key: cord-0647786-844f0p46
authors: Kilic, Mukremin; Bergeron, P.; Kosakowski, Alekzander; Brown, Warren R.; Agueros, Marcel A.; Blouin, Simon
title: The 100 pc White Dwarf Sample in the SDSS Footprint
date: 2020-05-30
journal: nan
DOI: nan
sha: 88733214d5cef3f9b541055363d14f305d6b8b36
doc_id: 647786
cord_uid: 844f0p46

We present follow-up spectroscopy of 711 white dwarfs within 100 pc, and present a detailed model atmosphere analysis of the 100 pc white dwarf sample in the SDSS footprint. Our spectroscopic follow-up is complete for 83% of the white dwarfs hotter than 6000 K, where the atmospheric composition can be constrained reliably. We identify 1508 DA white dwarfs with pure hydrogen atmospheres. The DA mass distribution has an extremely narrow peak at $0.59~M_{odot}$, and reveals a shoulder from relatively massive white dwarfs with $M=0.7$-$0.9~M_{odot}$. Comparing this distribution with binary population synthesis models, we find that the contribution from single stars that form through mergers cannot explain the over-abundance of massive white dwarfs. In addition, the mass distribution of cool DAs shows a near absence of $M>1~M_{odot}$ white dwarfs. The pile-up of 0.7-$0.9~M_{odot}$ and the disappearance of $M>1~M_{odot}$ white dwarfs is consistent with the effects of core crystallization. Even though the evolutionary models predict the location of the pile-up correctly, the delay from the latent heat of crystallization by itself is insufficient to create a significant pile-up, and additional cooling delays from related effects like phase separation are necessary. We also discuss the population of infrared-faint (ultracool) white dwarfs, and demonstrate for the first time the existence of a well defined sequence in color and magnitude. Curiously, this sequence is connected to a region in the color-magnitude diagrams where the number of helium-dominated atmosphere white dwarfs is low. This suggests that the infrared-faint white dwarfs likely have mixed H/He atmospheres.

It took astronomers more than half a century to identify the first three white dwarfs and understand their nature (Holberg 2009 ). Starting with the detection of the companion of Sirius in 1862, only two other white dwarfs, 40 Eridani B and Van Maanen 2 were identified by the 1920s. Interestingly, these white dwarfs reveal a relatively broad mass range, with M = 0.97±0.01, 0.51± 0.04, and 0.68 ± 0.02 M , respectively (Holberg et al. 2016) .

Thanks to large scale proper motion (e.g. Luyten 1976 ) and imaging surveys (e.g., Green et al. 1986 ), the kilic@ou.edu number of confirmed white dwarfs reached ∼ 2 × 10 3 in the late nineties (McCook & Sion 1987 . The next decade saw a ten-fold increase, thanks to the Sloan Digital Sky Survey spectroscopy (Eisenstein et al. 2006; Kleinman et al. 2013; Kepler et al. 2019) , and this decade saw another ten-fold increase thanks to the Gaia Data Release 2 astrometry (Gaia Collaboration et al. 2018; Gentile Fusillo et al. 2019) . Before Gaia, the only volume-limited and nearly-complete white dwarf sample extended only up to 20 pc, and included 139 systems (see Holberg et al. 2016; Hollands et al. 2018 , and references therein).

Volume-limited surveys provide unbiased estimates of the luminosity and mass functions of white dwarfs, which map the star formation history, the initial-final mass relation, the effects of close binary evolution, and the changes in the white dwarf cooling rate as a function of temperature and age. Studying the mass distribution of 298 DA white dwarfs with T eff ≥ 13, 000 K in the magnitude limited Palomar-Green Survey (Green et al. 1986 ), Liebert et al. (2005) found a primary peak at 0.57 M along with a smaller peak from low-mass white dwarfs at 0.4 M , and a broad high-mass shoulder centered at 0.78 M .

Magnitude-limited surveys are biased against the intrinsically fainter and more massive white dwarfs. Correcting for this bias, Liebert et al. (2005) found that the broad high-mass component accounts for the 22% of the hot DA white dwarfs in their sample, and they suggested binary mergers as a potential explanation for their numbers. White dwarf mass distributions obtained from the SDSS spectroscopy also show similar peaks (for example see Fig. 10 in Kleinman et al. 2013 ), but the contribution from massive white dwarfs is underestimated given the SDSS spectroscopic survey selection. Kilic et al. (2018) attempted to constrain the mass distribution using the 100 pc volume-limited white dwarf sample from Gaia. Based on pure hydrogen atmosphere model fits, they found a bimodal mass distribution with peaks at 0.6 and 0.8 M , and estimated a contribution of ∼ 11% from massive white dwarfs. They attributed these to the remnants of main-sequence and post-mainsequence mergers. El-Badry et al. (2018) also found an excess of massive white dwarfs in the SDSS DA white dwarf sample, and attributed this excess to a flattened initial-final mass relation that favors the formation of massive white dwarfs. On the other hand, Hollands et al. (2018) did not find any evidence of an overabundance of massive white dwarfs among the 139 systems in the 20 pc Gaia white dwarf sample.

To constrain the frequency of massive white dwarfs in the solar neighborhood, we initiated a spectroscopic follow-up survey of the 100 pc Gaia white dwarf sample within the SDSS footprint. Here we present the results from this spectroscopic survey. Section 2 describes our sample selection and follow-up observations, whereas section 3 presents our model atmosphere analysis highlighting the model fits for different spectral types. We discuss the properties of our 100 pc white dwarf sample, including the DA white dwarf mass distribution and the infrared-faint (IR-faint) white dwarfs in section 4. We conclude in section 5.

The 100 pc Gaia sample includes more than 10 4 white dwarfs (Gaia Collaboration et al. 2018; Kilic et al. 2018; Jiménez-Esteban et al. 2018; Gentile Fusillo et al. 2019 ), Figure 1 . A color-magnitude diagram showing the 100 pc Gaia white dwarf sample within the SDSS footprint. This sample contains 4016 white dwarfs with G magnitudes ranging from 12.1 to 20.6. The bifurcation in the white dwarf sequence due to the atmospheric composition ) is clearly visible. and it is a challenge to obtain spectroscopy of the entire sample. To make our survey feasible, we limited our follow-up to the SDSS imaging footprint so that we can take advantage of the prior spectroscopy from the SDSS and other surveys that focused on white dwarfs (e.g., Bergeron et al. 1997 Bergeron et al. , 2001 McCook & Sion 1999; Kilic et al. 2006 Kilic et al. , 2010 Gianninas et al. 2011; Limoges et al. 2015) .

To obtain a clean 100 pc white dwarf sample within the SDSS footprint, we used the SDSS Data Release 9 (DR9) catalogue matched with Gaia DR2. The SDSS DR9 footprint covers 14,555 square degrees of the northern hemisphere sky, primarily at high |b| 30 • Galactic latitudes, as detailed in Ahn et al. (2012) . We used the recommendations outlined in Lindegren et al. (2018) to remove non-Gaussian outliers in color and absolute magnitude, and limited our sample to objects with > 10σ significant parallax, G BP , and G RP photometry. We perform a simple cut in (G BP − G RP , M G ) space to select our sample of white dwarfs. Our selection is optimized for reliability rather than completeness; it keeps isolated white dwarfs and unresolved double degenerates, but removes the majority of the white dwarf + main-sequence binaries.

For completeness, we provide the ADL query that we used to define our sample in the appendix. This query returns 4016 white dwarfs within 100 pc and the SDSS footprint. Table 1 presents the Gaia source ID, coordinates, parallax, proper motions, and magnitude for each object. Figure 1 shows these sources in a Gaia colormagnitude diagram. The white dwarf sequence extends from M G = 8.6 to 16.5 mag, with the apparent G magnitudes ranging from 12.1 to 20.6. The split in the white dwarf sequence due to the atmospheric composition is clearly visible .

We cross-matched this sample with the SDSS DR14 spectroscopic catalog , and found 1045 white dwarfs with SDSS spectra. We found spectroscopy of 119 additional white dwarfs in Kilic et al. (2006 Kilic et al. ( , 2010 , 345 objects in the papers by the Montréal, group (e.g., Limoges et al. 2015) , and 26 objects with data from the Supernovae Type Ia Progenitor Survey survey (Napiwotzki et al. 2001) . We found spectral types for 117 additional objects in the literature (Dufour et al. 2017 ).

Spectral typing of white dwarfs based on lowresolution spectroscopy is relatively easy for stars hotter than about 6000 K. This is because hydrogen lines are clearly visible at these temperatures. Hence, the absence or presence of Hα and/or Hβ is usually sufficient to constrain the atmospheric composition. Helium lines are visible for white dwarfs hotter than 11,000 K, and additional lines from C 2 , Ca, and Mg are also visible in DQ and DZ white dwarfs, respectively. Hydrogen lines disappear below about 5000 K, and the majority of the white dwarfs below this temperature show featureless spectra; DC spectral type. Hence, optical spectroscopy is not useful for constraining the atmospheric composition of cooler white dwarfs, unless they are metal-rich. Therefore, we limit our spectroscopic follow-up survey to white dwarfs with T eff ≥ 6000 K, where our data can reliably constrain the atmospheric composition.

