Discovery of Two Polars from a Crossmatch of ZTF and the SRG/eFEDS X-ray Catalog

Magnetic CVs are luminous Galactic X-ray sources but have been difficult to find in purely optical surveys due to their lack of outburst behavior. The eROSITA telescope aboard the Spektr-RG (SRG) mission is conducting an all-sky X-ray survey and recently released the public eROSITA Final Equatorial Depth Survey (eFEDS) catalog. We crossmatched the eFEDS catalog with photometry from the Zwicky Transient Facility (ZTF) and discovered two new magnetic cataclysmic variables (CVs). We obtained high-cadence optical photometry and phase-resolved spectroscopy for each magnetic CV candidate and found them both to be polars. Among the newly discovered magnetic CVs is ZTFJ0850+0443, an eclipsing polar with orbital period $P_\textrm{orb} = 1.72$ hr, white dwarf mass $M_\textrm{WD} = 0.81 \pm 0.08 M_\odot$ and accretion rate $\dot{M} \sim 10^{-11} M_\odot$/yr. We suggest that ZTFJ0850+0443 is a low magnetic field strength polar, with $B_\textrm{WD} \lesssim 10$ MG. We also discovered a non-eclipsing polar, ZTFJ0926+0105, with orbital period $P_\textrm{orb} = 1.48$ hr, magnetic field strength $B_\textrm{WD} \gtrsim 26$ MG, and accretion rate $\dot{M} \sim 10^{-12} M_\odot$/yr.


INTRODUCTION
Magnetic cataclysmic variables (CVs) are compact object binaries in which a highly magnetized white dwarf (WD) accretes from a Roche-lobe filling donor, typically a late-type main-sequence star. Magnetic CVs are interesting for two reasons: 1) they may be the dominant contributors to the Galactic ridge hard X-ray emission (Hailey et al. 2016) and 2) the origin of the strong (B ∼ 1-100 MG) magnetic fields in accreting WDs is uncertain (Wickramasinghe & Ferrario 2000;Schreiber et al. 2021). More broadly, they are rich laboratories for studying accretion under the influence of a strong magnetic field.
CVs typically consist of a WD accreting from a donor via an accretion disk (e.g. Warner 1995;Hellier 2001). In non-magnetic CVs, the secondary fills its Roche lobe and develops a teardrop-like shape with the tip positioned at the Lagrangian L1 point. Matter leaves the secondary star through this point and forms an accretion stream after exiting the donor star. This stream extends out until a point known as the "circularization radius". The circularization radius is the point where the matter in the accretion stream intersects itself as it orbits the primary. The material then forms an accretion disk around the white dwarf and makes its way to the surface through viscous dissipation of energy.
In magnetic CVs known as intermediate polars (IPs; B WD ≈ 1 − 10 MG), the magnetic field pressure is comparable to the ram pressure of the accreted material. As a result, the disk is truncated at the Alfvén radius (also arXiv:2206.04714v1 [astro-ph.HE] 9 Jun 2022 known as the magnetospheric radius). In IPs, the Alfvén radius is smaller than the circularization radius so that a partial disk forms. The accreted material initially flows through the disk but is channeled along field lines onto the white dwarf surface inside the Alfvén radius.
In magnetic CVs known as polars (B WD 10 MG), the magnetic field is strong enough that the Alfvén radius is larger than the circularization radius (e.g . Hellier 2001;Mukai 2017). Matter can build up at the Alfvén radius, in a region called the stagnation region (also referred to as the threading region), before being channeled by WD magnetic field lines onto the surface (e.g . Cropper 1990;Mukai 2017).
Extensive literature and evolutionary models exist for non-magnetic CVs (e.g. Knigge et al. 2011). In the canonical picture of non-magnetic CVs, these systems are formed through common envelope evolution. Angular momentum loss (AML) of the binary system then drives its evolution as the white dwarf accretes matter from its secondary companion. At orbital periods above ≈ 3 hrs, magnetic braking dominates over gravitational radiation as the dominant contributor to AML. Magnetic braking is thought to shut off at the point when the donor star becomes fully convective, leading to the observed period gap (P orb ≈ 2-3 hrs). Below this gap, gravitational radiation dominates the loss of angular momentum. Few CVs have been found at orbital periods below ≈ 80 mins (known as the "period bounce"), thought to correspond to the point where the donor star becomes degenerate and expands as it loses mass.
There is typically no mention of WD magnetic fields in this evolutionary model of CVs. The discovery of many magnetic CVs within the period gap, and the large number of polars, at periods below 2 hours, has led to new ideas on how magnetic CVs form and evolve (e.g. Belloni et al. 2020;Schreiber et al. 2021).
Magnetic CVs have previously been difficult to find via optical surveys alone. Both magnetic and non-magnetic CVs have historically been discovered through their novae or dwarf novae outburst behavior. The former occurs when a thermonuclear ignition of hydrogen occurs on or near the surface of the accreting white dwarf. The latter occurs when a thermal instability in the accretion disk leads to a temporary increase in accretion rate (Hellier 2001). However, searching via optical outbursts alone is inefficient for finding magnetic CVs. The magnetic field disrupts the disk or eliminates it entirely, which prevents a thermal instability (Hameury & Lasota 2017). Novae can still occur in magnetic CVs, but are rare. As a result, optical-only surveys lead to a ∼ 1/100 rate of discovery for magnetic CVs (e.g. Szkody et al. 2021). However, a recent volume-limited (d < 150 pc) study of CVs discovered via various techniques found 36% of CVs to be magnetic .
Both magnetic and non-magnetic CVs are strong Xray emitters. The source of X-rays in magnetic CVs is typically thermal bremsstrahlung from the shock of material accreting onto the WD surface (e.g . Cropper 1990;Wickramasinghe & Ferrario 2000;Mukai 2017). The resulting thermal bremsstrahlung temperature is calculated via the following equation: which for a white dwarf of mass 0.8M is 36 keV -well in the regime of hard X-rays. The source of X-rays in non-magnetic CVs can be difficult to disentangle: the hot WD photosphere of a recent nova, the optically thick boundary layer, or accretion disk wind shock of non-magnetic CVs can also lead to X-ray emission (Mukai 2017).
X-ray surveys help overcome the observational bias of optical-only surveys in finding CVs by uncovering both the magnetic and non-magnetic populations (e.g. Motch et al. 1996;Bernardini et al. 2017;Halpern et al. 2018). Many magnetic CVs were discovered through the transformative all-sky Roentgensatellit X-ray survey (ROSAT; Truemper 1982;Voges et al. 1999;Boller et al. 2016). The ongoing eROSITA telescope aboard the Spektr-RG mission (SRG; Sunyaev et al. 2021;Predehl et al. 2021) is projected to go ∼30 times deeper than ROSAT with improved localization (∼5 arcsec) of X-ray sources, guaranteeing discoveries of new magnetic CVs, among other objects, all over the sky.
In this work, we crossmatched the eROSITA Final Equatorial Depth Survey (eFEDS; Salvato et al. 2021) catalog with forced photometry of ZTF Data Release 5 (DR5) 1 . We discovered two new polars: ZTFJ0850+0443 and ZTFJ0926+0105. In Section 2, we present an overview of the SRG/eFEDS catalog and ZTF archival photometry. In Section 3, we outline our methodology for finding notable objects within the crossmatched dataset. In Section 4, we present followup high-cadence photometry and spectroscopy and analyze all data for ZTFJ0850+0443. We present data and analysis for ZTFJ0926+0105 in Section 5. Finally, in Section 6, we place this work in the context of previous CV studies and discuss the utility of X-ray/optical searches for finding otherwise elusive CVs.

