Open Access
Issue
A&A
Volume 662, June 2022
Article Number A116
Number of page(s) 12
Section Stellar structure and evolution
DOI https://doi.org/10.1051/0004-6361/202142813
Published online 28 June 2022

© S. Ok and A. Schwope 2022

Licence Creative CommonsOpen Access article, published by EDP Sciences, under the terms of the Creative Commons Attribution License (https://creativecommons.org/licenses/by/4.0), which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

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1. Introduction

Cataclysmic variable stars (CVs) are accreting binary systems that transfer material via Roche lobe overflow from a late-type main-sequence star onto a white dwarf (WD). In the subgroup known as the polars, the white dwarf’s magnetic field strength is higher than B >  10 MG and suppresses the formation of an accretion disk. Mass transfer occurs along magnetic field lines (Warner 1995).

The material falling radially goes through a strong adiabatic shock at a certain distance above the surface, which heats the infalling plasma to several tens of keV, which subsequently cools via thermal plasma radiation at X-ray wavelengths and optical cyclotron radiation (Cropper 1990). The X-ray spectra of the polars are well described with a plasma that has a multi-temperature and variable density structure (e.g., Cropper 1990; Fischer & Beuermann 2001). Polars are essential objects to understand the processes of mass transfer in the presence of a strong magnetic field, the generation of strong magnetic fields in close binaries, and the last steps of stellar evolution in the presence of a strong magnetic field.

V496 UMa or MASTER OT J132104.04+560957.8 was first identified as a CV by Yecheistov et al. (2012) when the system changed brightness by ∼2 mag from 18.41 mag to 16.43 mag within 30 min. Based on photometric observations, the system was tentatively identified as a non-eclipsing polar (Kato 2012). It was confirmed as a polar based on its spectral properties by Littlefield et al. (2015, 2018). Optical spectra showed strong hydrogen Balmer and strong He II 4686 Å emission lines, and a non-stellar continuum that decreased blueward of 5000 Å. Radial velocities and time-resolved photometry showed periodic variability at a period of 91 min, identified as the orbital period. Interestingly, the medium-resolution spectra obtained by Littlefield et al. (2018) showed emission–absorption line-reversals at certain phases of the binary. Long-term Catalina Real-time Sky Survey (Drake et al. 2009) photometric observations revealed pronounced brightness variations during 2007–2012 (Littlefield et al. 2018). The orbital light curve of the binary showed a double-peaked structure, with the amplitude of the second hump being strongly variable.

Precise and uninterrupted optical photometric data were available from the Transiting Exoplanet Survey Satellite (TESS; Ricker et al. 2014). These data allow us to study such variations in much greater detail, which was a prime motivation for this study. These data, along with unpublished XMM-Newton X-ray observations of the source, promise deeper insight into the accretion physics of this unusual polar.

We thus present an analysis of archival XMM-Newton, TESS, and the Zwicky Transient Facility (ZTF) observations obtained between 2017 and 2021, when the system was in different accretion states. Our aim is to further explore the thermal, temporal, and geometric behavior of the object by analyzing the combined data set. In Sect. 2 we give the details of the observations. Section 3 contains our analysis and results. We conclude with a discussion of our results in Sect. 4.

2. Observations

2.1. TESS observations

TESS is a space-based observatory providing high-precision light curves for long uninterrupted time intervals. TESS is equipped with four identical refractive cameras with a combined field of view (FOV) of 24 × 96 deg. Each of the 2k × 2k CCDs on the satellite has a scale of 21 arcsec per pixel. V496 UMa was observed in two sectors, and the photometric data for our target comes in two parts, named s0015-1001235444 and s0016-1001235444. The observations were made between August 15, 2019, and September 12, 2019, and were carried out in the high-cadence mode with a time resolution of two minutes. We used the Presearch Data Conditioning (PDC) light curves of this star produced by the TESS Science Processing Operations Centre (SPOC), which we downloaded from the Mikulski Archive for Space Telescopes1.

