Searching for Cataclysmic Variable Stars in Unidentified X-Ray Sources

First, we select candidates of the WD/low-mass main-sequence star binary systems from the GAIA DR2 source list (Gaia Collaboration et al. 2018). In the GAIA color–magnitude diagram, AR Scorpii, CTCV J2056-3014 and the typical CV systems are located between the main sequence and the cooling sequence of the WD (Figure 1). In this work, therefore, we limit the range of the search with a color of 0.5 < G_BP − G_RP < 1.5 (G_BP and G_RP are blue and red magnitude defined by the GAIA photometric system, respectively) and a magnitude of 9 < M_G < 12. We do not limit the range of the parallax, but restrict the magnitude of the error with a cut parallax_over_error > 5 in the query. To obtain a clean sample, we refer to Lindegren et al. (2018) and apply the conditions that

• 1.  
  phot_bp_mean_flux_over_error >8
• 2.  
  phot_rp_mean_flux_over_error >10
• 3.  
  astrometric_excess_noise <1
• 4.  
  phot_bp_rp_excess_factor <2.0+0.06* power(phot_bp_mean_mag-phot_rp_mean_mag,2)
• 5.  
  phot_bp_rp_excess_factor >1.0+0.015* power(phot_bp_mean_mag-phot_rp_mean_mag,2)
• 6.  
  visibility_periods_used >5.

We downloaded a catalog of the GAIA sources using astroquery (Ginsburg et al. 2019).

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We search for a possible X-ray counterpart of the selected GAIA sources in (i) the ROSAT all-sky survey bright source catalog (Voges et al. 1999), (ii) the second Swift-XRT point-source catalog (Evans et al. 2020), and (iii) XMM-Newton DR-10 source catalog (Webb et al. 2020). We select the GAIA sources that are located within 10'' from the center of the X-ray source, and then we remove the sources that have been already identified as a CV or other types of objects by checking the catalogs of CVs (Ritter & Kolb 2003; Coppejans et al. 2016; Jackim et al. 2020; Szkody et al. 2021; Sun et al. 2021) and the SIMBAD astronomical database. ⁸

After selecting the GAIA sources that are potentially associated with unidentified X-ray sources, we cross match them with sources observed by the Zwicky Transient Facility DR-8 objects (hereafter ZTF; Masci et al. 2019). We select a potential candidate of CVs based on (i) identification of a signature of an outburst and (ii) a periodic search with a Lomb–Scargle periodogram (hereafter LS; Lomb 1976). We download the light curves from the Infrared Science Archive, ⁹ and use the r-band data to search for a periodic signal. We apply the barycentric correction to the photon arrival time using astropy. ¹⁰ We find, on the other hand, that since the ZTF observation for our candidates (Section 3) provides only 500–1000 data points during 2018–2021 observations, the data quality may not be enough to study the detailed properties of the light curve (e.g., identifying eclipse feature, Section 3.1).

The Transiting Exoplanet Survey Satellite (hereafter TESS; Ricker et al. 2014) provides the light curves of the sources by monitoring for a month, and also photometric data of sources that are out of the field of view of ZTF. For our targets, TESS full-frame images (hereafter FFIs) provide the data taken every 10 minutes or 30 minutes, for which Nyquist frequencies are F_N ∼ 72 and ∼24 day⁻¹, respectively. We extract the light curve of the pixels around the source region from TESS-FFIs using TESS analysis tools, eleanor (Brasseur et al. 2019; Feinstein et al. 2019) and Lightkurve (Lightkurve Collaboration et al. 2018). We note that since several GAIA sources are usually located at one pixel, TESS data alone cannot tell us which source produces the periodic signal in a light curve extracted from TESS-FFIs. To complement ZTF and TESS observations, we carry out photometric observations for some of our targets with the Lulin One-meter Telescope (hereafter LOT) in Taiwan.

