A Systematic Search for Short-period Close White Dwarf Binary Candidates Based on Gaia EDR3 Catalog and Zwicky Transient Facility Data

Galactic short-period close white dwarf binaries (CWDBs) are important objects for space-borne gravitational-wave (GW) detectors in the millihertz frequency bands. Due to the intrinsically low luminosity, only about 25 identified CWDBs are detectable by the Laser Interferometer Space Antenna (LISA), which are also known as verification binaries (VBs). The Gaia Early Data Release 3 (EDR3) provids a catalog containing a large number of CWDB candidates, which also includes parallax and photometry measurements. We crossmatch the Gaia EDR3 and Zwicky Transient Facility public data release 8, and apply period-finding algorithms to obtain a sample of periodic variables. The phase-folded light curves are inspected, and finally we obtain a binary sample containing 429 CWDB candidates. We further classify the samples into eclipsing binaries (including 58 HW Vir-type binaries, 65 EA-type binaries, 56 EB-type binaries, and 41 EW-type binaries) and ellipsoidal variations (209 ELL-type binaries). We discovered four ultrashort period binary candidates with unique light-curve shapes. We estimate the GW amplitude of all of our binary candidates, and calculate the corresponding signal-to-noise ratio (S/N) for TianQin and LISA. We find two (six) potential GW candidates with S/Ns greater than 5 in the nominal mission time of TianQin (LISA), which increases the total number of candidate VBs for TianQin (LISA) to 18 (31).


INTRODUCTION
Close White Dwarf Binaries (CWDBs) are an important branch of the evolution channel of main-sequence star binaries (Gokhale et al. 2007). The formation of such binaries involves a stage of the common envelope, a complicated stage where complicated physical processes such as mass transfer, angular momentum loss, and even gravitational wave radiation. The theoretical simulation of the CWDBs evolution is challenging, with major issues still under debate. For example, it is not clear whether a second common envelope stage is involved in the formation of a CWDB. Since there are many subclasses of CWDBs, there could be a variety of evolution channels. The searching and identification of new close white dwarf binaries have the potential to provide observational evidence for the binary evolution models and are important for the research of stellar physics, milli-Hertz gravitational-wave astronomy, and Galactic evolution. (Parsons et al. 2016;Rebassa-Mansergas et al. 2017;Lagos et al. 2020;Ren et al. 2020;Hernandez et al. 2021Hernandez et al. , 2022Lagos et al. 2022).
Depending on the components type and mass transfer, CWDBs can be divided into several sub-populations (Ren et al. 2020;Inight et al. 2021;Kruckow et al. 2021): Post-Common Envelope Binaries (PCEBs), binary systems that contains a white dwarf and a main-sequence star; Cataclysmic Variables (CVs), interactive white dwarf binaries; and Double White Dwarfs (DWDs).
Short-period CWDBs have orbital periods of less than 60 minutes, emitting gravitational wave (GW) in the millihertz-frequency band, becoming ideal sources for the space-borne gravitational wave observatories like the Laser Interferometer Space Antenna (LISA) (Amaro- Seoane et al. 2017) and TianQin (Luo et al. 2016;Gong et al. 2021), therefore, they are also known as verification binaries (VB) Huang et al. 2020). The known classical verification binaries catalog includes 11 AM CVn-type binaries, 13 detached double white dwarfs, and 1 hot subdwarf binaries ). Up to now, a total of ∼ 87 candidate verification binaries are all found in the electromagnetic band (Huang et al. 2020;Burdge et al. 2019aBurdge et al. , 2020aKilic et al. 2021;Chandra et al. 2021;Brown et al. 2022).
In addition, there are other potential GW sources such as Helium star binaries, short-period CVs, exoplanets, brown dwarfs, and substellar companies (Amaro- . From the perspective of the formation pathways, these verification binaries and other potential GW sources experienced mass exchange phases via Rochelobe overflow and mass loss via the ejection of a common envelope (CE) in evolution (Götberg et al. 2020;Amaro-Seoane et al. 2022). For example, there may be two different channels for the formation of DWDs: if the mass transfer stage is stable, it will be directly generated from CVs after a CE phase. If the mass transfer is unstable, the second CE stage takes place after the CVs, and then it will evolve into a WD+Helium-star, and finally form a DWD (Amaro- . It is noteworthy that El-Badry et al. (2021b) recently found evidence that the progenitors of extremely low mass white dwarfs (ELM WDs), AM CVn systems, and detached ultracompact binaries may be evolved CVs (El-Badry et al. 2021b,c). The Galactic foreground is mainly composed of DWDs, but other Galactic binaries also contribute to the Galactic foreground (Boileau et al. 2021), for example, CVs, stripped star binaries (Götberg et al. 2020), WD+Mdwarfs, etc. In addition to searches from individual observations, one can perform CWDB search with a larger scale. Several surveys can be used to pick potential CWDB candidates, like the Catalina Real-time Transient Survey (CRTS) (Breedt et al. 2014), Global Astrometric Interferometer for Astrophysics (Gaia) (Geier et al. 2017;Gentile Fusillo et al. 2021;Rebassa-Mansergas et al. 2021;El-Badry et al. 2021a;Torres et al. 2022), the Op-tical Gravitational Lensing Experiment (OGLE) (Wevers et al. 2016), the Palomar Transient Factory (PTF) (van Roestel et al. 2017(van Roestel et al. , 2018Burdge et al. 2019b), the All Sky Automated Survey for SuperNovae (ASAS-SN) (Rivera Sandoval et al. 2022), the Transit Exoplanet Survey Satellite (TESS) Pichardo Marcano et al. 2021a;Hernandez et al. 2022), the Large Sky Area Multi-Object Fiber Spectroscopic Telescope (LAMOST) (Wang et al. 2022b), and most recently the Zwicky Transient Facility (ZTF) (Ofek et al. 2020;Coughlin et al. 2020;Burdge et al. 2020a,b;Szkody et al. 2020Szkody et al. , 2021Kupfer et al. 2021;Keller et al. 2022;McWhirter & Lam 2022). The repeated observations of the same sources can reveal the optical variability, and some of these surveys can be used, and have been used, to determine the periodicity.
In this paper, we present a search for CWDBs from a combination of survey data. We first select potential variable sources from the Gaia EDR3 catalog, then apply periodic analysis from time domain photometric data from ZTF data to determine the properties of the binaries.
The structure of this article is organized as follows. In Section 2, we elaborate the classification and the characteristics of the different sub-classes of close white dwarf binaries and the status quo of potential gravitational wave sources for these subtypes. In Section 3, we describe how to select our initial samples based on the Gaia H-R diagram, and further select the variable sample by the Gaia Variability Metric. In Section 4, we describe how we use three period-finding algorithms to search for periodic samples from ZTF light curves. In Section 5, we analyze five different variability types of binaries in our binary sample and compare our sample with the CWDBs catalog of other surveys. In Section 6, we discuss four interesting binaries. The overall parameter distribution and GW properties of the final sample are also discussed. Finally we summarize in Section 7.