We checked the apertures used to extract the light curves and found that two more sources fall into the same source extraction region in sector 16. Both objects are ∼10 arcsec away from our source. The coordinates of these objects obtained by Gaia DR3 (Gaia Collaboration 2021) are RA1 = 13:21:06.03342, Dec1 = +56:09:54.8807 (source ID 1565396011799316352) and RA2 = 13:21:04.78039, Dec2 = +56:10:09.4925 (source ID 1565396007503248000), respectively. The G brightness values of these objects are 20.65(2) and 17.60(1).

We re-extracted the light curve by setting a new aperture for sector 16 using the Python sub-package lightkurve (Lightkurve Collaboration 2018). We used the same aperture value for sectors 16 and 15, and thus left the bright source with Gaia ID 1565396007503248000 outside of the new aperture. The newly extracted light curve comprising the observations obtained in the two sectors is shown in Fig. 1.

thumbnail Fig. 1.

TESS light curve of V496 UMa obtained in 2019 with 2 min time resolution. (a) The red line displays the binning time of 45 min. In the range of JD 2458739.1 and JD 2458741.4, the brightness of V496 UMa displays increases and decreases suddenly. (b) shows the sudden decrease in brightness, while (c) focuses on the increase.

2.2. Gaia observations

In Gaia DR3 (Gaia Collaboration 2021) V496 UMa is indicated by ID 1565395908719728384. The brightness is 17.27 ± 0.03, 17.31 ± 0.09, and 16.86 ± 0.08 in the G, GBP, and GRP passbands, respectively. Gaia measured the parallax of V496 UMa as 1.307 ± 0.060 mas. We used the distance to the system of 758 ± 33 pc, as determined by Bailer-Jones et al. (2021).

2.3. The Zwicky Transient Facility observations

We searched the Zwicky Transient Facility (Masci et al. 2019) database for data from V496 UMa. V496 UMa has three years of coverage (see Sect. 3.3) between March 2018 and June 2021. All data points were obtained with 30 s exposure time, and in total, we found 566 data points in the g, 544 points in the r, and 1556 points in the i passbands.

2.4. X-ray observation

The XMM-Newton observations of V496 UMa took place on March 12, 2017, (OBSID 0803500101), about two years before the TESS observations. They lasted 29 ks, and thus covered 5.36 photometric cycles. The EPIC-pn and EPIC-mos cameras (Strüder et al. 2001; Turner et al. 2001) were operated in full-frame mode with the thin filter. The optical monitor (OM) was set in the fast mode with an intrinsic time resolution of 0.5 s without using a filter.

Data were reduced using the XMM-Newton SAS version 15.0.0. The EPIC-pn data were processed with the epchain task to generate calibrated event lists. All times were corrected to the Solar System barycenter using the barycen task. Finally, the photon list was filtered to only include photons with energies between 0.2 keV and 10.0 keV for the EPIC-pn and EPIC-MOS instruments. Our source extraction region was a circle centered on the source, and the best extraction radius was found with the eregionanalyse task. The source extraction radii were 45 and 30 arcsec for the EPIC-pn and EPIC-MOS instruments. An annulus was positioned around the object to extract the background photons. The radius of the inner ring of the annulus was determined as 50 arcsec, and the radii of the outer ring of the annulus were 110 arcsec.

Background-subtracted X-ray light curves were produced with the task epiclccorr with 50 s time bins. In addition, we calculated the hardness ratio (HR) obtained from different energy bands and used the HEASARC LCURVE tool, a subpackage of XRONOS (Stella & Angelini 1992), and to display time-dependent light and hardness ratio curves (see Sect. 3.2.2).

One observation with the OM lasted 1200 s. A total of ten such observations were made that also cover more than five orbital cycles. Between the exposures are short gaps without data that last 335 s. The OM data were reduced using the task omfchain to produce background-subtracted light curves with ten-second time bins (see Sect. 3.2.1).