First, we produce an LS periodogram for each source by taking into account the Gaussian and uncorrelated errors that are usually provided in the archival data (or by usual data processing). We search for a possible periodic signal in 1 day⁻¹ < f < 50−150 day⁻¹, in which the maximum frequency depends on the time resolution of the observation. We estimate the false alarm probability (hereafter FAP) of the signal with the methods of Baluev (2008) and of the bootstrap (VanderPlas 2018). For an accreting system, it is proposed to investigate the effect of the time-correlated noise on the LS periodogram (VanderPlas 2018). Based on the correlated noise model of Delisle et al. (2020), we, therefore, produce an LS periodogram with different parameters of the noise model (Appendix A). We find that the LS periodogram of TESS data is insensitive to the time-correlated noise model. For ZTF data, although the noise model can change the shape of the LS periodogram, it is less effective in the periodic signals presented in this study (Table 1); but see Section 3.1 and Appendix A for ZTF18aampffv, in which one periodic signal may be related to time-correlated noise. In Section 3, therefore, we present an LS periodogram created with the time uncorrelated noise. The correlated noise model and some results of the LS periodogram are presented in Appendix A.

4XMM J172959.0+522948 (hereafter, 4XMMJ1729) is an unidentified X-ray source, and its position is consistent with GAIA DR2 1415247906500831744 (hereafter G141, Figure 2). Based on the parallax measured by GAIA, the distance to this source is ∼532 pc. There is a nearby source (GAIA DR2 1415247906499736448), whose position from our target is separated by ∼2''. Since the GAIA G-band mean magnitude of the nearby source, ∼20, is larger than G141 (∼18.3 mag), contamination will have less influence on the optical light curve observed for our target.

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Figure 2 (top right panel) shows the r-band light curve for G141 measured by ZTF (ZTF18aampffv). We find in the figure that the target frequently repeats small outbursts or transitions between high and low states on a timescale of months, which may indicate an accreting system. The amplitude is δ m > 2, which is relatively large compared to those seen in the ZTF light curves for other candidates presented in this study. We search for a potential periodic signal in the ZTF light curve with the LS periodogram (left panel of Figure 3), and find a significant signal at f_ZTF ∼ 46.9991(9) day⁻¹ (∼0.021 day), where the uncertainty denotes the Fourier resolution of the observation (namely, the inverse of the time span covered by the observation).

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The TESS observation covered the source region several times (Table 2). The middle panel of Figure 3 shows an LS periodogram of the light curve of the TESS data, sector 50 (Figure 2). The time resolution of sector 50 is about 10 minutes, and it has the capability of searching for a signal of f_ZTF ∼ 47 day⁻¹. We find, however, that the LS periodogram is dominated by the signal with ∼22 day⁻¹, which is indicated by 2F₀ in the figure, its harmonics and aliasing signals. We check the data of sector 47, which also does not show a significant periodic signal at f_ZTF. Since the data of sectors 17 and 24–26 were taken approximately every 30 minutes, they cannot be used to search for a periodic signal of f_ZTF. The signal of ∼22 day⁻¹ is confirmed in all data (although sector 40 also covers the source, the data is contaminated by unusually high background emission or noise).

To collect evidence of a binary nature, we carried out a photometric observation with LOT (2021 October 4 and 5, Table 2). The light curve clearly shows that G141 is an eclipsing binary system (Figure 4), and the observation covered three eclipse events that repeat at a frequency of F₀ = 11 ± 4 day⁻¹, suggesting that G141 is a binary system with an orbital period of P_orb ∼ 0.09 day. With the time resolution of ∼ 2 minutes for the LOT data, we estimate that each eclipse lasts ∼15 minutes, and the eclipse profile does not change during the observation. With the LOT data, we were unable to confirm a periodic signal corresponding to f_ZTF ∼ 47 day⁻¹.

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The top panel of Figure 5 shows the folded light curve of the TESS data with a frequency of F₀ ∼ 11 day⁻¹, and clearly shows an eclipsing feature at the orbital phase of ∼0.2 in the light curve. We also find the secondary eclipse around the orbital phase ∼0.7, which is shallower than that of the primary eclipse. This illustrates that the signal of the second harmonic (F₁ = 2F₀ ∼ 22.296 day⁻¹) is stronger than that of the fundamental signal in the LS periodogram.

