Measuring White Dwarf Variability from Sparsely Sampled Gaia DR3 Multi-epoch Photometry

White dwarf stars are ubiquitous in the Galaxy, and are essential to understanding stellar evolution. While most white dwarfs are photometrically stable and reliable flux standards, some can be highly variable, which can reveal unique details about the endpoints of low-mass stellar evolution. In this study, we characterize a sample of high-confidence white dwarfs with multi-epoch photometry from Gaia Data Release 3. We compare these Gaia light curves with light curves from the Zwicky Transiting Facility and the Transiting Exoplanet Survey Satellite to see when Gaia data independently can accurately measure periods of variability. From this sample, 105 objects have variability periods measured from the Gaia light curves independently, with periods as long as roughly 9.5 days and as short as 256.2 s (roughly 4 minutes), including seven systems with periods shorter than 1000 s. We discover 86 new objects from the 105 target samples, including pulsating, spotted, and binary white dwarfs, and even a new 68.4 minute eclipsing cataclysmic variable. The median amplitude of the absolute photometric variability we confirm from Gaia independently is 1.4%, demonstrating that Gaia epoch photometry is capable of measuring short-term periods even when observations are sparse.


INTRODUCTION
As the endpoints of all stars below roughly 8 M ⊙ , white dwarfs are extremely common.Their ubiquity and relative simplicity mean that white dwarf stars play an important role as flux standards, which are needed for precise absolute photometry and spectroscopy (e.g., Calamida et al. 2022).
Binary systems with at least one white dwarf star can tell us about stellar ages and close binary evolution (e.g., Rebassa-Mansergas et al. 2007;Heintz et al. 2022).These objects can also be progenitors of Type Ia supernovae, which are important distance indicators (Maoz et al. 2015).Binaries with short periods (less than roughly 1 hour) are also potential * NSF Graduate Research Fellow candidates for gravitational waves detectable with the Laser Interferometer Space Antenna (LISA, Burdge et al. 2020).
There are a number of ways binaries with a white dwarf can be photometrically variable.Eclipsing systems are the most dramatic, where one star passes in front of the other (e.g., Hallakoun et al. 2016).Eclipsing white dwarfs, which can be used to measure the masses and radii of the system components (Parsons et al. 2017(Parsons et al. , 2018)), are still relatively rare so any increase in the sample is valuable.Eclipses are not necessary to detect close binaries, as hot stars in the system can create a reflection effect from reprocessed heating off a cool companion (e.g., Schaffenroth et al. 2022).In addition, cataclysmic variables (CVs) are highly variable white dwarfs with stochastic mass-transfer from a Rochelobe-filling main-sequence companion (Warner 1995).
Magnetic white dwarfs can also exhibit strong photometric changes, such as cold (e.g., Brinkworth et al. 2013;Kilic et al. 2015) or hot (e.g., Hoard et al. 2018) spots corresponding to the surface rotation period.Measuring these rotation periods can help to investigate the angular momentum loss during white dwarf formation (Fuller et al. 2019).
Pulsating white dwarfs are variable due to non-radial pulsations as they cool through different instability strips that depend on their surface composition (Winget & Kepler 2008a;Fontaine & Brassard 2008;Hermes et al. 2017c).With enough identified pulsation modes, asteroseismology affords the opportunity to significantly constrain the interiors of white dwarfs, including global rotation rates (e.g., Hermes et al. 2015Hermes et al. , 2017b) ) and core composition (e.g., Giammichele et al. 2018;Chidester et al. 2022).Motivated by the need to find and constrain new variable white dwarfs, we analyze here a new data product from Gaia Data Release 3 (DR3), which features multi-epoch light curves for sources classified as variable via a machine learning algorithm trained on constant objects (Eyer et al. 2023).This new Gaia DR3 dataset includes photometric time series in the Gaia G, G BP , and G RP bands.Previous efforts have focused on literature cross-matches of DR3 variables (Gavras et al. 2023;Rimoldini et al. 2023), as well as specific object types (Gaia Collaboration et al. 2023a;Marton et al. 2023).
In Section 2 we discuss our target selection for variable white dwarfs in Gaia DR3, and in Section 3 describe our period-finding analysis.In Section 4 we explain our classification of new white dwarf variables, including new (eclipsing) binaries, spotted (magnetic) white dwarfs, and pulsating white dwarfs, all with coherent periodicities detected from Gaia DR3 photometry independently and confirmed in multiple datasets.We discuss the strengths and limitations of Gaia for period analysis in Section 5 and conclude in Section 6.

