Characterization of the Galactic White Dwarf Population in the Next Generation Virgo Cluster Survey

Transcription

1 Characterization of the Galactic White Dwarf Population in the Next Generation Virgo Cluster Survey by Nicholas Fantin A thesis submitted to the Department of Physics, Engineering Physics & Astronomy in conformity with the requirements for the degree of Master of Science Queen s University Kingston, Ontario, Canada August 2016 Copyright c Nicholas Fantin, 2016

2 Abstract Halo white dwarfs remain one of the least studied stellar populations in the Milky Way because of their faint luminosities. Recent work has uncovered a population of hot white dwarfs which are thought to be remnants of low-mass Population II stars. This thesis uses optical data from the Next Generation Virgo Cluster Survey (NGVS) and ultravoilet data from the GALEX Ultraviolet Virgo Cluster Survey (GU- ViCS) to select candidates which may belong to this population of recently formed halo white dwarfs. A colour selection was used to separate white dwarfs from QSOs and main-sequence stars. Photometric distances are calculated using model colourabsolute magnitude relations. Proper motions are calculated by using the di erence in positions between objects from the Sloan Digital Sky Survey and the NGVS. The proper motions are combined with the calculated photometric distances to calculate tangential velocities, as well as approximate Galactic space velocities. White dwarf candidates are characterized as belonging to either the disk or the halo using a variety of methods, including calculated scale heights (z> 1kpc),tangentialvelocities (v t >200 km/s), and their location in (V,U) space. The 20 halo white dwarf candidates which were selected using Galactic space velocities are analyzed, and their colours and temperatures suggest that these objects represent some of the youngest white dwarfs in the Galactic halo. i

3 Acknowledgments First, I would like to thank my supervisor, David Hanes, and my co-supervisor, Pat Côté, for their knowledge, direction, and support throughout my time at Queen s. Their infectious enthusiasm truly reinforced my love of astronomy. Thank you to Stephen Gwyn, Luciana Bianchi, and the NGVS team for their contributions to this thesis. I would also like to thank the Queen s support sta (Loanne, Tammie, Kyra, Gord, Peg), my fellow graduate students, Terry Bridges, and anyone else at Queen s who has helped me out along the way. I would also like to thank the Dunlap Institute, Suresh Sivanandam, and Stephane Courteau for organizing the incredible Dunlap Mauna Kea School. The biggest thank yous go to my Mom, Heather, my Dad, Patrick, my sister, Kathryn, and my late dog Oreo, for their love and support. I would also like to thank my best friends Ryan, Benen, and Spencer for all of the great times I had at Queen s. I am also grateful for the continued support from my friends in Toronto: Rachelle, Mark, Djurdja, Madi, and Lyndsay. Finally, I would like to thank Ashley for thinking I can actually dance. You ve been by my side ever since and I couldn t have done this without you. ii

4 Contents Abstract Acknowledgments Contents List of Tables List of Figures i ii iii vi vii Table of Acronyms 1 Chapter 1: Introduction Motivation Contributions Organization of Thesis Chapter 2: Galactic White Dwarfs White Dwarfs and the Study of the Milky Way White Dwarf Properties Formation and Composition Spectral Types Physical Properties White Dwarf Surveys within the Virgo Cluster Region The Sloan Digital Sky Survey GALEX Selecting Halo White Dwarfs Motivation Previous Results Using Kinematics Globular Clusters and the Inner Halo Chapter 3: The Data: Constructing an Optical-Ultraviolet Catalog 27 iii

5 3.1 The Next Generation Virgo Cluster Survey Extracting Point Sources The GALEX Ultraviolet Virgo Cluster Survey Caveats Matching the Catalogs Creating a UV-Optical Catalog Multiple Matches Spurious Matches Chapter 4: White Dwarf Candidates within the NGVS Field Selection Procedure Choosing Colours Contaminants Comparison to SDSS-GALEX AIS Matching Chapter 5: Photometric Properties Magnitude Distributions Model Comparison Photometric Distances Deriving Proper Motions Method Estimating the Uncertainty Comparison to the USNO Catalog Using QSOs Results Chapter 6: Selecting Candidate Halo White Dwarfs Colours and Magnitudes: Comparing to the TRILEGAL Model Using g-band Magnitudes Using a Colour-Magnitude Selection Using Photometric Distances Kinematics: Using Proper Motions Tangential Velocities Galactic Space Velocities Chapter 7: Discussion Halo White Dwarfs and Stellar Evolution Models Matching E ects Photometric Astrometric Sources of Bias iv

6 7.3.3 Radial Velocities Analysis of Halo Candidates Chapter 8: Summary and Conclusions Future Work Bibliography 103 v

7 List of Tables 2.1 Common white dwarf spectral types and their dominant characteristics Various parameters for the NGVS including the exposure times, magnitude limits, seeing, and background constraints Velocity dispersions for typical thin and thick disk populations in km/s compared to the dispersions from Figure 6.5 Table: Binney & Merrifield (1998) Properties of halo white dwarf candidates selected based on their Galactic space velocities. All velocities are in km/s vi

8 List of Figures 2.1 Sirius B, a white dwarf, (lower left) and its companion Sirius, an A-type main sequence star (center). Image: NASA A typical spectrum for white dwarfs with a Hydrogen atmosphere (DA, top), Helium atmosphere (DB, bottom), and an atmosphere dominated by metals (DZ, middle). Prominent spectral features are also highlighted, such as the Balmer Series, He I, and Ca H&K. Figure: Verbeek et al (2012) Theoretical line profiles for the Balmer series from H (bottom) to H8 (top) at various temperatures and log g. Thedashedlineindicateslog g=7.0 and the solid line is log g=9.0. Figure: Tremblay & Bergeron (2009) Temperature (top) and log g (bottom) distributions for DA and DB white dwarfs in the SDSS. The surface gravity is in units of cm/s 2 Figure: Kleinmann et al. (2013) Mass distribution for disk white dwarfs from Palomar Green Survey (Top) and SDSS DR7 (Bottom) Figures: Liebert et al. (2005); Kleinmann et al. (2013) The Galactic Space Velocity coordinate system. Figure: Carroll & Ostlie (2006) vii

9 2.7 U and V velocities in km/s for white dwarfs from (Top) Kawka & Vennes (2006) and (Bottom) Oppenheimer et al. (2001). The velocity ellipsoids for a thin disk, a thick disk, and a halo population are plotted where the disk components are centered at (U,V) = (0,0) and the halo is at (-220, 0). The squares represent selected halo candidates. Figure: (Top) Kawka & Vennes (2006), (Bottom) Oppenheimer et al. (2001) Colour-Magnitude diagram for the globular cluster M4 using HST filters. The circled region represents recently formed white dwarfs. Figure: Kalirai (2012) The Next Generation Virgo Cluster Survey (NGVS) field in J2000 equatorial coordinates. The yellow lines correspond to a single Megacam pointing, and the grid totals 117 separate pointings. The background is composed of real NGVS images and was taken from the NGVS graphical search tool The transmission curves for the filters used in the NGVS with a typical DA white dwarf spectrum for reference (black) The concentration index for NGVS Sources (grey) and stellar objects from SDSS (black). A sharp stellar sequence centered on i =0,and aclusterofbackgroundgalaxiescanbeseentowardsfainterg-band magnitudes. Only 100,000 point sources from the NGVS are plotted for clarity. The dashed lines indicate the chosen point source range used in this thesis and is in agreement with Durrell et al. (2014) viii

10 3.4 The sky coverage for the GUViCS catalog is shown in RA and DEC (J2000) compared to the NGVS footprint (yellow). The dashed circles represent the targeted GUViCS pointings, and the colour indicates the exposure time of the image. The red circles indicate exposure times between 800 and 1500 seconds, the cyan circles represent images with MIS depth (exposure time seconds), the dark blue circles indicate images with exposure times greater than s. Black areas represent fields that were avoided due to the presence of a bright foreground star. As a reference, the fields from the far-infrared survey HeViCS are shown in green. Figure: Voyer et al. (2014) Colour-colour diagrams of spectroscopically confirmed objects from the SDSS that have been matched to the NGVS. The blue points indicate white dwarfs from Kleinmann et al. (2015), the red points are QSOs from Paris et al. (2014), the cyan points are blue stragglers and blue horizontal branch stars from Scibelli et al. (2014), and the stars were queried using the SQL search in SDSS DR12. The separation between the objects is poor when compared to the (g-i), (NUV-g) diagram in Figure (g - i), (NUV - g) colour-colour diagram for the matched NGVS- GUViCS point source objects (grey), spectroscopically confirmed SDSS WDs (blue circles), QSOs (red squares), and stars (magenta triangles). The black dashed lines indicate the chosen colour cuts applied to the NGVS-GUViCS data in order to select white dwarf candidates while minimizing contamination from other objects ix

11 4.3 Model tracks from Bianchi et al. (2009a) are plotted to show ideal locations for the WDs (blue), QSOs (red), and for stars of various surface gravities (magenta). The WD track is for a log g = 8.0for temperatures between 15,000 and 200,000 K. The model QSO colours are a function of redshift, with values between 0 and 5. Model stars with log g = 5, 4, 3 are indicated by the solid, dashed, and dotted magenta lines, respectively. The black dashed lines indicate the chosen colour cuts applied to select white dwarf candidates Magnitude distributions for the white dwarf candidates selected in Chapter 4 compared to the SDSS spectroscopic selection from Kleinman et al (K13) and GALEX AIS photometric selection from Bianchi et al. (2011) (B11) g-band magnitude distribution for the white dwarf candidates (green) and the TRILEGAL white dwarfs (white) Photometric distances for the white dwarf candidates selection in Chapter 4.1. Absolute magnitudes were calculated using the TLUSTY colour-magnitude relationship in combination with the Megacam (g - i) colours obtained as part of the NGVS. The distances were calculated using the distance modulus with the absolute and apparent g-band magnitudes as they have the least uncertainty. Error bars are aresultoftheuncertaintiesinthe(g-i)colour x

12 5.4 Comparison between proper motions in Right Ascension (RA) derived using NGVS-SDSS positions and the proper motion catalog given by Munn et al. (2014). The root-mean-square deviation between the NGVS and SDSS proper motions in RA is 12.9 mas/yr Comparison between proper motions in Declination (DEC) derived using NGVS-SDSS positions and the proper motion catalog given by Munn et al. (2014). The root-mean-square deviation between the NGVS and SDSS proper motions in DEC is 12.7 mas/yr Comparing the total proper motion measured from the NGVS-SDSS matching technique to the proper motions derived by Munn et al. (2014). The root-mean-square deviation about the one-to-one line (red) is 9.6 mas/yr Calculated proper motions for stars (yellow), white dwarfs (blue), and QSOs (red) using the NGVS-SDSS positions Proper motion in RA and DEC for white dwarf candidates in the NGVS dataset (black). QSOs are also plotted to show they display minimal change in position between the two catalogs The relative contribution to the white dwarf population by each of the three Galactic components A TRILEGAL CMD for white dwarfs from each Galactic component. The black line was visually chosen to separate halo and disk white dwarfs Calculated scale heights as a function of g-band magnitude. The dashed line indicated the chosen scale height which separates disk and halo white dwarfs xi