3. Analysis and results

3.1. Optical photometry obtained with TESS and XMM-Newton/OM

V496 UMa displays a highly variable behavior of the optical light curve. The light curve shape is characterized by two alternating humps with different brightness (see Fig. 2, upper panel and Littlefield et al. 2018).

thumbnail Fig. 2.

TESS light curves of V496 UMa. (a) and (b) show folded TESS light curve of V496 UMa. The black and red dots indicate a continuous observation period of approximately two months. (c) Power spectrum of V496 UMa. The highest amplitude frequency indicates the 91-min period.

To determine periodic changes in the light curve, we first computed a Fourier transform using the Period04 software by Lenz & Breger (2004). We searched for significant peaks in the frequency interval from 0 d−1 up to the Nyquist frequency of short cadence TESS data (360 d−1). The power spectrum shows just one main period at f = 15.81384(7) cycle d−1 (P = 91.0594(4) min) plus integer harmonics. To check for further possible periodicities, the leading term in the Fourier series computed by Period04 was subtracted from the original data (pre-whitening), and another power spectrum was computed. No further periodicity was found in the pre-whitened data. The uncertainty of the dominant frequency was then computed via the least squares method in Period04 with the treatment of Montgomery & Winget (1999). The power spectrum is displayed in the bottom panel of Fig. 2.

The main or first hump was always present in the light curves, and its arrival times were used to derive an improved optical ephemeris. We fit these bright humps with a Gaussian to obtain the times Tmax of their centers and their errors. The same process was applied to the XMM-Newton OM light curve (see Fig. 6). Using both XMM-Newton/OM and TESS, a weighted linear regression between the times Tmax and the cycle numbers were used to derive

(1)

where the numbers in parentheses give the uncertainties in the last digits. The residuals of this linear fit are shown in Fig. 3. The error of the period obtained from the Fourier transform is larger than that from the linear regression. We therefore accept the results from the linear regression as our final timing solution.

thumbnail Fig. 3.

O − C variation of the main photometric hump in V496 UMa with respect to the ephemeris of Eq. (1), based on data from the OM on board XMM-Newton and on TESS. The inset shows the TESS residuals only.

The ephemeris given in Eq. (1) improves the previous period determination of Littlefield et al. (2018) considerably. While the period they derive is , our new value has a factor of ∼60 smaller error. This improvement was possible using the quality of the TESS data and the time base of the combined TESS and XMM-Newton/OM data.

In the following, all phases refer to the ephemeris given in Eq. (1). We note that the previous period value deviates by 3.8σ (of the old larger error) from our new value. The time difference between the two ephemerides is 2426.64783 days which corresponds to 38375.046 cycles according to our new period. Hence, our phase zero is later than the old value by 0.046 phase units.

We used our new ephemeris to create an epoch-phase diagram that shows all the data obtained with TESS in a compact format (see Fig. 4). TESS observations cover about 800 photometric cycles. The long-term light curve of V496 UMa shows the overall stability of the light curve pattern on the one hand, with some marked variability on the other hand. There are changes in the overall brightness affecting both humps, and there are occasions when apparently only the second hump was found to be strongly variable. This behavior was already reported by Littlefield et al. (2018) based on ground-based time series. The continuous TESS data offer new insight into the frequency and the duration of such changes.

thumbnail Fig. 4.

Cycle–Cycle Mod 2 diagram of V496 UMa for all high-cadence TESS data. Two consecutive cycles are drawn consecutively from the beginning. The color bar shows the flux density. The left panel shows data obtained in sector 15; the right panel shows data obtained in sector 16. All data were folded using the ephemeris given in Eq. (1). The wide white gaps in the two graphs show where TESS did not receive data.