CLOSE WHITE DWARF BINARIES AND POTENTIAL GRAVITATIONAL WAVE SOURCES
There are two evolutionary pathways for primordial binaries: (1) The so-called wide binary, about 75% of wide binaries have relatively large orbital separations, and there is no interaction in the Hubble time-scale, which is similar to the evolution of a single star (Ren et al. 2020).
(2) The remaining 25% are close binaries, which have to undergo a phase of mass transfer (Ren et al. 2020). After the ejection of the common-envelope (CE) phase, at least one star in the close binary evolved into a white dwarf, and due to complex physical pro-cesses such as angular momentum loss or gravitational wave radiation, which will be generated sub-classes such as PCEBs, CVs, and DWDs.
In this paper, we will focus on the Galactic ultracompact white dwarf binary candidates that can generate gravitational wave radiation, potential gravitational wave sources, and the progenitors of GW sources. These targets are formed by the evolutionary pathway of the primordial binaries after the CE stage (Kruckow et al. 2021). We will focus on the classification and the characteristics of each sub-type of CWDBs: PCEBs, CVs, and DWDs, respectively.

Post-Common Envelope Binaries
PCEBs are detached or semi-detached binary systems in which a white dwarf and main-sequence star that is rapidly engulfed in a common envelope, and the orbital periods range from hours to a day. The companion stars in the PCEBs system are low-mass main-sequence stars, such as several brown dwarfs, M-dwarfs, hot subdwarfs, etc. Brown dwarf companion stars are difficult to search from optical band data alone, while M-dwarf and hot subdwarf companions are in the majority. Hot subdwarfs are under-luminous for their high temperature (Heber 2016;Lei et al. 2020;Culpan et al. 2022). They are divided into two main spectroscopic: B-type subdwarfs (sdB, a core helium-burning star and thin hydrogen envelope), and O-type subdwarfs (sdO). Hot subdwarf binaries with white dwarf companions that exit the common envelope phase at orbital periods of less than two hours will overflow their Roche lobes while the sdB is still burning helium (Kramer et al. 2020;Li et al. 2022).

Cataclysmic Variables
Cataclysmic variables are short-period (P orb ≤ 6 h) semi-detached binary star systems in which a low-mass companion star transfers mass to a white dwarf (WD) primary via stable Roche lobe overflow(RLOF, Knigge et al. 2011;Hillman et al. 2020;Schreiber et al. 2021Schreiber et al. , 2022. The two stars are close enough that the companion completely fills its Roche lobe, and the outer layer of its envelope is gradually stripped from its surface and forms an accretion disk around the white dwarf. The CVs can be further divided into several sub-types: classical novae, dwarf novae, polar (AM Her-type star, Kolbin & Borisov 2020;Kolbin et al. 2022), intermediate polar (DQ Her star, Norton et al. 1999) and AM Canum Venaticorum system(AM CVn, Nelemans et al. 2001a;Postnov & Yungelson 2014;Ramsay et al. 2018;Wong & Bildsten 2021), etc.
For the polar (B ∼10-200 MG) and intermediate polar (B ∼1-10 MG), the primary is a highly magnetized WD, and the accretion disk can be entirely disrupted. There are differences between polar and intermediate polars, the rotation of the white dwarf is synchronized with the orbital period of the companion in the polars, while the latter is not synchronized.
The AM CVn systems are short-period ultra-compact binaries in which a massive white dwarf accretes heliumrich matter from a hydrogen-deficient donor star. For AM CVn systems, the donors star are degenerate or semi-degenerate, and the orbital periods are in the range of 5-68 minutes (Kalomeni et al. 2016;Green et al. 2018Green et al. , 2020van Roestel et al. 2021a,b;Duffy et al. 2021).

Double White Dwarfs
Double white dwarfs are the remnants of the second common envelope event in the evolution of close binaries. DWDs lose angular momentum through gravitational wave radiation, which will decrease the separation between the two white dwarfs and may eventually merge. Several relics can be associated with the double white dwarf merging event, such as type Ia supernovae (Nelemans et al. 2001b;Toonen et al. 2012;Shen et al. 2018;Liu et al. 2018;Rebassa-Mansergas et al. 2019;Maselli et al. 2020), neutron stars (Accretion-Induced Collapse events, Yu et al. 2019;Liu & Wang 2020;Ablimit 2022;Wang et al. 2022a) and high-mass WDs (Cheng et al. 2020). The exact outcome depends on the type of core of the two white dwarfs.
Extremely low-mass WDs are double-degenerate helium-core WDs with masses M ≤ 0.3M . ELM WD systems are formed after severe mass loss, which limits that these systems most likely formed through binary interactions (Li et al. 2019). Because it is difficult to evolve into ELM WD from an isolated star in the Hubble timescale. The ELM survey is systematic search research for ELM WD binaries. This survey selects candidates by using SDSS color-cutting, then carried out the targeted spectroscopic follow-up of ELM WD candidates. The ELM survey successfully discovered 124 detached double-white dwarfs (DWDs) (Brown et al. 2010;Kilic et al. 2011;Brown et al. 2012;Kilic Figure 1. The location of the sample selection on the Gaia color-magnitude diagram. In all panels, scatter points and the overlaid 2D histogram shows the stellar density of the Gaia 200 pc background sources. (a) The red solid lines show the color-cut range that we defined, using the lower edge of the main sequence as an upper limit and the upper edge of the WD cooling sequence as a bottom limit, and using a color-cut GBP − GRP < 1.0 as a right color limit. The blue dashed lines show a color-cut and absolute magnitude selection scheme for searching hot subdwarfs using Gaia data proposed by Geier et al. (2019). The green dashed lines show the color-magnitude diagram selection scheme for searching ELM-WD candidates based on Gaia DR2 data by Pelisoli & Vos (2019). (b) The red scatter points shows all samples under the initial query conditions. (c) The red scatter points shows the variable samples after using the Gaia variability metric select condition. (d) The red scatter points shows the final binary samples after examining ZTF light curve data. Brown et al. 2013;Gianninas et al. 2015;Brown et al. 2016Brown et al. , 2020bKosakowski et al. 2020;Brown et al. 2022), including eleven systems which are strong candidate LISA-detectable gravitational-wave sources Kilic et al. 2014;Brown et al. 2020aBrown et al. , 2022.