13 6.4 Calculated tangential velocities for the NGVS white dwarf candidates. The blue line indicates a tangential velocity of 200 km/s, which was the cut used to separate disk and halo white dwarfs Galactic space velocities for white dwarf candidates, along with the 2 velocity ellipsoids for the thin disk (dashed), thick disk (dot-dashed), and the halo (dotted red). The 1 velocity ellipsoid for the halo is indicated by the black dotted line Galactic space velocities and associated error-bars for white dwarf candidates Disk and Halo contributions calculated from each method described in Chapter A comparison between IFMRs studied by Bianchi et al. (2011). Figure: Bianchi et al. (2011) The di erence between the brightest and dimmest objects within a double match scenario as a function of the magnitude of the brightest object. The red circle highlights a case where 2 objects of similar magnitude were matched to a single UV source, whereas the blue circle highlights objects for which the magnitude of faintest source lies near the NGVS survey limit The e ect the colour selection from Chapter 4 has on the temperature of the selected white dwarfs A comparison between the colour-absolute magnitude relationships of a DA and DB white dwarf in SDSS band-passes from Holberg & Bergeron (2006) xii

14 7.6 Colour-absolute magnitude relationships for DA white dwarfs with different values of log g The SDSS spectrum of halo white dwarf candidate 7 with common spectral lines indicated. The strong, broad, Balmer series is present indicating that it is a DA. Figure: SDSS DR12 (Alam et al. 2015). 95 xiii

15 Table of Acronyms Table 1: Summary of frequently used acronyms and variables Acronym Meaning NGVS Next Generation Virgo Cluster Survey GUViCS GALEX Next Generation Virgo Cluster Survey SDSS Sloan Digital Sky Survey USNO United States Naval Observatory µ Proper motion log g Surface Gravity in cgs units (cm/s 2 ) WD White dwarf M Solar Mass FWHM Full-Width at Half Maximum CMD Colour-Magnitude Diagram RA Right Ascension DEC Declination QSO Quasi-Stellar Object (Quasar) UV Ultraviolet eff Central e ective wavelength BHB Blue Horizontal-Branch BS Blue Straggler IFMR Initial-Final Mass Relationship PSF Point-Spread Function AGB Asymptotic Giant Branch RMS Root-Mean-Square iii

16 1 Chapter 1 Introduction 1.1 Motivation Although 95% of stars end their lives as white dwarfs, the white dwarfs in the Galactic halo remain largely unstudied (Cojocaru et al. 2015). This is a result of their faint optical luminosities. Much of our knowledge from this population has come from the Sloan Digital Sky Survey (SDSS) (York et al. 2000), however, many of the white dwarfs are expected to be fainter than the survey limits. Moreover, halo white dwarfs, unlike their main-sequence counterparts, cannot be selected based on their metallicity. This is because the metals sink below the photosphere on short timescales. The only reliable method to select halo white dwarfs is through their kinematics. Recently, Kalirai (2012) discovered a population of hot white dwarfs with halo-like velocities. These stars are thought to be young white dwarfs that are formed from low-mass population II progenitors. These objects have temperatures between Kand20000K.Thehightemperatureoftheseobjectsmeansthattheirspectral energy distribution will peak in the ultraviolet. The Next Generation Virgo Cluster Survey (NGVS) and its ultraviolet compliment, the GALEX Ultraviolet Virgo Cluster

17 1.2. CONTRIBUTIONS 2 Survey (GUViCS), provide an ideal dataset for selecting and studying these young halo white dwarfs. This is a result of the photometric depth of both datasets, and that the large baseline allows for the separation of the white dwarfs from QSOs in colour-colour space. The NGVS can also be combined with the SDSS to provide second-epoch optical data, which can be used to derive proper motions. Combining all of these opportunities will allow for the selection of halo white dwarfs within the NGVS footprint. 1.2 Contributions This thesis uses data that was obtained as part of the Next Generation Virgo Cluster Survey (NGVS), the GALEX Ultraviolet Virgo Cluster Survey (GUViCS), and the Sloan Digital Sky Survey (SDSS). The NGVS research group includes faculty, research scientists, post-docs, and students from Canada, France, and the USA. Team members who contributed to the data used include Patrick Côté (NRC Herzberg Institute of Astrophysics, Canada), Laura Ferrarese (NRC Herzberg Institute of Astrophysics, Canada), Stephen Gwyn (NRC Herzberg Institute of Astrophysics, Canada), Jean-Charles Cuillandre (CFHT, USA), and David Hanes (Queen s University, Canada). The GUViCS team consists of 8 astronomers and is led by Alessandro Boselli (P.I., LAM, France) and co-pi: Samuel Boissier (LAM, France). Model tracks for the white dwarfs, QSOs, and main sequence stars as well as feedback and suggestions were provided by Luciana Bianchi (John s Hopkins University, Baltimore).

18 1.3. ORGANIZATION OF THESIS 3 Finally, the proper motion data from SDSS used in this thesis was acquired at the United States Naval Observatory and published by Munn et al. (2014). 1.3 Organization of Thesis This thesis is organized as follows: Chapter 2 provides the necessary background information on white dwarfs and the methods used to detect and characterize them. Chapter 3 describes the datasets used and the methods employed to construct an optical-uv catalog within the NGVS footprint. Chapter 4 describes the methods used to select white dwarf candidates within the NGVS footprint, while Chapter 5 describes various photometric and kinematic properties of the candidates. Chapter 6 uses various methods to characterize each candidate as either a disk or a halo white dwarf, and Chapter 7 discusses the results. Chapter 8 summarizes the results and discusses the future prospects for work on halo white dwarfs.

19 4 Chapter 2 Galactic White Dwarfs White dwarfs represent the final evolutionary stage of stars with initial masses less than 8 M (Doherty et al. 2015). This means that roughly 95% of stars will end their lives as a white dwarf, including our Sun (Althaus 2010). This section motivates the study of white dwarfs, with particular emphasis on those belonging to the Galactic stellar halo. The observational properties of a white dwarf are presented in Chapter 2.1, while Chapter 2.2 details the importance of white dwarfs in the study of the Milky Way. This Chapter concludes by presenting methods and result from previous surveys which attempted to select white dwarfs in the Galactic stellar halo. 2.1 White Dwarfs and the Study of the Milky Way The study of white dwarfs began with the discovery of Sirius B (seen in Figure 2.1 ) by Alvan Graham Clark in 1862, which had previously been hypothesized by Friedrich Bessel in 1838 (Carroll & Ostlie, 2006). In 1915 the temperature of Sirius B was measured to be almost three times higher than its companion star, yet the radius was smaller than that of the Earth. Since the discovery of Sirius B, over Galactic

20 2.1. WHITE DWARFS AND THE STUDY OF THE MILKY WAY 5 Figure 2.1: Sirius B, a white dwarf, (lower left) and its companion Sirius, an A-type main sequence star (center). Image: NASA white dwarfs have been discovered (see Chapter 2.3), with the total number left to be discovered thought to be close to one hundred million (van Oirschot et al. 2014). White dwarfs are important to the study of the Milky Way because they are ubiquitous, long-lasting, and have well-studied properties (Cojocaru et al. 2015). They are also test-beds for physics in extreme environments. Since white dwarfs do not produce energy via nuclear fusion, a di erent type of pressure must exist in order to prevent gravitational collapse. This pressure is called electron degeneracy pressure and is a result of the Pauli Exclusion Principle, which states that no two electrons in a gas can occupy the same quantum state (Winget & Kepler 2008). The electrons resist collapse as increasing the electron density requires energy to raise an electron to a higher energy level. Hence, white dwarfs present a real-life application of the Pauli Exclusion Principle (Van Horn 1979).

21 2.1. WHITE DWARFS AND THE STUDY OF THE MILKY WAY 6 As the mass of a white dwarf increases, so too does its internal kinetic energy. This is a result of the Pauli Exclusion Principle. At higher masses, the electrons become relativistic until they reach the speed of light, which results in a maximum attainable kinetic energy. This also imposes a maximum mass for which electron degeneracy pressure can counteract the gravitational collapse. This mass is called the Chandrasekhar mass and is equal to 1.4M (Chandrasekhar 1933). In binary systems mass can be deposited onto the white dwarf by its companion, allowing the white dwarf to grow in mass. When white dwarfs exceed this mass they tend to explode as Type 1a supernovae. Since this mass limit is universal, and a result of the underlying physics within the white dwarf, the resulting supernovae have similar light-curves. Type Ia supernovae have been used as standard candles to study the cosmological constant,, and have shown that the expansion of the universe is accelerating (Perlmutter et al, 1997, 1999; Schmidt et al. 1998). White dwarf properties also provide information regarding the boundary conditions of stellar evolution since they represent the final evolutionary state of 95% of stars. For example, the zero-age main-sequence masses of the progenitors range from 0.8-8M and white dwarf masses are typically 0.6M, which means that mass loss must play an important role during post-main-sequence evolution (Winget & Kepler 2008). The progenitor mass range is determined by the onset of helium core burning. Below 0.8M the core never reaches a high enough temperature to ignite the helium, and above 8M the carbon will ignite to produce neon. The ability to measure accurate masses thus has an important role in the formation of stellar evolution models. The age of the Milky Way and its components can also be measured by studying

22 2.2. WHITE DWARF PROPERTIES 7 the properties of white dwarfs. This is because the evolution of a white dwarf consists of only a cooling process, and this process is well understood (Fontaine, Brassard & Bergeron 2001). Thus, the temperature of a white dwarf determines its age, and the coolest white dwarfs represent the remnants of the oldest stellar populations in the Milky Way (Winget et al. 1987). Using the white dwarf luminosity function and cooling models, Leggett, Ruiz & Bergeron (1998) calculated the age of the Galactic disk to be 8±1.5 Gyr. Hansen et al. (2002) used a similar method on white dwarfs in globular clusters to estimate the age of the Galactic halo to be 12±1.5 Gyr. Kalirai (2012) also used four field halo white dwarfs to estimate the age of the so-called inner halo, that is the halo population closest to the Sun, and found it to have an age of 11.4±0.7 Gyr. 2.2 White Dwarf Properties The importance of white dwarfs in the study of our Galaxy underscores the need for accurate determination of their physical properties. This section presents the results of previous studies of their various properties, such as mass, surface gravity, temperatures, and spectral type. However, it begins by describing the formation process and its e ect on these properties Formation and Composition White dwarfs form at the end of the asymptotic giant branch (AGB) phase as the star expels its shell leaving an exposed core (D Antona & Mazzitelli, 1990). Three di erent formation scenarios exist, with each scenario leading to a di erent core composition:

23 2.2. WHITE DWARF PROPERTIES 8 Table 2.1: Common white dwarf spectral types and their dominant characteristics. Spectral Type DA DB DC DO DQ DZ Spectral Characteristics Only strong hydrogen absorption (Balmer Series) Only HeI absorption No discernible features, continuous spectrum Strong HeII lines, also H lines present Carbon features Metal lines only 1. The most common way to form a white dwarf is to eject the stellar envelope during the planetary nebula phase. The progenitors are not massive enough to fuse Carbon or Oxygen, and so the exposed core is composed of these two elements. This method is the most dominant formation scenario. 2. A helium core can be produced if the mass loss of the progenitor is quick enough to prevent helium burning. This would occur in progenitors with masses <1 M. The resulting white dwarf is composed of the helium core which failed to ignite. 3. The final scenario involves high mass progenitors for which the carbon core ignites. The resulting white dwarf is composed of oxygen, magnesium, and neon, which are products of the carbon burning process. Oxygen-Neon white dwarfs are thought to be formed primarily in binary stars as the mass transfer may be able to grow the progenitor to a high enough mass to ignite the core (Willems & Kolb, 2004).