TARGET SELECTION AND OBSERVATIONS
We set out to select and analyze all apparently isolated white dwarf stars flagged as photometrically variable in Gaia DR3 (Gaia Collaboration et al. 2023b).A new, expanded data product in DR3 is the release of multi-epoch, multicolor (G, G BP , G RP ) light curves for roughly 10.5 million objects with anomalously large scatter in their many Gaia visits (a.k.a.transits) that make them high-probability candidate variables (Eyer et al. 2023).These objects are cataloged in Gaia DR3 with the entry phot variable flag set to VARIABLE; full light curves are available through the Gaia Datalink Service (Cánovas & de Bruijne 2022), which we accessed using astroquery.gaia(Ginsburg et al. 2019).
In order to focus on isolated white dwarfs, we first restrict the 10.5 million variables in DR3 to be near the white dwarf region of the Gaia color-magnitude diagram by requiring M G > (4.5 × G BP − G RP ) + 9.0, similar to the absolute magnitude selection of Hollands et al. (2018).This excludes many white dwarfs in close binaries, such as CVs (Pala et al. 2020) and post-common-envelope (WD+dM) binaries.
We then cross-match this down-selected sample with the Gaia DR3 catalog of candidate white dwarfs of Gentile Fusillo et al. (2021).This cross-match results in a final sample of 1333 objects, 1217 of which are high-confidence single white dwarfs (with P WD > 0.75, see Table 1); only 42 objects have P WD < 0.3.We expect minor contamination from our color cuts from non-isolated white dwarfs, especially CVs with low-luminosity donors.
We further cross-match this sample with the Montreal White Dwarf Database (Dufour et al. 2017) and SIMBAD (Wenger et al. 2000) by matching coordinates for each source (precessing the Gaia DR3 epoch to J2000).This cross-match was done in order to collect as much supporting information as possible including literature references and spectroscopic classifications.Relevant information found in this cross match is listed in Table 2.
We compare the Gaia multi-color light curves of our 1333 objects with two other long-baseline photometric surveys.First, we use the Python package Lightkurve (Lightkurve Collaboration et al. 2018;Saunders 2020) to download any 20-second-and 2-min-cadence PDCSAP light curves of our objects as seen by the Transiting Exoplanet Survey Satellite (TESS, Ricker et al. 2015).This provides at least one month of nearly continuous TESS data for 698 objects in our sample, most brighter than roughly G = 17.0 mag.
Where available, we also download light curves within a 1.4-arcsecond search radius of our targets from Data Release 12 of the Zwicky Transient Facility (ZTF, Bellm et al. 2019).This provides long-baseline ZTF observations for 992 objects across all magnitudes in our sample, all with declinations north of −20 degrees.We also search for light curves in the south from the All-Sky Automated Survey for Su-perNovae (ASAS-SN, Shappee et al. 2014;Kochanek et al. 2017) and the Asteroid Terrestrial-impact Last Alert System (ATLAS, Tonry et al. 2018) projects.However, any objects without TESS photometry in the south mostly had upper limits on photometry due to their faintness, so we did not use their light curves in our analysis here.

PERIOD-FINDING ANALYSIS
We analyze the Gaia light curves and ZTF and TESS light curves, when available, simultaneously.All available light curves are visually inspected for signatures of variability in both the time and frequency domain, informed by the spectroscopic classification of the white dwarf if known.
We analyze every light curve in the frequency domain by computing Lomb-Scargle periodograms (Astropy Collaboration et al. 2013) using astropy (Astropy Collaboration et al. 2013, 2018, 2022).We also separate the light curves by band-pass filters (G, G BP , G RP , g, r, T from Gaia, ZTF, and TESS, respectively) to search for color-dependant variability.We initially classify frequencies as significant if their amplitude exceeds five times the mean amplitude of all frequencies in the periodogram, a relatively conservative limit given prior sporadically sampled datasets (Breger et al. 1993;Guidry et al. 2021).For simplicity, we use a constant frequency step size for Gaia and ZTF data: 10 −8 Hz, which corresponds to a critical sampling of 1157 days, consistent with the length of the typical Gaia and ZTF datasets.The step size for the TESS periodogram frequencies is set by the inverse of the TESS light curve baseline, oversampled by a factor of 10.All periodograms are computed to the TESS 2-min Nyquist frequency of 4160 µHz.
We use all available survey information in addition to our coherent period analysis to attempt to classify as many variable candidate white dwarfs in our sample as possible (see Figure 1 and top-line summary in Table 1).The amount of information differs significantly from source to source.For example, only 586 of 1333 objects have a spectral type in the literature listed from either MWDD (Dufour et al. 2017) or SIMBAD (Wenger et al. 2000).Therefore, our classification for 86 of 105 objects in Table 2 listed as "likely" is based on the limited information available and requires spectroscopic follow-up to truly confirm the variability classification.Literature information for the 105 white dwarfs in this study with significant variability measured from their Gaia DR3 light curve.

Class
[hr] [hr] Likely Binary [hr] [hr] Likely Spot  Most variables are categorized by their periods of variability (from 100 − 1500 s for pulsating white dwarfs, to minutes to days for spotted white dwarfs), as well as their position in the color-magnitude diagram (e.g., CVs are composed of a composite spectra mixing some fraction of a white dwarf, main-sequence star, and accretion disk, and are considerably over-luminous to an isolated white dwarf).Using the colormagnitude position along with any periods constrained from the survey light curves allows us to suggest likely classifications for the subset of objects in this manuscript; we will present full classification of all 1333 objects in a future publication.
We devote our attention here to objects where at least one Gaia light curve successfully identifies the period of variability of a candidate white dwarf.We consider Gaia to successfully recover a period if the Gaia-G periodogram has its highest peak matching (to within 0.05 µHz) the highest peak of an independent ZTF and/or TESS periodogram, or an independent Gaia bandpass light curve.
Regardless of its significance (we discuss further in Section 5), we use the highest-amplitude of the periodogram of the available Gaia, ZTF, and TESS datasets as an initial guess for a linear-least-squares (LLS) fit of a sinusoid to the data using the Python package lmfit (Newville et al. 2016).This process returns the best-fit period, amplitude, and phase of a single sinusoid to the light curve, as well as associated uncertainties.All reported periods in the main text of this manuscript are the LLS fits of the Gaia DR3 G-band photometry.
In total we find 105 candidate white dwarfs which have photometric variability periods that can be correctly measured from their Gaia DR3 light curve independently.Of these 105 objects, 72 have data from ZTF and 65 have data from TESS (including 32 with both ZTF and TESS data).Based on our classification (see Section 4), we show where these 105 objects sit in the Gaia color-magnitude diagram in Figure 1.Because binary systems and objects with cool spots both show sinusiodal variability, we use mass and temperature estimate fits to Gaia photometry by Gentile Fusillo et al. ( 2021) (listed in Table 2) to distinguish between these objects.We classify candidate white dwarfs with an effective temperature of > 31,000 K or a photometrically determined mass < 0.525 M ⊙ (which cannot have formed as single-stars within a Hubble time) as binaries; all other sinusoidally variable white dwarfs are classified as rotationally modulated spots.Since not all spotted white dwarfs are strongly magnetic (e.g., Hermes et al. 2017b), the only way to absolutely distinguish between a spot or binary is to use follow-up spectroscopy to search for radial-velocity variability.
Previous spectroscopy exists for just 36 of our 105 targets.Our photometric classifications lacking spectroscopic constraints will suffer some ambiguity.For example, WD J202932.51+070107.70 is hotter than 31,000 K and exhibits absorption from ultra-highly excited metals, but is likely variable due to a magnetic spot (Reindl et al. 2021).Similarly, the > 100,000 K white dwarf WD J095125.94+530930.72 is likely spotted, based on a lack of radial-velocity variation (Werner et al. 2019).Still, classifying as binaries the sinusoidal variables with T eff > 31,000 K or M WD < 0.525 M ⊙ will be appropriate for the vast majority of our objects.