Gaia Color-Magnitude Diagram Selection
Gaia Early Data Release 3 (Gaia EDR3, Lindegren et al. 2021) contains more than 1.8 billion sources (the magnitude range from G = 3 − 21) with astrometric and photometric data based on the first 34 months of observations by the Gaia satellite. The astrometric data in the Gaia EDR3 provides positions, proper motions, and parallaxes ( ) for 1.468 billion sources, and the photometric data includes 1.544 billion sources which have magnitudes of photometric three-passbands G (phot g mean mag), G BP , and G RP (the BP and RP are defined by the blue and red photometers).
Thanks to the excellent astrometry measurement ability of Gaia, it can provide an accurate estimate of stars' parallax. Compared with the Gaia DR2, the accuracy of parallax measurements of the Gaia EDR3 is improved by 20-30 percent on average. Meanwhile, the photometric observation ability enables the Gaia EDR3 to also provide color G BP − G RP , and the G-band apparent magnitude of stars. Therefore, we can use the color-magnitude diagram to select our sample of object sources. Based on the distribution characteristics of known CWDB systems in the H-R diagram (Pelisoli & Vos 2019;Inight et al. 2021), we find that the absolute magnitudes of these systems are dimmer than main sequence (MS) stars and brighter than single white dwarfs. We decide to apply the first cut in the color-magnitude diagram between the MS and white dwarf cooling sequence (WDCS). We further apply a selection condition on color G BP −G RP < 1.0 to favor bluer objects, as white dwarfs are expected to have high temperatures. These first selection conditions are illustrated in Figure 1(a) as red solid lines. The corresponding equations are as follows: G abs < 11.5 + 2.7 (G BP − G RP ), where G abs = G + 5 * log10 [( + 0.029)/1000] + 5 is the absolute magnitude (Pelisoli & Vos 2019). Our cutting scheme includes the selection range of extremely lowmass white dwarf candidates (green dashed lines in Figure 1(a)), and includes hot subdwarf stars (Geier et al. 2019) (blue dashed lines in Figure 1(a)).
To ensure that the red and blue photometry are not subject to random noise, we follow Pelisoli & Vos 2019) and filtered on the errors of both G BP and G RP flux measurements to be larger than 10 (phot bp/rp mean flux over error > 10). We also apply a signal-to-noise ratio (SNR) threshold of 5 on the parallax measurements (parallax over error > 5).
The filter conditions for the threshold of parallax over error > 5 are often adopted for searches with Gaia data, for example, the search for ELM-WD candidates (Pelisoli & Vos 2019), the search for pulsating white dwarfs (Guidry et al. 2021), the search for evolved-CVs (El-Badry et al. 2021b), and the search for AR Scorpii-type binary systems (Takata et al. 2022). Since the motivation of this work is to obtain reliable candidate GW sources, we conclude that precise measurement of parallaxes is very important so that the estimation of GW SNR can be trustworthy. By applying this filter, we exclude a large number of sources with positive and negative spurious parallaxes, especially near the color BP-RP ∼ 1 in the Gaia H-R diagram. Lindegren et al. (2018Lindegren et al. ( , 2021 proposed to apply the quality filter parameters selection condition on Gaia DR2, and Pelisoli Pelisoli & Vos 2019) used similar conditions to the study of ELM-WD candidates. In this work, we apply the flux excess factor phot bp rp excess factor, E as the quality filter parameters to the selection: where G is the G-band mean magnitude (phot g mean mag), and u is defined by parameters the value of the chi-square statistic of the astrometric solution, astrometric chi2 al, and the number of good observations, astrometric n good obs al: u = astrometric chi2 al/(astrometric n good obs al − 5), (7) We plan to search for periodicity from the ZTF timedomain photometric data. However, the geographical site of ZTF put a limit on the archived data, so we apply a final cut in declination of δ > −28 deg Graham et al. 2019;Masci et al. 2019;Dekany et al. 2020). For further details on the initial-cut selection criteria, please see Appendix A.

Gaia Variability Metric
In the above section, in order to obtain clean initial samples, we have used a series of selection conditions, such as the the error of parallax measurements, and the quality of filtering parameter. Now our samples are accompanied with precise distance measurement and reliable photometric data. In this step, we aim to identify the variable sources that are most likely to be binaries. Therefore, we apply a further selection to the candidates from another dimension: photometric variability. The period search relies on the change of luminosity over time, and we can discard candidates with stable magnitudes, please see Appendix A. We apply a cut in the Gaia variability metric to select variable sources in the initial sample. We adopt the "variable amplitude" proposed by Deason et al. (2017) based . Empirical Gaia variability metric as a function of G-band magnitude for all initial samples, with the exponential fit proposed by Guidry et al. (2021) for Gaia EDR3 delineated in green. The 1.5 percent most variable samples are marked in red, and 15 ultra-compact binaries reported by Burdge et al. (2020a) are marked as blue stars. on the root mean square (RMS) dispersion of flux. A number of studies have adopted the Gaia variable metric and successfuly identified different types of variable sources, including large-amplitude variables (Mowlavi et al. 2021), short-period cataclysmic variable (spCV) (Abrahams et al. 2020), pulsing white dwarf (Guidry et al. 2021), hot subdwarf stars (Barlow et al. 2022), and birth of the extremely low mass white dwarfs (El-Badry et al. 2021b,c). Following Guidry et al. (2021) and El-Badry et al. (2021b), we use the G-band photometris to further filter candidate with Gaia variability metric (or the variability amplitude proxy A proxy,G , see Mowlavi et al. (2021)), V G : where n obs is the number of observations contributing to the G photometry (phot g n obs), σ G is the error on Gband mean flux (phot g mean flux error ), G is the G-band mean flux (phot g mean flux). Figure 2 shows the Gaia variability metric distribution of the 823231 objects in the initial sample. One can notice from Figure 2 that the Gaia variability metric is actually dependent on the G-band magnitude. This is because for dimmer objects, the associated SNR will be smaller, leading to a larger contribution from random fluctuation. In order to select the mostprobable variable sources from the initial sample, we follow Guidry et al. (2021) and define the VARINDEX to cut the top 1% most variable CWDBs for Gaia EDR3: where A = 8.31 × 10 −9 , α = 0.794, B = 0.0005, and C = 0.00962. In Figure 3, we show the distribution of the VARINDEX over G-band magnitude. We obtained the variable sample, which contains the 12480 strongest candidate variables with VARINDEX > 0.00, as shown in Figure 1(c). It corresponds roughly to the 1.5% highest VARINDEX systems. We conclude that this choice is reasonable, since if we list the VARINDEX values of the 15 ultra-compact binaries reported by Burdge et al. (2020a), 13 of them are associated with VARINDEX > 0.00, as shown in Figure 3. Even though 2 sources are discarded in this stage, this selection retains most of the interesting sources while greatly shrinking the sample size.

Variable Sample
We used the Gaia Variability flags to select 12480 candidates (see Table 1), which is defined as a variable sample of objects for period search. We imposed a photometric color selection of G BP − G RP < 1.0, this is different from the color-cut scheme used by Pelisoli & Vos (2019) to search for ELM candidates.
Pelisoli & Vos (2019) used a color-cut criteron of G abs > 20.25(G BP − G RP ) − 7.15 to search for blue targets to reduce contamination sources such as faint red stars scattered from the main sequence. We are indeed interested in "blue" objects for the Gaia source catalog because we expected short-period CWDBs have higher temperatures due to tidal heating , especially those candidates whose orbital period is less than 60 min may become strong GW sources. However, we are also interested in other potential gravitational wave source candidates, such as short-period CVs and substellar companies (Amaro- . It is worth noting that our variable sample includes some outbursting objects, such as nonmagnetic CV (dwarf nova), magnetic CV (irregular variability on a wide range of timescales), and QSO (red-shifted emission lines) (Pelisoli & Vos 2019), but these sources are considered as contamination in this study.

ZTF Light Curves
The ZTF is a time-domain survey using the 48-inch (P48) Schmidt telescope at Palomar Observatory 1 . Its camera has a field of view of 47 square degrees, and it can scan the entire northern visible sky (Southern sky dec > −28 deg.) at a rate of ∼ 3750 deg 2 per hour Graham et al. 2019;Masci et al. 2019;Dekany et al. 2020). ZTF can reach a 5σ limiting apparent magnitude of ∼ 20.8 mag in the g band, ∼ 20.6 mag in the r band, and ∼ 20.2 mag in the i band in a 30s exposures.
For the selected variable sample, we cross match the coordinate with the ZTF data, by downloading light curve data from the ZTF Public Data Release 8 (ZTF DR8) 2,3 .