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4XMMJ1729 was covered by the field of view, when XMM-Newton observations were carried out for two stars (HD 150798 and HD 159181) in 2002. We extract the data in the standard way using the most updated instrumental calibration, tasks emproc for MOS and epproc for PN of the XMM-Newton Science Analysis Software (XMMSAS, v19.0.1). Although the observation was carried out with a total exposure of about 20 ks, the quality of the data is insufficient to measure the spectral properties, since (i) the target is located at the edge of the field of view in all EPIC data and (ii) the observation is significantly affected by background flare-like events. We create an LS periodogram for the light curve (Figure 2) of PN data; we do not analyze MOS data due to an insufficient count rate. As can be seen in Figure 3, the window effect dominates the periodogram, and a significant periodic signal at f_ZTF ∼ 47 day⁻¹ is not identified, although an indication may exist. Figure 5 shows the X-ray light curve folded with the orbital period F₀ = 11.148 day⁻¹. Although a lower count rate is observed at ∼0 ∼ 0.3 orbital phase, a deeper observation is required to investigate the eclipse feature in X-ray bands.

We obtain an ∼5 ks Swift observation for 4XMMJ1729 (Table 3). We extract a cleaned event file with Xselect under HEASoft v6.29 and fit the spectrum with Xspec v12.12. Since we could not constrain the spectral model because of insufficient photon counts, we fit the spectrum with a single power-law function (Table 3). Using the distance measured by GAIA (Table 1), we estimate the luminosity in the 0.3–10 keV band as ${L}_{X}={4.5}_{-1.3}^{+1.9}\times {10}^{31}{(d/532\,\mathrm{pc})}^{2}\,\mathrm{erg}\,{{\rm{s}}}^{-1}$ (hydrogen column density of ${N}_{{\rm{H}}}={1.9}_{-1.9}^{+5.4}\times {10}^{21}\,{\mathrm{cm}}^{-2}$ and photon index of ${\rm{\Gamma }}={0.5}_{-0.5}^{+0.6}$).

Table 3. Summary of Swift X-Ray Observations

GAIA	Data	Date/Exposure	NH	Photon Index	Luminosity
DR2		(MJD)/(ks)	1022(cm2)		1031(erg s−1)
G141	TOO	59558/4.7	${1.9}_{-1.9}^{+5.4}$	${0.5}_{-0.5}^{+0.6}$	${4.5}_{-1.3}^{+1.9}$
G453	TOO	59529–59534/2.0	${1.4}_{-1.4}^{+2.5}$	${1.6}_{-0.6}^{+0.7}$	${5.5}_{-1.5}^{+2.0}$
G207	Archive	57046–57047/3.2	0.3 (fixed) a	${0.9}_{-1.0}^{+1.0}$	${0.5}_{-0.3}^{+0.8}$
G205	Archive	57796–57806/9.1	${4.0}_{-2.0}^{+5.2}$	${2.4}_{-0.9}^{+1.1}$	${1.4}_{-0.6}^{+3.4}$
G216	Archive	57210–57309/10	4.0 (fixed) a	${1.8}_{-0.4}^{+0.4}$	${1.2}_{-0.3}^{+0.4}$
G432	Archive	56011–56074/1.1	13 (fixed) a	${0.3}_{-1.4}^{+1.1}$	${14}_{-8.0}^{+24}$
G454	TOO	59591/2.5	0.75 (fixed) a	$-{0.2}_{-1.6}^{+1.0}$	${5.5}_{-3.2}^{+14}$

Note.

^a N_H is estimated from the sky position using the hydrogen column density calculation tool "N_H" under HEASoft, and is fixed during the fitting process.

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We have not found a significant periodic signal with f_ZTF ∼ 47 day⁻¹ in TESS, LOT, or XMM-Newton data. In Appendix A, therefore, we carry out a further investigation of the LS periodogram of the ZTF data and find the possibility that the signal is caused by the time-correlated noise.

GAIA DR2 4534129393091539712 (hereafter, G453) is selected as a possible counterpart of the ROSAT source, 1RXS J185013.9+242222. We obtain an ∼2 ks Swift observation for 1RXS J185013.9+242222 in 2021 November, and we estimate the luminosity of ${L}_{X}\sim {5.5}_{-1.5}^{+2.0}\,\times {10}^{31}{(d/322\,\mathrm{pc})}^{2}\,\mathrm{erg}\,{{\rm{s}}}^{-1}$ in the 0.3–10 keV band by fitting the spectrum with a power-law model (${N}_{{\rm{H}}}={1.4}_{-1.4}^{+2.5}\,\times {10}^{21}\,{\mathrm{cm}}^{-2}$ and ${\rm{\Gamma }}={1.6}_{-0.6}^{+0.7}$, Table 3).