eFEDS Catalog
We began with the catalog of eFEDS Galactic sources. Salvato et al. (2021) searched for optical counterparts to the eFEDS X-ray sources by crossmatching to the DECam Legacy Survey (DECaLS) LS8 catalog, part of the DESI Legacy Imaging Survey (Dey et al. 2019). The median separation between the X-ray source and optical counterpart, divided by the mean X-ray positional error (i.e. the eROSITA/SRG uncertainty in the localization of the X-ray source), is reported in Salvato et al. (2021) to be 1.22. For the crossmatch to ZTF data, we use the coordinates of the LS8 optical counterpart. Given the superior depth of DECaLS (23.4 mag), we crossmatch the sources to the LS8 catalog instead of the ZTF catalog (21 mag).
Galactic sources in eFEDS are mainly identified through two methods as described in Salvato et al. (2021): 1) SDSS redshifts being z < 0.002 and/or 2) Gaia parallaxes with good significance: π/σ π > 3. The Renormalised Unit Weight Error (RUWE) < 1.4 can also be used. The actual method described in Salvato et al. (2021) is complex, and uses a combination of NWAY, a tool based on Bayesian statistics, and AS-TROMATCH, a tool based on the Maximum Likelihood Ratio.
In the eFEDS Main Catalog, 24774/27369 (90.5%) of X-ray sources are reported to have a reliable optical counterpart. Of those sources, 2976 are classified with the label LIKELY GALACTIC or SECURE GALACTIC. It is this sample that we further investigate with ZTF.

ZTF Data
The Zwicky Transient Facility (ZTF) is a photometric survey that uses a wide 47 deg 2 field-of-view camera mounted on the Samuel Oschin 48-inch telescope at Palomar Observatory with g, r, and i filters (Bellm et al. 2019a;Graham et al. 2019;Dekany et al. 2020;Masci et al. 2019). In its first year of operations, ZTF carried out a public nightly Galactic Plane Survey in g-band and r-band (Bellm et al. 2019b;Kupfer et al. 2021). This survey was in addition to the Northern Sky Survey which operated on a 3 day cadence (Bellm et al. 2019a). Since entering Phase II, the public Northern Sky Survey is now at a 2-day cadence. The pixel size of the ZTF camera is 1" and the median delivered image quality is 2.0" at FWHM.
We use forced photometry from ZTF Data Release 5 (DR5). Lightcurves have a photometric precision of 0.01 mag at 13-14 mag down to a precision of 0.1-0.2 mag for the faintest objects at 20-21 mag. While both raw photometry and forced photometry are PSF-fit photometry, the forced photometry calculates photometry of the object on difference images by forcing the location of the PSF to remain fixed according to the ZTF absolute astrometric reference. This allows one to obtain flux estimates below the detection threshold and therefore probe deeper than the standard photometry. For bulk download, we use a database of forced photometry files (Mróz, Burdge, et al. in prep).