Period Finding
The 12480 variable samples are not necessarily binary systems. To verify the binary nature of the system, the identification of the light curve period is necessary. To do so, we first cross-match the variable sample from Gaia data with the public ZTF 8th release data and identified 10938 sources that are accompanied by ZTF light curves. Then, we perform a period search procedure on the three time-series data: the ZTF-g band data, the ZTF-r band data, and the combined g + r band light curves.
(i) The Lomb-Scargle periodogram is based on the Fourier transform and is used to detect and characterize the periodic component in unevenly sampled time-series data and generate a signal power spectrum (VanderPlas 2018). The Lomb-Scargle normalized periodogram at frequency f is defined as (Lomb 1976;Scargle 1982;Leroy 2012).
where ω = 2πf , σ 2 is the variance of the photometry, y k is the photometry at corresponding observation times t k (k = 1, ..., N ),ŷ is the mean of the photometry, and τ is the time-offset which is defined by Eq. (3) from Leroy (2012).
(ii) The Conditional Entropy algorithm is a period-finding method to find the period of an astronomical (irregularly sampled) time series data based on minimizing the conditional Shannon entropy when the light curve folded at the trial period (Graham et al. 2013a). The expression of the conditional entropy H c (m i | φ j ) can be defined as (Graham et al. 2013a).
where m is the normalized magnitude, φ is the phase (trial period), p(m i , φ j ) is the density of points that fall within the bin located at phase φ j and magnitude m i , and p(φ j ) is the density of points that fall within the phi range. The CE algorithm determines the period through folding the phase of the light curve at each trial frequency, then estimating the conditional entropy of the partitioned phase-folded light curve corresponding to the trial frequency. In this paper, we used 10magnitude bins and 20-phase bins in calculating the period of ZTF sources using the CE algorithm.
(iii) The Box-Least Squares algorithm is based on a simplified box-shaped model of a strictly periodic transit, which is characterized by using only five parameter estimators to find the best model (Kovács et al. 2002). The parameters used are the period (P ), the transit duration as a fraction of the period (q), the phase offset of the transit (φ 0 ), the difference between the outof-transit brightness and the brightness during transit (δ), and the out-of-transit brightness (y 0 ). The frequency spectrum of BLS can be defined by the amount of Signal Residue (SR) of the time series at any given trial period (Kovács et al. 2002): where the equations of s and r are shown in Kovács et al. (2002), which can be used to estimate the photometric magnitude and the transit depth (Panahi & Zucker 2021). The light curve of eclipsing binaries may generate the secondary eclipse, however, the secondary eclipse is in some cases too shallow to be detected. The BLS algorithm searches for the periodic dips in brightness for extrasolar planets, especially for the secondary eclipse.
The LS algorithm has the advantage of being very fast to execute, but the CE and the BLS algorithms can report a more accurate period and are more robust against noises. Therefore, we apply LS period search to all 10938 sources, but only apply CE and BLS analysis if the sources show reliable periodic features. The search strategy of the period is separated into two stages: the rough search and the fine search.
(1) In the first stage of the rough search for the period, the LS algorithm can quickly calculate each source with have good ZTF light curve data in the Variable sample, however, LS has a different sensitivity to objects with eclipsing binaries and sinusoidal sources, and LS is more sensitive to the latter, which results in that eclipsing binaries have twice the real period, and there exists a peak at half of the true frequency in the frequency spectra, as shown in Figure 5.
(2) In the second stage of the fine search for the period, we visually inspected the phase-folded lightcurves of 10938 sources and determined that 826 of them are promising periodic sources (see Table 1), which we define as the periodic sample. In this search, we adopt the cuvarbase implementation of the BLS and CE algorithms, please see Appendix C 5 . A maximum frequency limit of 480 times per day is adopted. For the minimum frequency, we adopt the limit as twice the inverse of the baseline, where the baseline is defined as the end time minus the start time of the time-series data (for further details, please see Appendix B Period Finding Burdge et al. (2020b) The classification criteria based on the Variable Stars Index catalog 6 can be divided into two main variability groups: extrinsic variable stars and intrinsic variable stars. Extrinsic variable stars can be divided into eclipsing, rotating (spots, reflections, and ellipsoidal shapes), and microlensing events, of which the first two groups have obvious orbital modulation characteristics. The two main types of intrinsic variable stars are pulsation and outburst, in which pulsation is mainly the physical change inside the star. Based on the classification criteria of variable stars, we studied the general characteristics of the light curve shapes for binary systems and expected the physical mechanism of the variations.
Through multiple stages of search and veto, we are now left with a periodic sample of 826 candidates. More than 93.38% of the variable sample are discarded, as they demonstrate irregular or non-variability and outburst characteristics, as shown in Figure 6. The physical origin of outbursting stars could be similar to the dwarf nova (CV) systems, especially the AM CVn-type systems (van Roestel et al. 2021c;Pichardo Marcano et al. 2021b). However, we have no reliable spectroscopic follow-up observations to confirm the binary nature of the systems. Therefore, we have to discard these sources for this study.

Binary Sample
According to the light curve shapes, the 826 candidates from the periodic sample can be further classified as eclipsing binary systems, such as the HW Virtype eclipsing binary, the EA-type eclipsing binary (Detached Algol-type binaries), the EB-type eclipsing binary (β Lyrae-type binaries) and EW-type eclipsing binary (W Ursae Majoris type binaries), ellipsoidal binary system (ELL-type lightcurve binaries), reflection system (Figure 4 (f) show the typical light curve shape of reflection binary: ZTF J183304.05+463705.42.), pulsation (the RR Lyrae type pulsating star and the delta Scuti type pulsating star), and rotation sinusoids 7 , etc.
The final selection is to pick up sources demonstrating the obvious binary feature, like orbital modulation characteristics by binary motion, or showing light curves consistent with ellipsoidal or eclipsing models (see Table 1). Eventually, we produce a binary sample with 429 sources in total, as shown in Figure 1 (  these, 220 are eclipsing binaries, and 209 are ellipsoidal binaries.

HW Vir-type Binaries
HW Virginis (HW Vir) systems are PCEBs composed of a sdO/sdB primary and a low-mass main-sequence star secondary (M-dwarf), e.g. sdB+dM systems for the prototype. HW Vir-type binaries mostly show variations in their orbital periods (<0.1 days), also called eclipse time variations (ETVs, Sale et al. 2020). The light curve of HW Vir systems shows that two distinct eclipses belong to the typical Algol-type eclipsing, but its light curve also has an out-of-eclipse variation, which is caused by the irradiation effect. Figure 4 (a) show the typical light curve shape of HW Vir-type binary: ZTF J234504.03+505754.82 (116.686 min). Among our eclipsing binary candidates, there are 58 HW Vir systems, accounting for 13.52% of all binary samples, as shown in Figure 7. We present the result of Gaia EDR3 data information of these candidates in Table 4, please see Appendix B.