We obtained optical spectroscopy of 711 white dwarfs using the 1.5m Fred Lawrence Whipple Observatory (FLWO) telescope, the MDM Hiltner 2.4m telescope, the Apache Point Observatory (APO) 3.5m telescope, the 6.5m Multiple Mirror Telescope (MMT), and the 8m Gemini South telescope. Table 2 presents the details of our observing program, including the instrument configuration and the number of targets observed at each telescope.

At the FLWO 1.5m telescope, we used the FAST spectrograph (Fabricant et al. 1998 ) with either the 600 l mm −1 or the 300 l mm −1 grating and the 1.5 slit to obtain spectroscopy of 81 targets with spectral resolutions of 2.3 and 3.6Å over the wavelength ranges 3550 -5530 A and 3500-7400Å, respectively. These observations were done between 2019 January and 2020 February. We found spectroscopy data for 100 additional targets in the FAST archive (Tokarz & Roll 1997) .

At the MDM 2.4m telescope, we used the OSMOS spectrograph (Martini et al. 2011) with the Blue VPH grism and the 1.2 inner slit to obtain spectroscopy of 158 targets with a spectral resolution of 3.3Å over the wavelength range 3975-6865Å. These observations were done between 2018 December and 2019 November as part of the MDM OSMOS queue.

At the APO 3.5m telescope, we used the Dual Imaging Spectrograph (DIS) with the B400 + R300 gratings and a 1.5 slit to obtain spectroscopy of 107 targets with spectral resolutions of 5.2 and 6.4Å in the blue and red channels, respectively. The blue and red channels cover the wavelength ranges 3400 -5500 and 5500 -9200Å, respectively. These observations were done between 2018 November and 2019 September. Unfortunately, the DIS blue channel suffered from contamination problems soon after our observing program started, and only seven of our targets have DIS blue channel data available. At the 6.5-m MMT, we used the Blue Channel Spectrograph (Schmidt et al. 1989 ) with the 500 l mm −1 grating and a 1 or 1.25 slit to obtain spectroscopy of 233 targets over the wavelength range 3700 -6850Å with spectral resolutions of 3.8 and 4.8Å, respectively. We obtained additional observations of 51 stars using the 300 l mm −1 grating, which provided spectra from the atmospheric cutoff (3200Å) to 7620Å with resolutions of 6.5 and 8.1Å for the 1 and 1.25 slits, respectively. These observations were done between 2018 November and 2019 October.

At the 8-m Gemini South telescope, we used the Gemini Multi-Object Spectrograph (GMOS) with the B600 grating and a 1 slit to obtain spectroscopy of 21 targets as part of the queue program GS-2020A-Q-222. Unfortunately, our program was cut short due to the COVID-19 pandemic, which prohibited observations of additional targets.

Our Gemini observations were done between UT 2020 Jan 21 and March 7. We binned the CCD by 4 × 4 to reduce the read-out time. This setup provided spectra over the wavelength range 3670 -6810Å, with a resolution of 2Å per pixel. GMOS on Gemini has 3 CCDs, with gaps between them. Our observing setup leads to gaps in spectral coverage between 4677-4703 and 5737-5765Å. These gaps can be eliminated by obtaining multiple exposures with different central wavelength configurations of the grating. Because these gaps have no impact on our spectral classification, and in order to save telescope time, we did not dither in wavelength to eliminate these gaps.

We reduced the data from all five telescopes using standard IRAF routines. About two dozen targets were observed on more than one telescope and several spectra with low signal-to-noise ratios were also omitted, resulting in a final sample of 711 objects with new spectroscopy data. Of these, 477 are DA, 6 are DB, 195 are DC, 7 are DQ, 27 are DZ, and 1 is a dwarf nova. Two targets are likely magnetic white dwarfs with uncertain spectral types (DAH or DBH), and are included in both the DA and DB samples.

The use of many different telescope and instrument combinations with different resolving powers can lead to systematic uncertainties in the physical parameters derived using the spectroscopic method (Liebert et al. 2005) . Here we do not use the spectroscopic method. We use the photometric method instead (see below), and we rely only on Gaia parallaxes, and SDSS and Pan-STARRS photometry. Hence, the multiple telescope and instrument combinations have no impact on the physical parameters derived in our analysis. We simply use each spectrum to confirm the spectral type and to constrain the atmospheric composition of each white dwarf.

The top panel in Figure 2 shows the color distribution of the entire 100 pc white dwarf sample in the SDSS footprint (solid line) and that of the objects with spectroscopy (shaded histogram). The bottom panel shows the completeness of the spectroscopic follow-up.

Combining our data with spectroscopy available in the literature, we have spectral classifications for 2361 (59%) of the 4016 white dwarfs in our sample. Given our survey selection bias for T eff ≥ 6000 K objects, our spectroscopic follow-up is significantly more complete for hotter stars. A log g = 8 pure hydrogen atmosphere white dwarf is predicted to have G BP − G RP = 0.734 mag at 6000 K. There are 2213 white dwarfs bluer than that color in our sample, including 1838 with spectra. Hence, our spectroscopic follow-up is 83% complete for white dwarfs hotter than about 6000 K.

We use the photometric technique as detailed in Bergeron et al. (2019) , who demonstrated that the SDSS ugriz photometric system or a combination of SDSS u and the Panoramic Survey Telescope and Rapid Response System (Pan-STARRS, Chambers et al. 2016) grizy photometry yield accurate parameters. Bergeron et al. (2019) also found that the Pan-STARRS photometry is superior to the SDSS photometry for white dwarf model atmosphere analysis. We follow the same approach and use the SDSS u and Pan-STARRS grizy photometry in our analysis.

We convert the observed magnitudes into average fluxes using the appropriate zero points, and compare with the average synthetic fluxes calculated from model atmospheres with the appropriate chemical composition. A χ 2 value is defined in terms of the difference between observed and model fluxes over all bandpasses, properly weighted by the photometric uncertainties, which is then minimized using the nonlinear least-squares method of Levenberg-Marquardt (Press et al. 1986 ) to obtain the best fitting parameters. The uncertainties of each fitted parameter are obtained directly from the covariance matrix of the fitting algorithm, while the uncertainties for all other quantities derived from these parameters are calculated by propagating in quadrature the appropriate measurement errors.

We fit for the effective temperature and the solid angle, π(R/D) 2 , where R is the radius of the star and D is its distance. Since the distance is precisely known from Gaia parallaxes, we can constrain the radius of the star directly, and therefore the mass based on the evolutionary models for white dwarfs. The details of our fitting method, including the model grids used are further discussed in Bergeron et al. (2019) and Genest-Beaulieu & Bergeron (2019). Here we supplement our model grid with the updated DZ and DQ white dwarf models from Blouin et al. (2018a) and . Since all of our targets are within 100 pc, we do not correct for reddening.

Figures 3 and 4 show our methodology for spectral classification based on model fits to four DA white dwarfs identified in this work. We picked these four stars to also demonstrate the observing setup differences between the different telescopes.

For each star, the top panel shows the SDSS u and Pan-STARRS grizy photometry (error bars) along with the predicted fluxes from the best-fitting pure hydrogen (filled dots) and pure helium (open circles) atmosphere models. The labels in the same panel give the Gaia Source ID, object name based on Gaia DR2 coordinates (for example J0100−2021 for the top left panel in Figure 3), and the photometry used in the fitting: ugrizy means SDSS u + Pan-STARRS grizy while ugriz means SDSS ugriz. Some filters were omitted in a few cases where for example they were contaminated by an M dwarf companion.

The middle panel, here and in the following figures, always shows the predicted spectrum based on the pure hydrogen solution, along with the observed Hα or Hβ profiles depending on the wavelength coverage of the observations. Note that we do not fit the spectroscopy data here. Instead, we simply over-plot the predicted hydrogen line profile (red line) from the photometric fit to see if a given spectrum is consistent with a pure hydrogen atmosphere composition. The spectral type of each object is also given in the middle panel, along with a temperature index based on 50,400/T eff . The bottom panel shows a broader spectral range for each star re- Figure 3 . Model fits to two new DA white dwarfs observed at the FLWO 1.5m and APO 3.5m telescopes. The top panels show the best-fitting pure hydrogen (filled dots) and pure helium (open circles) atmosphere white dwarf models to the photometry (error bars). Each object is labeled based on its Gaia Source ID, object name based on Gaia DR2 coordinates, and the photometry used in the fitting: ugrizy means SDSS u + Pan-STARRS grizy while ugriz means SDSS ugriz. The atmospheric parameters of the favored solution is highlighted in red. The middle panels, here and in the following figures, always show the predicted spectrum (red lines) based on the pure hydrogen solution. The bottom panels show a broader wavelength range for each instrument, revealing additional Balmer lines in the blue for one of these targets.

vealing the presence of additional Balmer lines in the blue, if such data are available.