Figure 4 shows a considerable decrease in the overall flux happening between cycles 268–300 and 430–470. The overall light curve shape with two humps remains more or less the same, although there is some suggestion that the second hump is affected more strongly than the first during the overall brightness reductions. To further investigate this behavior, we extracted the brightness of the two humps per cycle. For this, we identified three phase intervals from the phase-folded light curve, 0.92–1.07 for the first hump, 0.36–0.55 for the second hump, and 0.68–0.72 for the faintest part of the light curve, which was used as the base flux or background and subtracted from the integrated flux in the two humps.

Figure 5 shows the variation of the two related humps in the same cycle, which displays a linear relation. In addition, this linear relationship is parallel to the line where the flux of the two humps is equal. The first hump always has more flux than the second hump and always has positive flux, while the second hump is consistent with zero flux at the lowest levels. The average flux ratio between hump 1 and hump 2 is 1.89.

thumbnail Fig. 5.

Diagram of hump 1 vs. hump 2. The average fluxes in the phase range 0.92–1.07 (hump 1) and 0.36–0.55 (hump 2) in each cycle were calculated. The average base corresponding between the 0.68–0.74 phase in each cycle was subtracted from the related humps. The red line shows the linear fit corresponding to the humps. The dashed line shows where the flux in both humps are equal.

The linear relation nevertheless shows a large scatter, implying that the distribution of matter onto one of the two poles that might be associated with the two light curve humps (if a two-pole scenario applies, see below for a discussion) instantaneously shows significant changes.

Since the system does not show an eclipse, it is difficult, if not impossible, from optical photometry alone to decide whether mass accretion occurs via one or two poles. Both geometries can produce a double-humped light curve. For instance, in a one-pole geometry, two humps may occur through stream obscuration and cyclotron beaming, while in a two-pole geometry, two humps occur through successive self-eclipses of the two poles.

X-ray observations play a crucial role in understanding which of these two scenarios occurs. The hydrogen column density in the direction of the object (NH) and hardness ratio (HR) behavior in the dips and bright humps can facilitate understanding of the proper geometry of the V496 UMa (see next section).

3.2. XMM-Newton observations

3.2.1. X-ray photometry

In Fig. 6 the light curves obtained with the XMM-Newton observatory at X-ray and optical–UV wavelengths are shown in the original time sequence. Similar to TESS in the optical, the light curves at X-ray wavelengths show a double-humped shape. The first hump is mainly constant in brightness, while the second hump is highly variable and unstable. These observations covered almost five complete photometric cycles, beginning with the second hump. The first hump is a factor of 1.3 brighter than the second hump during the first two photometric cycles (0.2−10 keV). The first and the second humps were separated by about 0.53 phase units in these cycles. During the last two cycles, the second hump was much fainter. In the phase interval 0.8–1.2 (hump 1) and 0.3–0.7 (hump 2) of the last two cycles the mean flux ratios increased to 2.3 and 2.6. The simultaneous OM observations show that weakening of the second hump in the optical to UV region starts (after JD 2458091.1) in the second full photometric cycle, which is one cycle earlier than observed at X-ray wavelengths.

We also generated energy-resolved, phase-folded X-ray light curves in the 0.2−0.5 keV, 0.5−2.5 keV, and 2.5−10 keV energy bands. These are displayed in Fig. 7, which shows the main hump as a rather stable feature in all bands with always the same width and similar brightness. A dip is seen in the soft energy band (0.2–0.5 keV) at phase ϕ = 0.81 with zero rates in all covered binary cycles. The width of the dip is about Δϕ = 0.037 (200 s). The dip is definitely not due to the donor star’s eclipse of the accreting white dwarf. Such a binary eclipse would be visible at all energies. Instead, the feature is more likely a stream dip, where the X-rays from the accretion region on the white dwarf are passing through the accretion stream that was raised out of the orbital plane. Its origin by photoelectric absorption in the stream naturally explains its energy dependence.

thumbnail Fig. 6.