CLASSIFIED WHITE DWARF VARIABLES
We attempt to classify the origin of the variability for the 105 candidate variable white dwarfs where we can measure a coherent, sinusoidal variability period from the Gaia light curves that matches a period detected in an independent dataset.Initially we inspect the Gaia DR3 machine learning output classifier (GaiaDR3Class), which is available for 62/105 objects.In most cases, however, this classifier simply says WD, revealing little about the specific nature of these objects.
We instead classify all objects based on variability period and position in the Gaia color-magnitude diagram, informed by past white dwarf variability studies (Hermes et al. 2017a;Reding et al. 2018).All discovery literature on our sources is collected in Table 2, and our full classification and variability information is collected in Table 3. Table 1 provides a summary of the overall sample and our analyzed sub-sample referenced in this manuscript.

Non-Eclipsing White Dwarf Binaries
Binary systems are often distinguishable from isolated white dwarfs because they are an unresolved pair of stars, making them over-luminous to single star cooling tracks, such as those shown in Figure 1.For this reason, overluminous objects with sinusiodal variability that have an effective temperature exceeding 31,000 K as determined by the hydrogen-rich-atmosphere fits from Gentile Fusillo et al. ( 2021) or a photometrically determined mass < 0.525 M ⊙ are categorized as binary systems.Objects without mass determinations from Gentile Fusillo et al. ( 2021) are likely over-luminous and also classified as binaries.Typical values for orbital periods of binary systems with a white dwarf paired with an M dwarf have been studied by Nebot Gómez-Morán et al. (2011), where SDSS data showed that post common envelope binaries containing a white dwarf and main sequence star have orbital periods ranging from 1.9 hr to 103.2 hr, with an average of approximately 10.3 hr.
We find 72 likely variable binaries in our sample, including seven eclipsing binaries (Section 4.3), with orbital periods ranging from 0.957 hr to 29.366 hr, with a mean of approximately 8.411 hr and a standard deviation of approximately 7.417 hr, consistent with the Nebot Gómez-Morán et al. ( 2011) distribution.
Three representative examples of variable binaries are shown in Figure 2.
The first object (WD J153938.12+270605.84,G = 16.6 mag) is a known DA+dM system with an orbital period of 5.72120 ± 0.00087 hr measured from the Palomar Transient Factory (PTF, Kao et al. 2016).We measure from Gaia DR3 photometry only P orb = 5.7213 ± 0.0053 hr, agreeing with the PTF measurement to within our estimated uncertainty.The second object (WD J041033.37−585203.63,G = 17.6 mag) is a newly discovered binary system with a sinusiodal pattern in both the Gaia G and TESS bands with a Gaia G band period of 2.87254 ± 0.00054 hr.The higher amplitude from the redder TESS data is indicative of flux reprocessing from a reflection-effect binary, though no spectroscopy exists for this target.Finally, WD J200937.02+165219.12 (G = 16.8 mag) is also likely a new reflection-effect binary with an orbital period of 2.49878 ± 0.00086 hr.
The shortest-period, likely detached new binary in our sample is WD J123955.40+834707.51 (G = 20.0 mag), which shows significant variability in ZTF at 0.95661 ± 0.00015 hr that is also seen in the Gaia G-band light curve at an amplitude exceeding 40%.No spectroscopy exists of this target, which has a position in the Gaia CMD consistent with a 7020 K, 0.27 M ⊙ white dwarf, suggesting it might be a new WD+WD binary containing at least one ELM white dwarf (e.g., Brown et al. 2022).There are also likely some binaries that are not detached in our sample.CVs are a class of accreting white dwarf binaries, and are often eruptive variables that show large brightening events from dwarf novae and other outbursts (Szkody et al. 2020(Szkody et al. , 2021)).We have not intended to search for new CVs among the 1333 high-confidence white dwarfs, which has been the focus of previous work on Gaia light curves using eruptions and outbursts (e.g., Gaia Collaboration et al. 2019).However, we have identified coherent periods in three objects classified as CVs in the literature.WD J083843.35−282701.14 (G = 17.6 mag) is a known CV (Halpern et al. 2017;Rea et al. 2017) for which we find a new potential period of variability of 16.109 ± 0.029 hr.This period differs slightly from the approximately 15-hr period of flux variability interpreted as the beat period between the orbital and spin periods (Rea et al. 2017), as well as the 14.7 ± 1.2 hr period of X-ray modulations observed by Halpern et al. (2017).WD J031413.25−223542.92(G = 18.2 mag) was studied by Warner (1980) and Bond et al. (1979).The Gaia DR3 data show a significant periodicity at 1.34947 ± 0.00017 hr, which is in close agreement with both studies.