J0010−2021( Figure 3 , left panels) is a relatively warm DA with several Balmer lines visible in its FAST spectrum, and a significant Balmer jump also visible in the u and g photometry. The photometry and Gaia parallax indicate a pure H atmosphere with T eff = 10, 049 ± 57 K and M = 0.554 ± 0.009 M . The predicted Hα line profile for these parameters provide an excellent match to the observed spectrum, indicating that this is a pure hydrogen atmosphere white dwarf. J0057+1756 (Figure 3 , right panels) is a cooler DA white dwarf with no significant Balmer jump visible in its photometry. The best-fitting pure hydrogen atmosphere solution has T eff = 6244 ± 29 K and M = 0.789 ± 0.011 M . Even though our APO data lack blue coverage for this object, the predicted Hα line profile from the photometric fit matches the observed spectrum, indicating that this is also a pure hydrogen atmosphere white dwarf. Note that we did not correct for telluric features, and the atmospheric B-band (6860-6890Å) is visible in our APO data.

Hydrogen lines become weaker with cooler temperatures. J0031+2218 (Figure 4 , left panels) is a cool DA white dwarf with only Hα and Hβ lines visible in our MDM spectrum. The best-fitting pure hydrogen atmosphere solution with T eff = 6056 ± 23 K and M = 0.629 ± 0.009 M provides an excellent match to the observed Hα line profile. J1301−0235 ( Figure 4 , right panels) is a slightly warmer and more massive (M = 1.079 ± 0.029 M ) DA white dwarf observed at Gemini. The quantum efficiency correction for the 3 GMOS CCDs is not perfect, resulting in slightly elevated flux levels for the reddest CCD with coverage beyond 5765Å. This has no impact on our spectral typing. Hα through Hδ are visible in our Gemini spectrum of J1301−0235, and the photometric solution provides a good match to the Hα line profile, indicating that this is also a pure hydrogen atmosphere white dwarf.

We present the figures for only four DA white dwarfs here. However, our model fits for all of the spectroscopically confirmed DA white dwarfs in our sample can be found in the online version of this article.

We present the physical parameters of all DA white dwarfs in our sample best explained by pure hydrogen atmosphere models in Table 3 . The small errors reported in this table represent the fact that both the photometric and parallax uncertainties are extremely small in most cases. Modern magnitude measurements such as SDSS or Pan-STARRS are quoted with extremely small uncertainties, sometimes as small as milli-magnitudes. However, as discussed in detail by Bergeron et al. (2019) , even though the photometric technique yields precise parameters, the true accuracy of the method is most likely dominated by the conversion from magnitudes to average fluxes (Holberg & Bergeron 2006) . For example, while the Pan-STARRS photometric system attempts to be as close as possible to the AB magnitude system, the Pan-STARRS implementation has an accuracy of only ∼ 0.02 mag according to Tonry et al. (2012) .

Figure 5 displays our fits to two of the newly identified magnetic DA white dwarfs found in our follow-up survey. J0326+1331 is a relatively warm and massive DA white dwarf with a significant Balmer jump. For magnetic white dwarfs, the Balmer jump is not reproduced well by our non-magnetic models. Our MDM spectrum of J0326+1331 reveals broad hydrogen lines that are split into multiple components due to the presence of a strong magnetic field. We do not fit for the field strength here, but simply compare the predicted Hα line profile from the photometric fit to the observed spectrum. The observed Hα line profile is weaker than expected due to the Zeeman-splitting, indicating that some of the weak-line objects with noisier spectra may be also magnetic.

J0154+2537 (right panels in Fig. 5 ) is one such system, where at first glance, our MMT spectrum looks noisy. However, a closer look at the Hα region shows that this line is much weaker than expected based on the photometric fit, but it is present, and is split into Note-This table is available in its entirety in machine-readable format in the online journal. A portion is shown here for guidance regarding its form and content. Figure 5 . Model fits to two new magnetic DA white dwarfs identified in this work. The symbols and panels are the same as in Figure 3 . We do not fit for the magnetic field strength here, but simply over-plot the predicted Hα line profile for the best-fitting non-magnetic, pure hydrogen atmosphere model in the middle panel for each star.

three components due to a magnetic field. This figure demonstrates the difficulty of identifying magnetic DA white dwarfs at cooler temperatures, and that some of the DC white dwarfs in our sample may be magnetic white dwarfs with weak lines that might have been lost in the noise. Table 3 includes the physical parameters of the magnetic DA white dwarfs, with masses ranging from 0.47 to 1.32 M . The median mass of the magnetic DA white dwarfs in our sample is 0.83 M . This is similar to the average mass, 0.87 M , of the magnetic white dwarfs presented in Kawka (2020) . Clearly, the mass distribution for the magnetic white dwarfs is significantly different than that of the normal DA white dwarfs. This is consistent with the idea that magnetic white dwarfs form as a result of merging binaries during common envelope evolution (Briggs et al. 2015) .

Ross 640 and L745-46A, are some of the best known examples of DA white dwarfs that have heliumdominated atmospheres. Hydrogen lines in these stars are heavily broadened through van der Waals interactions in helium dominated atmospheres (Giammichele et al. 2012; Rolland et al. 2018 ).

There are 13 white dwarfs in our sample that show hydrogen lines, but their spectral energy distributions are best explained by a helium-rich atmosphere. Figure  6 shows our model fits to one of these DA(He) white dwarfs. J1646+0308 clearly shows Hα and Hβ. However, the best-fit photometric solution for a pure hydrogen atmosphere has T eff = 12, 041 K and M = 0.86 M . At that temperature, a pure hydrogen atmosphere white dwarf would display significantly deeper Balmer lines (top panel) than observed, and the photometry would also show evidence of a significant Balmer jump between the u and g filters, which is not observed. However, the spectral energy distribution and the observed Hα line profile can both be explained by a He-dominated atmosphere with T eff = 10, 290 K, M = 0.617 M , and trace amounts of hydrogen with log H/He = −4.5. Table 4 presents the best-fit atmospheric parameters for the DA(He) white dwarfs in our sample. The model fits for all 13 are available in the online version of this article. Nine of these are clearly He-dominated DAs, based on the Hα line profiles being inconsistent with a pure hydrogen atmosphere solution. However, for four of these objects, J1611+1322, J1628+1224, J2104+2333, and J2138+2309, our interpretation of a He-dominated atmosphere depends on the quality of the photometry, in particular in the u−band. Figure 6 . Model fits to the He-rich DA white dwarf J1646+0308. The top panel shows the observed (black) and predicted Hα line (red) for the best-fitting photometric solution with a pure hydrogen atmosphere. The spectral energy distribution clearly favors a He-rich solution (second panel), which provides an excellent match to the Hα line profile (third panel). The bottom panel shows the entire spectral range of our observations, revealing Hα and Hβ lines much weaker than expected for a typical DA white dwarf at these temperatures. Figure 7 . Model fits to two of the DC white dwarfs in our sample. The symbols and panels are the same as in Fig. 3 . Even though both hydrogen and helium atmosphere solutions match the photometry, pure hydrogen atmosphere models predict significant Hα absorption features that are not observed (middle panels). Hence, these two stars clearly have He-dominated atmospheres.

These four stars appear as normal DA stars. Using the spectroscopic method, we find that the spectroscopic solution is also consistent with the pure hydrogen photometric solution. However, the spectroscopic method has a degeneracy between a high log g and a high helium content (see Figure 18 in Bergeron et al. 1991) . Given the temperature range of 8530 -11,060 K for these four stars, the observed Balmer jump between the u and g filters is smaller than expected for pure hydrogen models. The best-fitting mixed atmosphere models have He/H ratios similar to GD 362, which was confirmed to have a helium-dominated atmosphere through high-resolution spectroscopy (Zuckerman et al. 2007 ). Higher quality u−band photometry or higher resolution optical spectroscopy (for the stars with T eff near 11,000 K) would be useful to confirm the atmospheric compositions for these four targets.