24 2.2. WHITE DWARF PROPERTIES Spectral Types White dwarfs also have di erent spectral types. The spectral type of a white dwarf depends on its temperature and atmospheric thickness. A description of common white dwarf spectral types can be seen in Table 2.1. The spectrum of typical DA, DB, and DZ white dwarfs can be seen in Figure 2.2 with spectral features highlighted. The spectral types are a result of the leftover elements from the cores of the progenitors. The light elements dominate the atmospheres as a result of the strong gravitational forces present, which allows them to float to the surface (Kepler et al. 2016). This process, called gravitational di usion, is very e cient and occurs over a very short time-frame (Fontaine & Michaud, 1979, Althaus et al. 2001). While white dwarfs may come in many di erent spectral types, the majority of the population are hydrogen rich and are thus classified as DAs. The Sloan Digital Sky Survey (SDSS) (York et al. 2000) provided a perfect dataset to test the relative abundances of each spectral type, as it provided spectra for white dwarfs over an immense area of the sky. Recent studies of white dwarfs (Kepler et al. 2015, Kleinmann et al. 2013, 2015) show that roughly 80% of white dwarfs in the SDSS are classified as a DA, 10% as a DB, 3% as a DC, 2% as a DZ, and 1% as a DQ. The remaining fraction is composed of unknown type, a mix of hydrogen and helium, or as a white dwarf with a main-sequence companion. The result is that DA white dwarfs do indeed dominate the total fraction of the white dwarf population. The spectral type of a white dwarf can also change throughout the cooling phase (Bergeron et al. 1997). This evolution is dictated by the thickness of the atmosphere, and is temperature dependent (Hansen & Liebert 2003). If a white dwarf has a thick

25 2.2. WHITE DWARF PROPERTIES 10 Figure 2.2: A typical spectrum for white dwarfs with a Hydrogen atmosphere (DA, top), Helium atmosphere (DB, bottom), and an atmosphere dominated by metals (DZ, middle). Prominent spectral features are also highlighted, such as the Balmer Series, He I, and Ca H&K. Figure: Verbeek et al (2012)

26 2.2. WHITE DWARF PROPERTIES 11 atmosphere dominated by hydrogen it will remain a DA throughout the entirety of the cooling process (Davis et al. 2009). However, white dwarfs with thin atmospheres may change spectral type as they cool. At high temperatures (> K) very few DB white dwarfs exist (Eisenstein et al. 2006). A helium convection layer is formed below K which can dredge helium up to the surface. This can result in a DA changing into a DB, and it is thought that up to 25% of DAs can undergo this change (Hansen & Liebert 2003). A further change can occur below 5000 K as the hydrogen and helium lines cease to be excited. The resulting spectrum becomes featureless and is described as a DC (Davis et al. 2009). Since gravitational di usion occurs on short time scales, the presence of heavy metals in the atmospheres of DZ white dwarfs has always been a topic of interest. Recently, these metals have been hypothesized to originate from the collision with rocky debris disks which survived the post-main-sequence phase (Dufour et al. 2013). These disks can be observed at infrared wavelengths, and have been discovered around many DZ white dwarfs. These observations can provide information regarding the composition of the leftover planetary systems (Dufour et al. 2013) Physical Properties The physical properties of a white dwarf can be calculated from its spectrum. This section will detail the procedure to calculate various physical parameters, such as mass, radius, temperature, and surface gravity, and will provide results based on recent surveys.

27 2.2. WHITE DWARF PROPERTIES 12 Temperature and log g Among all of the properties that can be derived for a white dwarf the temperature and surface gravity (log g) provide the best description of the star (Althaus, 2010). These properties can be derived using absorption line profiles. This is advantageous as the line profile is highly dependent on these atmospheric parameters, and the physics behind the profiles is well understood (see Tremblay & Bergeron 2009; Bergeron et al. 1992; Barstow et al. 2003; Vennes et al. 2005; Schulz & Wegner 1981). The e ect of the temperature and surface gravity on the line profile can be seen in Figure 2.3, which uses the Balmer series as an example. Figure 2.3 shows that the depth of the line increases at lower temperatures and the width of the line increases with surface gravity. The broadening of the spectral lines is a result of Stark (or pressure) broadening. This e ect occurs as a result of collisions between charged particles within the white dwarfs atmosphere, and their electric fields result in the spectral line being split. This process is stronger at higher atmospheric temperatures and densities (surface gravity), and thus the observed line profiles can be fit with model profiles which return predicted values for T eff and log g (Bergeron et al. 1992). Kleinman et al. (2013) used spectral fitting to determine various parameters of the known white dwarf sample within the Sloan Digital Sky Survey. The results can be seen in Figure 2.4, and are sorted by type. The result is that the distribution of surface gravitiesis very narrow and peaks at logg=8.0. The temperature distribution shows the total number of white dwarfs increases towards lower temperatures. The number of DB white dwarfs increases below K and this is thought to be the result of

28 2.2. WHITE DWARF PROPERTIES 13 Figure 2.3: Theoretical line profiles for the Balmer series from H (bottom) to H8 (top) at various temperatures and log g. The dashed line indicates log g=7.0 and the solid line is log g=9.0. Figure: Tremblay & Bergeron (2009). the onset of a convective layer below the hydrogen layer which dredges up the helium (Liebert et al. 2005; Koester & Kepler 2015). Mass and Radius The mass of a white dwarf can be measured in multiple ways, the easiest of which is using its orbital parameters if it happens to be in a binary system. Since this is not always the case, masses are estimated using white dwarf evolutionary models. Liebert et al. (2005) used cooling models from Wood (1995) to derive a relationship between log g and mass. A similar exercise was performed on the SDSS white dwarfs

29 2.2. WHITE DWARF PROPERTIES 14 Figure 2.4: Temperature (top) and log g (bottom) distributions for DA and DB white dwarfs in the SDSS. The surface gravity is in units of cm/s 2 Figure: Kleinmann et al. (2013)

30 2.2. WHITE DWARF PROPERTIES 15 Figure 2.5: Mass distribution for disk white dwarfs from Palomar Green Survey (Top) and SDSS DR7 (Bottom) Figures: Liebert et al. (2005); Kleinmann et al. (2013)

31 2.3. WHITE DWARF SURVEYS WITHIN THE VIRGO CLUSTER REGION 16 by Kleinman et al. (2013) using evolutionary models created by Renedo et al. (2010). The results of both surveys can be seen in Figure 2.5, and both show that the distribution of masses peaks at 0.6M. This result has been consistent throughout many similar studies, and will be important for the model tracks used in this thesis. One fundamental result which helps to convert the measured log g into a mass is the use of the mass-radius relationship since the surface gravity is a function of both the mass and radius. This relationship was first developed by Chandrasekhar in 1933 as a result of the degenerate state of the white dwarf and states that the radius scales as M 1 3 (Provencal et al. 1998). This theoretical relationship can be tested independently by studying white dwarfs in binary systems since their orbital parameters can provide mass and radius determinations (Holberg 2012). Provencal et al. (1998) tested the theoretical mass-radius relationships from Wood (1995) by calculating the mass and radius of 10 white dwarfs in binary systems and 11 field white dwarfs with precise parallax measurements. The results agreed with the theoretical predictions made by the Wood (1995) model and further corroborated the white dwarf mass-radius relationship. 2.3 White Dwarf Surveys within the Virgo Cluster Region This thesis uses data from the Next Generation Virgo Cluster Survey (NGVS) (Ferrarese et al. 2012) which is located at a high Galactic latitude (b 75 ). This section describes the largest UV/optical surveys which overlap with the sky coverage of the NGVS. The survey will be introduced and explained in detail in Chapter 3.

32 2.3. WHITE DWARF SURVEYS WITHIN THE VIRGO CLUSTER REGION The Sloan Digital Sky Survey The Sloan Digital Sky survey (York et al. 2000) is a spectroscopic and photometric survey which covers most of the Northern sky using a 2.5m Ritchey-Chrétien telescope at the Apache Point Observatory in New Mexico. Since its first data release in 2003 (Abazajian et al. 2003) the SDSS has provided an unparalleled combination of sky coverage and depth in the Northern Hemisphere. The photometry is provided in 5 optical bands, ugriz, with 95% detection limits of 22.3/23.3/23.1/22.3/20.8 AB magnitude and spectroscopy to approximately 18th magnitude in the g-band. The SDSS has provided the largest and most extensive catalog of white dwarfs to date. Using the first data release, Kleinman et al. (2004) discovered a total of 2551 white dwarfs. Most recently, Kepler et al. (2016) used Data Release 12 to increase the total number of spectroscopically confirmed white dwarfs to over The methods employed to select white dwarfs in the SDSS use a combination of colour cuts and spectral fitting (Eisenstein 2006). First, colour cuts are made in order to select the bluest stars in the SDSS catalog since this region of colour-colour space represents the hottest stars and separates the white dwarfs from the QSOs and mainsequence stars. For example, Eisenstein (2006) used (g-r) < 0.2 and -2 < (u-g) < *(g-r) to select white dwarf candidates. Next, the selected spectra are fit to calculate a temperature and surface gravity. The white dwarfs are then selected by choosing objects with high surface gravity measurements (Kleinman et al. 2004). The resulting catalogs are published and publicly available from CASJobs on the SDSS servers. The SDSS fully covers the Virgo Cluster region explored in this thesis. Querying

33 2.3. WHITE DWARF SURVEYS WITHIN THE VIRGO CLUSTER REGION 18 the SDSS database yielded 146 spectroscopically confirmed white dwarfs within the NGVS field. These white dwarfs will be used as a test dataset to select white dwarf candidates within the NGVS (see Chapter 3) GALEX The search for white dwarfs has also been done using the 50cm Galaxy Evolution Explorer (GALEX) ultraviolet space telescope (Martin et al. 2005). GALEX covers the ultraviolet portion of the electromagnetic spectrum from nm. The original GALEX mission consisted of a deg 2 All-Sky Imaging Survey (AIS), a 1000 deg 2 Medium Imaging Survey (MIS), and an 80 deg 2 Deep Imaging Survey (DIS) using two bands: The Far-Ultraviolet (FUV) and the Near-Ultraviolet (NUV). These bands can be seen in Figure 3.2 in Chapter 3. The 95% detection limits of the AIS/MIS/DIS are 20.5/23.5/25.5 NUV AB magnitude respectively. White dwarf selection using GALEX was done by Bianchi et al. (2011) by matching AIS/MIS and SDSS photometry since GALEX lacked spectroscopic measurements. Colour cuts of (FUV-NUV) < were used to select the hottest stars in the sample and an additional colour cut of (NUV-r) > 0.1 separates the stars from QSOs. This method was aimed to select the hottest white dwarfs (T eff K) since they are brightest in the UV bands. Within the NGVS field the resulting selection process yielded 175 white dwarf candidates. However, the process makes no attempt to distinguish white dwarfs from hot sub-dwarf stars and includes contamination (see Chapter 4.3 for more discussion). Of the three contiguous GALEX surveys, only the AIS surveyed the Virgo

34 2.4. SELECTING HALO WHITE DWARFS 19 Cluster region. This means that the selected white dwarf candidates are brighter than NUV 20.0 AB magnitude. 2.4 Selecting Halo White Dwarfs Motivation Despite their importance to Galactic formation and evolutionary models, halo white dwarfs are one of the least studied populations of stars. This is due to their small radii and faint optical luminosities. In the early 2000 s the population was considered as a potential contributor to the dark-matter content in the Milky Way (ex. Oppenheimer et al. 2001), however, this view is now considered to be unlikely (Reid 2005). However, despite the belief that the halo white dwarf population does not account for asignificantportionofthedarkmattercontent,theycanstillprovideinformation regarding Galactic formation as well as stellar evolution models of Population II stars (Rowell & Hambly 2011). Halo white dwarfs can also be used to estimate the age of the halo by studying the white dwarf luminosity function and looking for the faintest objects (Harris et al. 2006; Hansen et al. 1999). The most extensive search for halo white dwarfs was performed by Rowell & Hambly in 2011 using data from the SuperCOSMOS Sky Survey. This survey covered nearly three quarters of the sky and obtained kinematic and photometric data for white dwarf candidates to a limiting magnitude of R Using a selection tool of v t > 200 km/s to select halo white dwarfs returned only 93 candidates, showing that this population continues to be largely undetected at these optical magnitudes. This thesis employs a similar method but uses data more than 5 magnitudes fainter in the g-band.