Objects of Interest
It is useful to plot the X-ray to optical flux ratio for the entire eFEDS catalog. A similar exercise was carried out by various studies (e.g. Agüeros et al. 2009;Greiner & Richter 2015) for the ROSAT catalog and proved to be an effective way for disentangling CVs from other Galactic X-ray sources such as M dwarfs and chromospherically active binaries such as BY Dra and RS CVn systems. Figure 1 shows the eFEDS X-ray flux versus DE-CaLS LS8 optical flux plot along with ZTFJ0850+0443 and ZTFJ0926+0105. Both systems stand out as being amongst the systems with the highest F X /F opt ratio. Figure 2 shows the advantage of a color cut in picking out CVs from active M dwarfs. By supplementing the X-ray to optical flux ratio with optical color information, M dwarfs cluster towards the upper right, while CVs cluster towards the upper left. The population in the lower center of the figure is generally comprised of the chromsopherically and coronally active BY Dra/RS CVn systems. 2

SAMPLE SELECTION
The goal of our study is to classify Galactic eFEDS/ZTF sources, with an emphasis on those with a high X-ray to optical flux ratio and a strong periodic signal in ZTF.
We adopt the value of optical flux, F opt , for our entire study, as the standard conversion of the DECaLS LS8 g magnitude from the AB magnitude system. We assume a flat SED and a reference wavelength of 5000 Angstrom. We define the following samples: 1. High X-ray to optical flux ratio. We obtain spectra for all objects with F X /F opt > 0.5.
2. Moderate X-ray to optical flux ratio and strong periodicity. We obtain spectra for all objects with 0.5 > F X /F opt > 0.025 percent that feature strong periodicity and pass a color cut. Our color cut eliminates the reddest objects which are likely to be active M dwarfs. We also report best-fit periods for the objects that do not pass the color cut.
2 The term BY Dra refers to chromospherically active binary stars on the main sequence, and should be distinguished from RS CVn binary stars which are evolved and therefore above the main sequence. However, the term RS CVn has been used in the literature to refer to both; see Eker (1992) for a summary of the nomenclature. 3. Low X-ray to optical flux ratio and strong periodicity. We compile a list periods for all objects that have F X /F opt < 0.025.
We define the significance of periodicity as the maximum Lomb-Scargle power subtracted by the median power, all divided by the median absolute deviation. We define "strong periodicity" as lightcurves where the significance is in the 86 th quantile. By this metric, approximately 10 percent of all objects in the eFEDS/ZTF footprint show strong periodicity. We define our color cut in the LS8 color bands and exclude objects with g − r > 1.4 as likely M dwarfs.
ZTFJ0850+0443 and ZTFJ0926+0105 stood out immediately from the first cut, with values of F X /F opt > 0.5. The Lomb-Scargle periodogram search of their lightcurves using gatspy also showed strong periodicity (VanderPlas 2016(VanderPlas , 2018. Both criteria prompted follow-up spectroscopy.
The full analysis of our findings from the above cuts will be reported in an upcoming study.

ZTFJ0850+0443
4.1. Data ZTFJ0850+0443 was found in both ZTF r and g band data to be a periodic source with high amplitude. The best-fit Lomb-Scargle period is 103.44 minutes (1.72 hr) in both bands. The folded lightcurve is shown in Figure  3.
We followed up ZTFJ0850+0443 with high-cadence photometry in r and g bands using the Caltech HIghspeed Multi-color camERA (CHIMERA; Harding et al. 2016) and u band using the Wafer-Scale Imager for Prime (WASP; Bilgi 2019). The WASP u-band data were only acquired over a single period, while the CHIMERA r-and g-band data were both acquired simultaneously over two orbital periods. The high-cadence data revealed the eclipse in ZTFJ0850+0443 as well as cyclotron beaming at two points during a single orbit as seen in Figure 4.
An identification spectrum of ZTFJ0850+0443 was acquired using the Dual Imaging Spectrograph on the 3.5m Apache Point telescope on 03 January 2022. That spectrum revealed strong He II 4686 compared to the Hβ Balmer line. This is strong evidence of a magnetic CV, although non-magnetic CVs can sometimes show this line behavior (Silber 1992;Oliveira et al. 2020). Additional spectra at three orbital phases were obtained on the Keck telescope using the Low-Resolution Imaging Spectrometer (LRIS; Oke et al. 1995) on 01 February 2022. A full orbit of ZTFJ0850+0443 was acquired on 07 March 2022 using LRIS. A summary of all data acquired for ZTF0850+0443 is presented in Table 1.

General Lightcurve Features
In Figure 4 we present the high-cadence photometry and spectroscopy of ZTF0850+0443 during notable orbital phases. The most prominent features of the highcadence lightcurve are 1) the eclipse and 2) the two broad bumps per orbital phase in the u, g, and r bands, one of which occurs around the eclipse and the other at phase φ ≈ 0.6.
As described in the Introduction, the magnetic field in polars channels accreted material directly from the threading region. The material is directed by the magnetic field out of the orbital plane through the "accretion curtain" and onto the WD surface via one or two magnetic poles; see Figure 11 of Littlefield et al. (2018). Furthermore, the strong magnetic fields in polars lead to beamed cyclotron emission as non-relativistic spiral around magnetic field lines (synchrotron emission is the relativistic analog). Cyclotron emission can manifest itself in optical lightcurves as broad 1-2 mag bumps (e.g . Cropper 1990;Hellier 2001). The data on ZTFJ0850+0443 points to it being an eclipsing polar. A visual aid to describe the system configuration is presented in Figure 5.
In most polars (≈ 95 percent), the WD spin is locked with the orbit. We searched to see if ZTFJ0850+0443 is an "asynchronous" polar (i.e. the WD spin period is not locked to the orbital period). After Gaussian smoothing of the high-cadence lightcurves, no separate WD spin period is seen, suggesting that ZTFJ0850+0443 is a (typical) tidally locked polar. For the most part, orbital periods of polars range between 1.5 and 4 hours, placing the 1.72 hr period of ZTFJ0850+0443 well within the range of most polars (e.g. Halpern et al. 2018;Pala et al. 2020;Abril et al. 2020).
In the following subsections, we walk through the orbit of ZTFJ0850+0443 and incorporate photometric and spectroscopic data to support our analysis.