Periodicities in Known Cataclysmic Variables
Finally, WD J130017.86−325805.23 (G = 20.3mag), is a CV candidate that has undergone at least two measured outbursts detected in CRTS (Drake et al. 2014).We lack TESS or ZTF coverage for this faint southern object, but all three Gaia band-passes have their highest periodogram peak at 2171.36 s (36.2 min).The amplitude of the signal exceeds 80% in all Gaia band-passes.Such large-amplitude periodic variations are not commonly observed as spurious signals in Gaia DR3 at such short periods (Holl et al. 2023), though we cannot independently rule out an instrumental origin for this 36.2-minvariability.We strongly encourage follow-up of this faint southern target.

Eclipsing White Dwarf Binaries
Eclipsing binaries often display near-total flux dropouts in randomly sampled light curves (Parsons et al. 2013), as the fainter companion passes in front of the brighter member.These eclipses should occur at exactly the same phase in a folded light curve, manifesting as stable, repeated photometric variability.The seven known and likely eclipsing systems are shown in Figure 3.
The top panels in Figure 3 detail three previously known eclipsing white dwarf binaries, in order of orbital period.WD J085746.18+034255.35(G = 18.3 mag) is a known eclipsing WD+dM with a measured orbital period of 1.562317 hr by the Catalina Sky Survey (CSS, Parsons et al. 2015), which is consistent with our measurement from Gaia DR3 photometry of 1.562316( 17) hr.This object shows both ZTF and Gaia dropouts, notable since the Gaia DR3 light curves have a reasonably aggressive outlier rejection (Eyer et al. 2023).WD J132518.18+233808.02(G = 18.2 mag) is also a known eclipsing DA+dM binary with an orbital period of 4.679 hr measured by CSS (Drake et al. 2010;Parsons et al. 2015) consistent with our measurement from Gaia DR3 photometry of 4.67901(39) hr.The lack of ineclipse data from Gaia is likely related to outlier rejection of the Gaia photometry 1 .WD J003352.64+385529.70 (G = 18.3 mag) was identified by Kosakowski et al. (2022) to have a strong 4.86-hr signal in ZTF, and has all the hallmarks of a WD+dM eclipsing binary, especially featuring ZTF dropouts in both the gand r-bands when folded on a period of 4.86465(31) hr.These dropouts align in phase space and show a decrease in amplitude of nearly 100%.
Our analysis identifies four new candidate eclipsing binaries.Most compact is WD J154008.28−392917.61,showing multiple low Gaia points when folded on the TESSdetermined period of 1.319(13) hr.We detail follow-up observations of this source in Section 4.3.1 and Figure 4. WD J130905.43−470852.39 (G = 18.3 mag) may be an eclipsing binary, having only Gaia light curves to analyze.When folded on a period of 3.32265(44) hr, the source shows dropouts in both the G and G RP bands with small uncer-1 Gaia DR3 Documentation Section 5.1.4:Photometric Calibration Figure 3.Following the same convention as Figure 2, we show phase-folded light curves of seven eclipsing binaries detected from their Gaia DR3 light curves.In this figure, ZTF and Gaia data are not binned, but TESS data are grouped into 251 bins.The first three systems are previously published eclipsing binaries containing a white dwarf (Drake et al. 2010;Parsons et al. 2015;Kosakowski et al. 2022).Four systems are newly discovered eclipsing binaries containing a white dwarf, including a new 1.3-hr eclipsing CV (WD J154008.28−392917.61,further detailed in Section 4.3.1 and Figure 4).With only sparse Gaia DR3 data, we do not claim to confirm binarity in WD J154008.28−392917.61,but include it as an interesting candidate.
tainties leading us to believe that these are genuine eclipses.Photometric fits to the Gaia CMD suggest this system has an extremely low-mass (<0.16 M ⊙ ), 11040 K white dwarf with a high probability of being a white dwarf (P WD = 0.91, Gentile Fusillo et al. 2021).With only sparse Gaia DR3 data and possibly long transit durations, we cannot confirm this system as eclipsing yet, but encourage further follow-up.
We are far more confident in the fidelity of the final two systems shown in Figure 3. WD J004502.35+503408.46 (G = 17.6 mag) is over-luminous to the isolated white dwarf position in the Gaia CMD (suggesting binarity) and features ZTF and Gaia dropouts suggesting an orbital period of 6.87794(72) hr.WD J202811.64+350525.08 (G = 17.9 mag), is also over-luminous and features ZTF dropouts when folded on a period of 10.3937(17) hr.There is also a strong Gaia-G sinusiodal pattern that aligns with the ZTF data with a minimum in the time of transit.

