatically different outcomes. The late stages of stellar evolution are critical to understanding the stellar evolution of stars. It gives insight into how the stars are formed, as well as the future state of similar stars and the evolution of galaxies. What Are Hot Subdwarf Stars The Hertzsprung-Russell diagram, or H-R diagram, was created in 1912 by Ejnar Hertzsprung, and refined in 1913 by Henry Norris Russell. It is a plot of luminosity, or power output, as a function of temperature for stars. Since absolute magnitude measures luminosity, and since spectral type is determined by temperature, the H-R diagram gives astronomers insight into stellar evolution. The H-R diagram shown below in Figure 1 can be plotted with surface temperature (with higher temperatures towards the left), spectral classification (OBAFGKM where O-types are the hottest and M-types are the coolest stars), or color on the horizontal axis, versus absolute magnitude or luminosity (in comparison to the Sun) on the vertical axis. Other information the H-R diagram provides includes stellar mass and radius.

14 2 There are five main regions where stars group together. The diagonal grouping that runs from the upper left to the lower right is called the main sequence. Main sequence (MS) stars are all stars that have nuclear fusion in their cores, in which hydrogen is being converted into helium. Most stars spend a majority of their lives on the main sequence, and depending on their initial masses can finish their lives quite differently. The mass of the stars, although not explicitly on the H-R diagram, are still inferred by a star s position on the main sequence curve. One can calculate a MS star s mass from the luminosity, called the mass-luminosity relation. This mass-luminosity relationship for MS stars is mathematically expressed as: L = ( M ) ).+ L "#$ M "#$ From the expression, the bigger the star s mass, the brighter the star, and the masses increase to the top left of the curve. While a star is on the MS, it is maintaining hydrostatic equilibrium where the hot core produces thermal pressure pushing outwards and is equally balanced by the inward pull from the gravitational collapse of the gas. Just above the MS curve is the region of stars called Giants. These stars have larger radii, as the name suggests, and in general greater luminosity than MS stars. The more massive stars will live much shorter lives, as they will burn through energy much quicker (since E = mc 2 ). A star will become a giant star after leaving the MS. To leave the MS means the star has started to lose hydrostatic equilibrium. This is because stars only have a limited supply of hydrogen for fusion, and at that transition point, has depleted its hydrogen supply in the core. Now there will be more helium in the core, and the star will begin fusion of the

15 3 shell of hydrogen surrounding the core. The core will begin to contract and the outer layers will expand. A star can also leave the MS and join the Supergiant branch, which is located above the Giant branch. Where a star ends up directly after the MS curve depends on the stars initial mass. After becoming a giant star or supergiant star, the star has several evolutionary channels. A star like the Sun will eventually become a white dwarf, where its outer layers are thrown outward as a planetary nebula, leaving behind the dense core. Stars that are ten times (or more) the mass of the Sun will explode in a supernova, leaving behind a neutron star (a star made entirely of neutrons), or a black hole. White dwarf stars are seen below the MS curve. As mentioned above, a white dwarf is the stellar remnant, the core of a star, which has expelled its outer layers. It is composed of electron-degenerate matter, which is where electrons are so densely packed together that they stop the collapsing of matter because of the Pauli Exclusion Principle. For a diagram representation of the stellar evolution of a 1 solar mass star, see Figure 2 below. Most of these diagrams do not however, depict the star that is the topic of this thesis: hot subdwarf stars.

16 4 Figure 1. This Hertzsprung-Russell diagram shows the placement of the hot subdwarf stars sdb and sdo on the extreme horizontal branch (EHB). (Heber U. 2009, ARAA, 47, 211) Since the discovery of hot subdwarf stars, the Hertzsprung-Russell diagram has been modified to include these stars. The modified diagram is pictured in Figure 1. Hot subdwarf stars are found at the blue end of the extreme horizontalbranch (EHB) which lies between the main sequence and the white dwarf sequence. It is believed the EHB stars are the evolutionary step after a star has undergone the red giant phase. There are two main types of these hot subluminous stars. The spectral type O subluminous stars (sdo) and the spectral type B subluminous stars (sdb). These