Pre-Eclipse
CVs, both magnetic and non-magnetic, typically feature strong emission lines due to accretion. ZTFJ0850+0443 is one of six polars (Littlefield et al. 2018) where line inversions are seen in the pre-eclipse phase. Figures 4 and 6 show that at phase φ = 0.93, the H Balmer and He I lines are absorbed redward of line center. The He II 4686 line is only slightly absorbed. This also the case in the non-eclipsing polar MASTER OT J132104.04+560957.8 (Littlefield et al. 2018) as well as the eclipsing polar FL Cet (SDSS J015543.40+002807.2) (Schmidt et al. 2005). Littlefield et al. (2018) attribute this phenomenon to absorption within the accretion curtain (i.e. within the magnetosphere), not the threading region as was suspected before MASTER OT J132104.04+560957.8 was discovered. The main reason for this is that threading region is confined to the orbital plane, while the accretion curtain comes out of the plane along with the white dwarf magnetic field lines. Since ZTFJ0850+0443 is an eclipsing system, the presence of line inversions supports the idea that this phenomenon is more common at higher inclinations (i → 90 • ).
Another notable feature seen at pre-eclipse is that the u-band flux drops while the r-and g-band flux increase ( Figure 4). This is due to the u passband being centered blueward of the Balmer jump. In the pre-eclipse occultation of accretion spot emission by the accretion curtain, cooler material passes in front of the dominant source of radiation. Thus, the Balmer jump transitions from emission to absorption.

Eclipse: A Likely One-Pole System
The lightcurve near eclipse can often be used to identify whether a polar has one or two accreting poles. We present the high-cadence lightcurve zoomed in around the eclipse in Figure 7. The data favors ZTFJ0850+0443 being a one-pole system, but we cannot discard the possibility of a second low-luminosity accreting pole.
In the single-pole case, the pole is eclipsed at φ = 0.966 as indicated by the sharp decline in the g-and r-band data. The sampling of the u-band data is insufficient to resolve this. The first shaded region (φ = 0.966 − 0.988) in Figure 7 corresponds to the gradual ingress of the ballistic stream. The pole exits eclipse at φ = 1.033 as indicated by the sharp rise in the g-and r-band data. The second shaded window (φ = 1.033 − 1.05) shows the gradual egress of the accretion curtain. We denote φ = 1.05 as the end of the accretion stream eclipse as that is the point where the total flux returns to its pre-eclipse value in r-and gband data. The u-band flux is larger post-eclipse due to the absence of pre-eclipse self-absorption by the accretion curtain. Previous observations and numerical simulations have been able to reproduce remarkably similar lightcurves (Breytenbach et al. 2019;Zhilkin et al. 2019).
In the case of two-pole accretion, two "steps" in the ingress and egress of the magnetic poles are often seen. However, our photometric sampling cadence (10 seconds) is too low to detect that. For example, a ∼ 0.1-second cadence was needed to see this in FL Cet (O'Donoghue et al. 2006) and a 1-second cadence for eRASStJ192932.9-560346 (Schwope et al. 2021). It could also be that the second pole is so faint at optical wavelengths that it would not appear in optical photometry at all. After all, no spectroscopic evidence aside from weak evidence in the Doppler tomograms (see Section 4.6) of a second pole is seen. Additional data (e.g. optical polarimetry, X-ray lightcurves, or higher cadence optical photometry) are needed to definitively classify this as a one-or two-pole system, although the current data more strongly support the one-pole model.
On the whole, the eclipse is shallowest in the u band and deepest in the r band. This has been attributed to the accreted material being channeled in the lowest energy configuration, which concentrates cooler material towards the center of the accretion stream. Hotter material is therefore more sparse and can still be seen while the cooler, concentrated material is eclipsed (see Figure 5 of Harrop-Allin et al. 1999) for the modeling of HU Aquarii). We note that in the case of HU Aquarii, modeling of this feature alone in optical lightcurves was insufficient to determine whether the system is accreting at one or two poles.