He I lines disappear below about 11,000 K and hydrogen lines disappear below about 5000 K. Hence, the absence of spectral features in DC white dwarfs hotter than 5000 K can be used to rule out a pure H composition and infer a He-dominated atmosphere. Figure 7 shows our model fits to two of the DC white dwarfs in our sample, where a pure hydrogen atmosphere can be safely ruled out. The photometry cannot distinguish between the pure hydrogen and the helium-dominated solution for J0008−0353 (left panels), as both provide acceptable solutions. However, the best-fitting pure hydrogen atmosphere solution has T eff = 6223 K, which would display a significant Hα line that is not observed in our MMT spectrum. Hence, J0008−0353 clearly has a He-dominated atmosphere. Similarly, the best-fitting pure hydrogen atmosphere model for J0348+8048 (right panels) requires a Hα line that is almost 50% deep compared to the continuum. Such a line is clearly absent in our MDM spectrum, also Note-The mixed atmosphere interpretation for J1611+1322, J1628+1224, J2104+2333, and J2138+2309 is based on the significance of the Balmer jump inferred from the u−band photometry. Analyzing the mass distribution of non-DA white dwarfs between 11,000 K and 6000 K, Bergeron et al. (2019) found an almost complete absence of normal mass non-DA stars based on pure helium atmosphere models, and concluded that pure He atmosphere white dwarfs must be extremely rare or non-existent in this temperature range. More reasonable mass estimates require additional electron donors in the form of hydrogen, car-bon, or other metals. In fact, they found that about 25% of the non-DAs in this temperature range are DQ stars contaminated by carbon, and another 25% are DZ stars contaminated by metals, and the rest are DC stars. Bergeron et al. (2019) and Rolland et al. (2018) revisited the suggestion that convective mixing is responsible for the sudden increase in the number of non-DA white dwarfs below 10,000 K. In this scenario, the relatively small amount of hydrogen in the upper layers is mixed with the underlying helium convection zone, resulting in Figure 8 . Model fits to two DQ white dwarfs observed at the MMT. The top and middle panels show the photometric and spectroscopic model fits, respectively. The bottom panels display the entire spectral range of the observations. The atmospheric models provide an excellent match to both photometry and spectroscopy for these two stars.

extremely small hydrogen abundances that, in general, do not produce a visible Hα line.

For the analysis of the DC white dwarfs in our sample, we follow Bergeron et al. (2019) and use mixed hydrogen and helium models where the hydrogen abundance is adjusted as a function of effective temperature. In the temperature range of DB stars (T eff ≥ 11, 000 K) we adopt log H/He = −5, and for cooler DC stars, we gradually increase the hydrogen abundance to log H/He = −3 at 6000 K following the predictions of the convective mixing scenario (Rolland et al. 2018 ). We assume log H/He = −5 for the He-rich solution of cooler DC stars. Table 5 presents the best-fit model parameters for the newly identified DB and DC white dwarfs in our sample.

For DC white dwarfs below 5000 K, there is no way to tell the composition based on optical spectra as both hydrogen and helium become invisible in their atmospheres. However, pure helium and mixed H/He models result in mass estimates below 0.5 and even 0.4 M for many of the cool DCs. Kowalski & Saumon (2006) demonstrated that the far red wing of the Lyman α line dominates the opacity in the blue part of the optical spectra of pure hydrogen atmosphere white dwarfs, and concluded that most cool DC stars should have pure hydrogen atmospheres. These models provide a much better fit to the u − g colors of the cool DC white dwarfs (see Figures 10 and 11 below) and provide more reasonable mass estimates of M > 0.5 M for the majority of these stars . This is why we adopted the pure hydrogen solution for the coolest DCs in our sample.

On the other hand, not all cool white dwarfs have pure hydrogen atmospheres. found that ≈ 25% of the DC white dwarfs cooler than 5000 K have helium-rich atmospheres. There are also DZ white dwarfs with clearly helium-rich atmospheres in the same temperature range. The atmospheric composition of each of the cool DCs should be constrained based on Figure 9 . Model fits to two DZ white dwarfs observed at the MMT and FAST. The top and middle panels show the photometric and spectroscopic model fits, respectively. The bottom panels display the entire spectral range of the observations. The atmospheric models provide an excellent match to both photometry and spectroscopy for these two stars.

a detailed analysis of each object, which is outside of the scope of this paper.

There are several DC white dwarfs in our sample that display significant absorption in the Pan-STARRS z and y−bands. These are the so-called IR-faint or ultracool white dwarfs that display collision induced absorption (CIA) from molecular hydrogen. We discuss these further in section 4.3.

We identify 7 new DQ white dwarfs in our survey. We rely on the photometric technique to determine the bestfit T eff and log g for these stars, and use the neutral C I lines or the C 2 Swan bands to fit for C/He. Given the abundances derived from the spectroscopic fit, we repeat our photometric and spectroscopic fits until a consistent solution is found. Figure 8 shows our model fits to two of these stars. The top and middle panels show our photometric and spectroscopic fits, respectively. The DQ models presented in provide an excellent match to both the photometry and spectroscopy data for these stars. Table 6 presents the best-fit model parameters for all 7 newly identified DQ white dwarfs in our sample. Six of these are cooler than 8000 K, and display strong C 2 Swan bands in their spectra. The remaining object, J0104+4650, is significantly hotter, and has a relatively noisy MDM spectrum that displays weaker lines. A higher signal-to-noise ratio spectrum would be helpful in confirming the nature of this system, and constraining its carbon abundance. The bestfit parameters for J0104+4650, T eff = 11, 257 ± 166 K, M = 0.997 ± 0.016 M , and log C/He = −3.21, place it in the second and more massive DQ white dwarf sequence as discussed in 

There are 27 newly identified DZ white dwarfs in our sample that display Ca H and K absorption lines. We rely on the photometric technique to determine the temperature and surface gravity for these stars, and fit the blue portion of the spectrum, including the Ca II H and K doublet and the Ca I resonance line, to find Ca/He. We use the red portion of the spectrum to constrain the H/He abundance ratio. The abundance ratios of the other heavy elements are scaled to the abundance of Ca to match the abundance ratios of CI chondrites. Figure  9 shows our model fits to two of these stars. The top and middle panels for each star show our photometric and spectroscopic fits, respectively. The bottom panels show the entire spectral range of the data.

J0422+0038 (left panels) is a cool DZ white dwarf that shows only Ca absorption features. The absence of a Hα absorption feature constrains the H/He ratio in this star, and our model fits provide an excellent match to both the optical spectra and the photometry of this star. The best-fit model has log H/He = −3 and log Ca/He = −9.34.

J1733+3013 (right panels) is a DZ with both Ca and Mg lines. Our FAST spectrum does not cover Hα, but Hβ is clearly absent in this star. Our best-fit model with log Ca/He = −7.85 reproduces most of the observed Ca absorption lines relatively well in the blue. The model fits for the rest of the DZ white dwarfs are presented in the online version of this article, and the best-fit parameters are presented in Table 7 . The Ca abundances for these stars range from log Ca/He = −11.3 to −7.9.

With the addition of 711 new spectra from our spectroscopic survey, we have spectral types for 2361 of the 4016 white dwarfs in the 100 pc white dwarf sample in the SDSS footprint. We classify 1539 (or 65%) as DA, including 85 magnetic white dwarfs, 13 DA(He) stars with He-dominated atmospheres, 1 DAB white dwarf (GD 323), 5 DA + M dwarf systems, and 9 with likely but uncertain DA: classification. We also identify 53 DB/DBA, 555 (or 24%) DC, 97 DQ, 115 DZ, 1 cataclysmic variable (ASASSN-14dx), and 1 dwarf nova (GD 552). Figure 10 shows the distribution of DA and non-DA stars in color-magnitude diagrams based on Gaia (left panel) and SDSS u and Pan-STARRS g photometry (right panel). The solid, dashed, and dotted lines show the cooling sequences for 0.6 M white dwarfs with pure hydrogen, pure helium, and mixed atmosphere models with log H/He = −5, respectively. The bifurcation in u − g colors is easily explained by the Balmer jump in pure hydrogen atmosphere white dwarfs. The Balmer jump suppresses the ultraviolet fluxes of these stars compared to their hydrogen-poor counterparts, resulting in redder u − g colors.

The split in the Gaia sequence is also explained by the presence of hydrogen (and/or other electron donors), but in this case it is the additional opacity from trace amounts of hydrogen in helium-dominated white dwarfs that affects their colors . The log H/He = −5 mixed atmosphere model sequence, for example, goes through the bulk of the DC white dwarfs in the Gaia color-magnitude diagram, except the coolest ones. Regardless of the reason (additional hydrogen or other electron donors), the differences in atmospheric composition can clearly explain the bifurcation seen in these color-magnitude diagrams. Figure 11 shows a color-color diagram of our white dwarf sample based on the SDSS u and Pan-STARRS g, r filters. DA and DB/DC white dwarfs form relatively tight color sequences in this diagram, with the main distinction between them being the Balmer jump visible in the u − g color for DA white dwarfs. On the other hand, the majority of the DQ (green) and DZ (magenta) white dwarfs appear as outliers with respect to the DA and DB/DC sequences. DZ white dwarfs suffer from metal absorption features mostly in the ultraviolet, which result in redder u − g colors compared to DC stars, whereas the Swan bands in DQ white dwarfs are strongest in the g−filter, resulting in bluer u − g and/or redder g − r colors compared to the DC white dwarfs. Hence, follow-up spectroscopy of the outliers in similar color-color diagrams may provide an efficient method to identify additional DQ and DZ white dwarfs in the solar neighborhood.