17 5 stars have canonical masses of ~0.5 M, blue colors, effective temperature (T.// ) from 20,000 K to 100,000 K, and logarithm of surface gravity (log g) between 4.0 to 6.5 dex. In general, therefore, hot subdwarf stars have higher surface gravity than the Sun, with log g = dex. They are core helium-burning stars with a thin hydrogen envelope, and are thought to evolve directly into white dwarf stars by avoiding the asymptotic giant branch (AGB) (Heber et al. 1984; Heber 1986). In other words, as these stars die, they increasingly resemble hot rocks, and become less like gaseous MS stars, such as the Sun. SdB stars spectroscopically form a homogenous class, have hydrogen dominated atmospheres, T.// between 20,000 K and 40,000 K, log g between 5.2 to 6.5 dex. SdO stars have a wide variety of spectra, have helium rich atmospheres, T.// between 40,000 K and 100,000 K, and a log g between 4.0 and 6.5 dex (Oreiro et al. 2004). It is unknown how these stars were able to lose enough mass to leave behind such a thin inert hydrogen layer after leaving the red giant branch. During the last stages in a red giant star, the hydrogen burning shell surrounding the core will continue to add helium into the core. As it continues to dump helium into the core, the core will continue to heat up. Eventually, the collapsing core will be so densely packed, that the core will become degenerate, halting the contraction. Yet the hydrogen burning continues, dropping more helium into the core, continuing to heat up the core, until there is a thermonuclear runaway. This is the helium flash. The helium is ignited and burned for just a few minutes but can release as much energy as an entire galaxy. The helium flash makes the star no longer degenerate, and then the star behaves as a gas again (Schneider and Arny 2009). After this, the red giant star moves to the horizontal branch, which is not the EHB but lies (not pictured) roughly between the giants and MS curve. It is a horizontal branch of stars with roughly the same luminosities but different temperatures. After this, the

18 6 star would then move up to the AGB. It is thought the hot subdwarf phase occurs right after the red giant phase, but in this case, the star has skipped the AGB phase and evolves into a white dwarf. Therefore, the red giant star must have lost all of its envelope at the tip of the red giant branch to make a hot subdwarf star. Figure 2. Diagram of the stellar evolution of a typical 1 solar mass star. The evolution starts on the MS curve, and progresses to the red giant branch (RGB), to the horizontal branch, to the AGB, planetary nebula phase, and down to the last stage white dwarf stars. (Carrol, B., Ostlie, D., 2007, Introduction to Modern Astrophysics, 2 nd ed.)

19 7 Formation Theories Currently, the exact channels that lead to the formation of hot subdwarf stars are still unknown. There are, however, three main leading theories: Roche Lobe overflow, Common Envelope phase, and two white dwarf mergers. The formation channels of hot subdwarf stars continue to be extensively studied. Most stars in the sky are in binary systems, which means two or more stars orbit around a common center of mass. Binary interaction between stars could result in the formation of hot subdwarf stars since it could explain the required mass loss. Binaries can be identified in several ways: resolving them visually, spectroscopically, photometrically, or in eclipsing systems. Since most stars are found to be in pairs or multiples, it is critical to understand how these stars interact with each other. If the distance between the two stars in a binary system is not too great, one phenomenon that could account for how hot subdwarf stars are formed is called Roche Lobe overflow (RLOF). There is a region of space around a star where gas will be gravitationally bound to that star. Consider the situation where there are two stars orbiting one another about their common center of mass, a relatively short distance apart compared to their sizes, and orbit in a circular path. The reference frame will be rotating with the binaries with the coordinate system centered at the common center of mass. Close to each star s center of mass, the gravitational equipotential is spherical. Further out, the equipotential surface will distort, as gravity from the stars begin to affect one another (Paczynski 1971). The distortion caused by the two stars will be roughly teardrop shaped and are referred to as Roche lobes. Figure 3 below shows the equipotential surfaces of this scenario. The shape of the Roche lobe depends on the mass ratio. Paczynski noted that one can measure the size of the Roche lobe by the average radius r which is