Follow-Up of a New Eclipsing CV
We obtained follow-up time-series photometry and spectroscopy for our most compact new eclipsing system (WD J154008.28−392917.61),located in the southern hemisphere (G = 17.3 mag).
We obtained high-speed time-series photometry using the ULTRACAM instrument (Dhillon et al. 2007) mounted on the 3.6-meter New Technology Telescope (NTT) telescope at the La Silla Observatory in Chile.This camera obtains simultaneous three-channel photometry with frame-transfer detectors; we used high-throughput Super-SDSS u s g s r s filters (Dhillon et al. 2021).We observed WD J154008.28−392917.61 over two consecutive nights, analysing here only the SDSS-g s data.We collected 9.0-s exposures on UT date 2023 March 16 with an average seeing of 0.8 arcsec.We collected 4.5-s exposures on UT date 2023 Mar 17 with an average seeing of 0.7 arcsec.All UL-TRACAM data were bias-subtracted and flat-field corrected using the HiPERCAM pipeline2 .
We also obtained follow-up spectroscopy of this system using the Goodman spectrograph (Clemens et al. 2004) mounted on the 4.1-meter SOAR Telescope in Chile.We collected eleven 10 min spectra using the 400-line grating with a 1-arcsec slit and the M1 grating setup on UT date 2023 May 24, yielding a resolution of roughly 4.4 Å.We extracted the data using the pypeit data reduction pipeline (Prochaska et al. 2020), and flux calibrated using the standard star EG 274.
We captured two primary eclipses with ULTRACAM, shown in the top two panels of Figure 4. Fitting the midtime of the eclipses with a Gaussian bounded by when the flux decreases below −20%, we find that the pri- mary eclipses occur at BJD TDB = 2460019.8887179(17)and 2460020.8778468(11),separated by 18 cycles of our TESSdetermined main periodicity of 1.319(13) hr.There is considerable out-of-transit variability, including an extended feature from a bright spot on the white dwarf, seen in many eclipsing CVs (e.g., Savoury et al. 2011;McAllister et al. 2019).
Our coadded spectrum in the bottom panel of Figure 4 confirms this is an accreting white dwarf binary.Broad Balmerline absorption from the white dwarf is visible, along with strong emission features from accretion, especially dominant at Hα.Our spectrum is not high-enough resolution to attempt a radial-velocity fit.We do not observe Zeeman splitting at the Balmer lines, though our limits are weak given the strong emission in the line cores.
A purported orbital period of 68.365 min is well below the CV period minimum of roughly 80 min, after which convective donor stars expand on further mass loss (Patterson 1984;Knigge et al. 2011;Kalomeni et al. 2016;McAllister et al. 2019).However, the full photometric phase coverage from TESS shown in Figure 3 reveals this is the correct period of recurrent variability.This makes WD J154008.28−392917.61among the shortest-period CVs known, similar to the 66.61-min CV SDSS J150722.30+523039.8 (Littlefair et al. 2007).These ultracompact CVs are likely descended from a previously de- tached white dwarf + brown dwarf binary.It is also possible the system descended from a low-metallicity, significantly evolved donor (Uthas et al. 2011).

Magnetic Spotted White Dwarfs
Spotted white dwarfs are difficult to distinguish from reflection-effect binaries like those discussed in Section 4.1.When spectroscopy is not available, we classify all objects with apparently mono-periodic variability and photometrically determined (Gentile Fusillo et al. 2021) masses >0.525 M ⊙ and temperatures <31,000 K as isolated white dwarfs with rotational modulation from magnetic spots.
The period of the spot-induced modulations corresponds to the rotational period at the star's surface (e.g., Brinkworth et al. 2013;Kilic et al. 2015;Hoard et al. 2018).We recover the periods of eight previously known spotted white dwarfs from the Gaia DR3 light curves independently, and identify 17 new likely spotted white dwarfs.The majority of the newly identified spotted white dwarfs (12/17) have effective temperatures between 6500 − 10,000 K, placing them inside the range of known DAHe strongly magnetic white dwarfs with Balmer-line emission (Greenstein & McCarthy 1985;Reding et al. 2020;Gänsicke et al. 2020;Walters et al. 2021;Reding et al. 2023;Manser et al. 2023), motivating future time-resolved spectroscopic followup.Our sample contains several known DAHe (see Table 2).WD J083531.17+533230.91 (G = 18.2 mag) is the only other spectroscopically confirmed strongly magnetic white dwarf in our sample, and appears to have a 2.16-hr period.
Examples of three spotted white dwarfs are shown in Figure 5.The top object WD J052026.35+381240.87 (G = 15.4) is a spectroscopically confirmed white dwarf from LAMOST claimed to be a DBA (Kong et al. 2019) but is likely a DAH; Gaia DR3 photometry shows it is likely rotating at 6.7856 ± 0.0046 hr.The second object (WD J195629.23−010232.67,G = 13.6 mag) has been known to be spotted (the white dwarf is highly magnetic with a complex field structure, shown in Maxted et al. 2000).We observe clear sinusoidal variability in the G data with a period of 34.898 ± 0.074 hr, in close agreement with the literature value from Brinkworth et al. (2005).The final object is WD J202932.51+070107.70 (G = 16.6 mag), a known DO white dwarf (Dreizler et al. 1995).This white dwarf was observed to have a ZTF g photometric variability period of 6.97882 ± 0.00012 hr from Reindl et al. (2021), which is close to our LLS fit to the Gaia-G data of 6.9572 ± 0.0022 hr.It is likely that the ZTF or Gaia data has selected an incorrect alias due to gaps in the data.
Figure 6 demonstrates Gaia DR3 light curves are able to recover the variability in two of the shortest-period spotted white dwarfs known.
The top panel details WD J031715.85−853225.56 (G = 14.8 mag), a well-studied, rapidly rotating, high-field magnetic white dwarf (Ferrario et al. 1997).The Gaia G peak occurs at the same period as the TESS data, to within the uncertainties of the LLS fits.The light curve from Gaia is sparsely sampled, with visits separated by 32.5 ± 8.8 d, where 8.8 d is the standard deviation of the time between visits.False-alarm probability lines for periodograms are estimated by holding the time sampling the same but randomly shuffling the fluxes with replacement 10,000 times, in an attempt to quantify the probability that the amplitude of a peak can be generated by pure noise (e.g., Greiss et al. 2014;VanderPlas 2018).For WD J031715.85−853225.56 at the top of Figure 6, none of our bootstrapped periodograms have a peak as high as the observed Gaia G periodogram, yielding a false-alarm probability of <0.1%.
In the bottom panel of Figure 6 we show Gaia and TESS peaks measured for the strongly magnetic, emissionline (DAHe) white dwarf WD J125230.93−023417.72 (G = 17.5 mag, Reding et al. 2020).While not statistically significant, the highest peak in the Gaia periodogram occurs at the known dominant period of 317.278 s (which is the first harmonic the 634.56-s rotation period, see Farihi et al. 2023).We bootstrap a false-alarm probability of 0.1% for this peak.
The shortest-period new spotted white dwarf in our sample is WD J115033.35−063618.07 (G = 16.4 mag).This spotted white dwarf features a highest peak in the G light curve matching the TESS-significant peak at 884.0679 ± 0.0094 s.Spectropolarimetry puts a 3σ upper limit on the magnetic field of LP 673-41 of <6 kG (Kawka & Vennes 2012), raising questions about the origin of the spot on this 8600 K white dwarf.The longest period spot appears on WD J124740.10+303007.41 (G = 17.9 mag), with a highest peak in the periodogram at 9.487 d in both its Gaia and ZTF light curves.