Donor Star Revealed
At phase φ ≈ 0.3, the H Balmer, He I, and He II emission lines begin to split before being distinguishably separated at φ ≈ 0.4 (Figure 4). The broad, blueshifted component traces the accretion onto the white dwarf. The narrow component, which at this phase is slightly redshifted, traces the irradiated face of the donor star. At phase φ ≈ 0.5, the narrow component in the H Balmer, He I, and He II emission lines is at line center and stronger than the blueshifted accretion spot emission lines (Figure 8).
At this point in the orbital phase, we are seeing directly into the irradiated face of the donor, confirming the origin of the narrow emission component. This phenomenon has been known since early studies of polars (e.g. Cropper 1990) and used to constrain binary parameters of the eclipsing polar BS Tri (Kolbin et al. 2022) when the traditionally used Na I 8183, 8195 doublet could not be spotted. The Na I 8183, 8195 doublet is not seen in ZTFJ0850+0443 due to the strong accretion continuum that dominates out to red optical wavelengths. At the same orbital phases that H Balmer, He I, and He II emission lines are split into broad and narrow components (center around φ = 0.5), Ca II 8498 and 8542 from the irradiated donor are seen in emission above the accretion continuum (Figure 8).
Na I, Ca II, H Balmer, He I, and He II lines from the donor star do not all arise from the same location. The H Balmer, He I, and He II lines likely arise from the tip of the Roche lobe and possibly into the accretion stream (e.g. Schwope et al. 2011). The Ca II lines roughly trace the center-of-light of the irradiated donor, somewhere between the center-of-mass and the tip of the Roche Lobe. The Na I lines tend to arise from deeper within the donor and more reliably trace the center-ofmass (e.g. Schwope et al. 2011). Therefore, in order to correctly use the Ca II lines to trace the radial velocity of the donor, we must apply a correction which we explain in detail in Section 4.7.

Doppler Tomography
Spectral lines in CVs vary as a function of orbital phase, often containing information about all system parameters which can be blended together. In CVs with an accretion disk, the disk, the accretion hot spot (where the accretion stream hits the disk), and irradiated face of the donor star can all contribute to the observed emission. Doppler tomography converts phase-resolved spectroscopy into a plot of observed radial velocity and line strength as a function of orbital phase. Doppler tomograms disentangle the contribution of the various CV components (e.g. accretion disk, accretion hot spot, donor star) to a given spectral line; see Marsh (2005) for a review of the method of Doppler tomography. We present Doppler tomogams and radial velocity curves of He II 4686 and Hβ in Figure 9.
We use the doptomog 3 code developed by Kotze et al. (2015). We show the "inverse" Doppler tomograms, which better illustrate the high-velocity components in magnetic CVs. Higher velocities are located closer in to the center of the diagram, while lower velocities are farther from center (traditional Doppler tomography flips this around).  The feature with an amplitude of 1000 km/s is the dominant component. The free-fall velocity at the surface of a white dwarf, assuming typical parameters (M WD = 0.6M , R WD = R Earth ) is ≈ 4000 km/s. By observing emission at 1000 km/s, we can infer that this emission is due to material within the accretion curtain as it approaches the WD surface. We do not know enough about the magnetic field configuration near the surface to know exactly where in the accretion curtain we are probing. A weak, diffuse component can also be seen towards the bottom right, which could be indicative of a second magnetic pole. This is the only possible Figure 7. High-cadence lightcurve of ZTFJ0850+0443 around the eclipse. In the one-pole accretion model, the accretion spot on the white dwarf is eclipsed by the donor star at φ = 0.966. The accretion stream is gradually eclipsed until totally disappearing at φ = 0.988. The accretion spot exits eclipse at φ = 1.033 and the accretion stream gradually re-emerges until being fully exposed at φ = 1.05. evidence for a second pole that we have in our current data.
The irradiated face of the secondary is clearly shown roughly between 300-400 km/s in both Doppler tomograms as well near φ = 0.5 in the radial velocity curves. The gap near φ = 0.3 is due to a small gap in our data acquisition. The radial velocity curves clearly show the pre-eclipse line inversion, where He II 4686 is hardly split, but Hβ is split into two components due to the intervening redshifted absorption.