20 8 defined so that 0 ) πr) is equal to the volume within the Roche lobe (Paczynski 1971). The formulae by Paczynski for the radius is calculated as follows: = log > 4 >? for 0.3 < > 4 >? < = B C 5 ) D ( > 4 > 4 E>? ) 4 D for 0 < > 4 >? < 0.8 The point where the two potential surfaces touch between the two stars, is called the inner Lagrangian point L 1. At this point, there is no net force acting on any mass at this point. The mass will stay at that position relative to the two stars and rotate with them. This location is unstable, however, and a slight perturbation will cause the mass to move. If the star fills its Roche lobe up to the L 1 Lagrangian point, then the companion star can then accept the over flowing mass and accrete this mass. This dynamical mass transfer can account for the thin hydrogen envelope observed in hot subdwarf stars (Han et al 2002, 2003).

21 9 Figure 3. Roche lobe equipotential surface diagram of two masses M 1 and M 2. L 1, the inner Lagrangian point is pictured between the two masses, at the apex of the tear-drop shape. The arrows indicate direction of force a test mass would experience at that location. (Boehm-Vitense 1989) It is possible that both stars can fill or overflow their Roche lobes. If one star is transferring matter to a companion star by means of RLOF, the companion star may not be able to accrete all the gas. The gas will then begin to build up and eventually fill its own Roche lobe. This is called the Common Envelope phase. There are now two (or more) stars that share an envelope of gas. Since the binary system is sharing this envelope, inside there is friction as the two stars orbit each other inside the matter. The stars will begin to spiral into each other and eventually this complex process will give orbital energy to the envelope and eject it (Paczynski 1976). The ejection of the common envelope can account for the mass loss.

22 10 The other theoretical possibility is in the merger of two helium white dwarf stars. The two stars will merge together to produce a single star, theoretically the hot subdwarf star. The formation of these single hot subdwarf stars were carefully calculated and modeled by Han et al (2002, 2003). It is theorized that should two helium white dwarf stars converge, and the merging be hot enough, it could ignite helium causing a helium flash. The result after which being a single sdb star (Saio and Jeffery 2000). Figure 4. The theoretical formation channels for hot subdwarf stars: Roche lobe overflow, Common Envelope phase, and two white dwarf mergers. (Heber 2009)

23 11 Hot Subdwarf Research There are many reasons to study hot subdwarf stars. Hot subdwarf stars are found in the disk and bulge of the galaxy, in elliptical galaxies, and in globular clusters. Hot subdwarf stars explain the UV-upturn, show insight into stellar interiors by studying their pulsations, and dominate the sky for magnitudes brighter than B = 18 in surveys of faint blue objects. A brief review follows. Hot subdwarf stars are found in globular clusters. In NGC 6752, these spectra were identical to the spectra of the hot subdwarf stars in the field of our galaxy (Heber et al. 1986). Globular clusters are very old, thought to have condensed soon after the Big Bang itself, which implies that hot subdwarf stars can also be very old. They can also be found in elliptical galaxies (Brown et al. 2008) and in the galactic bulge (Zoccali et al. 2003), which are both also old stellar populations. An unexpected discovery in early-type galaxies is called the UV-upturn. It is an excess of ultraviolet light coming from these galaxies. This is unexpected because elliptical galaxies have little to no star formation, so they aren t expected to have many hot stars. The mystery was solved when observations concluded the UV-upturn was due to the prominence of hot subdwarf stars (Brown et al. 1997). More perplexing are the cases in which gas-giant planets orbit a hot subdwarf. This is astonishing, since to do this, the gas-giant planet must have undergone the red giant phase and survived. An example of this is a giant planet that orbits the star V391 Pegasi, a pulsating subdwarf B star (Silvotti et al. 2007). Studying pulsations in stars allows investigation into their interiors, in much the way seismology shows geologists what is inside Earth. This is called asteroseismology. Some hot subdwarf stars pulsate, and so are of interest to asteroseismology. The first of the two main types of hot subdwarf stars that were