Pulsating White Dwarfs
Pulsating white dwarfs are variable due to non-radial pulsations, with periods typically ranging from 100 − 1500 s, amplitudes up to several percent, and usually multiple, non-harmonically related periods present at the same time (Fontaine & Brassard 2008;Winget & Kepler 2008b).DA white dwarfs are unstable to pulsations in a narrow temperature range between roughly 13,500 − 10,500 K (Hermes et al. 2017c).These hydrogen-atmosphere pulsators are commonly known as ZZ Cetis and DAVs.
From Gaia DR3 photometry alone we are able to independently identify the periods for two new candidate pulsating white dwarfs and confirm the periods of two known DAVs.All objects lie within the empirical DAV instability strip in the Gaia color-magnitude diagram (Figure 1), and their Lomb-Scargle periodograms are shown in Figure 7.As with our spotted white dwarfs in Figure 5, we bootstrap falsealarm probabilities to assess the significance of a peak in the periodogram and quantify the likelihood a peak cannot arise from noise alone.The significance lines in Figure 7 are the 99.9% confidence line (<0.1% false alarm); false-alarm probabilities for all objects in this manuscript are listed in Table 3.While none of our pulsating white dwarfs have formally significant peaks, the chance that the highest peak in the periodogram exactly matches significant peaks in an independent ZTF or TESS dataset is exceptionally low; our periodograms all have step sizes of 0.01 µHz and run beyond 4000 µHz, giving hundreds of thousands of trial frequencies.In three of the four cases in Figure 7, the false-alarm probability is <10%.
We find WD J120650.89 −380549.23 (G = 15.7 mag) is a new pulsating WD with a pulsation period at 259.9127 ± 0.0013 s in G with a 8.1% false-alarm probability that is also significantly detected in TESS.WD J215823.88-585353.81 (G = 15.8 mag) is a known DAV with multiple detected modes from rotational splittings revealed by TESS at 310.27 s, 309.79 s, and 309.31 s (Romero et al. 2022).The highest peak in the G RP periodogram is consistent with this pulsational variability, at a period of 310.0049± 0.0021 s, though this peak has a marginal 28.9% false-alarm Figure 7. Panels of periodograms for the four objects we classify as Gaia-detected pulsating white dwarfs, all with periods <400 s.The photometric bands in these figures are G, GBP, GRP, g, r, T (Gaia G, BP, and RP bands, ZTF g and r bands, and the TESS photometry band, respectively).A bootstrapped 99.9% confidence lines is shown as a horizontal dashed line in gray (see description in Section 4.4).The false-alarm probabilities of all four Gaia peaks are all between 2.5% and 28.9% (see Table 3).
probability.WD J082924.77−163337.25 (G = 17.6 mag) was identified as a variable white dwarf in Guidry et al. (2021).We detect variability consistent with pulsations in both the Gaia-G and ZTF-g light curves at 359.0045 ± 0.0025 s, with just a 2.5% false-alarm probability.Finally, WD J195227.88+250929.18(G = 15.1 mag), is a known DAV with a dominant pulsation period of 256.2 s (Kepler 1984;Fontaine et al. 1980).Our analysis agrees closely with peak in G BP at 255.999 ± 0.001 s and a 3.7% false-alarm probability of matching peaks in ZTF and TESS.
The four white dwarfs with likely pulsations detected in their Gaia light curves all have periods <400 s; longer-period modes are likely unstable over long baselines (Hermes et al. 2017c), suggesting longer-period modes will be hard to detect from Gaia data independently.However, pulsating white dwarfs appear to be the most numerous white dwarfs flagged as variable in Gaia DR3.There is an overdensity of points in Figure 1 near the DAV instability strip relative to the 200pc sample of white dwarfs in the background.In fact, of the 883 candidate white dwarfs that are flagged as photometrically variable in Gaia DR3 with P WD > 0.98 and  2021), nearly half (422) have effective temperatures near the DAV instability strip boundaries (13,500 >T eff > 10,500 K).Literature searches of this sample reveal at least 50 are already-known DAVs, and at least 120 that can be photometrically confirmed with TESS, ZTF or ASAS-SN data; this analysis will be presented in a future publication.