A striking feature visible in Figures 10 and 11 is that the cooling sequences for 0.6 M pure helium and mixed H/He atmosphere white dwarfs fail to match the colors of the bulk of the cool DC white dwarfs with u − g > 0.8 mag, or T eff < 6000 K. Hence, a photometric analysis based on helium-rich models produce mass estimates that are too low (see Figure 12 in Bergeron et al. 2019 ). On the other hand, the pure hydrogen atmosphere models including the red wing of the Lyman α line (Kowalski & Saumon 2006) provide a much better fit to the u − g colors of the cool DC white dwarfs in Figures 10  and 11 and provide more normal mass estimates, justifying our use of pure hydrogen model fits for the coolest (T eff < 5000 K) DCs in our sample.

A caveat in our analysis is that some of the cool DCs likely have helium-dominated atmospheres. Comparing the pure hydrogen, pure helium, and mixed H/He at- mosphere solutions for each star, found the fraction of helium-rich DCs to be around 25%. Based on the u − g colors, the fraction of DC stars that have helium-rich atmospheres appears to be small in our sample. However, a detailed model atmosphere analysis of individual DC white dwarfs is required for reliable constraints on their atmospheric parameters.

In the following sections, we present the DA white dwarf mass distribution, and then discuss the properties of the DC white dwarfs, specifically the so-called IRfaint white dwarfs in our sample. Figure 12 shows a color-magnitude diagram of all spectroscopically confirmed DA white dwarfs in our sample. The DA white dwarf sequence ends at an absolute magnitude of M G ≈ 15, which corresponds to T eff = 5000 K for 0.6 M white dwarfs. Hα disappears below this temperature. Excluding the DA white dwarfs with weak lines, mixed atmospheres, e.g., DA(He) stars, uncertain spectral types, or M dwarf companions, we have 1508 spectroscopically confirmed DA white dwarfs in our sample that are best-fit by pure hydrogen atmosphere models. Most of these DA white dwarfs form a tight sequence around M = 0.6 M , but a significant contribution from fainter and more massive white dwarfs, many of which are on the the crystallization sequence (also referred to as the Q-branch, Gaia Collaboration et al. 2018; Tremblay et al. 2019) , is also clearly visible. Figure 13 . The white dwarf mass distribution (black solid histogram) based on 1337 spectroscopically confirmed DA white dwarfs hotter than 6000 K in the 100 pc sample and the SDSS footprint. Dotted and dashed lines show the bestfitting Gaussians to the main peak and the broad shoulder, and the red line shows the composite of the two. Figure 13 shows the mass distribution of our DA white dwarf sample. Since our spectroscopic completeness falls significantly beyond 6000 K, we limit our mass distribution to 1337 stars with T eff ≥ 6000 K. We estimate the uncertainties in each mass bin based on a Monte Carlo analysis where we replace the mass of each white dwarf M with M + g δM , where δM is the error in mass and g is a Gaussian deviate with zero mean and unit variance. For each of 1000 sets of modified masses for the entire sample, we calculate the mass distribution, and we take the range that encompasses 68% of the probability distribution function as the 1σ uncertainties for each mass bin.

Remarkably, the mass distribution has an extremely narrow peak and a broad shoulder. Fitting two Gaussians to the observed distribution, we find that the mean peak is centered at 0.59 M with a 1σ spread of only 0.035 M , whereas the contribution from massive white dwarfs is best-fit with a Gaussian at 0.76 M and a 1σ spread of 0.15 M .There is also a low mass peak around 0.35 M in the mass distribution, but it is smaller than previously observed in magnitude-limited samples like the PG survey (Liebert et al. 2005 ). This is not surprising as low-mass white dwarfs are over-represented in magnitude-limited surveys due to their larger radii and luminosities. A caveat here is that our mass estimates for low-mass white dwarfs may be erroneous since they were based on the assumption of a single star, and that low-mass white dwarfs are usually found in binary systems (Marsh et al. 1995; Kilic et al. 2020) . Hence, further observations would be useful for constraining the binary nature of these systems and the mass distribution below 0.5 M . Figure 14 compares the DA mass distributions for T eff ≥ 6000 K (left panel) and a more restrictive T eff ≥ 10, 000 K (right panel) sample of stars against the predictions from a 10 Gyr old disk population with a constant star-formation rate (SFR, solid line) and a Gaia magnitude limit of G = 20. We use a Salpeter mass function (Salpeter 1955) , assume solar metallicity, and that the stars evolve in isolation. We use the mainsequence + giant-branch lifetimes from Hurley et al. (2000) to decide if a star evolves into a white dwarf within 10 Gyr, and if so, to estimate its cooling age.

We calculate the final white dwarf masses based on the latest MIST-based piece-wise initial-final mass relation (IFMR) from Cummings et al. (2018) , and use the evolutionary models 1 similar to those described in Fontaine et al. (2001) with (50/50) C/O-core compositions, q(He) ≡ M He /M = 10 −2 , and q(H) = 10 −4 , to estimate their temperatures. Just like in the observed samples, we only include white dwarfs with T eff ≥ 6000 K (left panel) or 10,000 K (right panel) in these simulations. We normalize the disk model to match the peak of the observed mass distribution at 0.59 M . Our simulations fail to account for the relatively large numbers of low-mass (M < 0.5 M ) white dwarfs. This is not surprising, as the majority of these low mass white dwarfs are likely in binary white dwarf systems (Marsh et al. 1995) , which are excluded from our synthetic populations.

This figure reveals remarkable differences between the mass distributions for the hot DAs and the overall population. The mass distribution for the hot DAs (right panel) shows a roughly linear decline in the number of massive white dwarfs beyond 0.7 M , and the 10 Gyr old disk model of single stars with constant star formation provides an excellent match to this mass distribution. Note that we simply scaled the model predictions to match the peak of the observed mass distribution, hence the excellent match between the observations and the predictions demonstrate that our choices of a Salpeter IMF, a constant SFR, the IFMR, and the white dwarf cooling models are appropriate for simulating white dwarf populations in the solar neighborhood. At 10,000 K, only white dwarfs more massive than 1 M would have crystallized. Hence, the uncertainties in the cooling models due to crystallization and its associated effects (see below) are mostly avoided for hot white dwarfs.

Even though both the hot DA and the overall DA mass distributions peak at 0.59 M , the latter (left panel) is significantly different: it shows a nearly constant number of massive white dwarfs between 0.7 -0.9 M , and then a sudden decrease to nearly zero at 1 M and beyond. The synthetic populations fail to match this distribution. This figure demonstrates that for cool white dwarfs there is a mechanism that leads to a pile-up of massive white dwarfs with M ∼ 0.8 M and a sudden disappearance of more massive white dwarfs. Liebert et al. (2005) interpreted the excess of massive white dwarfs in the Palomar-Green Survey of DA white dwarfs as evidence of binary evolution. Toonen et al. (2017) performed binary population synthesis calculations to show that up to 23% of the white dwarfs in the solar neighborhood might have descended from binary mergers during (post-)main-sequence evolution. Recently, Temmink et al. (2020) found that binary mergers can account for 10-30% of all single white dwarfs. However, they found that these mergers should not significantly alter the shape of the white dwarf mass distribution. Now that we have a precise mass distribution based on 1337 spectroscopically confirmed white dwarfs with T eff ≥ 6000 K in a volume-limited sample, we can directly compare the predictions from the binary population synthesis calculations to see if mergers can explain the over-abundance of massive white dwarfs in our sample.

We use the binary-star evolution (BSE) algorithm of Hurley et al. (2002) to track the evolution of 10 5 mainsequence binaries with primary masses randomly drawn between 0.8 and 8 M from a Salpeter mass function and the secondary masses drawn from a uniform mass ratio distribution between 0 and 1. We assume constant star formation rate, and track the evolution of these systems over 10 Gyr. We perform simulations with two different period distributions; lognormal and flat (Toonen et al. 2017) . We use the evolutionary times from BSE to estimate the cooling age of each single white dwarf that formed through mergers, and estimate its current temperature based on the white dwarf cooling models. Figure 15 top panel shows the predicted mass distribution for single white dwarfs that form as a result of mergers. The results from the lognormal and flat period distributions are shown as solid and dotted lines, respectively. The overall shapes of the predicted mass distributions are similar; both predict a dominant peak around 0.6 M with a tail towards higher masses. The main difference between the simulations using lognormal and flat period distributions is the number of systems that form through mergers (see, Toonen et al. 2017 , for a detailed discussion). To see if mergers can help explain a significant portion of the massive white dwarfs in our sample, we compare our DA mass distribution against the predictions for blended populations of 70% white dwarfs from a 10 Gyr old disk population that evolved in isolation + 30% single white dwarfs that formed through mergers. We picked 30% contribution from mergers, as this is the upper limit in the binary population synthesis calculations from Temmink et al. (2020) . Figure 15 bottom panel shows a comparison between our 100 pc DA white dwarf mass distribution against these blended populations, the solid red line for the lognormal period distribution and the dotted line for the flat period distribution. Note that both observations and simulations shown here are restricted to white dwarfs with T eff ≥ 6000 K. Just like in Figure 14 , we normalize the synthetic populations to match the peak of the observed mass distribution at 0.59 M .