24 12 discovered to pulsate were the sdb stars (Kilkenney et al. 1997). These pulsations have low amplitudes and are multi-periodic, reaching around a few mmag (millimagnitudes), with short periods between 80 and 600 seconds. Interestingly, these pulsations were theorized at about the same time (Charpinet et al. 1996). These stars are now known as V361 Hya stars (Kilkenney 2007). The discovery of longperiod pulsations has since followed from the discovery of the short-period pulsators. The long-period pulsating sdb stars have periods ranging from 2000 to 9000 seconds. These stars are now known as V1093 Her stars (Green et al 2003). SdO stars have also been observed to pulsate. The short-period pulsations are due to p-mode (pressure mode) pulsations. P-mode pulsations are due to the κ mechanism, which is when the opacity of a layer in the star increases with compression. Somewhere in the star, some of the stellar material gets pulled in by gravity and falls inward. As the material falls inward, the material compresses and the temperature increases. The heated-up material becomes opaque to radiation, trapping the heat. The temperature will continue to increase until there is enough pressure to push back outwards. Since this is a gas, it will expand, cool, and become more transparent, releasing the energy and the pressure that was below. Gravity wins again and pulls down the material and the cycle repeats. Hence, pulsation. However, the Kramers Law ρ κ T ).+ shows that as the material moves inward, increasing the density and temperature, the opacity κ will become smaller. This means the opacity actually decreases with compression. Yet, we do see such pulsations in stars, so the opacity must increase with compression, perhaps under special conditions (Carrol and Ostlie, 2007).

25 13 S.A. Zhevakin first found the conditions necessary for the κ mechanism to work as is needed. There are partial ionization zones where some of the work done on the gases is spent on ionizing gases rather than increasing the temperature. Density in Kramer s Law now dominates and the mechanism works (Carrol and Ostlie, 2007). The long-period pulsations are due to g-mode (gravity mode) oscillations. These oscillations are produced by internal gravity waves (Carrol and Ostlie, 2007). The gravity tends to smooth out the material but there are differences in pressure and composition, and gravity will act on those differently. There is an oscillatory motion as the gravity acts as the buoyant force to restore the star to equilibrium. Each type of oscillation provides its own insight into the stellar structure of the star. The p-mode oscillations provide information on the surface of the star while the g-mode oscillations probe deep inside the interior of the star. Thereby studying the pulsations of hot subdwarf stars gives valuable information about the conditions on the inside of the star and the surface. Pulsating hot subdwarf stars do not have to confine to one or the other though. There are a small handful of cases of hot subdwarf stars that pulsate in both p and g-modes (Schuh et al. 2006).

26 RESEARCH PROGRAM This thesis reports a survey to find variability in the brightness, or apparent magnitude, of a set of hot subdwarf stars. We selected the hot subdwarf stars from the Palomar-Green Catalog of Ultraviolet Excess Stellar Objects, described below. For each hot subdwarf star, we examined whether their apparent magnitudes changed as a function of time. A plot of a star s apparent magnitude as a function of time is called its light curve. Light curves measured from the Catalina Real- Time Transient Survey (CRTS) (Drake et al. 2009), which is funded by the National Science Foundation and so is publicly available. The CRTS light curves were made in visible light, and are a series of hundreds of apparent magnitudes of the stars, measured on the average of about every ten days for 8-9 years, beginning in For each CRTS light curve, the mean apparent magnitude was calculated, as well as the standard deviation of the variance about the mean. This tells how much the star changes in brightness. The next few sections will discuss the types of variability we can expect, the Palomar-Green Catalog, the Catalina Real-Time Transient Survey, and the calibration that shows how accurate the CRTS is for this purpose. Palomar-Green Catalog The Palomar-Green (PG) Catalog of Ultraviolet Excess Stellar Objects was published by Richard Green, Maarten Schmidt, and James Liebert in 1986 (Green et al. 1986). The survey looked specifically for quasars, although it is dominated by hot, high-gravity stars in the late stages of stellar evolution, such as hot subdwarf stars and white dwarf stars. All these objects are blue in color and have ultraviolet excesses, which means that they have a larger ratio of the intensities of