35 2.4. SELECTING HALO WHITE DWARFS 20 Figure 2.6: The Galactic Space Velocity coordinate system. Figure: Carroll & Ostlie (2006) Previous Results Using Kinematics The ability to select halo white dwarfs relies on their kinematics, as opposed to di erent spectral features which can be used to separate disk and halo main-sequence stars. This is a result of gravitational di usion which allows the metals to sink below the photosphere of the white dwarf (Cojocaru et al. 2015). The result is that disk and halo white dwarfs can be separated using Galactic space velocities. Galactic space velocities (U, V, W) are the velocities of a star in Galactocentric coordinates. The geometry can be seen in Figure 2.6. The direction of the vectors in Figure 2.6 represent the direction of positive velocities. Positive U velocities represent motion away from the Galactic Center, positive V represents motion with the Galactic Disk rotation, and positive W is towards the North Galactic Pole.

36 2.4. SELECTING HALO WHITE DWARFS 21 The Galactic space velocities can be used to determine a lower limit to the number of halo objects in a kinematic sample of stars. This is because in these coordinates the average space velocity of a pure halo population with respect to the local standard of rest, that is the velocity which an object in the position of sun would travel if it were in a perfectly circular orbit around the Galactic center, is (U,V,W) = (0, -220, 0) km/s. This is a result of the lack of combined rotation in Galactic halo which yields mean velocities of zero in U, V, and W. However, the halo population will have an average V velocity of 220 km/s as a result of the rotation of Sun about the Galactic Center. This method has been used multiple times in order to determine whether the halo contributes to the local white dwarf population. These white dwarfs would have high space velocities, but their orbits happen to currently place them within the solar neighborhood. An example of such work includes Kawka & Vennes (2006), who used a catalog of high proper motion white dwarf candidates from the revised New Luyten Two-Tenths catalog (Salim & Gould 2003). They calculated distances using colour-absolute magnitude relations, and U and V velocities from the measured proper motions. They over-plotted typical velocity ellipsoids from the thin disk (solid ellipse), the thick disk (dashed ellipse), and the halo (dotted ellipse) from Chiba & Beers (2000) in order to determine which Galactic component each white dwarf belonged to. This method returned zero halo white dwarfs and suggested that every white dwarf within their sample belonged to the disk. Their results can be seen in the top panel of Figure 2.7. This result has also been corroborated by Sion et al. (2014) who used a sample of white dwarfs within 25 pc and found no compelling evidence that this sample included a halo white dwarf.

37 2.4. SELECTING HALO WHITE DWARFS 22 Figure 2.7: U and V velocities in km/s for white dwarfs from (Top) Kawka & Vennes (2006) and (Bottom) Oppenheimer et al. (2001). The velocity ellipsoids for a thin disk, a thick disk, and a halo population are plotted where the disk components are centered at (U,V) = (0,0) and the halo is at (-220, 0). The squares represent selected halo candidates. Figure: (Top) Kawka &Vennes(2006),(Bottom)Oppenheimeretal.(2001).

38 2.4. SELECTING HALO WHITE DWARFS 23 The largest survey used to characterize halo white dwarfs was done by Oppenheimer et al (2001) using the SuperCOSMOS Sky Survey. This survey covered 4000 deg 2 at the Southern Galactic Cap and provided photometry and proper motions for stars with R < Since the survey was at high Galactic latitude the U and V velocities could be described solely from the proper motions in RA and DEC. Using the U and V velocities Oppenheimer (2001) selected 38 stars with halo-like velocities, and these candidates can be seen in the bottom panel of Figure 2.7. The work was corroborated by Salim et al. (2004) who improved the photometric and astrometric measurements for the sample. The common theme throughout the studies which attempt to identify halo white dwarfs is that they are rare. The studies presented above found very few candidates, particularly Rowell & Hambly (2011) who identified less than 100 potential halo candidates out of their sample of white dwarfs. This thesis will use photometric data which is more than 5 magnitudes fainter than the Oppenheimer et al. (2001) study in order to determine whether a sample of halo white dwarfs can be identified. Various methods will be presented, including tangential velocities, U-V velocities, and photometric distances Globular Clusters and the Inner Halo Globular clusters o er a unique study of population II because they allow for a study of many stars at once, all of which are at similar distances, ages, and compositions. Using the distances an accurate HR diagram can be created, which allows for a comprehensive study of their stellar population. Since they contain some of the oldest stars in the Milky Way, the population is composed of low-mass stars in the

39 2.4. SELECTING HALO WHITE DWARFS 24 late stages of their evolution, as well as the remnants of the intermediate mass stars. This allows for a large study of white dwarfs at di erent positions along the cooling sequence. Kalirai et al. (2009) used ultra-deep Hubble Space Telescope (HST) imaging to study the white dwarf cooling sequence of Messier 4 (M4). The study revealed over 2000 white dwarfs within the cluster. M4 has an estimated age of 12.5 Gyr and lies at a distance of 2.2 kpc in the direction of the Scorpius constellation (Kalirai 2012). The colour-magnitude diagram derived from the HST imaging can be seen in Figure 2.8. The circled region in Figure 2.8 displays the location of the hottest white dwarfs in M4. These also represent the most recently formed white dwarfs in the cluster. Kalirai (2012) used the Keck Telescope to obtain spectroscopic measurements for six of these newly-formed white dwarfs, as well as four white dwarfs from Pauli et al. (2006) which had halo-like Galactic space velocities. Fitting the spectra of the white dwarfs from Pauli et al. (2006) revealed temperatures between K and K, suggesting that they formed between million years go. These white dwarfs are similar to the six recently formed white dwarfs from M4, which had cooling ages of approximately 100 Myr.

40 2.4. SELECTING HALO WHITE DWARFS 25 Figure 2.8: Colour-Magnitude diagram for the globular cluster M4 using HST filters. The circled region represents recently formed white dwarfs. Figure: Kalirai (2012)

41 26 Chapter 3 The Data: Constructing an Optical-Ultraviolet Catalog This chapter details the data sets used as part of this thesis and how they were used to construct a joint optical-uv catalog. An overview of the acquisition, telescopes, and instruments are presented, including relevant parameters associated with the final catalogs. 3.1 The Next Generation Virgo Cluster Survey The optical data used in this thesis was obtained as part of the Next Generation Virgo Cluster Survey (NGVS) (Ferrarese et al. 2012). The NGVS is a deep optical multi-band survey of the Virgo Cluster. The footprint covers 104 deg 2 centered on M87 (l=283.78, b=74.49) and extends to the virial radius of both the Virgo A and B substructures. The footprint of the survey can be seen in Figure 3.1. The NGVS was acquired using Megacam, which is a high-resolution imaging camera mounted at the prime focus of the 3.6m Canada-France-Hawaii telescope. Megacam is ideal for this type of survey as it provides a large field of view with uniform

42 3.1. THE NEXT GENERATION VIRGO CLUSTER SURVEY 27 Figure 3.1: The Next Generation Virgo Cluster Survey (NGVS) field in J2000 equatorial coordinates. The yellow lines correspond to a single Megacam pointing, and the grid totals 117 separate pointings. The background is composed of real NGVS images and was taken from the NGVS graphical search tool.

43 3.1. THE NEXT GENERATION VIRGO CLUSTER SURVEY 28 Figure 3.2: The transmission curves for the filters used in the NGVS with a typical DA white dwarf spectrum for reference (black). image quality and also has good sensitivity in the near-uv. Megacam is composed of 36 CCDs, each measuring 2048 x 4612 pixels, and has a field of view of 0.90 deg 2. The NGVS was carried out in 3 optical (u*, g, r ) and 2 near infrared (i and z ) bands resulting in wavelength coverage from nm. The transmission curves can be seen in Figure 3.2 with the spectrum of a DA white dwarf overlaid to show how the filters line up with its spectral features. The truncation of the white dwarf spectrum at 3800 Å is a result of the limits of the SDSS u-band. These filters are similar, but not identical, to filters used in the Sloan Digital Sky Survey (York et

44 3.1. THE NEXT GENERATION VIRGO CLUSTER SURVEY 29 Table 3.1: Various parameters for the NGVS including the exposure times, magnitude limits, seeing, and background constraints. Filter Exposure Times (s) NGVS Point Source Limits (mag) SDSS Point Source (mag) Median FWHM (arcsec) Moon Illumination u 11 x (S/N = 5) apple10% g 5x (S/N = 10) apple10% r 7x (S/N = 10) 23.1 apple1.0 apple40% i 5x (S/N = 10) any z 8x (S/N = 5) any al. 2000), however, magnitudes measured in one filter set can be transformed using relationships described in Ferrarese et al. (2012). All optical magnitudes quoted in this thesis will be in the Megacam system unless otherwise noted. This thesis will exploit the high image quality, depth, and seeing obtained as part of the NGVS. The resolution of an image is described by the full-width half max (FWHM) of the point spread function (PSF) of an unresolved source, such as a star. During the NGVS acquisition the FWHM in all bands never exceeded 1, and is particularly sharp in the g and i -band with median FWHMs of 0.77 and 0.52 respectively. This leads to very precise astrometric positions, which are crucial for deriving proper motions (see Chapter 5). Table 3.1 shows the exposure times achieved in the NGVS. One important aspect of the project was that the final dataset was created by stacking images. This practice is used to increase the signal-to-noise by creating the equivalent of a long exposure image by adding the flux from multiple short exposures. The total number of images, and the exposure time of each image, are listed in column 2. Once the images have been stacked, SExtractor (Bertin & Arnouts 1996) was used to extract a catalog of

45 3.1. THE NEXT GENERATION VIRGO CLUSTER SURVEY 30 objects. The sub-exposures were also dithered, which is a process that shifts the pointing of the images, to allow for the removal of cosmic rays and to fill in the gaps between images. The depth achieved in the NGVS is instrumental to detecting white dwarfs as they are faint in the optical region of the spectrum. The point-source magnitude limits of the NGVS survey can be seen in Table 3.1. These limits are also compared with SDSS and show that the NGVS detects sources that are >2 magnitudesfainter. However, when the surveys are compared at equal signal-to-noise limits this di erence is even larger. The u and g-band images were also taken under the darkest sky conditions (apple10% moon illumination) in order to minimize the background light detected, however, the i and z images were taken under any sky conditions as the sky is not as bright in the near-infrared Extracting Point Sources After the SExtractor was run on the processed stacked images, a catalog of sources was created. This catalog included every object observed in the NGVS including galaxies, stars, and QSOs. The white dwarfs, as well as any stellar object, detected in this survey are at a large enough distance that they will be detected as point sources. Thus, in order to decrease contamination from resolved sources, the point sources must be extracted from the master catalog. The point source extraction was done in accordance with Durrell et al. (2014) who used the NGVS to study the spatial distribution of globular clusters in the Virgo Cluster. At the distance of the Virgo Cluster many of the globular clusters were expected to be point sources (Durrell et al. 2014). In order to extract point sources,

46 3.1. THE NEXT GENERATION VIRGO CLUSTER SURVEY 31 Figure 3.3: The concentration index for NGVS Sources (grey) and stellar objects from SDSS (black). A sharp stellar sequence centered on i = 0, andacluster of background galaxies can be seen towards fainter g-band magnitudes. Only 100,000 point sources from the NGVS are plotted for clarity. The dashed lines indicate the chosen point source range used in this thesis and is in agreement with Durrell et al. (2014). the authors used the concentration index, i, which is the di erence between the 4-pixel and 8-pixel aperture i-band magnitudes of an object. These magnitudes were calculated by summing all of the flux within a specified aperture. Since each pixel covers on the sky, the 4-pixel diameter of 0.75 should cover most of the flux within the seeing disk. When the aperture over a point-source is doubled there

47 3.1. THE NEXT GENERATION VIRGO CLUSTER SURVEY 32 will only be a negligible amount of flux added as a result of the residual light left over from the background subtraction. This results in concentration values above zero. A negative concentration index occurs when the background subtraction is overestimated. The result is that for a true point source the concentration index should be roughly zero. The i-band was used to calculate the concentration index of an object because it was taken under the best seeing conditions. The resultant PSF of objects in the i-band is more concentrated than in any other band obtained in the NGVS. In order to quantify the range of concentration index needed to extract point sources, a set of known point sources was queried from the SDSS. These objects were all spectroscopically classified as stars, and should thus be point-sources. The resulting plot of concentration index versus g-band magnitude can be seen in Figure 3.3, where the black triangles represent the stars from the SDSS. By visually inspecting Figure 3.3 a concentration range of 0.1 < (i 4 i 8 ) < (3.1) was chosen, where i 4 and i 8 are the 4-pixel and 8-pixel i-band magnitudes respectively. The chosen range can be seen as the dashed lines in Figure 3.3, and is in agreement with Durrell et al. (2014). Applying the concentration criterion to all NGVS point sources leads to a catalog of 5,345,653 objects. This catalog will be referred to as the NGVS point-source catalog for the remainder of this thesis.