Even though the blended populations help increase the number of M ∼ 0.8 M white dwarfs produced in the simulations and provide a better fit to the observational data in that mass range, the overall fit to the mass distribution is still problematic as these blended populations also produce more of the M ∼ 0.7 and > 1 M white dwarfs. The observed sample shows significant deficits for both M ∼ 0.7 and > 1 M white dwarfs compared to the model predictions.

Merger populations can also reveal themselves through their kinematics. Double white dwarf merger products should have higher velocity dispersion because they would be part of an older population that is kinematically heated up (Coutu et al. 2019; Cheng et al. 2020) . Studying the kinematics of hot (T eff > 13, 000 K) DA white dwarfs from the PG survey and the SDSS DR4 white dwarf catalog (Eisenstein et al. 2006) , Wegg & Phinney (2012) found that the transverse velocity dispersion decreases from σ ∼ 50 km s −1 for 0.5 M white dwarfs to ∼20 km s −1 for 0.8 M white dwarfs. This is consistent with the expectations from single star evolution as the progenitors of lower mass white dwarfs belong to an older population where the disc heating is significant.

Wegg & Phinney (2012) did not find any high mass white dwarfs traveling at > 50 km s −1 in their young DA sample, and concluded that the observed kinematics are consistent with the majority of high mass white dwarfs forming through single star evolution. This is similar to the conclusions reached by Cheng et al. (2020) , who estimate that the fraction of massive white dwarfs that form through double white dwarf mergers is around 10% in the 0.8-0.9 M mass range. The exception to this is the massive DQ white dwarfs that display significantly larger transverse velocities, with 45% displaying velocities in excess of 50 km s −1 (Coutu et al. 2019 ). Hence, Figure 16 . Cumulative distribution of transverse velocities for DA white dwarfs with cooling ages (assuming single star evolution) younger than (left panel) and older than (right panel) 2 Gyr and with M = 0.5-0.7, 0.7-1, and > 1 M . many of the massive DQ white dwarfs are likely produced through double white dwarf mergers. Figure 16 shows the cumulative distribution of transverse velocities for our DA white dwarf sample split into three mass ranges, which correspond to the main peak in the mass distribution (0.5-0.7 M ), the broad shoulder at 0.7-1 M , and very massive white dwarfs with M > 1 M . The left and right panels show the distributions for the young and old DA samples with cooling ages (assuming single star evolution) younger than and older than 2 Gyr, respectively. The transverse velocities are based on Gaia DR2 parallaxes and proper motions.

Looking at the cumulative transverse velocity distribution for the younger DAs (left panel), the velocity dispersion decreases for 0.7-1 M white dwarfs compared to the 0.5-0.7 M population. This is similar to what is seen in Wegg & Phinney (2012) , which suggests that the mergers are unlikely to explain the number of 0.7-1 M white dwarfs. On the other hand, the velocity distribution for the most massive white dwarfs with M > 1 M shows an excess of higher velocity objects compared to the 0.7-1 M sample: 10 of the 44 hot DA white dwarfs with M > 1 M have V trans > 50 km s −1 . This would indicate a substantial contribution from mergers for the most massive white dwarfs, and is consistent with the results from Temmink et al. (2020) and Cheng et al. (2020) , who found that the fraction of > 1 M white dwarfs that come from mergers is ∼30%.

The transverse velocity distribution for the older DAs (right panel) is remarkably different. Here the distributions for the 0.5-0.7 and 0.7-1 M white dwarfs are Figure 17 . Synthetic color-magnitude diagrams for pure hydrogen atmosphere white dwarfs for a 10 Gyr old disk population and assuming a constant star formation rate. The top panel is for stars that evolved in isolation, whereas the bottom panel includes single white dwarfs that formed through mergers. Each panel displays the same number of stars as in Figure 12 , for a fair comparison. The solid line shows the cooling sequence for a 0.6 M pure hydrogen atmosphere white dwarf.

almost identical, but the velocity distribution for the M > 1 M cool DA sample in Figure 16 is significantly different: it is missing the high velocity tail visible in Figure 18 . Stellar masses as a function of effective temperature for all spectroscopically confirmed white dwarfs in the 100 pc sample and the SDSS footprint. The parameters have been determined using photometric fits to the SDSS u and Pan-STARRS grizy photometry and Gaia DR2 parallaxes. Solid curves are theoretical isochrones, labeled in units of 10 9 years, obtained from cooling sequences with C/O-core compositions, q(He) ≡ M (He)/M = 10 −2 , and q(H) = 10 −4 , while the dotted curves correspond to isochrones with the main sequence lifetime taken into account. The lower blue solid curve indicates the onset of crystallization at the center of evolving models, while the upper one indicates the locations where 80% of the total mass has solidified. The dashed curve indicates the onset of convective coupling. Note that the low-mass DA white dwarfs in this diagram are most likely in unresolved degenerate binary systems, and their mass estimates may be erroneous since they were based on the assumption of a single star. the velocity distributions of the M < 1 M stars. This means that we are missing the oldest (and therefore the coolest) massive DA white dwarfs. Based on the velocity distributions for both hot and cool DAs, we can safely conclude that mergers cannot explain the relatively large numbers of M ∼ 0.8 M white dwarfs, and we must look for an alternative explanation for these systems.

Another way to demonstrate this is through colormagnitude diagrams. Figure 17 displays synthetic colormagnitude diagrams for pure hydrogen atmosphere white dwarfs for a 10 Gyr old disk population with constant SFR and a Gaia magnitude limit of G = 20. The top panel assumes evolution in isolation, whereas the bottom panel includes single white dwarfs that form through mergers. A comparison with Fig. 12 shows that none of the simulated populations, including the one with the mergers, can explain the observations.

Tremblay et al. (2019) identified a pile up in the cooling sequence of white dwarfs in Gaia color-magnitude diagrams, and demonstrated that the latent heat of crystallization causes this pile up. The release of latent heat results in a slowdown in the evolution of a white dwarf. Since massive white dwarfs crystallize first, the effects of crystallization is most significant in their number distribution (see also Bergeron et al. 2019) . Bergeron et al. (2019) note that the most significant effect of crystallization is actually the Debye cooling phase, where the transition from the classical regime to the quantum regime occurs. In the quantum regime, the specific heat decreases with cooling, rapidly depleting the thermal energy reservoir of the star, and making it essentially disappear from view as a black dwarf. Again, this is most significant for massive white dwarfs.

Our sample contains 44 DA white dwarfs with T eff > 10, 000 K and cooling ages less than 2 Gyr, and only 15 DAs with T eff = 6000-10,000 K and cooling ages more than 2 Gyr. A remaining question is whether the near absence of M > 1 M DA white dwarfs at cooler temperatures is due to those stars turning into massive DC stars or not. Figure 18 shows the stellar masses as a function of temperature for all spectroscopically confirmed DA and non-DA white dwarfs in the 100 pc sample and the SDSS footprint. We restrict this figure to the objects with T eff < 30,000 K, where the photometric technique is the most reliable (Genest-Beaulieu & Bergeron 2019). Theoretical isochrones, with and without the main sequence lifetime taken into account , are shown as solid and dotted curves, respectively. The nearly horizontal isochrones for massive white dwarfs at cooler temperatures indicate the Debye cooling regime, where the thermal reservoir of the star is rapidly depleted. This occurs below about T eff = 6000 K for M ≥ 1 M white dwarfs.

The lower solid blue curve marks the region where crystallization starts at the center of the white dwarf, and with further cooling, the solidification front moves upward. By the time ∼ 80% of the star has solidified, most of the latent heat would have been spent, and the upper solid blue curve marks this limit of 80% crystallization. The dashed curve marks the onset of convective coupling, when the convection zone first reaches into the degenerate interior, where all of the thermal energy of the star resides. Convective coupling significantly changes the cooling rates of white dwarfs, as evidenced by the sudden change in slope of the isochrones shown here. Figure 18 demonstrates that the pile up of massive white dwarfs seen in our 100 pc sample is clearly due to delays in cooling from the latent heat of crystallization. We see an enhanced number of white dwarfs between the two solid blue curves, where most of the latent heat of crystallization would have been released.