As can be seen in the right panel of Figure 6, the ZTF light curve (ZTF18abikbmj) shows several outbursts with a recurrent timescale of a year. In fact, 1RXS J185013.9+242222 has already been recognized as a dwarf nova by previous observation of the outburst. ¹¹ Since no detailed investigation for this source has been carried out, we searched for possible orbital modulation in the photometric data.

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First, we searched for periodic signals in a quiescent state in the ZTF data, but we did not find any obvious periodic signals (except for the window effects) in the periodogram (Figure 7). TESS observed this source in 2020 June during a stage of the small outburst (Figure 6), and the data was taken approximately every 30 minutes. We extract the light curve with 4 pixels around the target (left panel of Figure 6). In the LS periodogram, we find two strong signals at 8.88(4) day⁻¹ (∼0.11 day) and 39.11(4) day⁻¹ (∼0.026 day), either of which is likely the aliasing of the sampling frequency. Since the extracted light curves with 4 pixels contain several sources (left panel of Figure 7), the TESS observation alone cannot support the detected signal originating from G453.

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We confirm the binary nature of G453 with LOT. We carried out the observations with r-band (2021 July 3) and g-band (2021 July 4) filters, for which one observation covered the source with an exposure of ∼2–2.5 hr (Table 2). As indicated in Figure 6, the LOT observation was also carried out during a small outburst, which could be a re-brightening after the large outburst occurred around MJD 59300. In the LS periodogram (Figure 7) and the observed light curve (Figure 8), we confirm evidence of periodic modulation at F₀ = 37.3 ± 1 day⁻¹, which is close to the TESS result.

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Although we cannot firmly conclude the origin of the periodic signal with the current photometric data, the signal F₀ is likely related to the orbital period. From the shape of the light curve taken by LOT, we can expect that the orbital period is double the photometric period, namely, P_orb ∼ 2 ×1/F₀ ∼0.05 day; e.g., the light curve with the r-band filter may be more consistent with modulation caused by the elliptical shape of the companion star that fills the Roche lobe, and an indication of double-peak structure with the different peak magnitudes in the g bands (Figure 9).

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Another possible origin of the signal F₀ is the superhump, which is a periodic variation observed emission from an eccentric disk after the outburst of CVs (Warner 1995). The period of the superhump is several percent longer (or sometimes shorter) than the orbital period. Although superhump is usually observed after a super-outburst of CVs (Osaki 2005; Kato et al. 2014; Hameury 2020), it has also been observed at normal outburst or re-brightening after a super-outburst (Zhao et al. 2006; Imada et al. 2012). The ZTF light curve of G453 suggests that there were several re-brightenings after the large outburst occurred around MJD 59300, and the LOT observation covered one of the re-brightening stages. Moreover, the previous observations for other dwarf novae confirm a beat signal between the orbital modulation and superhump (Patterson et al. 2000; Kato et al. 2010). In the periodogram of the TESS data for G453 (middle panel of Figure 7), we notice a periodic signal at ∼1.34 day⁻¹ (∼0.75 day), which is confirmed only at the source region, with a significance greater than the 99% confidence level. This signal can be explained by the beat signal, if the difference between the orbital period and the superhump period is ∼ 3%–4% (i.e., 1.34 ∼ × 39 day⁻¹). The TESS light curve folded with F₀ is presented in Figure B2.