48 3.2. THE GALEX ULTRAVIOLET VIRGO CLUSTER SURVEY The GALEX Ultraviolet Virgo Cluster Survey The ultraviolet catalog used in this thesis was constructed as part of the GALEX Ultraviolet Virgo Cluster Survey (GUViCS) (Voyer et al. 2014). The catalog is a combination of archival data from the original GALEX surveys (AIS, MIS, DIS), the Nearby Galaxies Survey (NGS), as well as PI programs. The Virgo Cluster region was covered mainly by the AIS in the original GALEX survey. In order to improve the depth of the UV data, the GUViCS team was awarded time in 2010 to cover the NGVS footprint to a depth equivalent to the MIS. GUViCS covers an area of 120 deg 2 centered on M87 and covers most of the NGVS field. Some regions were avoided due to the presence of bright stars in order to prevent saturation of the detectors. The sky coverage can be seen in Figure 3.4, with the NGVS field indicated in yellow. The GUViCS survey contains UV photometry obtained from the GALEX satellite in both the near-ultraviolet ( eff =2316Å) and far-ultraviolet ( eff =1539Å) bands, and is a combination of multiple observations. In order to maximize the point-source depth, only the detection with the highest signal-to-noise for a given object was retained. The resulting catalog contains NUV data to a depth of m NUV =23.1,and FUV data to a depth of m FUV = The ability to take data in the FUV was lost in early 2010 and was therefore unavailable during the GUViCS follow-up observations. This thesis will therefore focus on the deeper NUV data in order to best match the depth of the NGVS. An important feature of the UV data is the FWHM of the PSF. Since the GALEX telescope was operated from space it had the advantage that the PSF is dominated by the properties of the telescope as opposed to the turbulence in the atmosphere.

49 3.2. THE GALEX ULTRAVIOLET VIRGO CLUSTER SURVEY 34 Figure 3.4: The sky coverage for the GUViCS catalog is shown in RA and DEC (J2000) compared to the NGVS footprint (yellow). The dashed circles represent the targeted GUViCS pointings, and the colour indicates the exposure time of the image. The red circles indicate exposure times between 800 and 1500 seconds, the cyan circles represent images with MIS depth (exposure time seconds), the dark blue circles indicate images with exposure times greater than s. Black areas represent fields that were avoided due to the presence of a bright foreground star. As a reference, the fields from the far-infrared survey HeViCS are shown in green. Figure: Voyer et al. (2014).

50 3.3. MATCHING THE CATALOGS 35 The PSF in the NUV band has a FWHM of 4-6 arcseconds, with a median of 5.3 arcseconds (Bianchi et al. 2014). The resolution of GALEX is dominated by the microchannel plate detector, which has 1.5 arcsecond pixels, as well as the telescope optics and the ground pipeline (Martin et al. 2003; Morrissey et al. 2007; Llebaria et al. 2008). This resolution was tolerable for the science goals of GALEX since they were extragalactic in nature. A point-source catalog was created and published by Voyer et al. (2014). The catalog consists of sources, of which fall within the NGVS footprint. This catalog will serve as the ultraviolet source catalog for the remainder of this thesis Caveats A feature of the GUViCS catalog is that during the creation of the point-source catalog the authors removed bright foreground stars which appeared in the SIMBAD database. This was done because the main science drivers of the catalog were extragalactic in nature. Since this thesis is focused on the ability to select stars, the catalog was combined with the hot star catalog of Bianchi et al. (2011) to supplement the GUViCS data. 3.3 Matching the Catalogs In order to create a unified UV-optical catalog for sources in the NGVS field, the NGVS and GUViCS catalogs were matched. This section details the matching procedure, as well as what was done in the event of a multiple match. A discussion about spurious matches is also presented.

51 3.3. MATCHING THE CATALOGS Creating a UV-Optical Catalog The UV and optical catalogs were matched using TOPCAT (Taylor 2005), which is software designed specifically to match astronomical catalogs. TOPCAT merges the catalogs using their equatorial coordinates (RA and DEC) and matches objects within a specified search radius. If there happen to be multiple objects within the specified search radius, TOPCAT will designate all of the objects in the search radius as a match and place them in a unique group. TOPCAT returns all objects which have at least one match between the NGVS and GUViCS catalogs in a list. The search radius chosen in this thesis was 3. This was chosen to coincide with work done by Bianchi et al. (2011) who matched GALEX and SDSS data. The 3 radius was chosen to match the large PSF of the GALEX observations. Applying the chosen search radius to the NGVS-GUViCS catalogs results in unique UV sources with at least one optical counterpart and unique optical sources with at least one UV counterpart. Removing the multiple matches leads to one-to-one matches, which will be used as the NGVS-GUViCS matched catalog for the remainder of this analysis Multiple Matches The depth of the NGVS combined with the large search radius means that there will be instances of multiple matches. When matching the two catalogs, there are two scenarios where a multiple match can occur. The first, and dominant case is multiple optical counterparts being attributed to a single GUViCS source. The second case is multiple GUViCS sources being attributed to a single NGVS source, however, this case is rare. The objects with multiple matches are discarded since the broad point

52 3.3. MATCHING THE CATALOGS 37 spread function of the UV object means that it may be a superposition of all possible optical counterparts within 3 arcsec. This would render meaningless colours and consequently these instances were removed (Bianchi et al. 2011). A discussion on the impact of this decision is presented in Chapter Spurious Matches The high spatial density of the optical data means that there is a possibility that two unique sources may be matched together. This case is termed a spurious match, and can happen as a result of the di erent wavelength regimes probed in the two surveys. For example, a faint QSO and a late-type star may lie within the match radius of a UV source. When viewed in the UV, the QSO would be detected, however, the QSO could be too faint in the optical to be detected. The opposite is true for late-type stars (such as an M-dwarf). This could lead to the UV detection of the QSO being matched to the optical detection of the late-type star. The likelihood of a spurious match was estimated in two ways. First, a collection of 1 square degree cutouts from the GUViCS sample were selected, and 1 degree was added to both their RA and DEC. The resulted tessellated cutout was then matched to the NGVS catalog and the spurious match rate was calculated as the total matches divided by the total number of points within the square degree o set. Repeating the exercise for 5 di erent pointings led to a spurious match rate of 2% A second method to estimate the spurious match rate was done using a Monte Carlo method. A 0.5 deg 2 field of both GUViCS and NGVS data was taken in order to represent the spatial density of both catalogs. The NGVS data was then replaced by an equal number of randomly generated coordinates using the random.uniform

53 3.3. MATCHING THE CATALOGS 38 function in Python. A nearest neighbors algorithm was applied to the resulting coordinates in order to determine the distance to the three nearest mock optical objects for each GUViCS object. If the distance to one of the three nearest neighbors was less than three arcseconds then it was considered to be a match. This exercise was repeated 100 times for each GUViCS point. The calculated average spurious match rate was 3%. Both methods show that the contamination from spurious results is approximately 2-3%. However, the resulting colours from spurious matches could be very odd depending on the types and magnitudes of the two objects. For this reason, a spurious match is not expected to contaminate the results presented in this thesis.

54 39 Chapter 4 White Dwarf Candidates within the NGVS Field This chapter describes the process used to select white dwarf candidates within the NGVS field using the matched NGVS-GUViCS catalog created in Chapter 3. The selection process using colour cuts is described in Section 4.1, while the possible contaminants are discussed in Section 4.2. Finally, a comparison to previous UVoptical selections methods is presented in Section Selection Procedure Choosing Colours A common way to separate di erent classes of astronomical objects is to use their colours. Di erent types of objects will have di erent colours depending on their spectral energy distribution. For example, Wien s Law, max = b T (4.1)

55 4.1. SELECTION PROCEDURE 40 where b = x 10 3 m K is a constant, shows that hot stars (T> K) will have a peak wavelength in the NUV band (290 nm). The resulting spectral energy distribution dictates that hot stars will brighter in the NUV band than in an optical band. The (NUV-g) colour will thus be numerically smaller, as numerically larger apparent magnitudes represent fainter objects. On the other end, cool stars will peak in the near-infrared, such as the i-band, and will be fainter in the NUV band. This will lead to a positive (NUV-g). This method will be used in the following analysis to separate newly formed white dwarfs, which have high temperatures, from other objects such as main-sequence stars and QSOs. First, a collection of spectroscopically confirmed white dwarfs, stars and QSOs from the SDSS were compiled. The white dwarfs were taken from Kleinman et al. (2015), the QSOs from Paris et al. (2014), and the stars were queried from SDSS DR12. Another class of objects called blue horizontal branch (BHB) stars and blue stragglers (BS) stars were taken from Scibelli et al. (2014). Blue horizontal branch stars are post-main-sequence stars which turn blue-ward on the Hertzsprung-Russell diagram after the onset of helium core burning. Blue stragglers are hot stars which stay on the main-sequence longer than predicted. Blue stragglers are thus bluer than the main-sequence turn-o point. Blue stragglers and blue horizontal branch stars are included due to their blue colours, as they may contaminate the white dwarf selection (see Chapter 3.2). The ability to select the white dwarfs is critically dependent on the capability to separate the di erent classes of astronomical objects. In order to see the value of the NUV filter, consider Figure 4.1, which shows a colour-colour diagram composed of strictly Megacam u*, g, and i filters. This colour-colour diagram shows that many

56 4.1. SELECTION PROCEDURE 41 Figure 4.1: Colour-colour diagrams of spectroscopically confirmed objects from the SDSS that have been matched to the NGVS. The blue points indicate white dwarfs from Kleinmann et al. (2015), the red points are QSOs from Paris et al. (2014), the cyan points are blue stragglers and blue horizontal branch stars from Scibelli et al. (2014), and the stars were queried using the SQL search in SDSS DR12. The separation between the objects is poor when compared to the (g-i), (NUV-g) diagram in Figure 4.2. of the spectroscopically confirmed white dwarfs (blue points) overlap with either the QSOs (red), the main sequence stars (magenta), or the blue horizontal-branch stars (black). Specifically, the main-sequence stars and BHB/BS stars occupy the same region of colour-colour space as many of the redder white dwarfs. After trying many di erent colour-colour combinations it was determined that

57 4.1. SELECTION PROCEDURE 42 Figure 4.2: (g - i), (NUV - g) colour-colour diagram for the matched NGVS-GUViCS point source objects (grey), spectroscopically confirmed SDSS WDs (blue circles), QSOs (red squares), and stars (magenta triangles). The black dashed lines indicate the chosen colour cuts applied to the NGVS- GUViCS data in order to select white dwarf candidates while minimizing contamination from other objects. the (g-i), (NUV-g) colour-colour diagram provided the best separation between the white dwarfs, BHBs, QSOs, and main sequence stars. The resulting plot can be seen in Figure 4.2. The dashed lines in Figure 4.2 show the location of the colour cuts applied to the NGVS-GUViCS catalog to select white dwarf candidates. These lines were selected in order to include as many confirmed white dwarfs, whilst minimizing the contamination from other objects.