EA-type Binaries
EA-type eclipsing binaries are also called detached Algol-type binaries. Based on the definition of the Variable Stars Index Catalog, the unique shape of light curves are that between eclipses the light curve remains almost constant or varies insignificantly. The explanation for this characteristic is that binaries have spherical or slightly ellipsoidal components, and the reflection effects or physical variations are also important factors.
Detached white dwarf binaries, can have different effective temperatures and can show eclipse variability in the photometric data. If the binary has a high inclination angle, then the phase-folded light curve will contain two eclipses, a deeper primary one and a shallower secondary one. The primary eclipse is generated when the brighter target is obscured by its companion, and the secondary eclipse is the opposite process. In some cases, however, the secondary eclipse is too shallow to be detected, and there is only a primary eclipse in one orbit. Out of 220 eclipsing binary candidates in the bi- nary sample, 167 sources illustrate both primary and secondary eclipses, and only primary eclipses are identified for the remaining 59 sources. Figure 4 (b) show the typical light curve shape of EA-type eclipsing binary: ZTF J200119.16+482301.88 (212.716 min). Among our eclipsing binary candidates, there are 68 EA-type eclipsing binaries, accounting for 15.15% of all binary samples, as shown in Figure 7. We present the result of Gaia EDR3 data information of these candidates in Table 5 in Appendix B.

EB-type Binaries
EB-type (β Lyrae-type) eclipsing binary systems have ellipsoidal components and light curves for which it is impossible to specify the exact times of onset and end of eclipses because of a continuous change of the system's apparent combined brightness between eclipses. The secondary minimum is observed in all cases, its depth usually being considerably smaller than that of the primary minimum. Figure 4 (c) show the typical light curve shape of EB-type eclipsing binary: ZTF J204328.19+230649.25 (712.524 min). Among our eclipsing binary candidates, there are 56 EB-type eclipsing binaries, accounting for 13.05% of all binary samples, as shown in Figure 7. We present the result of Gaia EDR3 data information of these candidates in Table 6 in Appendix B.

EW-type Binaries
EW-type eclipsing binaries are also known as W Ursae Majoris type binaries, which are composed of ellipsoidal components almost in contact, and eclipses in binary systems with components filling their Roche-lobes. The depths of the primary and secondary minima of the light curves are almost equal or differ insignificantly. The amplitude variations of light are usually less than 0.8 mag and the orbital periods are usually shorter than one day. Figure 4 (d) show the typical light curve shape of EW-type eclipsing binary: ZTF J082516.60+432931.35  (309.922 min). Among our EW-type eclipsing binary candidates, there are 41 EW-type eclipsing binaries, accounting for 9.56% of all binary samples, as shown in Figure 7. We present the result of Gaia EDR3 data information of these candidates in Table 7, please see Appendix B.

ELL-type Binaries
ELL-type binaries (ellipsoidal variables) are noneclipsing reflection effect binaries consisting of a hot white dwarf and a cooler companion (typically an M dwarf) (El-Badry et al. 2021b). The variability amplitudes are usually less than 100 mmag. In the ellipsoidal modulation system, the shape of the light curve has the characteristics of quasi-sinusoidal variability and shows two different minima in one orbit. This quasi-sinusoidal variation light curve is produced by tidal deformation, in which case the two sides of the tidally disturbed star have different temperatures, and the hotter side is brighter than the colder side. There are two different minima in the light curve, which is mainly caused by the gravity darkening effect. Figure 4 (e) show the typical light curve shape of ELL-type eclipsing binary: ZTF J213329.86+512721.88 (264.770 min). We identify 209 candidates to be ellipsoidal variables, which account for 48.72% of the binary sample, as shown in Figure 7. We present the result of Gaia EDR3 data information of these candidates in Table 8 in Appendix B.

Comparison to the other catalogs
Our screening scheme provides a candidate catalog covering different types of close white dwarf binaries, which provides observational evidence for the study of the evolutionary channels of white dwarf binaries.
Several studies feature the search of CWDB systems. We compare our samples and cross-check the identified binaries with these works. Burdge et al. (2020a,b) used the Pan-STARRS1 catalog and ZTF photometric data to search for potential sources for milli-Hz band gravitational wave detectors. They successfully discovered sixteen ultra-compact binaries, including eight eclipsing systems, two AM CVn systems, and six ellipsoidal variations systems. Two of the sources, namely ZTF J213056.69+442046.58 (orbital period 39.340 min) and ZTF J205515.96+465106.45 (orbital period 56.348 min), are also identified in our search. Both sources are mass-transferring WD+sdB systems, and their light curves have similar shapes, which are typical ellipsoidal variables (see Kupfer et al. (2019Kupfer et al. ( , 2020aKupfer et al. ( ,b, 2022 for further details). We analyzed the reason why only two sources in our sample overlap with the 15 ultra-compact binaries reported by Burdge et al. (2020a). We checked the Gaia astrometric parameters of these 15 ultra-compact binaries and found that only three sources are measured with parallax over error > 5, which means that most sources are filtered out by our initial selection criteria for lack of reliable distance estimation, see Section 3.1 for further details.
El-Badry et al. (2021b) selected sources in the Gaia color-magnitude diagram and searched for largeamplitude ellipsoidal variability using ZTF photometric data. Their motivation is to find the progenitor of extremely low-mass white dwarfs and AM CVn systems. In El-Badry et al. (2021b), the authors reported 51 candidates, of which 21 sources obtained many-epoch spectra, and all 21 sources were confirmed to be completely or nearly Roche lobe filling binaries, 13 showing evidence of ongoing mass transfer. Our 22 ellipsoidal variable candidates reported by El-Badry et al. (2021b), and 11 sources have been confirmed by spectra. The initial query conditions we used for sample selection in Gaia EDR3 are different from El-Badry et al. (2021b). Keller et al. (2022) used the published catalog compiled by Gentile Fusillo et al. (2019) to identify eclipsing white dwarf binaries. They used the BLS algorithm to search for sources with periodic light curve variability in the ZTF data, and their search revealed 18 new binaries. The cross-check between our binary sample and these 18 binaries reveals five binaries to be overlapped. Keller et al. (2022) used samples from the Gaia white dwarf catalog, which contains 486641 sources. They cross-matched Gaia white dwarf catalog with ZTF DR3 data and finally obtained 276074 sources that have at least two ZTF epochs. We used the variable sample which was selected after the Gaia Variability Metric cut to cross-match the ZTF DR8 data. This leads to the discard of a large fraction of faint sources and could explain the difference in reported samples. Wang et al. (2021) systematically searched for periodic variables in the hot subdwarf catalog from Gaia DR2 using ZTF data. Their targets come from a catalog of 39,000 hot subdwarf candidates provided by Geier et al. (2019). In their search, they found 67 HW Vir binaries and 496 sources with reflection effects or pulsation, plus a few eclipsing and ellipsoidally modulating binaries. Our selection criteria in Gaia color-magnitude diagram include the hot subdwarf region in Section 3.2 of Geier et al. (2019). Therefore, our candidates will inevitably overlap with Wang et al. (2021). However, the catalog is not publicly available, therefore we can not check the extent of overlap.