Just like the DA white dwarfs, the mass distribution for the non-DA stars is also dominated by 0.6 M white dwarfs, with a small number of massive DC white dwarfs also present. Including trace amounts of hydrogen in our DC white dwarf fits leads to normal mass estimates for these stars, with no bias towards mass estimates lower than 0.5 or 0.4 M at the cool end of the distribution.

Interestingly, there are only four massive DC white dwarfs with masses near 1 M . Three of these, J1621+0432, J1039−0325, and J1105+5225, are warmer than 13,000 K. Hence, to be classified DC, they must be strongly magnetic DAH or DBH white dwarfs. The remaining object, J0930+0628, has T eff = 6418 ± 54 K and M = 1.01 ± 0.02 M assuming a composition of log H/He = −3.2. J0930+0628 appears to be the only genuine DC white dwarf more massive than 1 M .

Note that there are a number of cool and massive DA stars in the 40 pc sample of Limoges et al. (2015, see their Fig. 21 ). However, the masses for those objects are mostly determined spectroscopically. For those in common (18 objects cooler than 8000 K and with M > 0.8 M based on spectroscopy), we find that the photometric mass is much smaller than the spectroscopic mass for all objects with spectroscopic masses above 0.9 M . This suggests that these objects are either double degenerate systems or He-rich DAs. The fact that the photometric and spectroscopic temperature estimates agree for most of these objects would favor the latter explanation. Alternatively, a relatively weak magnetic field can also broaden the lines without displaying explicit Zeeman splitting in the low-resolution spectra, leading to erroneously high mass estimates. However, two of these objects, J1022+4600 and J1420+5322, have photometric mass estimates below 0.5 M , and therefore they are likely in binary systems.

To check if the current evolutionary models (Fontaine et al. 2001 ) provide a reasonable match to the significance of the pile up of M ∼ 0.8 M white dwarfs in the 100 pc sample, we show the observed (top panel, similar to Figure 18 ) and the predicted (bottom panel) DA white dwarf mass and temperature distribution for a 10 Gyr old disk population with a constant star formation rate in Figure 19 . These are the same evolutionary models used in Bergeron et al. (2019) and Tremblay et al. (2019) .

Since our spectroscopic follow-up is severely incomplete beyond 6000 K, here we restrict our comparison to stars with T eff ≥ 6000 K. Gaia's limiting magnitude also comes into play below this temperature. A 1 M pure hydrogen atmosphere white dwarf is predicted to have M G = 15 mag at 6000 K. Hence, Gaia DR2 catalog suffers from incompleteness issues, even within 100 pc, for massive white dwarfs below this temperature. We limit our simulations to objects brighter than G = 20 mag to account for this bias.

A complication in the comparison and simulations shown in Figure 19 is the spectral evolution of white dwarfs; the atmospheric composition of a white dwarf changes throughout its evolution due to several different mechanisms (see Blouin et al. 2018a , for a detailed discussion). Given the white dwarf luminosity function, our sample is dominated by stars cooler than 10,000 K, where we also observe an increase in the ratio of non-DA to DA stars due to convective mixing. This means that Figure 19 . Observed (top, similar to Fig. 18 ) and predicted (bottom) white dwarf mass and temperature distribution for a 10 Gyr old disk population with a constant star formation rate based on the current evolutionary models. Also shown are the same isochrones, crystallization, and convective coupling curves as in Figure 18 . We limit this figure to stars hotter than 6000 K, since our follow-up spectroscopy is severely incomplete below that temperature. a fraction of the DA white dwarfs turn into non-DAs below 10,000 K. We account for spectral evolution in our simulations by assuming 1/3 of all DAs below 10,000 K turn into non-DAs, essentially removing them from our simulated sample.

A comparison of the observed and the predicted mass and temperature distributions of our 100 pc white dwarf sample shows that the synthetic population is significantly different from the observed one in two major ways: 1-There is no significant pile-up of M ∼ 0.8 M white dwarfs, and 2-Massive white dwarfs with M > 1 M do not disappear quickly enough.

Even though the evolutionary models that include crystallization predict a slow down in the cooling at the right location in the mass versus effective temperature diagram, where a pile up of ∼ 0.8 M white dwarfs is observed Bergeron et al. 2019) , the estimated delay in evolutionary times is clearly insufficient to produce any significant pile-up in the synthetic populations. In addition, the synthetic populations predict a significant population of massive white dwarfs at cooler temperatures that are simply absent in the observational sample.

Studying the number density and velocity distribution of massive white dwarfs on the Q branch, Cheng et al. (2019) arrived at a similar conclusion, and found that the cooling delay from crystallization alone is not sufficient and suggested 22 Ne settling as a source of extra cooling delay. In addition, the effects of phase separation and 16 O sedimentation are currently not included in the evolutionary models (Fontaine et al. 2001 ). Additional factors such as the uncertain Coulomb plasma parameter at the liquid-solid phase transition, the C/O profile in the core, and the thickness of the surface hydrogen and helium layers also play a role in the cooling rates of these objects . Hence, our observational data clearly point to the onset of crystallization and its associated effects to explain the properties of the observed white dwarf mass distribution, but the current evolutionary models are missing important physics related to this process.

Among the 555 DC white dwarfs identified in our sample, there are a handful of known IR-faint white dwarfs that show optical and near-infrared flux deficits, presumably due to the CIA from molecular hydrogen. Even though we tend to refer to them as ultracool, implying they have temperatures below 4000 K, it is unclear if the majority of them are actually this cool, as mixed H/He atmosphere model fits indicate temperatures as high as ∼ 5500 K for some of them (Kilic et al. 2010; Gianninas et al. 2015) .

For example, Blouin et al. (2018b) performed a detailed model atmosphere analysis of J0804+2239, a DZ white dwarf with significant absorption in the nearinfrared. J0804+2239 is within 100 pc, and included in our sample. Blouin et al. (2018b) find best-fit parameters of T eff = 4970 ± 100 K, log g = 7.98 ± 0.05, and log H/He = −1.6 ± 0.2. Hence, the term "IR-faint" is more appropriate for these objects.

We identify four additional white dwarfs with optical and near-infrared flux deficits in the 100 pc sample and the SDSS footprint. Figure 20 shows the spectral energy distributions for these four stars. Solid lines and dots show the monochromatic fluxes and the synthetic photometry for the best-fit model, respectively. Three of these objects, J0928+6049, J1147+2220, and J1727+0808 are spectroscopically confirmed DC white dwarfs with SEDs that peak in the r− or i−band and with flux deficits visible in the Pan-STARRS z and y bands. The remaining object, J2138−0056 does not have follow-up spectroscopy, but it clearly shows a significant flux deficit in the near-infrared based on the UKIRT Infrared Deep Sky Survey (UKIDSS, Lawrence et al. 2007 ) JH photometry. If available, we also include the near-infrared photometry in our model fits. These fits indicate temperatures as low as 2774 K and hydrogen abundances of log H/He ≈ −3. Note that this abundance corresponds to roughly the maximum intensity of the H 2 -He CIA.

The intensity of CIA is controlled by the photospheric density and the H 2 abundance. The former decreases and the latter increases with an increase in the H/He ratio, which implies that there is a degeneracy between high and low hydrogen abundances below and above log H/He ≈ −3 (Blouin et al. 2018b) . For example, in-stead of the solution shown in Figure 20 , the spectral energy distribution of J2138−0056 can also be fitted with a model that has T eff = 4630 K, M = 0.429 M , and log H/He = −2. The model degeneracy is not an issue for the other three stars; the infrared flux deficit is much stronger in these stars, including the Pan-STARRS z− and Y −band photometry. Their spectral energy distributions require the maximum possible CIA to reproduce the flux deficit, so there is a unique solution for these objects.

Our mixed H/He atmosphere models barely replicate the broad-band photometry for IR-faint white dwarfs, and no model can currently match the observed spectra. In addition, the relatively low temperature estimates force our model solutions to have relatively large radii to match the observed fluxes, which in turn require M ∼ 0.2 M and log g ∼ 7 for these objects. In fact, many of the previously known IR-faint white dwarfs with parallax measurements seem over-luminous and require relatively large radii and small masses (e.g., Bergeron & Leggett 2002; Gianninas et al. 2015) .

Using the clean sample of extremely low-mass (ELM, M ∼ 0.2 M ) white dwarfs from Brown et al. (2020) , we estimate that the local space density of "observed" ELM white dwarfs is 100 to 200 kpc −3 depending on the choice of Galactic scale length parameters (see Brown et al. 2016 , for a detailed discussion). This means that there should be 0.4-0.8 ELM white dwarfs with T eff = 9000-22,000 K within 100 pc of the Sun. Limiting the sample to the SDSS footprint lowers this estimate by about 3×.