Binary Parameters
In order to solve for the full mass and radius parameters of the system, we assume a circular orbit. Our constraining equations are the following: 1) the Roche lobe equation from Eggleton (1983), 2) the binary star mass function, 3) the relationship between the mass ratio and the correction applied to the RVs derived from Ca II lines, 4) an R(M ) relation derived from modern CV evolutionary tracks, and 5) the eclipse of the system.
The Roche lobe equation (Eggleton 1983) is: where a is the orbital separation of the system: a 3 = G(M 1 +M 2 )P 2 orb /4π 2 and q is the ratio of the donor star mass to the white dwarf mass: q = M 2 /M 1 . We adopt this mass ratio convention consistently throughout this study.
The binary star mass function is: where M 1 is the mass of the accreting white dwarf and M 2 is the mass of the donor. K 2 is the radial velocity of the donor, which we must infer from the observed radial velocity of the Ca II lines, K 2 . As discussed earlier, these lines originate from the center-of-light of the irradiated (day) side of the donor star, which is not a good approximation for the center-of-mass of the donor star. We obtain K 2 = 360 ± 15 km/s from a least-squares fit to the observed line profiles (Figure 11). The statistical error of 15 km/s arises from instrumental precision and low signal-to-noise in measuring the line position at certain phases. We assume the entire donor star is co-rotating around the center of mass of the system at the same orbital period. To determine the relationship between K 2 and K 2 , we assume the center-of-light of the donor star is located εR L from the center-of-mass of the donor star. The factor ε can be thought as being the coordinate on the axis between the donor center-of-mass and the tip of the Roche lobe. Therefore, the semi-major axis of the center-of-light is a 2 = a 2 − εR L and the observed radial velocity is K 2 = 2π(a 2 − εR L )/P orb . Since K 2 = 2πa 2 /P orb , we can solve for the correction factor: K 2 /K 2 = 1 − εR L /a 2 . Since a = a 2 (1 + q), we write: and therefore the RV correction is a function of the mass ratio q = M 1 /M 2 and ε, the coordinate on the axis between the donor center-of-mass and the tip of the Roche lobe. A value of ε = 0 corresponds to the donor center-of-light being located at the donor center- of-mass and a value of ε = 1 corresponds to the donor center-of-light being located at the tip of the Roche lobe.
In order to determine reasonable values of ε, we constructed a simple binary star model using PHOEBE (Prsa & Zwitter 2005;Prsa et al. 2016) consisting of a 15,000 K primary star (average of WDs in CVs at this orbital period, e.g. Pala et al. 2022) irradiating a 3000 -4000 K donor star at a typical CV orbital separation. This model with a single source of radiation serves as the lower limit of possible radiation for the donor. In polars, radiation from the accretion stream, accretion curtain, and accretion pole can also irradiate the donor. In our simple model, the center-of-light (location of mean intensity) is at ε = 0.45, which serves as a lower limit.
We then turn to empirical findings to place an upper limit on ε. We consider the analysis of He II, Ca II, and Na I lines of the donor star in HU Aquarii (Schwope et al. 2011). Doppler tomography of those lines showed that the Ca II lines precisely probe the center-of-light, located approximately at values of ε = 0.5 − 0.85. Therefore, we adopt the range ε = 0.45 − 0.85, combining the simple analytical model and empirical results. We overplot this range on our PHOEBE model in Figure  10. A full treatment of radiation from the white dwarf, accretion spot, accretion curtain, accretion stream, and efficiency of irradiation of the donor are beyond the scope of this study.
In order to obtain an R(M ) relation, we use the CV donor star evolutionary tracks from the Knigge et al. (2011) set of models. They account for the inflated radius of the donor star due to the rotation it undergoes while in the binary system.
The final component is the eclipsing nature of the system. Given the typical system parameters of polars, we know the inclination of the system must be i 78 • for the system to be eclipsing. Chanan et al. (1976) showed Figure 11. Radial velocity (RV) measurements of the irradiated face of the donor star as a function of orbital phases, K 2 . RV measurements are obtained at orbital phases where 1) Ca II is strong enough to be seen above the continuum or 2) the narrow component of H Balmer lines is not blended with the broad accretion component. Table 2.
System Parameters for ZTFJ0850+0443 System Parameter Estimated Value 1.724 ∆t ecl (sec) 415 ± 5 M (M /yr) ∼ 10 −11 ε = (a2 − a 2 )/RL 0.65 ± 0.20 that if the eclipse timing is well-constrained, then the mass ratio q is a function of the inclination i in Roche lobe filling systems. We find the eclipse duration to be 415 ± 5 sec, measured at the sharp dropoff and sharp rise as described in Section 4.4. The Chanan et al. (1976) geometry, however, assumes a point source located at the center of the white dwarf and not on the surface, as is that case in polars. This however, leads to a negligible systematic that is contained within the statistic error bars on the measurement of all system parameters.
We then solve for all equations simultaneously via a vectorized least-squares approach implemented with scipy to find the final best-fit values. This is equivalent to minimizing the error in Equation 3, Equation 4.7, R L = R(M 2 ), and the eclipse timing equation from Chanan et al. (1976) simultaneously. We present the final values for the binary system in Table 2.
The largest uncertainty in our white dwarf mass estimate stems from the uncertainty in radial velocity (which scales to the third power in Kepler's binary system equation). While this is limited by our estimates of the location of the donor center-of-light (parameterized by ε), we find that we can still reasonably constrain the mass of the white dwarf.

Magnetic Field Strength
There are three common ways to determine the magnetic field strength of a polar as outlined by Cropper (1990): 1) Cyclotron humps in the optical spectrum, 2) Zeeman splitting of emission lines in the optical spectrum, 3) Optical polarization measurements. In the case of ZTF0850+0443, we do not detect the first two and have not acquired optical polarization data to test the third criterion.
Why don't we see any cyclotron harmonics? The wavelengths of cyclotron harmonics (e.g. Ferrario et al. 2015;Mason et al. 2019) are given by the following formula: where λ n is in Angstrom and θ is the viewing angle of the cyclotron beaming. In cases where cyclotron humps are seen in the optical, it is usually the n = 3 or n = 4 harmonics that are seen (Cropper 1990;Wickramasinghe & Ferrario 2000). Since lower-order harmonics are less prominent, the absence of seeing cyclotron harmonics at optical wavelengths often implies low magnetic field strength. Ferrario et al. (1993) and (Wickramasinghe & Ferrario 2000) showed that in polars with field strengths of B 20 MG, cyclotron harmonics (n = 2, 3, 4) can only be seen in near-infrared spectra and not at all in optical spectra.
When infrared spectra are not available, infrared photometry has been shown to be insightful for magnetic field characterization of low-field polars (Harrison & Campbell 2015;Wickramasinghe & Ferrario 2000). Mason et al. (2019) discovered CRTS J035010.7 +323230, a polar that did not show any of the typical magnetic field diagnostics outlined by Cropper (1990). CRTS J035010.7 +323230 stood out by showing a strong infrared excess with WISE W3 and W4 magnitudes higher than W2 and W1 points. The authors argued this was indicative of a low-field ( 10 MG) polar. We see exactly the same behavior in ZTF0850+0443, with a clear infrared excess in the WISE W3 and W4 bands. We reproduce a spectral energy distribution in Figure 12 compiled from all data in CDS which includes photometry from SDSS, PANSTARRS, Gaia, WISE, GALEX, and UKIDSS, among others surveys. We propose that ZTF0850+0443 must be viewed at a high enough angle (sin θ ∼ 1) from the magnetic pole so that cyclotron beaming can be observed in its optical lightcurve. What we see in the optical is likely a blend of many low-order cyclotron harmonics in the lightcurve bumps at phase φ = 0.6 and φ = 1. The fundamental (n = 1) harmonic is then in the mid-infared (∼ 10 − 20µm) with strong n = 2, 3, 4 harmonics in the nearinfrared. We suggest that ZTF0850+0443 is a low-field (B 10 MG) polar, potentially adding to a small pool of polars with such low magnetic field strengths.