Notes on Individual Objects
We selected four sources with special light curve shapes from the candidates, which are ZTF J2351+6305, ZTF J1611+6308, ZTF J1813+4251, and ZTF J0112+5827. The four newly discovered CWDB candidates have distinct light curve variability. Three sources are accompanied by an orbital period of less than 60 minutes and that of the other source is about 81 minutes. To understand the composition of these candidates and to explain the feature of the light curves, we will apply a large aperture telescope for time-domain photometry and spectral follow-up observations. ZTF J235115.32+630528.23 (ZTF J2351+6305) is an ultra-short period binary candidate. Its phase-folded light curve shows ellipsoidal variation characteristics (as shown in Figure 8), and the BLS period is 42.985 minutes. It has a color of G BP − G RP = 0.59 mag and a magnitude of G abs = 6.24 mag. It may be a masstransferring and recently-detached CV, which is a progenitor of ELM-WDs or AM CVn systems. El-Badry et al. (2021b) has systematically studied such systems. Among their 51 candidates of evolved CVs and bloated proto-ELM WDs, the shortest orbital period is 2 hours. This candidate has a shorter orbital period than reported by El-Badry et al. (2021b). The donor of evolved CVs has high temperatures (4700 < T eff < 7000K), which can be confirmed by spectral follow-up observation.
ZTF J161133.96+630831.67 (ZTF J1611+6308) has a period of 49.708 min. The ZTF phase-folded light curve shows a deeply-eclipsing white dwarf binary characteristic and the eclipse depth is greater than 2.5 mag, as shown in Figure 9. ZTF J1611+6308 has a color of G BP − G RP = 0.19 mag and magnitude of G abs = 11.26 mag. The Catalina Sky Survey 8 observed ZTF J1611+6308 between 2005 and 2013, and we obtained clean raw photometric data of CSS for ZTF J1611+6308. Figure 9 shows the phased ZTF light curves for the g-band, r-band, and i-band, and the phased CSS light curve. The light curve has a deep eclipse, but there is no secondary eclipse, and the eclipse duration is about 2.5 minutes as shown in the bottom panel of Figure 9. We used twice the period to fold the light curve, and the primary and secondary eclipses appeared at the same depth. The evolution of the light curve is predicted to be dominated by a white dwarf, while the companion star is a low luminosity target, such as a brown dwarf or an M dwarf . The classification of the system can be further confirmed by spectrum and high-speed photometric observation.  ZTF J181311.10+425150.51 (ZTF J1813+4251) is a cataclysmic variable candidate with a period of 51.161 min.
The light curve is a fully eclipsing binary system characteristic that is similar to the ZTF J1946+3203 (Burdge et al. 2020b), which exhibits strong ellipsoidal variations owing to the tidal deformation and eclipse effect as shown in Figure 10. ZTF J1946+3203 is a singlelined spectroscopic eclipsing binary, which is composed of a hot He WD or an sdB and a low luminosity He WD companion star. In the color-magnitude diagram, ZTF J1813+4251 is located in the classical CV region at G BP − G RP = 0.79 mag, and an absolute magnitude of G abs = 9.36 mag, which is significantly different from the position of ZTF J1946+3203. We obtained clean raw photometric data of CSS and ZTF for ZTF J1813+4251, as shown in the upper panel of Figure 10. Further observations of ZTF J1813+4251 are needed to measure the radial velocity and to strongly constrain the masses, radii, and temperatures using high-speed photometry. Once confirmed, this may be the shortest orbital period CV system ever observed. During the preparation of this manuscript, Burdge et al. (2022) reported the observation of this source. They found that ZTF J1813+4251 is a transitional CV, and this binary consists of a star with a temperature comparable to that of the Sun but a den- ZTF i mag Figure 11. The light curves of ZTF J011242.48+582757.60. The top panel shows the raw ZTF g-band (dark cyan) and r-band (dark red) light curves. The middle and bottom panels show the phase-folded light curves for ZTF J0112+5827 in g and r-bands, which show a clear difference between the two bands. The r-band exhibit two obvious spikes in one phase, between two spikes there is a transit phase.
sity 100 times greater owing to its helium-rich composition, accreting onto a white dwarf. These transitional CVs have been proposed as progenitors of helium CVs (Burdge et al. 2022). ZTF J011242.48+582757.60 (ZTF J0112+5827) is a CV candidate, which has a color of G BP − G RP = 0.9 mag and magnitude of G abs = 10.19 mag. The light curve of ZTF J0112+5827 shows typical large-amplitude ellipsoidal variation in the g-band, and the period com-puted by the BLS algorithm is 80.9 minutes, however, its r-band light curve shows an unusual two spikes in one period, as shown in Figure 11. We propose a possible hypothesis to explain the unusual light curve of ZTF J0112+5827: This is a polar (AM Her-type star) or intermediate polar 9 . The accreted mass moves along  (j), we show the one-dimensional histogram over Gaia BP-RP color, the Gaia G-band apparent magnitude, the distance, and the orbital period, respectively. Other panels (b, d, e, g, h, i) show the correlation distribution between the two parameters for different types of binaries.
the magnetic lines in the direction of the white dwarf's magnetic poles. The two spikes of the light curve in one period are generated by the accretion point, which is similar to a rare eclipsing polar BS Tri system (Kolbin et al. 2022). Future high-time resolution spectral observations will be needed to verify the formation of the unusual light curve of the binary system.

Parameters Distribution of CWDBs
In order to better understand the distribution characteristics of photometric parameters and source parameters of different types of candidates in our binary sample, we display their statistical histograms and correlations in Figure 12.  (2019) based on Gaia DR2 data to search ELM-WD candidates. The solid red line is the cooling model offset by −0.75 mag for 0.21M and 0.69M white dwarf. We use the publicly available WD models package provided by Cheng et al. (2020). The black scatter points show the Gaia 200 pc background sources. The five colors scatter points show the different types of light curve shapes in the final binary samples searched using ZTF data, and the black circles show the binaries in the Binary sample whose period is less than 100 min, which are potential GW source candidates.
appear to be bluer. Other variability types of binaries are mainly distributed at BP-RP > 0 mag, where ELLtype binaries are generally distributed between 0.2 mag < BP-RP < 1.0 mag. Figure 12 (c) shows the apparent magnitude distribution of Gaia/G-band of different types of candidates, which scatters between 16-18 mag.
In Figure 12 (f), we show the distance distribution of all binary candidates, HW Vir binary and EW-type binaries are mainly between 1.0 kpc to 2.5 kpc, EA-type binary at 0.5-2.0 kpc, the EB-type binary at 1.0-2.0kpc. Figure 12 (j) shows the orbital period distribution of these binary candidates. We find that for most types of binaries, the orbital periods are mostly less than 9 hours, while EB-type binary exhibits a peak at around 10 hours. We can explain the period distribution by the fact that the viewing angle will be decreasingly small for wider seperated eclipsing binaries. The ELL-type does not subject to this selection bias as they do not rely on eclipsing observation. The HW-type are also not affected as the component size are usually larger, corresponding to a larger viewing angle.
Other panels (b, d, e, g, h, i) in Figure 12 show two dimensional distribution for different types of binary systems. For example, from Figure 12 (d) and (e), we find an apparent cut in the upper right corner. This is most likely due to the choice of the Gaia variability metric.