To estimate the number of cool ELM white dwarfs, we use the evolutionary models for solar-metallicity progenitors from Istrate et al. (2016) . We predict N ∼ 1 ELM white dwarf with 4000 < T eff < 6000 K, but we find 20 IR-faint white dwarfs in our sample. Hence, we can safely conclude that the majority of the IR-faint white dwarfs cannot be extremely low mass. Figure 21 shows near-infrared color-magnitude diagrams for the non-DA white dwarfs in our sample. The left panel is solely based on the Pan-STARRS data, whereas the right panel uses H−band data from the UKIDSS Large Area Survey, and Kilic et al. (2010) for the majority of the IR-faint white dwarfs. We matched our list of non-DA white dwarfs with the Large Area Survey from the UKIDSS Data Release 11, and found 244 objects with near-infrared observations. IR-faint white dwarfs, including the four newly identified systems presented here, are marked with open circles. We also show the cooling sequences for pure hydrogen, pure helium, and mixed H/He atmosphere white dwarfs, for reference.

Strikingly, 17 of the 20 IR-faint white dwarfs shown in this figure form a sequence in these color-magnitude diagrams. This is the first time such a sequence is clearly observed in a color-magnitude diagram. The cooling sequence for 0.2 M white dwarfs with log H/He = −3 comes closest to matching this sequence, but the match is not perfect in either diagram.

The IR-faint white dwarf sequence is connected to a region in the M g versus g − z color-magnitude diagram where the number of DC white dwarfs appears to be low. There are a significant number of DC white dwarfs blueward of g − z = 0.5 mag, and there are also a large number of them redward of g −z = 0.9 mag, but the DC white dwarf population is significantly depleted in between these two colors. This color range corresponds to ≈ 5000-6000 K for 0.6 M pure hydrogen white dwarfs. This is the same temperature range where Bergeron et al. (1997 Bergeron et al. ( , 2001 found depleted numbers of heliumrich stars compared to their hydrogen-rich counterparts (see also . This is likely related to the spectral evolution of white dwarfs and transformation of helium-rich white dwarfs to hydrogen-rich composition, and vice-versa, through some yet unexplained phenomenon (Malo et al. 1999; Chen & Hansen 2012) .

We interpret the observed sequence of IR-faint white dwarfs in Figure 21 as a cooling sequence of white dwarfs with mixed H/He atmospheres. Given that the sequence is so tight indicates that these stars probably have similar hydrogen abundances, around log H/He = −3. In addition, the analysis by Bergeron et al. (2019) indicates that some of the warmer DC stars (above 6000 K) have such trace amounts of hydrogen in their atmospheres. Hence, it is possible that such an IR-faint white dwarf sequence due to CIA is unavoidable.

Clearly, a large fraction of the warmer DC white dwarfs turn into hydrogen-rich DC stars below 5000 K, otherwise we would see a lot more objects with CIA absorption, but a few of those likely retain their heliumdominated atmospheres, and end up on the IR-faint white dwarf cooling sequence instead.

In summary, we see a mix of hydrogen-and heliumatmosphere white dwarfs above 6000 K. These are the DA and DC/DQ/DZ white dwarfs, respectively. Since hydrogen lines disappear below 5000 K, we have to rely on other indicators for composition, like the presence of metals, the red wing of the Ly α line, and CIA. There are three possible outcomes for cool DC white dwarfs below 5000 K: 1-The color-magnitude diagram suggests that most cool white dwarfs evolve as pure hydrogen atmospheres through some unknown process. 2-Some evolve as IR-faint white dwarfs on a cooling sequence with hydrogen abundances that are typical of some of the hotter DC and DZ white dwarfs, whose origin is likely convectively mixed DAs. 3-Some also evolve as DC white dwarfs with almost pure helium atmospheres, with hydrogen abundances low enough to produce no visible CIA signatures. The progenitors of the latter likely have very little hydrogen, potentially DQ stars or cooled off DB stars.

We present the results from a follow-up spectroscopy survey of the 100 pc white dwarf sample in the SDSS footprint. Our follow-up is complete for 83% of the white dwarfs hotter than 6000 K. We perform a detailed model atmosphere analysis of each white dwarf, and use this sample to constrain the DA white dwarf mass distribution, which displays an extremely narrow peak at 0.59 M and broad shoulder up to 0.9 M .

Surprisingly, the number of massive white dwarfs remains roughly constant in the 0.7-0.9 M range. The predictions from single and binary population synthesis studies fail to match this over-abundance of massive white dwarfs. The location of the pile-up of ∼ 0.8 M white dwarfs in the mass versus temperature diagrams and the disappearance of M > 1 M white dwarfs from these samples are consistent with the expectations for crystallization and related effects. The former is explained by a delay in cooling due to the release of latent heat of crystallization, whereas the latter is explained by enhanced cooling in the quantum regime where massive white dwarfs quickly disappear from the sample. However, we find that the current evolutionary models are unable to match the significance of the pile-up of ∼ 0.8 M and the sudden disappearance of the more massive stars.

We suggest that additional cooling delays from 16 O sedimentation upon crystallization and 22 Ne gravitational settling likely play a significant role in the evolution of white dwarfs, and that convective coupling may lead to even faster cooling than currently predicted.

We also discuss the prevalence of IR-faint white dwarfs in the 100 pc sample and the SDSS footprint. We find 20 IR-faint white dwarfs that show significant flux deficits in the optical and/or near-infrared. We demonstrate that these white dwarfs form a sequence in colormagnitude diagrams. In addition, the IR-faint white dwarf sequence seems to be connected to a region in the color-magnitude diagrams where the number of heliumdominated atmosphere white dwarfs is low. This suggests that the transition of helium-rich white dwarfs into hydrogen-rich atmospheres, and vice-versa, may also explain the appearance of IR-faint white dwarfs, and that IR-faint white dwarfs likely have mixed H/He atmospheres.

Based on observations obtained at the Gemini Observatory, which is operated by the Association of Universities for Research in Astronomy, Inc., under a cooperative agreement with the NSF on behalf of the Gemini partnership: the National Science Foundation (United States), National Research Council (Canada), CONI-CYT (Chile), Ministerio de Ciencia, Tecnología e Inno-vación Productiva (Argentina), Ministério da Ciência, Tecnologia e Inovação (Brazil), and Korea Astronomy and Space Science Institute (Republic of Korea).

Facilities: MMT (Blue Channel spectrograph), FLWO:1.5m (FAST spectrograph), Gemini (GMOS spectrograph), APO (DIS), MDM (OSMOS)

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This work is supported in part by the NSF under grant AST-1906379, the NSERC Canada, the Fund FRQ-NT (Québec), and the Smithsonian Institution. SB acknowledges support from the Laboratory Directed Research and Development program of Los Alamos National Laboratory under project number 20190624PRD2.We thank B. Kunk, E. Martin, and A. Milone for their assistance with observations obtained at the MMT Observatory, a joint facility of the Smithsonian Institution and the University of Arizona.This work is based on observations obtained at the MDM Observatory, operated by Dartmouth College, Columbia University, Ohio State University, Ohio University, and the University of Michigan. We thank J. Rupert for obtaining the MDM data as part of the OS-MOS queue.This research is based in part on observations obtained with the Apache Point Observatory 3.5-meter telescope, which is owned and operated by the Astrophysical Research Consortium.

The ADL query used to select our sample of 100 pc white dwarfs in the SDSS footprint is given below. SELECT g.source id, g.ra, g.dec, parallax, parallax over error, pmra, pmra error, pmdec, pmdec error, phot g mean mag, phot g mean flux over error, phot bp mean mag, phot bp mean flux over error, phot rp mean mag, phot rp mean flux over error, phot g mean mag + 5.0*log10(parallax/100.0) AS M G, s.ra,s.dec, u mag, u mag error, g mag, g mag error, r mag, r mag error, i mag, i mag error, z mag, z mag error, clean flag FROM gaiadr2.gaia source AS g, gaiadr1.sdssdr9 original valid AS s, gaiadr2.sdssdr9 best neighbour AS xs WHERE g.source id = xs.source id AND s.sdssdr9 oid = xs.sdssdr9 oid AND parallax > 10.0 AND parallax over error > 10.0 AND phot bp mean flux over error > 10 AND phot rp mean flux over error > 10 AND astrometric n good obs al > 5 AND (SQRT(astrometric chi2 al/(astrometric n good obs al -5.0)) < 1.2 OR SQRT(astrometric chi2 al/(astrometric n good obs al -5.0)) < 1.2*exp(-0.2*(phot g mean mag -19.5))) AND phot bp rp excess factor BETWEEN 1.0 + (0.03*POWER(phot bp mean mag -phot rp mean mag, 2.0)) AND 1.3 + (0.06*POWER(phot bp mean mag -phot rp mean mag, 2.0)) AND phot g mean mag + 5.0*log10(parallax/100.0) > (3.333333*(phot bp mean mag -phot rp mean mag) + 8.333333)