Accretion Rate
We can estimate the accretion rate of ZTF0850+0443 assuming conversion from potential energy to X-ray luminosity. Assuming a ∼10 percent efficiency of this energy conversion (e.g. Rosswog & Brüggen 2007): Assuming the standard white dwarf mass-radius relation (e.g. Hellier 2001), for an X-ray flux of 2 × 10 31 erg/s and a mass of M WD ≈ 0.81M , we obtainṀ ∼ 10 −11 M /yr.

ZTFJ0926+0105
5.1. Data ZTFJ0926+0105 was found in ZTF data to be a periodic source with high amplitude in both r and g bands Figure 13. Folded lightcurve of ZTF0926+0105 (P orb = 1.48 hr) over ZTF forced photometry.
( Figure 13). We followed up ZTFJ0926+0105 with highcadence photometry using CHIMERA. Data were acquired over 3.5 hours, but all orbital phases could not be completely covered due to transient clouds. The best-fit period of the r-band data is 88.53 min, while the best-fit period of the g-band data is 89.10 min. The average of the two is 88.81 min (1.48 hr).
An identification spectrum was acquired using the Double Spectrograph (DBSP; Oke & Gunn 1982) on the Hale telescope on 08 January 2022. This spectrum showed strong H Balmer, He I, and He II lines in emission. He II 4686 fulfilled the criteria of Silber (1992) for being a magnetic CV candidate, prompting us to acquire follow-up spectroscopy. Phase-resolved spectra were taken on the Keck telescope using the Echelle Spectrograph and Imager (ESI; Sheinis et al. 2002) on 01 February 2022. Eight 10-minute spectra were taken consecutively with ∼11 minutes between the starting point of each spectrum. Table 3 summarizes all data taken and the contribution of each dataset.

Lightcurve and Spectral Analysis with Doppler Tomography
We see cyclotron beaming once per orbital phase in the g and r high-cadence lightcurves of ZTFJ0926+0105 ( Figure 14). The large factor by which the flux increases, combined with the orbital period of 1.48 hr, is characteristic of few objects other than polars. No eclipse or any other notable features are seen. We also see a prominent cyclotron bump in the phase-resolved spectra of ZTFJ0926+0105 ( Figure 14). The phase where the bump is most prominent coincides with the maximum in the photometry, confirming cyclotron beaming as the source of the high-amplitude variation. We only see one cyclotron harmonic around 8800 Angstrom, and discuss the implications for determining the magnetic field strength in Section 5.3.
Aside from the prominent cyclotron bump, the phaseresolved spectroscopy of ZTFJ0926+0105 is much like Figure 14. Cyclotron beaming is seen once per orbital phase in the high-cadence CHIMERA photometry (top) as well as phase-resolved spectroscopy around 8800Å (bottom).
that of ZTFJ0850+0443, revealing emission from both the accretion curtain and the face of the irradiated donor star.
We produce Doppler tomograms for ZTFJ0926+0105 in order to disentangle the two components. Both the He II 4686 and Hβ tomograms reveal large, approximately 750 km/s amplitude radial velocities. We attribute such large radial velocities to the accretion curtain, as was the case with 1000 km/s radial velocities in ZTFJ0850+0443. Since ZTFJ0926+0105 is viewed at a more face-on inclination, the observed radial velocity should be lower.
Both Doppler tomograms of ZTFJ0926+0105 ( Figure  15) reveal the irradiated face of the donor star at approxmiately 300 km/s, particularly the Hβ tomogram. This coincides with the presence of Ca II lines (see Figure 14) which also stem from the irradiated face of the donor star like in ZTFJ0850+0443. While we could estimate radial velocity measurements of the donor star in ZTFJ0926+0105, the lack of an eclipse prevents us from obtaining a precise estimate of the white dwarf mass.