The Gold Sample of CWDBs
In the H-R diagram, the sub-types of CWDB are mostly located in the region between MS and WDCS. We divided the volume according to the types of close binary stars in the H-R diagram and defined three gold samples, namely PCEBs gold sample, CVs gold sample, and DWDs gold sample. Inight et al. (2021) established a volume-limited sample for all sub-types of CWDB, which can be used to study the population of WD binaries. The reference samples provide four types of gold samples: WD + M (M-type main-sequence star), WD + AFGK (A, F, G, or K-type star), CV, and DWD. Our gold samples are not established by spectral type. We define the gold samples based on Gaia selection source conditions proposed by Geier et al. (2019) and Pelisoli & Vos (2019) and combined them with the white dwarf cooling model. We show the distribution characteristics of these binary candidates in the H-R diagram in Figure  13, and their sky distribution in Figure 14.
Geier et al. (2019) applied a color-cut and absolute magnitude selection to define a distribution range of hot subdwarf candidates in Gaia DR2, as shown in Figure 13 (the red dashed lines). We further define the sdB binaries (or PCEBs) in this region as the gold sample (see Table 2). We have a total of 85 hot subdwarf binary candidates as gold samples, of which 6 have orbital periods less than 100 min. Note-The above four Gold samples are empirically based on the distribution of candidates in the Gaia H-R diagram. There have crossover regions in the segmentation criteria of the four Gold samples, which result in repeated statistics for some sources, for further details , see Figure 13.
The CV gold sample established by Inight et al. (2021) shows that it is widely distributed below the MS star and the BP-RP colour index G BP − G RP > 0 in the Gaia H-R diagram (the detailed analysis is shown in Section 4.3 of Inight et al. (2021)). From the point of view of the time-domain photometry observation, it can be found that the light curve of CV can be divided into three main types: ELL-type binary, EA-type binary, and the outbursting class. Our short-period CWDB catalog only retains the EA-type or ELL-type binaries formed by the transit process, excluding the flare sources of the irregular class. Most CVs have orbital periods P orb 14 h. We have 224 candidates as CV gold samples in our catalog (see Table 2), of which 7 have periods less than 100 minutes.
Pelisoli & Vos (2019) proposed a method to select ELM candidates catalog from Gaia DR2 data, which is based on the distribution of the known samples in the Gaia H-R diagram and the prediction of the theoretical model. We define the CWDB candidates in Pelisoli's color-cutting criterion as the gold samples of ELM binaries (see Table 2). In our CWDB catalog, 45 candidates belong to the gold sample of ELM binaries, of which 9 have orbital periods less than 100 minutes. A binary system consisting of two white dwarfs has a color similar to that of a single white dwarf, but a DWD system is brighter than a single WD. One can expect that DWDs appear above single WDs (up to 0.75 mag) in the H-R diagram. In Figure 13, we use the cooling model contours (−0.75 mag) of 0.2 M and 0.69 M single WDs to define the gold sample of DWDs. We use the publicly available WD models package provided by Cheng et al. (2020). The WD models package is available at GitHub. 10 . According to the definition of the DWD gold sample, we have 11 candidates, including 6 ultra-short periods (P orb ≤ 100 min) DWDs.

GW Signals of Binary Systems
Galactic ultracompact binaries are the most numerous GW sources expected to be detected by future spacebased GW detectors such as TianQin and LISA Huang et al. 2020;Amaro-Seoane et al. 2022). The loudest signals can be detected individually, while a large number of the unresolved GW signals will superpose to form the DWDs foreground for the spacebased GW detectors (Huang et al. 2020;Liang et al. 2022;Lu et al. 2022). Once the short-period DWDs candidates in our final catalog are confirmed, it can help to expand the population of verification binaries. 10 https://github.com/SihaoCheng/WD models The GW radiation from DWDs can be considered as quasi-monochromatic signal sources, which can be described by seven parameters: frequency f GW = 2/P orb , the dimensionless amplitude A, ecliptic coordinates (λ, β), orbital inclination ι, polarization angle Ψ S , and initial orbital phase φ 0 (Huang et al. 2020). The primary and secondary masses (m 1 and m 2 ), luminosity distance (d), and orbital period (P orb ) of double white dwarfs can be derived from electromagnetic (EM) observations, and can be used to estimate the amplitude of the gravitational wave signal (Huang et al. 2020): where M = (m 1 m 2 ) 3/5 (m 1 + m 2 ) −1/5 , G and c are the chirp mass, the gravitational constant and the speed of light, respectively. The characteristic strain can be defined by the dimensionless GW amplitude A and the frequency of GW radiation f GW : where N cycle = f GW T obs is the number of binary orbital cycles observed during the mission, T obs is the integration time (or observation time) of the detectors.
To estimate the SNR (ρ) of GW signals from DWDs, we use the expression defined as Korol et al. (2017) and Huang et al. (2020), and the average amplitude defined by where F 2 + (λ, β, Ψ S ) and F 2 × (λ, β, Ψ S ) are the orbit averaged detector responses (Cornish & Larson 2003;Huang et al. 2020). S n (f s ) is the sensitivity curve of the detector in a Michelson channel. The sensitivity curve of TianQin can be expressed analytically as Eqs. (13) of Huang et al. (2020), and the sensitivity curve of the detector of LISA from Robson et al. (2019).
In order to estimate the SNR of binaries under the actual observation conditions of the detectors, we consider the effective observation time of the GW detectors. For TianQin, the 5-year mission adopts the observation mode of three-month observation plus three-month shutdown protection, which effectively corresponds to 2.5 years of observation time (Luo et al. 2016;Huang et al. 2020). For LISA, based on the performance of LISA Pathfinder, LISA Science Group expects that LISA will have a duty cycle of about 0.75, which means that in its  (15), the observation time T obs of TianQin is set as 2.5 years, and that of LISA is set as 3 years.

4-year mission, its effective observation time is 3 years (Amaro Seoane et al. 2022). In equation
In this work, we discovered 429 CWDB candidates. In order to calculate the SNR of these sources, we need to obtain the source parameters. The sky location (λ, β) of sources can be used the ecliptic longitude (ecl lon) and ecliptic latitude (ecl lat) from Gaia EDR3 data.
Using BLS and CE to analyze the ZTF light curve, we can calculate the trustworthy orbital period of binary candidates. We compared the period values obtained by the two algorithms after independently calculating three groups of ZTF photometry data, and finally estimated the average orbital period and retained it to three decimal places. The luminosity distance can be determined using trigonometric parallaxes from Gaia EDR3 (Lindegren et al. 2021;Kupfer et al. 2018). See Table  3 for further details of potential GW candidates. We assume that the primary mass m 1 obeys a uniform distribution U (0.5, 0.7) M , and the secondary mass m 2 obeys a uniform distribution U (0.2, 0.4) M according to Burdge et al. (2020b), and we fix ι = π/3, Ψ S = π/2 for all new candidates, since there are currently no measurements of these parameters.
We report the estimated TianQin/LISA SNR for the sources in the sample in Table 3. The first part of the Table 3 shows the first 24 candidates with periods less than 100 minutes in our binary sample, which are defined as potential GW candidates (for further details on their light curves, please see Appendix D). The later part of the Table 3 shows the recently discovered GW sources by other surveys that is not summarised in Huang et al. (2020). Figure 15 shows the characteristic strain of gravitational radiation of our newly discovered binary samples and other classic verification binaries and the sensitivity of TianQin and LISA. As illustrated in Figure  15, most sources of our sample fall below the sensitivity curves of TianQin and LISA, about 10 candidates fall above the LISA sensitivity curve, and about 16 candidates fall above the LISA sensitivity curve after 4 years of observations. In estimating the GW signals of candidates, we fixed some source parameters as constants, and the mass was uniformly distributed (we remark that for some binary systems this assumption might be unphysical), the current uncertainty in the SNR and GW amplitude of all sources originate from the uncertainty of distance measurement (mainly due to the standard error of parallax, parallax error). In our binary sample, the light curve shapes of potential GW candidates located above or near the sensitivity curve are mainly EA-type and ELL-type binaries. We adopt a low SNR threshold of 5 as the minimum standard for GW signals detected by TianQin and LISA. For TianQin, we found two new candidates VBs, namely ZTF J0526+5934 (SNR ∼ 12) and ZTF J2007+1742 (SNR ∼ 7), plus other newly discovered GW sources in the later part of Table 3, bringing the total number of VBs to 18 for TianQin. For LISA, we found 6 new VBs candidates, bringing the total number of VBs to 31 for LISA.