58 4.1. SELECTION PROCEDURE 43 The resulting colour cuts were chosen by visually inspecting the locations of the spectroscopically confirmed objects in the (g - i), (NUV - g) plane with the goal of minimizing contamination from QSOs and hot sub-dwarfs (see section 4.2 for further discussion). A magnitude cut of g < 24.5 was also imposed in order to minimize the contamination by objects with large photometric errors. The black dashed lines in Figure 4.2 & 4.3 show the location of the colour cuts used to select white dwarf candidates. First, all objects with (g - i) < -0.3 are selected, which represents the bluest objects in the data set. The second cut is indicated by the diagonal dashed lines and is used to separate the bluest main sequence and sub-dwarf stars from the white dwarfs. A further cut is made on the UV data by only selecting objects with uncertainties below 0.3 mag. Applying these colour cuts results in the selection of 852 white dwarf candidates. In order to confirm the selected region, a series of model evolutionary tracks for white dwarfs, stars, and QSOs was plotted in the same colour-colour plane. The models originate from Bianchi et al (2009) and were modified to fit the Megacam and GALEX filters used in this thesis. The white dwarf model is derived from the TLUSTY model (Hubeny & Lanz, 1995) and the main sequence stars are modeled using a Kurucz model (Kurucz, 1993) which produces model absolute magnitudes as afunctionoftemperatureandlogg. The QSO model is a function of redshift, and was provided by Luciana Bianchi (see Bianchi et al. 2009, 2011). The location of the models in colour-colour space can be seen in Figure 4.3. Comparing Figure 4.2 with Figure 4.3 shows that the models and observations are in good agreement. A further addition to the white dwarf candidates was made using the results from Bianchi et al. (2011). This is required because the GUViCS catalog removed many

59 4.1. SELECTION PROCEDURE 44 Figure 4.3: Model tracks from Bianchi et al. (2009a) are plotted to show ideal locations for the WDs (blue), QSOs (red), and for stars of various surface gravities (magenta). The WD track is for a log g =8.0fortemperatures between 15,000 and 200,000 K. The model QSO colours are a function of redshift, with values between 0 and 5. Model stars with log g =5,4,3 are indicated by the solid, dashed, and dotted magenta lines, respectively. The black dashed lines indicate the chosen colour cuts applied to select white dwarf candidates. bright stars during the creation of their point-source catalog. A further 42 candidates were added by applying the same colour cuts to the shallower GALEX AIS data, bringing the total number of candidates up to 894, of which 52 are spectroscopically confirmed by the SDSS.

60 4.2. CONTAMINANTS Contaminants As Figure 4.2 shows, objects that are not white dwarfs can fall within the same region of the g-i, NUV-g plane as a white dwarf. The main source of contamination in the bluest regime are O sub-dwarfs (sdo), while towards redder colour, the main contamination is from QSOs with high UV fluxes. sdo stars are thought to be the cores of red giant stars which ejected their surrounding shell prior to reaching the AGB-phase (Geier 2006). They are also very blue, however, they are very rare and not expected to strongly contaminate the white dwarf candidates. The contamination rate for QSOs was estimated by matching the white dwarf candidates to the NGVS Master Spectroscopic Catalog (MSC), which is a compilation of all available spectroscopic redshifts for objects within the NGVS footprint. The catalogs included within the MSC include the SDSS DR12, NED, and VCC, as well as a number of NGVS PI programs that targeted the Virgo Cluster with a variety of telescopes including KEck, AAT, and MMT. Matching the white dwarf candidates to the MSC returns 66 matches, of which 60 are classified as stars and 6 are classified as extragalactic. The extragalactic sources are all located in the red portion of the selection region. In order to quantify the contamination by sdo and other hot stars, the white dwarf candidates were matched to SDSS DR12. Matching the two catalogs returned 59 matches, of which 52 were classified as WDs and 7 were classified as di erent types of hot stars. These stars are all bright (brighter than g 18) and therefore will not a ect the selection of halo white dwarfs performed in Chapter 5 as these are much fainter.

61 4.3. COMPARISON TO SDSS-GALEX AIS MATCHING Comparison to SDSS-GALEX AIS Matching A similar exercise was performed by Bianchi et al. (2011), for which GALEX data release 5 was matched with SDSS DR7. The authors used a colour cut of (FUV - NUV) < 0.13 to select hot stars, and (NUV - r) < 0.1 to separate the single star candidates from the binary candidates (see Fig 5). This selection method di ers from the one presented in this thesis for two reasons. First, the r-band data for the NGVS was never completed over the whole field (Raichoor et al. 2014). Second, the GALEX FUV detector was out of commission when the GUViCS data was taken, and thus the data is shallow and incomplete over the NGVS field. One of the main downfalls with the SDSS-GALEX matching is that some of the hottest and faintest white dwarfs detected in the UV will not appear in SDSS (Bianchi et al. 2011). At the magnitude limit of the GUViCS data (NUV 23), which is equivalent to the MIS data used in the SDSS-GALEX matching, Figure 4.3 shows that the hottest WDs have typical (NUV - g) = This means that optical data must be complete to g 24.5 to allow for the detection of the hottest white dwarfs. Since the depth of SDSS is only 23.1 in the g-band, many of these hot white dwarfs would not have been detected. By contrast, the depth of the NGVS optical data (g 26) means that all of the white dwarfs detected in the GUViCS data should also appear in the NGVS data. The ability to recover sources that were selected by Bianchi et al. (2011) provides aquickcheckofthecolourselectionsusedinthisanalysis. Ofthe28319classifiedhot star candidates from Bianchi et al. (2011), 179 fall within the NGVS footprint. Of the 179 sources, 126 fall within the region of colour-colour space used to select white

62 4.3. COMPARISON TO SDSS-GALEX AIS MATCHING 47 dwarfs detailed in Figure 4.3. Matching these 126 objects to the catalog obtained in Chapter 3.1 returns 84 sources. The remaining 42 are lost because the GUViCS catalog removed all bright foreground stars that were matched to the SIMBAD catalog as discussed in Chapter 3. These objects do appear in the NGVS catalog and were appended to the list of white dwarf candidates. This check shows that all objects classified as white dwarfs in the shallower GALEX-SDSS matching are also classified as white dwarfs in this thesis. The number also show that the SDSS-GALEX matching was not su cient to select white dwarfs below g 21 as a result of the shallow NUV data. Also, even with the deeper NUV data provided by GUViCS, the shallower optical data acquired by the SDSS would not detect some of the hottest white dwarfs due to their faint optical luminosities. Thus, the combination of deep optical data from the NGVS and the NUV data from GUViCS will return the highest number of white dwarfs in this Galactic region.

63 48 Chapter 5 Photometric Properties This chapter presents various properties of the white dwarf candidates extracted in Chapter 4 including magnitude distributions (Section 5.1), photometric distances (Section 5.2) and proper motions (Section 5.3). 5.1 Magnitude Distributions The first photometric property that will be explored is the distribution of magnitudes in the GALEX NUV, Megacam g, and Megacam i bands for the white dwarf candidates. These distributions can be seen in Figure 5.1, where they are compared to the photometric selections made in the Bianchi et al. (2011) using GALEX-SDSS matching (B11), and the SDSS spectroscopic selections made by Kleinman et al. (2013) (K13). Figure 5.1 highlights the depth of both the NGVS and GUViCS data, as the candidates selected in this work agree with previous spectroscopic and photometric classifications to a depth of g Below g 19.0 the selection method described in Chapter 4 selects more than five times the number of previously discovered objects. The distribution also peaks at g 21.5, which is below the spectroscopic threshold of the SDSS and the photometric limit of the GALEX AIS.

64 5.1. MAGNITUDE DISTRIBUTIONS 49 Figure 5.1: Magnitude distributions for the white dwarf candidates selected in Chapter 4 compared to the SDSS spectroscopic selection from Kleinman et al (K13) and GALEX AIS photometric selection from Bianchi et al. (2011) (B11).

65 5.1. MAGNITUDE DISTRIBUTIONS Model Comparison TRILEGAL is a stellar population synthesis code developed by Girardi et al. (2005) which generates a mock photometric catalog along a chosen line-of-sight based on input model evolutionary tracks. TRILEGAL has the ability to simulate surveys in a variety of photometric bands, which makes it a particularly useful model when comparing matched catalogs that contain di erent photometric systems. A mock catalog was created in order to compare with results obtained using the selection criteria in Chapter 4. The mock catalog was centered on the galactic coordinates of M87, which is approximately the center of the NGVS field. The total area of the catalog was selected to be largest the model will allow, 10 deg 2, in order to best match the size of the NGVS footprint. A limiting magnitude of 26 in the g-band was chosen to also match the NGVS. All other input parameters were left at the default option, including a Chabrier IMF, a Milky Way extinction model, and a three component Galactic model including a squared hyperbolic secant thin and thick disk and an oblate halo. Due to the high Galactic latitude of the NGVS, the field will not include any bulge stars and so bulge parameters were not included. The resulting catalog contains various parameters for the mock stars including apparentmagnitudes inthefivemegacambands,temperature,log g, and mass. White dwarfs were selected based on their log g, and any mock star with a log g>7.5 was considered to be a white dwarf. A magnitude cut was also imposed on the (g-i) < -0.3 color to match the selection criteria that was imposed on the NGVS data. The resulting magnitude distribution can be seen in Figure 5.2. The data has been binned in 0.5 magnitude bins and displayed as a surface density, instead of a total

66 5.1. MAGNITUDE DISTRIBUTIONS 51 Figure 5.2: g-band magnitude distribution for the white dwarf candidates (green) and the TRILEGAL white dwarfs (white). count, in order to account for the smaller area of the mock catalog. The resulting surface densities of the mock catalog follow the same distribution as the real data to a depth of g=22.5, however, the mock data consistently over-predicts the surface density throughout this regime. Below g=22.5 the mock data over-predicts the data by a factor of 10 or more. The magnitude distribution in the g-band su ers from incompleteness below g 22 as a result of the completeness limit of the GUViCS survey (NUV 23.1). The white