27 15 ultraviolet-to-blue light than even the hottest normal stars have. The PG survey covered 10,714 square degrees, about 1/4 th the celestial sphere, using the Palomar Schmidt 18-inch telescope. More than half the survey, 53%, consisted of hot subdwarf stars, which included sdb and sdo types. The rest consisted of hot white dwarf stars, cataclysmic variables, planetary nebulae, quasars, and other extragalactic objects. A total of 1874 objects of all kinds were found by the Palomar-Green survey, and hence are listed in the Palomar-Green Catalog (Green et al. 1986). Green et al (1986) classified the hot subdwarfs and white dwarfs with the following spectral classifications, some of which they devised themselves: sdb: Subdwarf B stars show that high-gravity Balmer series absorption over a wide range of colors. sdb-o: sdb stars with a suggestion of He I λ4471 in absorption. sd: Usually implies a lower signal-to-noise observation in which two or three Balmer absorption lines of moderate gravity are present. sdoa: Not conventional sdo stars, but showing spectra with dominant hydrogen Balmer absorption along with pronounced He I λ4471 and often He I λ4026. sdob: Spectrum dominated by He I and He II lines and generally showing hydrogen Balmer absorption. sdod: Cooler subdwarf stars with pure He I absorption spectra, characterized by the weakness or absence of hydrogen Blamer lines and He II λ4686, while showing the singlet λ4388 about equal in strength to the triplet λ4471. sdo: A spectrum in which He II λ4686 and often He I λ4471 were identified, at a signal to noise ratio somewhat too low for a more detailed description.

28 16 DAn: Have hydrogen Balmer absorption at the very high surface gravities characteristic of hot white dwarf stars. The subtype numbers (n) are the indices from 0 to 9 denoting effective temperature adopted by Sion et al. (1983). DBn: Degenerates with spectra showing only neutral helium absorption. DAO, DAB, DBA: Degenerates with atmospheres mixed with hydrogen and helium composition. O denotes the presence of He II λ4686, B denotes He I. The order of the letters denotes the dominant atmospheric constituent first. DO: Helium atmosphere degenerates with spectra dominated by ionized helium absorption. DC, DZ: Helium-atmosphere white dwarf stars. These stars show no weak carbon features, they do show metallic features. Note: caution is advised due to incompleteness in this color range, and higher signal-to-noise spectra not provided. Catalina Real-Time Transient Survey The Catalina Real-Time Transient Survey (CRTS) is an astronomical survey that uses three ground-based telescopes to search for transient objects. Its original purpose was to search for near-earth asteroids, but since making their data publicly available, many other purposes are being found. It is the precursor for the giant, deep, time-resolved surveys of the future, such as the Large Synoptic Survey Telescope, currently under construction in Chile and among the national observatories largest projects.

29 17 The CRTS uses three ground based telescopes, which are the Catalina Sky Survey (CSS), the Mount Lemmon Survey (MLS), and the Siding Springs Survey (SSS). Each telescope has its own range of sky it surveys, and each telescope avoids the Galactic plane due to the crowding of stars. Together, the three telescopes cover about 33,000 square degrees of sky. The CRTS takes photometry from unfiltered images then does a transformation to V, the visual band. This is highly dependent on source color. The color correction for blue objects is small but can be very large for red objects (Drake et al. 2009). Converting the unfiltered apparent magnitudes to V are done with the transformation equations of Bessel and Brett (1988). The comparison stars used are G0-G8 dwarf stars from the all-sky 2MASS Point Source Catalog (Cutri et al. 2003). It is noted that these comparison stars as well as the transformation equations used were chosen for the best choice for asteroids. Caution is advised for using apparent magnitudes from CRTS brighter than 13 th magnitude (V ~ 13), due to source saturation and nonlinearity of the response (Drake et al. 2009). Types of Variability There exists a great variety of variability in stars that is valuable to many subfields in astronomy. A variable star is one that has luminosity or spectroscopic changes. This may be due to the natural evolution of a star s life, where the star enters into a phase in its life where it pulsates. A star can be variable because it has a companion star that orbits it and the eclipsing dip in their light curves is observed. There is the irradiation effect where a hot star heats up the facing side of a companion. Erupting stars are called cataclysmic variables (CV), where a lowmass, main-sequence star loses mass to a WD companion. Pulsating stars are of central interest to asteroseismology, as described above.