We find these three candidates that do not show frequent outbursts, but the observed brightness drops suddenly and stays at a low luminosity state with a timescale of months. Figure 10 shows the light curves of GAIA DR2 2072080137010352768 (hereafter G207), 2056003803844470528 (G205), and 2162478993740496256 (G216) measured by ZTF, which are named ZTF 18abrxtii, 18aayefwp, and 17aaapwae, respectively. For G207 (top panel of Figure 10), for example, a sudden drop in brightness occurred around MJD 59050 and the source stayed in a low luminous state for ∼50 days. These three GAIA sources are selected as the optical counterparts of Swift sources. Using the distance measured by GAIA, the X-ray luminosity in the 0.3–10 keV energy band is estimated to be ${L}_{X}\,\sim {0.5}_{-0.3}^{+0.8}\times {10}^{31}{(d/313\,\mathrm{pc})}^{2}\mathrm{erg}{\,{\rm{s}}}^{-1}$ for G207, $\sim {1.4}_{-0.6}^{+3.4}\,\times {10}^{31}(d/595\mathrm{pc}{)}^{2}\mathrm{erg}{\,{\rm{s}}}^{-1}$ for G205, and $\sim {1.2}_{-0.3}^{+0.4}\,\times {10}^{31}(d/429\,\mathrm{pc}{)}^{2}\mathrm{erg}{\,{\rm{s}}}^{-1}$ for G216, respectively (Table 3).

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For these three targets, we can detect significant periodic signals in the ZTF and TESS data (Tables 1 and 2). The photometric periodic signals in the ZTF light curves are f_ZTF = 28.575(1) day⁻¹ (∼0.035 day) for G207, 24.595(1)day⁻¹ (∼ 0.041 day) for G205, and 22.175(1) day⁻¹ (∼0.045 day) for G216, respectively. We also obtain consistent periodic signals in the TESS light curves.

We carried out photometric observations for the three sources with LOT. For G207 (Figure 11), although the data fluctuation is significant, we find an eclipsing feature in the light curve. Figure 11 shows that the source became fainter around MJD 0.034 (+59475.6) and MJD 0.094 (+59475.6), and the time interval between the two epochs is consistent with an integer multiple of the photometric period of 1/f_ZTF ∼0.035 day. The orbital period, however, will be double the photometric period, since the observation in the left panel of Figure 11 should cover another eclipse if the orbital period is ∼0.035 day. ZTF/TESS light curves may indicate a secondary eclipse with a shallower depth (Figure B2).

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For G216 (Figure 12), the light curve indicates periodic modulation, and the time interval between two strong peaks is consistent with the photometric period of 1/f_ZTF ∼ 0.045 day, and the LOT light curve is consistent with theTESS/ZTF light curves (Figure B2). Hence, G216 is a binary system with an orbital period of 0.045 day. For G205, we could only carry out an ∼40 minute observation with LOT. The data, therefore, is not enough to constrain the orbital period of the source.

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GAIA DR2 4321588332240659584 (hereafter G432) is selected as a candidate for a counterpart of the Swift point source, 2SXPS J192530.4+155424, and the X-ray luminosity is measured as ${L}_{X}\sim {1.4}_{-0.8}^{+2.4}\times {10}^{32}{(d/582\,\mathrm{pc})}^{2}\mathrm{erg}\,{\mathrm{cm}}^{-2}{{\rm{s}}}^{-1}$ in the 0.3–10 keV band (Table 3). As compared with the ZTF light curves of other candidates in this study, the optical emission from this source (ZTF18aazmehw) is more steady with an amplitude of variation of less than ∼1 mag (right panel of Figure 13). In the LS periodogram of the ZTF light curve, we confirm a periodic signal at a frequency of f_ZTF =18.5521(9) day⁻¹ (∼0.054 day).

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TESS observed the region around G432 in 2019 July (sector 14) and 2021 June (sector 40), for which data were taken approximately every 30 minutes and 10 minutes, respectively. Figure 14 shows an LS periodogram for the data of sectors 14 and 40. The LS periodogram (left panel) clearly indicates a periodic signal at F₀ = 18.553(1) day⁻¹, which is consistent with the finding from ZTF. The folded light curve with f_ZTF (right panel of Figure 14) may be described by the main peak plus a small secondary, rather than a pure sinusoidal curve, although the significance of the secondary peak is small. In the LS periodogram, we can see the signals at the second harmonics (F₁ = 2F₀) and the effect of aliasing with the data sampling frequency of F_s ∼ 145 day⁻¹, namely, F_b = F_s −F₀ ∼126 day⁻¹ and F_b1 = F_s − F₁ ∼ 108 day⁻¹