67 5.1. MAGNITUDE DISTRIBUTIONS 52 dwarfs selected in Chapter 4 have typical (NUV-g) colours between -1 and 1 (see Figure 4.2), with numerically higher values indicating lower temperatures. This means that the cooler white dwarfs with (NUV-g)=1 are lost below g Three other scenarios exist that could explain an over-prediction by the model. First, some UV candidates were lost as a result of being matched to multiple optical sources. As discussed previously, these objects were removed since the GUViCS PSF could potentially be a superposition of the optical sources within the search radius. This would lower the total number of candidates, and could explain the discrepancies between the model and the real data. A second scenario which could explain the over-prediction is the cut in the (NUV-g). The TRILEGAL model is not currently equipped to generate a mock catalog with both Megacam and GALEX filters simultaneously and thus a corresponding (NUV-g) cut which matched the one presented in Chapter 4 could not be imposed. This cut could potentially lower the total number of objects predicted by the model. The final scenario involves the uncertainties in the UV data. The GUViCS catalog contains objects with NUV magnitude uncertainties as large as 0.3 mag. By imposing a magnitude cut on the NGVS-GUViCS data some of the white dwarfs with larger uncertainties may not fall within the selected region shown in Figure 4.2. Large discrepancies at faint magnitudes have also been found by Bianchi et al. (2009, 2011). The authors suggest that the reason for the over-prediction is caused by the chosen initial-final mass relation (IFMR). This relation, despite it being very important to our understanding of stellar evolution, is not well constrained (Bianchi et al. 2011). The IFMR determines the mass of the white dwarf based on the initial mass of the progenitor. White dwarfs have a very well constrained mass regime,

68 5.2. PHOTOMETRIC DISTANCES M, however, the progenitor masses vary from M meaning that a small change in white dwarf mass has a large influence on the inferred progenitor mass (Bianchi et al. 2011). Since the progenitor mass influences the total lifetime of astaritwillalsoa ect the total number of white dwarfs which are produced. 5.2 Photometric Distances The ability to determine the distance to a star is essential in order to study its kinematics. As Figure 5.1 shows, the white dwarf candidates in this work are all fainter than g 18. Hipparcos (ESA 1997) obtained parallax measurements for stars brighter than V 12, and so parallax measurements would not have been acquired for the white dwarf candidates (Perryman et al. 1997). In the absence of parallax measurements, an estimate of the distance to these candidates can be made using theoretical colour-magnitude relations. Distances to a subset of candidates were made using the TLUSTY model (Hubeny & Lanz 1995) cooling curve seen in Figure 4.3. This model returns absolute magnitudes for a given temperature and surface gravity. The end result is that a relationship between the (g-i) colour and the absolute g-band magnitude is created. With an absolute magnitude the distance can be calculated using the distance modulus, d =10 0.2(m M+5 Ag) (5.1) where m is the apparent magnitude in a given band, M is the absolute magnitude,

69 5.2. PHOTOMETRIC DISTANCES 54 and A g is the extinction caused by interstellar material in the g-band. A g was taken to be zero since the NGVS surveys a high Galactic latitude. The model makes two very important assumptions. First, it only considers pure hydrogen atmospheres (DA). Recent spectroscopic surveys have shown that DAs are the dominant type of white dwarfs, however, one must be wary of the presence of other types. For example, Kepler et al. (2015) reported 8441 spectroscopically confirmed WDs in SDSS DR10 of which 6887 are DAs and 450 are helium dominated DBs. A quick check of the Kleinman et al (2013) catalog which had previously been matched to the NGVS reveals that 96/110 WDs have been classified as DAs. Moreover, DAs tend to dominate in the high-temperature range which is probed in the model (> K). Hansen & Liebert (2003) show that convection in the He layers of white dwarfs will deposit He in the upper atmosphere. The authors suggest that this process will increase the fraction of DB WDs below K, but that DAs will dominate the total population of hot white dwarfs. The second assumption is that the surface gravity (log g) isequalto8.0,whichis typical for an average white dwarf. This was presented in Figure 2.4, which showed that white dwarfs have typical log g values between 7.5 and 8.5. The e ect of these two assumptions will be discussed in Chapter 7. With these caveats in mind, the estimated photometric distances for the subset of white dwarf candidates that have (g-i) < -0.5 can be seen in Figure 5.3. The (g-i) color was used as these bands had the highest signal-to-noise of all bands. The error bars are obtained as a result of the uncertainty in the (g-i) colour. Figure 5.3 shows the TLUSTY model predicts that the majority of the hot white

70 5.2. PHOTOMETRIC DISTANCES 55 Figure 5.3: Photometric distances for the white dwarf candidates selection in Chapter 4.1. Absolute magnitudes were calculated using the TLUSTY colourmagnitude relationship in combination with the Megacam (g - i) colours obtained as part of the NGVS. The distances were calculated using the distance modulus with the absolute and apparent g-band magnitudes as they have the least uncertainty. Error bars are a result of the uncertainties in the (g-i) colour.

71 5.3. DERIVING PROPER MOTIONS 56 dwarfs present in the NGVS footprint lie at distances between 200 and 2500 parsecs. The distances calculated in Figure 5.3 suggest that the white dwarf population in the NGVS is composed of both disk and halo white dwarfs. The distances will be used to characterize the white dwarf population in Chapter Deriving Proper Motions This section describes the method used to derive proper motions for a subset of the white dwarf candidates Method By definition, proper motion is the change in position of an object in the sky over time attributed to its own (space) velocity. This indicates that in order to calculate the proper motion, the position of an object must be precisely calculated from separate images taken over a long enough baseline so that the motion can be observed. The two catalogs used to calculate the change in position over time of the white dwarf candidates are the SDSS and the NGVS. The first step to calculate the proper motions for objects in the NGVS is to acquire epochs, that is the date at which the image was taken, from both the NGVS and SDSS datasets. The epochs for the SDSS positions were queried from the PhotoObjAll catalog in Data Release 12 (DR 12) and are returned in modified Julian day (MJD). The NGVS epochs were compiled by Stephen Gwyn for each NGVS pointing, also in modified Julian day. Taking the di erence between the epochs yields the baseline between each observation. The SDSS positions and uncertainties of each object are also provided as part of the PhotoObjAll catalog, and the NGVS positions were

72 5.3. DERIVING PROPER MOTIONS 57 provided with the NGVS catalog. A typical uncertainty in position for an SDSS object is roughly Deriving the positions and epochs from the NGVS was not as straightforward as for the SDSS. This is because the final NGVS images were created by stacking individual images with shorter exposure times, whereas the SDSS images are composed of a single image. As part of the acquisition process, some NGVS pointings had images taken over a period of years. The result is that objects with high proper motion will be smeared in the direction of motion. In order to compensate for this e ect, only pointings with all images taken within 3 months of each other were used to calculate proper motions Estimating the Uncertainty Comparison to the USNO Catalog In order to check the accuracy of the method, the resulting proper motions were compared to the catalog published by Munn et al. (2014). Their proper motions were derived by comparing positions using SDSS data and follow-up observations with the Steward Observatory Bok 90-inch telescope located at the United States Naval Observatory (USNO). The data was acquired in the r-band with an average baseline of six years with statistical uncertainties between 5 mas/yr for brighter objects and 15 mas/yr for the faintest objects. The data is complete to r 22.0 and constitutes the deepest available proper motion catalog to cover the NGVS footprint.

73 5.3. DERIVING PROPER MOTIONS 58 Figure 5.4: Comparison between proper motions in Right Ascension (RA) derived using NGVS-SDSS positions and the proper motion catalog given by Munn et al. (2014). The root-mean-square deviation between the NGVS and SDSS proper motions in RA is 12.9 mas/yr.

74 5.3. DERIVING PROPER MOTIONS 59 Figure 5.5: Comparison between proper motions in Declination (DEC) derived using NGVS-SDSS positions and the proper motion catalog given by Munn et al. (2014). The root-mean-square deviation between the NGVS and SDSS proper motions in DEC is 12.7 mas/yr.

75 5.3. DERIVING PROPER MOTIONS 60 Figure 5.6: Comparing the total proper motion measured from the NGVS-SDSS matching technique to the proper motions derived by Munn et al. (2014). The root-mean-square deviation about the one-to-one line (red) is 9.6 mas/yr.

76 5.3. DERIVING PROPER MOTIONS 61 Comparisons between the proper motions derived as part of this thesis and proper motions from the USNO catalog can be seen in Figures 5.4 and 5.5. The red line represents a perfect agreement between the two catalogs. The root-mean-square (rms) deviation from the one-to-one line in RA and DEC is 12.9 mas/yr and 12.7 mas/yr respectively. Combining the proper motions in RA and DEC results in Figure 5.6, where the rms deviation is 9.6 mas/yr. This shows that the mean di erence between the Munn et al. (2014) proper motions and those calculated using the NGVS positions is approximately 10 mas/yr Using QSOs In order to quantify the uncertainty associated with the method described above, a collection of QSOs were compiled from Paris et al. (2014). QSOs were selected as they are point-sources, but they are extragalactic in nature and therefore must have negligible proper motions. The calculated proper motions for the collection of QSOs can be seen in the bottom panel of Figure 5.7, where they are compared to stars and white dwarfs. The distribution of QSOs shows minimal spread around zero proper motion, however, the maximum observed proper motion for a QSO is 10 mas/yr. This suggests that the uncertainty associated with the NGVS proper motions is 10 mas/yr, which is in agreement with the calculated rms deviation about the one-to-one line shown in Figure 5.6.

77 5.3. DERIVING PROPER MOTIONS Results Figures 5.7 and 5.8 show the resulting proper motions of the white dwarf candidates. Many of the white dwarf candidates show very little proper motion. This is because they are mostly part of a disk population, and hence they have Galactocentric velocities comparable to the Sun. The spread of points towards negative µ RA and negative µ DEC is consistent with solar reflex motion, suggesting that these objects belong to the Galactic halo. This is because stars in the halo do not rotate in the Galactic disk with the Sun. The measured proper motion is therefore a result of the relative motion between the Sun and the halo stars. An estimate of the tangential velocities, as well as Galactic space velocities, will be provided in Chapter 6 as a tool to separate potential halo white dwarfs from their counterparts in the Galactic disk.

78 5.3. DERIVING PROPER MOTIONS 63 Figure 5.7: Calculated proper motions for stars (yellow), white dwarfs (blue), and QSOs (red) using the NGVS-SDSS positions.

79 5.3. DERIVING PROPER MOTIONS 64 Figure 5.8: Proper motion in RA and DEC for white dwarf candidates in the NGVS dataset (black). QSOs are also plotted to show they display minimal change in position between the two catalogs.

80 65 Chapter 6 Selecting Candidate Halo White Dwarfs This Chapter uses a combination of models and observations in order to classify the white dwarf candidates as belonging to either the Galactic disk or halo. 6.1 Colours and Magnitudes: Comparing to the TRILEGAL Model TRILEGAL provides simulated stellar magnitudes for a mock catalog at a given Galactic longitude and latitude using input stellar evolution models. This section will detail two ways to distinguish halo white dwarfs from disk white dwarfs using TRILEGAL: first using only g-band magnitude distributions, and second using a colour-magnitude selection. One feature of TRILEGAL is that is it categorizes the mock stars as being in a thin disk, a thick disk, or the halo. The following analysis was done by extracting the white dwarfs from each of the three Galactic components that are being probed by the NGVS.

81 6.1. COLOURS AND MAGNITUDES: COMPARING TO THE TRILEGAL MODEL Using g-band Magnitudes The first method used to determine the prevalence of disk and halo white dwarfs is to use their relative contribution to the total population as a function of g-band magnitude. This distribution can be seen in Figure 6.1. As expected, the relative fraction of halo white dwarfs (green) increases towards fainter magnitudes, while the fraction of disk white dwarfs declines. The discreteness of the plot arises as a result of small number statistics. In order to quantify the total number of expected disk and halo white dwarfs, the fractions obtained in Figure 6.1 were applied to the g-band magnitude distribution of white dwarf candidates (see Figure 5.1). The results yield 674 disk white dwarfs and 220 halo white dwarfs, or a 75% disk and a 25% halo contribution Using a Colour-Magnitude Selection The second method used to characterize the white dwarf population is to separate them in a colour-magnitude diagram. A colour-magnitude diagram of the mock white dwarfs from TRILEGAL can be seen in Figure 6.2. The black line indicates a visually chosen line which separates the halo population (green) from the majority of the disk population (red and yellow). Applying the chosen colour-magnitude cut to the white dwarf candidates yields 715 disk white dwarfs and 179 halo white dwarfs, or an 80%-20% contribution from the disk and halo respectively.