30 Method Investigation into finding candidates for variability of the hot subdwarf 18 stars from the PG catalog started with analysis of the data from CRTS. A linear least squares regression was fitted against the data with the goal to minimize the squared error. The least squares regression will be the model used to predict how much a stars brightness should vary based on the average magnitude of the star. This is the best fit line for the data. The equation of the regression curve is f(x, β) = β N + β O x. The solution therefore minimizes the squared error: SE = S TUN r R B where r is the residual. The difference between the data and the predicted value by the model is: r R = y R f(x R, β) Minimizing the squared error is essential since the regression curve should be as close to the data as possible. The closer the line fits the data, the better the model. Therefore, finding a line that will reduce the distance between each data point and the predicted value, will produce the best model. Once the best fit line is computed, then the standard deviation about the mean can be calculated. For residuals, the standard deviation (σ) is computed as follows: σ = (y R f(x i, β)) B n 2 To make the analysis more easily manageable, the sample of 985 stars was split in approximately half. For each half, a plot was made of the variability of

31 19 each star. (See Figures 5 and 6.) In both these plots, the variability for each star was found by performing a least-squares linear regression, with standard deviations calculated for the light curves of the individual stars. To find the best candidates for variability, we plotted each star s standard deviation about the mean of its light curve versus its mean apparent magnitude. The stars with statistically significant variability will have the highest standard deviations. A discussion on how to determine which stars are statistically significant follows in the next section.

32 OBSERVATIONS AND ANALYSIS Analysis Part I Figure 5. This figure shows the first half of each star's average magnitude against their standard deviation.

33 Table 1: PG highest stars on Figure Label Identifier A PG B PG C PG D PG E PG F PG Table 2: PG hot subdwarf stars and related objects significant variance 4 σ 5 σ +6 σ PG PG PG PG PG PG Figure 5 shows the results of plotting the stars magnitude against the standard deviation. Table 2 lists the labeled stars in order with the PG star identifier. Table 3 lists each star s standard deviation. The higher the standard deviation the more statistically significant the star s variability becomes. From the discussion earlier about CRTS, a calibration must be performed in order to ensure the data are accurate.

34 Analysis Part II 22 Figure 6: This figure shows the second half of each star's average magnitude against their standard deviation

35 Table 3: PG highest variable stars on Figure Label Identifier A PG B PG C PG D PG E PG Table 4: PG hot subdwarf stars and related objects significant variance 4 σ 5 σ +6 σ PG PG PG PG PG Figure 6 show the results of plotting the stars magnitude against the standard deviation. Table 4 lists the labeled stars in order with the PG star identifier. Table 5 lists each star s standard deviation.

36 24 Calibration In order to determine whether a star is variable, one needs to compare their apparent magnitudes to those of stars that do not either intrinsically nor extrinsically change brightness. A standard star in theory will have no variance. However, stars always how some small amount of variability, due to scintillation from differential refraction from turbulence in Earth s atmosphere, which is also called twinkling. This variation can be accounted for, however. Landolt compiled an extensive and carefully conducted UBVRI photoelectric survey for standard stars along the celestial equator (Landolt 1992a, 1992b). The observations produced a list of standard stars between V = 11.5 and V = The search for standard stars continued and more standard stars have since been identified and increased the range of magnitudes between V = 8.90 and V = (Landolt 2009). Some of Landolt s standard stars had ultraviolet excesses such that they were included in the PG catalog. In order to calibrate the photometry from the CRTS, only the PG standard stars were chosen for the calibration, as they would be a natural choice to which to compare our list of hot subdwarf stars. Figure 7 is a graph showing this calibration of the photometry of the PG standard stars. We plot the V magnitude as measured by the CRTS against the variance about the mean for each star. A true standard star should have no variance in brightness, hence since there does appear to be some small variance in the brightness of the standard stars in Figure 7, this is attributed to atmospheric extinction and scintillation. Other possible causes for variance are due to unfiltered photometry transformations to V magnitude, and the calibration from G dwarf stars. Magnitudes brighter than V = 13 are to be viewed with caution, as those stars are bright enough to have saturated the detectors used by CRTS, which may explain why there is higher variance on the bright end of Figure 7 (Drake et al.