GAIA-DETECTED PERIODS
We use Gaia DR3 epoch photometry, which includes photometric time series data in the G-, G BP -, and G RP -bands (Eyer et al. 2023).Each time-series data point is a socalled field-of-view transit, after an object has passed through nine consecutive CCD observations, each separated by 4.85 s (Roelens et al. 2018).As the Gaia spacecraft spins, objects will then be re-observed at a cadence separated by 1 hr 46 min (Roelens et al. 2017).The time sampling after this revisit is considerably longer, and different for each source, set by the Gaia scanning law (e.g., Boubert et al. 2021).
We analyze the revisit cadence of these observations by creating a histogram of the average time between each obser-vation, shown in Figure 8.We ignore the revisit timescale of 1 hr 46 min (set by the 6-hr spin period of Gaia, as discussed in de Bruijne 2012) by excluding time between observations of less than 0.3 days, and find an average time of 49.7±12.5 d between observations for the full sample of 1333 objects (the uncertainty is set by the standard deviation of these revisit times).Of the 105 objects where we can measure variability from the Gaia light curves independently, the average revisit time is 44.2 ± 10.3 d.Our subset of 105 objects has slightly less time between observations, only a few more Gaia-G data points (with an average number of points of 49±17 compared to 41 ± 14 for the full sample), and is slightly brighter (with an average magnitude of G = 17.0 ± 1.2 mag compared to G = 17.2 ± 1.6 mag for the full sample).The distributions in Figure 8 show we are not heavily biased towards objects with frequent revisits set by the Gaia scanning law.The average and standard deviation in the revisit times between FoV transits for each object is included in Table 3.Among the 72 of 105 objects with ZTF data, the average object has 393 ZTF visits, which is completely consistent with the typical sky coverage of the average fields in ZTF DR12.
We also analyze short-period variability in the Gaia DR3 light curves, which is measured as the object moves from one CCD to the next every 4.85 s (e.g., Roelens et al. 2018).Included in DR3 are per-CCD least-squares fits listed as "Frequency" for objects flagged as vari short timescale, for select objects with candidate variability periods shorter than 0.5 d.The inverse of the vari short timescale frequency is listed in Table 2 as P G,S , and we check each period generated by our LLS fit (P G,DR3 in Table 3) against P G,S .In our final 105 object sample, 65 objects are flagged in Gaia DR3 as short-timescale sources, and 55 of these 65 (85%) have P G,S that matches P G,DR3 to within 3% (after which the agreement is never better than 22%).
We compare the Gaia DR3 short-timescale analysis against our LLS fits by object type.We find that of our 72 binary objects, 48 of 53 (91%) with vari short timescale data have P G,S that matches our determinations of P G,DR3 , and of the spotted white dwarfs, 5 of 7 with short-timescale analysis match.For all variable types, the Gaia DR3 shorttimescale analysis returns 55/60 (92%) matches for objects with vari short timescale between 0.278 and 2.78 hours, and routinely does poorly for periods longer than 3 hr.
We also attempt to assess the reliability of the Gaia variability identifier (Eyer et al. 2023).Gaia uses a machine learning algorithm trained on non-variable objects and then tested against training sets (built from various published catalogues of variable stars) to confirm how effectively this algorithm can identify variable objects.Objects are categorized as variable when there is a large value for the ratio of the difference in magnitude from the average for that object to the interquartile range of the magnitude.These objects are then passed through one of two paths in the machine learning process to be sorted into a specific Gaia "class," discussed in depth in Rimoldini et al. (2023).This Gaia class is listed in Table 2.
We find that this "class" is not generally useful, as most are simply "WD."There is one case where this class correctly identifies a known CV (WD J130017.86−325805.23).The Gaia "class" also marks two objects as "S" or stars with short-timescale variability: WD J083843.35−282701.14 (a known CV with P G,S that matches P G,DR3 at 16.109 ± 0.029 hr) and WD J233923.79−485350.19 (a likely new binary system with P G,S that matches P G,DR3 at 2.52962 ± 0.00075 hr).
The new eclipsing CV WD J154008.28−392917.61 also has a Gaia "class" of CV.
Finally, we note that Gaia epoch photometry may contain spurious periodicities due to scan-angle-dependent signals, especially in marginally resolved, fixed-orientation pairs of stars separated by <0.5 arcsec (Holl et al. 2023).Although previous work has only explored signals up to 10 days, and most signals determined here are below that, we investigate the likelihood that any of our detections are spurious.
All 1333 white dwarf candidates in our sample have information in the vari spurious signals table from Holl et al. (2023), including important metrics that can reveal close binarity, the Spearman rank correlation coefficient with corrected flux excess factor (r exf,G ) and the Image Parameter Determination model (r ipd,G ).Only three white dwarfs have both r exf,G and r ipd,G values >0.8 (WD J020426.03+571026.62, WD J031047.57−100153.85, and WD J100643.74−221757.86),none of which are included in our subset of 105 white dwarfs with variability measured independently from Gaia.In our subset of 105 objects, only one has r ipd,G > 0.6 and that is WD J003512.88−122508.84, which has confirmed variability from TESS (Reding et al. 2023).We conclude that contamination from spurious Gaia scanning-law-dependent periods is unlikely in our sample of white dwarfs.