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In addition to the periodic signals related to F₀ and 2F₀, the periodogram shows other signals at F_u = 32.17(4) day⁻¹ (∼0.031 day) and its harmonics F_u /2. This signal clearly appears in the TESS data of sector 40. To check which pixel of the TESS-FFIs causes the signal, we extract the light curve of each pixel around the sources for the observation of sector 40. We find that a significant signal with F_u can be detected at one pixel where the power of the signal with F₀ becomes the maximum. The periodic signal with F₀ can be seen in other pixels but the power of the signal is lower than that at the pixel where the F_u signal is found. Hence, the signal, F_u , may be related to our target, although other optical sources located in the same pixel (right panel of Figure 13) cannot be ruled out as the origin of the signal. We note that the LS periodogram of TESS data is insensitive to the time-correlated noise model discussed in Appendix A.

If the signal F_u is related to G432, then the origin may be related to the harmonics of F₀. Although the frequency F_u = 32.17(4) day⁻¹ cannot be described by a simple relation with F₀, the frequency F_s − F_u ∼ 6F₀, where F_s ∼ 145 day⁻¹ is the data readout frequency, indicates that the signal F_u is related to the 6th harmonic of the fundamental frequency. It is not trivial, however, why the modulation of the 6th harmonic is more evident than those of the 2nd–5th harmonics. If the frequency F_u is independent of F₀, the signal would be related to the spin of the WD. We cannot find a significant periodic signal at the frequency F_u in the data of sector 14. This may be due to a large uncertainty of each data point of the observation or the true signal is F_s − F_u ∼ 111 day⁻¹ (∼13 minutes) for which the data of sector 14 cannot identify. If F_u and F₀ are related to the WD spin and orbital period, respectively, G432 could be a candidate for IP due to the fact that the X-ray emission dominates the UV emission, which is a typical property of the emission of IPs (Section 4.1). A data set taken with a higher cadence is required to identify the origin of F_u .

We select GAIA DR2 4542123181914763648 (hereafter G452) as a candidate for the optical counterpart of 1RXS J172728.8+132601, for which a 2.5 ks Swift observation measures the X-ray luminosity of ${L}_{X}={5.5}_{-3.2}^{+14}\,\times {10}^{31}{(d/502\mathrm{pc})}^{2}\mathrm{erg}{\,{\rm{s}}}^{-1}$ with N_H = 7.5 × 10²¹ cm² (Table 3). As the ZTF light curve (ZTF18abttrrr) shows (left panel of Figure 15), the source repeats outbursts on a timescale of years; the outburst that occurred in 2021 was alerted as being a GAIA transient source, AT 2021aath (GAIA21eni, Hodgkin et al. 2021), which was identified as a polar type CV. Nevertheless, since there is no detailed binary information for the target in the literature, we searched for a possible periodic signal in the ZTF light curve. After removing the data of the outburst from the light curve, the LS periodogram shows a significant periodic signal at f_ZTF = 8.6499(8) day⁻¹ (∼0.115 day).

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TESS observation for the region around G452 was carried out in 2020 May and June (sectors 25 and 26) during the outburst around MJD 59000 (Figure 15). We extracted the TESS-FFI light curve and removed a long-term trend caused by the outburst from the light curve. We found a periodic signal with F₀ = 8.65(2) day⁻¹, which is consistent with the result of the ZTF observation. The right panel of Figure 15 shows the folded light curves of the ZTF and TESS data, which can be described by sinusoidal modulation. As Figure 15 shows, we also observe a shift in the TESS light curve from the ZTF light curve, which may be due to the effect of an outburst during the TESS observation. We do not find another significant periodic signal in the TESS data, which may be consistent with a spin–orbit phase synchronization of the polar.

We searched for a possible periodic signal of 29 GAIA DR2 sources, which are potential counterparts of an unidentified X-ray source. Table 4 presents four sources, for which TESS-FFI data provides a periodic signal; however, not enough data points or no data are available for ZTF observations. As we have mentioned, there are two observational modes for TESS-FFIs, in which the data readout time intervals are ∼48 and ∼144 day⁻¹, respectively. As shown in Table 4, GAIA DR2 5360633963010856448 and 5964753754945126528 were observed by two observational modes, and the periodic signal F₀ reported in Table 4 is identified in both data sets. For GAIA DR2 2031371479242995584 and 1981213682883140864, on the other hand, data from only one observational mode is available, and we cannot discriminate between the true frequency and the aliasing. We note that due to one pixel of the TESS observations containing several GAIA sources, we cannot rule out that the periodic signal is related to another source.