Magnetic Field Strength and Accretion Rate
We can at best put a lower limit on the magnetic field strength of ZTF0926+0105. We are primarily limited by the resolution and flux calibration of our data at blue optical wavelengths. In the phase-resolved spectroscopy, we see a single prominent cyclotron feature at phase φ = 0.68. This harmonic is well-fit by a Gaussian centered at 8800 Angstrom. There are no other cyclotron harmonics seen at phase φ = 0.68, where the maximum cyclotron continuum should occur. After performing a power-law continuum fit, subtracting the single cyclotron feature and possible template spectra of the donor, no other cyclotron harmonics bumps emerge. The bump-like features at 6400 Angstrom and 5100 Angstrom are in the spectra at all phases, suggesting they are not cyclotron features which should be beamed only once per orbital phase.
Using Equation 4.9, we must assume both a viewing angle and cyclotron harmonic number to find the magnetic field strength. Such a strong cyclotron feature like the one we see at 8800 Angstrom is unlikely due to a harmonic higher than n = 4 (e.g. Cropper 1990). The viewing angle must also be large (θ 60 • ) for the beaming to be as high amplitude as we see in the spectroscopy and photometry. We therefore place a lower limit of B 26 MG on the magnetic field strength of ZTF0926+0105. Near-infrared spectroscopy could be used to search for the lower harmonics and place stronger constraints on the field strength.
We can estimate the accretion rate of ZTF0926+0105 assuming conversion from potential energy to X-ray luminosity as we did with ZTF0850+0443. Adopting a ∼10 percent efficiency of this energy conversion and the standard white dwarf mass-radius relation (e.g. Hellier 2001), for an X-ray flux of 4 × 10 30 erg/s and a mass of M WD ≈ 0.8, we obtainṀ ∼ 10 −12 M /yr. 6. DISCUSSION

Placement on the HR Diagram
We overplot ZTFJ0850+0443 and ZTFJ0926+0105 on a Gaia Hertzsprung-Russell (HR) diagram ( Figure 16). We note that ZTFJ0850+0443 has a parallax divided by parallax error (π/σ π ) value of 2.8. This is lower than the value adopted by some authors to claim a precise distance measurement (π/σ π > 3 or even π/σ π > 10, depending on the study). We plot all sources in Gaia EDR3 within 100 pc of the Sun with parallax π/σ π > 10. On average, the locations of ZTFJ0850+0443 and ZTFJ0926+0105 are consistent with the mean position of polars as found by Abril et al. (2020).

Current CV Population and SRG
All CVs are X-ray emitters, to some extent (Mukai 2017). While magnetic CVs typically have higher Xray luminosities than their non-magnetic counterparts, the eFEDS dataset is deep enough to reveal new X-ray Figure 16. Gaia EDR3 HR diagram composed of sources within 100 pc with an exceptional parallax measurement (π/σ/π > 10). The three CVs in this work are significant outliers which reside between the main sequence and WD tracks.
detections of non-magnetic CVs. Table 4 presents a list of all SDSS CVs in the eFEDS footprint alongside the objects reported in this paper. This list of CVs is by no means exhaustive, and there are CVs and CV candidates in the Open Catalysmic Variable Catalog (Jackim et al. 2020) that are not in the SDSS list. However, a complete analysis of all CVs in the eFEDS field is beyond the scope of this study.
Even from this modest sample, the efficiency of discovery of magnetic CVs is greatly increased by incorporating X-ray data from eFEDS/SRG. Neither of the two polars were listed as SDSS CVs, and ZTF0850+0443 was even previously misclassified as a quasar based on its GALEX color information (Warwick et al. 2012).
An all-sky eROSITA/SRG release will be vital for constructing a volume-limited survey similar to that of Pala et al. (2020). Volume-limited samples are one way of eliminating observational bias from constructing a full picture of CVs and their evolution, as was shown by Pala et al. (2020). Introducing X-ray information eliminates another observational bias and provides another property that can be used to study CVs. ZTFJ0850+0443 and ZTFJ0926+0105 were also detected in the "hard" sample of the eFEDS catalog (2.3-5 keV) and fulfill at least one of the criteria to be classified as X-ray variables in the eFEDS data release (Salvato et al. 2021). Schwope et al. (2021) identified an eclipsing polar through an eROSITA/SRG crossmatch with Gaia using a proprietary eRASS dataset. We showed here that the public eFEDS dataset revealed a similarly interesting object when crossmatched with ZTF.
Our findings show that the eROSITA/SRG X-ray survey is vital in supplementing ZTF for the discovery of new CVs. Making use of Gaia, we can obtain precise luminosities of the objects we find. The upcoming Gaia DR3 will be useful in this context.

CONCLUSION
We have discovered two polars: ZTFJ0850+0443 (eclipsing, P orb = 1.72 hr) and ZTFJ0926+0105 (noneclipsing, P orb = 1.48 hr), through a crossmatch of the eFEDS dataset and ZTF archival photometry. We suggest that ZTFJ0850+0443 is likely a low-field polar with magnetic field B WD 10 MG. The accreting white dwarf in ZTFJ0850+0443 has a mass of M WD = 0.81 ± 0.08M and accretion rate ofṀ ∼ 10 −11 M /yr, both typical values of polars. ZTFJ0926+0105 has a more typical magnetic field strength of polars, B WD 26 MG, and accretion rate ofṀ ∼ 10 −12 M /yr. Because it is not eclipsing, we cannot place robust measurements on the white dwarf mass.
This study is part of a larger follow-up analysis of the eFEDS/ZTF footprint. Studies such as this are useful in overcoming observational biases in previous opticalonly searches for CVs, and will directly lead to accurate volume-limited studies of CVs such as that by Pala et al. (2020). This in turn will test our knowledge of the origin of magnetic fields in WDs, compact object accretion, and binary star evolution.