DISCUSSION & CONCLUSIONS
We analyze 105 white dwarf candidates for which Gaia is capable of detecting accurate periods from DR3 photometry.These periods of variability range from 9.5 d to as short as 256.2 s (roughly 4 min), including seven objects with periods shorter than 1000 s.We obtained this result by comparing Gaia multi-band photometry to data from ZTF and TESS to identify significant periods within the Gaia data.Analysis of the Gaia photometry resulted in the discovery of new pulsating, spotted and binary white dwarfs.This includes a new 68.4-mineclipsing cataclysmic variable, which has a period well below the CV period minimum of roughly 80 min (Knigge et al. 2011) and is one of the shortest-period CVs known.
Our overall analysis demonstrates that Gaia epoch photometry is precise enough to detect short-term, low-amplitude periods even when observations are sparsely sampled.The absolute median amplitude of the photometric variability we confirm from Gaia independently is 1.4%, with an average period of roughly 12 hr.This is notable compared to the distribution of time between observations, which is on average roughly 44 d.We find that overall, the 105 variables that are significant in Gaia are slightly brighter and sampled more often than the full sample of 1333 objects, but the distributions of magnitudes or number of points are not significantly biased in either parameter space, as shown in Figure 8.
The likelihood that the highest peak in two independent periodograms match is small, given that there are more than 10 5 frequency elements in each periodogram.This is the basis for which we claim Gaia has detected a periodicity.Still, we have bootstrapped estimates that a peak in the periodogram can be caused by noise alone and find that 33/105 objects have significant peaks in their Gaia light curves, with a <0.1% false-alarm probability.Nearly half the sample, 50/105, have peaks with a false alarm <1%.Only three have >35%, but all 105 have Gaia peaks with a <41% false-alarm probability (Table 3 details this value for all objects in our sample).Our work provides an empirically determined set of cutoffs for which variability in a Gaia DR3 light curve is likely to be genuine, and it also represents a useful value for future analysis of sparsely sampled, high-precision photometry from large surveys like the Vera C. Rubin Observatory and its Legacy Survey of Space and Time (LSST; Ivezić et al. 2019), as well as the Nancy Grace Roman Space Telescope (Akeson et al. 2019).
Previous spectroscopy exists for only 36 of the 105 objects discussed in this paper, so follow up is encouraged for most of these sources.There are many objects of interest that would expand sample sizes of rare object types.Some notable examples include WD J123955.40+834707.51 (G = 20.0 mag), which may be a new WD+WD binary containing an ELM white dwarf, and WD J130017.86−325805.23 (G = 20.3mag) which is a candidate CV with recorded outbursts (Drake et al. 2014) but shows a dominant photometric period of 36.2 min closer to the orbital period of AM CVn binaries (see Section 4.1).There are also multiple candidate eclipsing binaries discussed in Section 4.3.Finally, one of the shortest-period new spotted white dwarfs we discovered here (WD J115033.35−063618.07)appears to have an 884.73-s spin period but a <6 kG magnetic field, raising questions about the origin of its fast rotation (see Section 4.4).
As Gaia continues to scan the sky, the methods discussed in this paper provide a foundation for analyzing short-period variables within even longer-baseline data.Verifying that Gaia data independently can be used to detect short periods will allow future work on sources with no additional spectro-scopic or photometric information.Increasing the numbers of rare variable stellar remnants, especially those in shortperiod binaries or with magnetic spots, will help constrain their space density and formation channels.

Figure 1 .
Figure 1.Color-magnitude diagram showing our sample of 1333 high-confidence white dwarf candidates flagged as photometrically variable in Gaia DR3 as black stars.The larger colored symbols show the 105 objects discussed in this manuscript which have variability periods measured from their Gaia light curves independently; the color for each point corresponds to the corresponding variability period.The background of this plot is a two-dimensional histogram of white dwarfs within 200 pc matching the magnitude distribution of the 1333 photometrically variable white dwarfs.Dashed red lines show the expected cooling tracks of a 0.6 M⊙ white dwarf at top and 1.2 M⊙ white dwarf at bottom; white dwarfs cool from the upper left to the lower right in this diagram.

Figure 2 .
Figure2.Phase-folded light curves of three representative variable white dwarfs from binarity, revealing orbital periods of 5.725 hr, 2.873 hr, and 2.500 hr, respectively.All folded light curves (ZTF g in blue, Gaia G in green, and TESS photometry in red) are phased to the same ephemeris.ZTF g and TESS data are grouped into 151 bins for each light curve.The larger amplitudes at redder wavelengths in these systems indicates they are all likely reflectioneffect binaries of a cool main-sequence star reprocessing flux from a nearby hot white dwarf.

Figure 4 .
Figure4.Follow up data for WD J154008.28−392917.61reveals deep primary eclipses in the two top panels.Follow-up spectroscopy (note the broken x-axis) confirms this is a 68.365-minCV, likely descending from a previously detached white dwarf + brown dwarf post-common-envelope binary (e.g.,Littlefair et al. 2007).

Figure 5 .
Figure 5.Following the same convention as Figure 2, we show phase-folded light curves of three magnetic spotted white dwarfs.ZTF-g and TESS data are grouped into 151 phase bins, whereas the Gaia data are not binned.

Figure 6 .
Figure 6.Lomb-Scargle periodograms showing two rapidly rotating spotted white dwarfs recovered in sparsely sampled Gaia DR3 light curves.At top is WD J031715.85−853225.56 (Ferrario et al. 1997); the 725 s variability period has a <0.1% false-alarm probability in the Gaia G light curve.At bottom is WD J125230.93−023417.72, which has a 0.1% false-alarm probability, with the highest peak in the periodogram at exactly the same period, within the uncertainties, as the known variability discovered by Reding et al. (2020).

Figure 8 .
Figure 8. Top left histogram shows the average time between Gaia DR3 observations (ignoring the 1 hr 46 min revisit) for the full sample of 1333 candidate white dwarfs flagged as variable in gray, inset in red by the 105 candidate white dwarfs in this manuscript where their variability period can be determined by Gaia independently.The top right panel shows the number of points in each G light curve, and the bottom left panel shows the G magnitude distribution of both samples.The bottom right panel shows the distribution of the 105 periods for objects detected by Gaia independently (note that the x-axis is log scale).Although we are slightly more sensitive to objects with more frequent visits, our sample of 105 sources covers most of this parameter space.

Table 1 .
Summary table of the full sample and a subset of Gaia-detected variable candidate white dwarfs.

Table 3 .
New variability information determined for the 105 white dwarfs in this study with significant variability measured from their Gaia DR3 light curve.

Table 3 continued
Table3(continued) RP ) band used in analysis instead of Gaia G band.Note that "Rev."(revisit) is the average time between two Gaia detections of a source, and "Std.Rev." is the standard deviation of this revisit time.