Among the four sources in Table 4, GAIA DR2 5964753754945126528 (hereafter G596), which shows a periodic signal F₀ ∼ 8.34 day⁻¹ (∼0.120 day) in the TESS data, is a promising candidate for a CV, and its location is consistent with the X-ray source, AX J1654.3-4337, which was discovered by the ASCA Galactic plane survey (Sugizaki et al. 2001). Swift and NuSTAR observations for this source were carried out in 2020 July–August with a total exposure of 6.7 and 26 ks, respectively. We extract the events and spectra of the source region with the command nupipeline under HEASoft v6.29 for the NuSTAR data and the package Xselect for the Swift data.

We group the spectral bins to contain a minimum of 20 counts in each bin, and fit the spectrum using Xspec v12.12 (Figure 16). We find that the spectrum in the 0.2–70 keV band is well fitted by the optically thin thermal plasma emission (tbabs*mekal model in Xspec) with a temperature of ${k}_{B}T={8.9}_{-1.5}^{+2.0}$ keV and absorption column density of ${N}_{H}\,={2.2}_{-0.07}^{+0.08}\times {10}^{21}\,{\mathrm{cm}}^{-2}$ (χ² = 164 for 188 dof). The luminosity in the 0.2–70 keV band is estimated to be ${L}_{X}\,={6.0}_{-0.5}^{+0.6}\times {10}^{31}{(d/462\,\mathrm{pc})}^{2}\,\mathrm{erg}\,{{\rm{s}}}^{-1}$. The X-ray emission with a plasma temperature of ∼10 keV suggests the emission from an accretion column on the WD surface, indicating a magnetic CV system. Moreover, the observed X-ray luminosity of < 10³² erg s⁻¹ indicates that the source is not a typical IP, for which the X-ray luminosity is typically >10³² erg s⁻¹.

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Figure 17 presents the folded light curve of F₀ =8.34 day⁻¹ extracted from the TESS-FFI data. We can see that the shape of the light curve shows a double-peak structure. Combined with the X-ray spectral properties, this optical emission likely originated from two magnetic poles heated by the accretion column, and the modulation is likely due to the WD spin. Since the TESS data did not indicate other periodic signals longer than this WD's spin signal within 10 days, G596/AX J1654.3-4337 may be a polar, although we cannot rule out the possibility of an IP. We do not find any periodic signal in the NuSTAR data, in which a window effect of the observation dominates the LS periodogram.

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Figures 18 and 19 compare the properties of our CV candidates with those of known CVs. Figure 18 shows the distributions of the orbital periods and GAIA G-band magnitudes (upper panel) or the X-ray luminosity in the 0.3–10 keV band (lower panel) of our candidates. In the figure, we can see the so-called period gap at P_orb ∼ 2–3 hr, in which less CVs have been detected (Spruit & Ritter 1983; Katysheva & Pavlenko 2003; Ritter 2010; Garraffo et al. 2018). The figure shows that the nonmagnetic systems (black-filled circle) have been detected with a period in the range of 0.01–1 day. Known IPs (red-filled circle) and polars (blue-filled circle), on the other hand, concentrate on orbital periods longer and shorter than the period gap, respectively. We find in the figure that the six CV candidates discussed in the current study are located below the period of the gap. This will be a selection effect because (i) there is a correlation between the orbital period and GAIA G-band magnitudes, as can be seen in the top panel of Figure 18, and (ii) we selected the candidates with the condition 9 < M_G < 12 of the G-band magnitudes (Figure 1). AX J1654.3-4337 (pink diamond), which is a polar candidate as discussed in Section 3.6, locates in or close to the period gap. As the bottom panel of Figure 18 shows, the X-ray luminosity of our candidate, L_X ∼ 10³¹⁻³² erg s⁻¹ is relatively larger among the CVs located below the period gap. This is because we searched candidates in the X-ray source catalogs of previous surveys, which may have missed many faint X-ray sources.