82 6.2. USING PHOTOMETRIC DISTANCES 67 Figure 6.1: The relative contribution to the white dwarf population by each of the three Galactic components.

83 6.2. USING PHOTOMETRIC DISTANCES 68 Figure 6.2: A TRILEGAL CMD for white dwarfs from each Galactic component. The black line was visually chosen to separate halo and disk white dwarfs.

84 6.2. USING PHOTOMETRIC DISTANCES Using Photometric Distances Photometric distances were calculated in Chapter 5 using a colour-magnitude relationship derived using the TLUSTY model (Hanz & Lubeny, 1995) for a DA white dwarf with a log g =8.0. Thesephotometricdistancescanbecombinedwiththehigh Galactic latitude of the NGVS field to derive model-dependent scale heights. Bovy, Rix & Hogg, (2012) used G-dwarf stars as tracers of the thin disk and found that the population was well fit by an exponential up to a scale height of 1 kpc. Using this value to crudely separate the disk population from the halo gives results that can be seen in Figure 6.3. Using the scale height of the Galactic thick disk to separate candidates results in 74% being classified as disk white dwarfs and 26% being classified as halo white dwarfs. 6.3 Kinematics: Using Proper Motions The di culty in selecting halo white dwarfs is exacerbated by the fact that they cannot be distinguished spectroscopically from their disk counterparts (Cojocaru et al. 2015). The Galactic halo is composed of population II stars which are more metal-poor than disk stars. A resulting estimate of the metallicity can thus provide atooltodistinguishbetweenmosthaloanddiskstars.thereasonthatthismethod cannot be used to distinguish white dwarfs is that they lack any surface metals due to the e ciency di usion (Cojocaru et al. 2015).

85 6.3. KINEMATICS: USING PROPER MOTIONS 70 Figure 6.3: Calculated scale heights as a function of g-band magnitude. The dashed line indicated the chosen scale height which separates disk and halo white dwarfs.

86 6.3. KINEMATICS: USING PROPER MOTIONS Tangential Velocities The first method used to separate halo white dwarfs from disk white dwarfs involves tangential velocities. The tangential velocity of an object is the velocity measured perpendicular to the line of sight. The tangential velocity, in km/s, is related to the proper motion, v t =kdµ, (6.1) where d is the distance in parsecs, µ is the proper motion in arcseconds/year, and k=4.74 is a constant. The tangential velocities for the subset of white dwarf candidates which have distances estimated from Chapter 5.2 and proper motions from Chapter 5.3 can be seen in Figure 6.4 as a function of g-band magnitude. The error bars are a result of the measurement errors both of the positions which are used to calculate the proper motion and of the colours which are used to calculate the distances of the candidates. In order to select the population of halo white dwarfs, a tangential velocity cut of 200 km/s is imposed. This value was chosen in accordance with Cojocaru et al. (2015) who used a population synthesis code to study the luminosity function of white dwarfs in the Galactic halo. The value of 200 km/s was chosen as it reflects typical heliocentric tangential velocities of a halo population. This cut is represented by the horizontal blue line in Figure 6.4.

87 6.3. KINEMATICS: USING PROPER MOTIONS 72 Figure 6.4: Calculated tangential velocities for the NGVS white dwarf candidates. The blue line indicates a tangential velocity of 200 km/s, which was the cut used to separate disk and halo white dwarfs.

88 6.3. KINEMATICS: USING PROPER MOTIONS 73 Applying the tangential velocity cuts shown in Figure 6.4 results in the classification of 13 halo white dwarfs and 118 disk white dwarfs, or a 90%-10% disk-halo contribution Galactic Space Velocities Coordinate Transformations Another method that can be used to separate disk and halo stars is to use their Galactic space velocities (U, V, W). Since these velocities are defined with respect to the Galactic center, a transformation from equatorial (RA and DEC) to Galactic coordinates (l, b) mustbeperformed. The transformation from motions in the Equatorial coordinate system to velocities in Galactic coordinates were done in accordance with Johnson & Soderblom (1987), but with J2000 coordinates. The Galactic space velocities are related to the motions in equatorial coordinates using the following transformations: U 6 V = B 6kdµ W kdµ (6.2) where U, V, and W are the Galactic space velocities in km/s, is the radial velocity in km/s, k=4.74 is a constant, d is the distance in parsecs, and µ and µ are the proper motions in RA ( ) anddec( )inarcsecond/yearrespectively. The transformation matrix, B, is equal to

89 6.3. KINEMATICS: USING PROPER MOTIONS 74 B = T A (6.3) where cos o +sin o 0 sin NGP 0 + cos NGP + cos NGP +sin NGP 0 T = 6+sin o cos o sin NGP cos NGP (6.4) cos NGP 0 + sin NGP and 2 +cos cos sin cos sin A 6+sin cos +cos sin sin 4 +sin 0 +cos (6.5) are used to transform the coordinates. In order to perform the transformation the location of the North Galactic Pole (NGP) in equatorial coordinates (J2000) is taken to be: NGP = NGP = The angle between the North Celestial Pole (NCP) and the great circle passing through the North Galactic Pole and zero degrees of Galactic latitude are taken to be

90 6.3. KINEMATICS: USING PROPER MOTIONS 75 o = Plugging these values into equation 6.4 gives 2 T = (6.6) The uncertainties in the space velocities are also calculated using the method of Johnson & Soderblom (1987): U 2 V 2 W = C 6(kd) b 12 b µ +( d µ d 4 )2 (kd) µ µ k 2 2 d 6b 22 b µ +( d µ )2 b d 32 b 33 (6.7) where represents the uncertainty in a given variable which is represented in the subscript. The elements of the matrix C are just the squares of the elements of B (c ij =b 2 ij). The Johnson & Soderblom (1987) method uses the parallax angle, ±, instead of the distance, and so the following conversions were made in the equations above: = 1 d (6.8) where the parallax angle is in arcseconds in order to achieve a distance in parsecs. The uncertainty is then found by propagating the error of, which yields

91 6.3. KINEMATICS: USING PROPER MOTIONS 76 = d d 2. (6.9) An important item to note is that the coordinate transformations require a radial velocity,, in order to be meaningful. Radial velocities are normally calculated using the red or blue shift of a spectral line. Unfortunately, radial velocities are not available for the white dwarf candidates selected in this work. Moreover, accurate radial velocities are di cult to determine due to the large surface gravities (log g =8.0)ofthewhitedwarfswhichcontributetoasignificantgravitationalredshiftof the spectral lines (Cojocaru et al. 2015). For example, Falcon et al. (2010) used a collection of white dwarfs in order to determine the mean gravitational redshift of a white dwarf. The authors determined that the mean gravitational redshift imposed is hv g i =37.50± 3.59 km/s. This means that any measured redshift is a combination of the actual radial velocity as well as the contribution from the surface gravity, and no precise method to disentangle the contributions exists (Cojocaru et al. 2015). With an absence of radial velocity measurements, is set to zero. This results in an underestimation of the derived U, V, and W velocities, however the contribution from the radial velocity to U and V is minimal at the Galactic latitude of the NGVS field (b 75 ). Plugging the central Equatorial coordinates of the NGVS field into equation 6.2 yields U 6 V = B 6kdµ = 6 4 W kdµ kdµ kdµ (6.10)

92 6.3. KINEMATICS: USING PROPER MOTIONS 77 Equation 6.10 shows that the coe cients associated with the proper motions are larger than those associated with the radial velocity. Plugging in typical values for the distance and proper motions also shows that a calculated radial velocity would be comparable to a tangential velocity (kdµ), suggesting that the U and V velocities are dominated by the proper motion at the Galactic latitude of the NGVS footprint. White Dwarf Candidates in the U-V Plane With this caveat in mind, the resulting U and V Galactic space velocities of the white dwarf candidates can be seen in Figure 6.5. The dot-dashed and dashed ellipses represent the2 velocity ellipsoids for the thick and thin disk populations respectively, while the dotted black line represents the 1 velocity ellipsoid for the halo, and the dotted red line represents the 2 velocity ellipsoid for the halo. These velocity ellipsoids were taken from Chiba & Beers (2000). In order to characterize the whole population, a Gaussian was fit to the U, V, and W velocity distributions. The resulting velocity dispersions were U =80km/s, V =80km/s,and W = 39 km/s. These velocity dispersions can be compared to the Milky Way thin and thick disk population from Edvardsson et al. (1993) shown in Table 6.1 in km/s. Since the velocity dispersions are higher than the expected values for the thick disk this suggests that there exists a collection of halo white dwarfs. However, since the U and V velocities are only 19 km/s larger than the expected thick disk velocities and the W velocities are equal, this suggests that the total population is dominated by disk white dwarfs. This can also be seen in the average V velocity, which is less than a typical thick disk population. The velocity ellipsoids were used to estimate lower limits for the size of the thin

93 6.3. KINEMATICS: USING PROPER MOTIONS 78 Table 6.1: Velocity dispersions for typical thin and thick disk populations in km/s compared to the dispersions from Figure 6.5 Table: Binney & Merrifield (1998) hv i U V W Thin Disk Thick Disk Halo This Work disk, thick disk, and halo populations by counting all of the objects which lie strictly within each velocity ellipsoid. The total number of white dwarfs which lie strictly within the 2 velocity ellipsoid for the halo is 20, or 16% of the total population included in Figure 6.5. Using the same approach for the thick disk yields 20 such objects, or 18% of the total population. One object lies within the overlapping region of the halo and thick disk ellipsoids. A population of 72 objects, or 58% lie within the 2 the 2 ellipsoid which represents the thin disk. Finally, 10 (8%) objects lie outside velocity ellipsoid of all three components, including four objects which have velocities that place them outside the range of Figure 6.5, and are not classified. Combining the selection results with the analysis of the velocity dispersions implies that the population of white dwarfs selected in Chapter 4 is composed mainly of disk white dwarfs, with the addition of a small population of halo white dwarfs. An analysis of the selected halo candidates, as well as a discussion as to whether or not they are truly halo white dwarfs is presented in Chapter 7.

94 6.3. KINEMATICS: USING PROPER MOTIONS 79 Figure 6.5: Galactic space velocities for white dwarf candidates, along with the 2 velocity ellipsoids for the thin disk (dashed), thick disk (dot-dashed), and the halo (dotted red). The 1 velocity ellipsoid for the halo is indicated by the black dotted line.

95 6.3. KINEMATICS: USING PROPER MOTIONS 80 Figure 6.6: Galactic space velocities and associated error-bars for white dwarf candidates.

96 81 Chapter 7 Discussion This chapter discusses the results from Chapters 5 & 6 and compares the model predictions to the results obtained using kinematics. An analysis of the halo candidates selected in Chapter 6 is presented in Chapter Halo White Dwarfs and Stellar Evolution Models The combination of deep optical and ultraviolet photometry, as well as the high Galactic latitude, makes the NGVS footprint an interesting location for identifying halo white dwarfs. Chapter 6 began by presenting theoretical predictions from the TRILEGAL population synthesis code for the total number of halo and disk white dwarfs expected within the NGVS footprint. The chapter finished by using tangential and approximate Galactic space velocities to characterize a subset of candidates as either a disk or a halo white dwarf. The results from each method are summarized in Figure 7.1. Figure 7.1 shows that the fraction of halo white dwarfs predicted by TRILEGAL

97 7.1. DISCUSSION 82 Figure 7.1: Disk and Halo contributions calculated from each method described in Chapter 6.