37 ). So long as the hot subdwarf stars magnitudes and their standard deviations are higher than the noise depicted here, the photometry can be trusted for accuracy. Figure 7 shows a total standard deviation of within ΔV = 0.1 magnitudes between V = 12.0 and V = Figure 7. Average magnitude of the PG standard stars from Landolt (1992a, 1992b) plotted against each stars standard deviation

38 List of Standard Stars 26 Table 5. PG Standard Stars from Figure 7. IDENTIFIER <V> σ NOTE PG PG PG PG A PG B PG PG A PG B PG C PG D PG E PG PG B PG C PG D PG PG V* UY Sex PG A PG B PG C PG PG B PG C

39 27 PG D PG PG A PG B PG C PG D PG E PG PG PG A PG B PG C PG D PG PG A PG B PG C PG D PG E PG F PG G PG PG PG A PG B

40 28 PG C PG E PG PG A PG B PG C PG E PG F PG PG PG A PG B PG PG A PG B PG List of PG Hot Subdwarf Stars Part I Table 6. PG Standard Stars from Figure 5. IDENTIFIER σ CSS MLS SSS NOTE PG PG PG PG PG

41 29 PG PG PG PG PG PG PG PG PG PG PG PG PG SD PG PG PG PG PG / PG / PG PG PG PG PG PG

42 30 PG / PG PG PG PG PG PG PG PG PG SD PG PG PG NAOF PG PG PG PG PG PG PG PG PG PG PG PG

43 31 PG PG PG PG PG PG PG PG PG PG PG PG SD PG SD PG PG PG PG PG PG PG PG PG PG PG PG

44 32 PG BSL PG PG PG TYC PG PG PG PG BSL PG PG PG PG PG PG BSL PG PG PG PG PG PG PG PG PG PG

45 33 PG PG PG PG PG PG PG PG PG PG PG PG BSL PG PG PG PG PG PG PG PG PG PG PG PG PG

46 34 PG PG PG PG PG PG PG PG PG PG PG PG PG SDSS J PG PG PG PG SD PG PG PG PG PG PG PG

47 35 PG PG PG PG PG PG PG PG PG PG SD PG SD PG PG PG PG SD PG PG PG PG PG SD PG PG PG PG PG

48 36 PG PG PG PG PG PG PG PG PG PG PG PG BSL PG PG PG PG PG PG PG PG BSL PG PG PG PG ML PG

49 37 PG PG PG SDSS J PG PG PG PG PG PG PG PG PG PG PG NAOF PG PG PG PG BSL PG PG BSL PG PG PG PG

50 38 PG PG PG PG PG PG PG PG PG PG PG ML PG PG PG PG PG PG PG PG PG PG PG PG PG PG

51 39 PG PG PG PG PG PG NAOF PG PG PG PG PG PG PG PG PG PG PG PG PG PG PG PG PG PG NAOF NAOF PG

52 40 PG PG PG PG PG BSL PG PG PG PG PG PG PG PG PG PG PG NAOF PG PG PG NAOF PG PG PG PG PG PG NAOF

53 41 PG PG PG PG PG PG PG BSL PG PG PG PG PG PG PG PG PG PG BSL PG PG PG BSL PG PG BSL PG PG BSL PG

54 42 PG PG PG BSL PG PG PG PG PG PG PG PG PG PG PG PG PG PG PG SD PG SD PG PG PG PG PG PG

55 43 PG PG PG PG PG PG PG PG PG PG PG PG PG PG PG PG PG PG PG PG PG PG PG PG BSL PG

56 44 PG PG PG PG PG PG PG PG PG PG PG PG PG PG PG PG PG PG PG PG PG PG PG PG PG