CONCLUSION
In this work, we have presented a catalog of shortperiod close white dwarf binary candidates based on the Gaia EDR3 catalog and the Zwicky Transient Facility photometry data. We defined a color-cutting criterion for selecting initial samples in the Gaia H-R diagram. In the Gaia EDR3 data, we searched 823231 high signal-tonoise ratio sources after using quality filtering parameters (Pelisoli & Vos 2019;Geier et al. 2019). We applied the Gaia variability metric (Guidry et al. 2021) to select 12480 most variable objects with high confidence from high-SNR samples.
We cross-matched the high-confidence variable source catalog with time-domain photometry data of the ZTF Public DR8 and analyzed the light curves of all variable sources. After analyzing the ZTF light curves, a total of 826 candidates were identified to have distinguishable periodic variability. Taking the shape of the light curve produced by the eclipse process of the binary system as the selection criterion, we found 429 binary candidates. The final catalog includes 58 HW Vir-type binaries, 65 EA-type binaries, 56 EB-type binaries, 41 EW-type binaries, and 209 ELL-type binaries.
We analyzed four short-period close white dwarf binary candidates with special light curves in the final catalog. ZTF J2351+6305 is an ellipsoidal variable binary with a period of less than 60 minutes (P orb = 42.985 min), which is similar to a mass-transferring and recently-detached CV (El-Badry et al. 2021b). ZTF J1611+6308 is a deeply-eclipsing white dwarf binary with an orbital period of 49.708 minutes. ZTF J1813+4251 is a short-period (P orb = 51.161 min) binary candidate near the classical-CV in the Gaia H-R diagram. ZTF J0112+5827 is a CV candidate similar to an eclipsing polar BS tri system (Kolbin et al. 2022) with a period of 80.912 minutes. We obtained the ZTF photometric data of these special candidates and analyzed their positions in the Gaia H-R diagram. The future follow-up observation of the spectra can be used to estimate the physical parameters such as masses, temperatures, and radial velocity semiamplitudes. The highspeed photometric observation can be used to solve the orbital parameters of the binary system, such as radius, inclination, semimajor axis, and orbital period.
We define the distribution of the Gold samples of close-WD binaries based on the sub-classes of stars in the Gaia H-R diagram. In the final catalog, a total of 429 close-WD binary candidates were divided into 85 PCEB Gold samples, 224 CV Gold samples, 45 ELM-WD Gold samples, and 11 DWD Gold samples.
We estimated the gravitational wave amplitudes and signal-to-noise ratios of all candidates in our binary sample. We found that we have two potential GW candidates with SNRs greater than 5 in the 2.5-year observation time of TianQin, which increases the total number of candidate VBs for TianQin to 18. For LISA, we have six new sources with SNRs of more than 5 in their 3-year effective observation time with a total of 4-year mission lifetime. The total number of LISA VBs has reached 31.
In future work, we aim to use multi-band spectral energy distribution to analyze the compositions and obtain the effective temperature and surface gravity of the binary systems to study their evolution process. We also plan to use LAMOST spectral and jointly fit the light curve to obtain the physical parameters and orbital parameters for our binary candidates to confirm their binary nature. Note-The position (λ, β) are the ecliptic coordinates, f is the GW frequency, A is the dimensionless amplitude, d is the luminosity distance.

ACKNOWLEDGMENTS
We thank Jian-dong Zhang, En-Kun Li, and Siyi Xu for their helpful comments and discussions. This This work has made use of data from the European Space Agency (ESA) mission Gaia (https://www. cosmos.esa.int/gaia), processed by the Gaia Data Pro-cessing and Analysis Consortium (DPAC, https://www. cosmos.esa.int/web/gaia/dpac/consortium). Funding for the DPAC has been provided by national institutions, in particular the institutions participating in the Gaia Multilateral Agreement. The ZTF data used in this study can be accessed from the ZTF Science Data System (ZSDS) (Masci et al. 2019)   Below we show the initial-cut selection criteria applied to Gaia EDR3 11 data through the following Astronomical Data Query Language (ADQL) query. Our ADQL query jobs are run in the Gaia@AIP 12 services or ARI's Gaia 13 services.

B. SHORT-PERIOD CWDBS CATALOGS
Below we show the Gaia photometric parameters and the orbital period parameters for all 429 objects in our binary sample. According to the types of the light curve, we can divide them into five tables: HW Vir-type binary candidates (see Table 4), EA-type binary candidates (see Table 5), EB-type binary candidates (see Table 6), EW-type binary candidates (see Table 7), and ELL-type binary candidates (see Table 8).  Note-The coordinates and basic photometric characteristics of the 58 HW Vir-type binary candidates discovered so far using ZTF data. Coordinates are taken from Gaia and are in J2000.0. The IAU name is provided in the catalog.    Table 5 continued Note-The coordinates and basic photometric characteristics of the 65 EA-type binary candidates discovered so far using ZTF data. Coordinates are taken from Gaia and are in J2000.0. The IAU name is provided in the catalog.    Note-The coordinates and basic photometric characteristics of the 56 EB-type binary candidates discovered so far using ZTF data. Coordinates are taken from Gaia and are in J2000.0. The IAU name is provided in the catalog.       Note-The coordinates and basic photometric characteristics of the 209 ELL-type binary binary candidates discovered so far using ZTF data. Coordinates are taken from Gaia and are in J2000.0. The IAU name is provided in the catalog.   Figure 16. Examples of the variability types of light curve shapes caused by the binary eclipse effect in our binary sample. All panels show the frequency spectra of the BLS and CE corresponding to the above (Figure 4) variability types of the HW Vir binary and EA-type binary.  Figure 18. Examples of the variability types of light curve shapes caused by the binary eclipse effect in our binary sample. All panels show the frequency spectra of the BLS and CE corresponding to the above (Figure 4) variability types of the ELL-type binary and Reflection binary. Figure 19. Phase-folded ZTF lightcurves of the potential GW candidates with an orbital period of less than 100 min, at GW amplitude and TianQin/LISA SNRs for these candidates described in Section 6.4.