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We can see in the figure that four candidates (G453, G205, G216, and G432) have an orbital period close to or shorter than ∼0.05 day, which is known as the minimum orbital period in the standard binary evolution of CVs (Ritter 2010). We note however that the orbital periods of G453, G205, and G432 may be double the values in the figure (Sections 3.3 and 3.4), and hence they may have an orbital period longer than the minimum period.

Figure 19 shows the distribution of the flux ratio of the UV band and X-ray band measured by Swift. As can be seen in the figure, the ratio is greater than unity for most of the nonmagnetic systems, which is understood by the emission from the boundary layer of the accretion disk. For magnetic CVs, on the other hand, the X-ray dominates the UV emission, which is a characteristic of emission from the accretion column (Mukai 2017). Several sources, on the other hand, have a ratio greater than 10, and the emission is probably dominated by blackbody emission from the pole with a temperature of < 50 eV.

We find that our candidates have relatively hard spectrum (F_UV/F_X ≤ 1) and the two hardest sources (G432 and G596) are classified as candidates for magnetic CVs. For G432, we identify two possible periodic signals (F₀ = 18.5 day⁻¹ and F_u = 32.2 or 111 day⁻¹) in the TESS data. With the UV/X flux ratio much smaller than unity, G432 may be a candidate for X-ray faint IP. For G596, the properties of the optical light curve and the X-ray spectrum are consistent with a polar, as described in Section 3.6.

In the unidentified X-ray source, we searched for new binary candidates that show emission properties similar to those of AR Scorpii, for which (i) no mass is probably transferred from the companion star to the WD, (ii) UV emission dominates the X-ray emission, and (iii) a magnetic WD heats up the companion star. With current photometric studies, however, we can conclude that these candidates do not belong to the AR Scorpii-type binary system. For example, three candidates (G141, G453, and G454) clearly show dwarf-nova-type outbursts, suggesting the existence of a mass transfer from the companion to the WD, and thus an accreting system. With a large optical variation (δ m ∼ 1.5), AR Scorpii contains a WD heating up the companion star. The optical curves of our candidates show a smaller magnitude variation (δ m < 1, e.g., Figure 12 for G216 and Figure 13 for G432), and do not show any clear evidence of heating. G596/AX J1654.3-4337 is a promising candidate for the magnetic system, but it is a polar, while AR Scorpii is an IP in the sense that the spinning period is different from the orbital period.

Finally, we note that out of our eight candidates, six systems have not experienced a large outburst in the last 4 years and have been missed in previous surveys. Our study, therefore, will suggest that a large population of WD binary systems with an inactive mass transfer could be discovered in future surveys.

In summary, we searched for new CV systems associated with the unidentified X-ray sources listed in the ROSAT, Swift, and XMM-Newton source catalogs. We selected the GAIA sources with a g-band magnitude of 9 < M_G < 12 and a color 0.5 < G_BP − G_RP < 1.5, and identified 29 sources that are potential counterparts of the unidentified X-ray sources. We carried out a photometric study with ZTF, TESS, and LOT observations, and constrained the orbital periods for the seven sources (Sections 3.1–3.5). Among the seven candidates, G141 and G207 are eclipsing binary systems, and G141 shows a secondary eclipse with a shallower depth. We identified three candidates (G141, G453, and G454), in which a mass transfer from the companion to WD is active, and they exhibit repeated outbursts (Figures 2, 6, and 15). For the other three candidates (G207, G205, and G216), on the other hand, it is observed that the source brightness suddenly drops and stays at a low luminous state (Figure 10), suggesting the mass transfer may be inactive. Based on the detection of two periodic signals in the light curve and UV/X-ray emission properties, we can classify G141 and G432 as IP candidates, although a spectroscopic study is required for confirmation. In addition to seven candidates, we confirmed that the unidentified ASKA source, AX J1654.3-4337 (G569), is a candidate for being a polar. With the current photometric studies, we could not find any candidate for the AR Scorpii-type WD binary, although we selected the GAIA sources that had a similar magnitude to AR Scorpii. AR Scorpii still remains a unique WD binary system, and a more sophisticated search (e.g., an optical survey for an unidentified X-ray source with high cadence) will be required to find a new AR Scorpii-type binary system.