X-ray and optical light curves of V496 UMa obtained XMM-Newton. The top two panels show the light curves obtained in the 0.2−0.5 keV and 0.5−10 keV ranges with time bins of 50 s. The OM data in the lower panel have time bins of 10 s. In the upper panel, red (hump 1) and blue (hump 2) shaded regions identify the phase intervals used to extract the X-ray spectra of the two humps.

thumbnail Fig. 7.

Energy resolved X-ray light curves of V496 UMa. They were folded according to Eq. (1). The light curves were extracted using time bins of 50 s.

3.2.2. X-ray spectroscopy

The X-ray spectra obtained with XMM-Newton were analyzed with version 12.8.2 of the XSPEC package (Arnaud 1996; Dorman & Arnaud 2001). Spectral fitting was performed for EPIC-pn and EPIC-MOS in the energy range of 0.2−10 keV. Mean spectra were extracted for the first and second hump for the time intervals shown in Fig. 6.

The background noise was high (RATE > 1) during the first 30 min of the observation (until the first minimum in the light curve), which was therefore excluded from our analysis. We used MOS1 and MOS2 data to analyze the mean spectra from hump 1 and hump 2, but not for time-resolved spectroscopy due to their low signal-to-noise ratio.

The spectrum of the first hump was obtained from the first five stable peaks seen on the light curve (see Fig. 6). The spectrum of the second hump was acquired only for the first two full occurrences due to the weakness of this feature during the last two photometric cycles. Both spectra were grouped with 25 counts per bin. In the spectral analysis, we used the χ2 statistics for model optimization.

Following Kuulkers et al. (2010) and Mukai (2017, and references therein), the bright phase spectra of polars can be described with optically thin thermal plasma emission from the post-shock plasma, sometimes with an additional blackbody component from the accretion-heated white dwarf atmosphere, and we follow this approach here as well.

We started to fit the first hump data using a single MEKAL plasma model (Mewe et al. 1985; Liedahl et al. 1995) with the metal abundances frozen at solar values (Wilms et al. 2000). V496 UMa is located at a very high galactic latitude and is a relatively distant object compared to the distribution of galactic hydrogen. We decided to include an absorption component to the MEKAL and to fix the absorbing column at the galactic value, NH, gal = 1.23 × 1020 atoms cm−2 (HI4PI Collaboration 2016). The combined simple model TBABS*MEKAL gave a bad fit to the data with a reduced χ2 = 2.14 (for 328/153 d.o.f.). The fit left an excess of photons in the soft spectral region, < 0.5 keV.

We then added a single blackbody (BB) model so that our new model is TBABS(BB+MEKAL). The fit yielded a chi-square value of 174.35 for 151 d.o.f., . The null hypothesis probability of rejecting the model was 9%. We thus accepted this model for the first hump (see Fig. 8).

thumbnail Fig. 8.

X-ray spectrum of V496 UMa. The spectrum was extracted from the first bright humps and grouped with 25 counts per bin using TBABS(BB+MEKAL) spectral models. The reduced chi-square value is 1.15.

A similar process was applied for the spectrum of the second hump. For this, we also started with a TBABS*MEKAL model. This initial fit yields a chi-square of 208.72 for 72 d.o.f. (χ2 = 2.89), and was thus rejected. The fit left an excess of photons mainly at soft energies below 0.8 keV. Then we added a BB model to describe this energy range better. The fit was improved substantially with a chi-square value of 83.93 and 70 d.o.f. Our reduced χ2 value decreased to χ2 = 1.19. The probability of rejecting the null hypothesis is 12%, and we thus accepted the emission model with a blackbody and a thermal component. The spectrum, the best-fit model, and the residuals are shown in Fig. 9.

thumbnail Fig. 9.

X-ray spectrum of V496 UMa. The spectrum was extracted from the first two peaks of the second hump, which can be seen in the light curve in Fig. 6, and grouped with 25 counts per bin. The same models as applied to the first bright hump were used. The reduced chi-square value is 1.20.

The best-fit model parameters are summarized in Table 1. Their errors were calculated with the error and steppar commands in XSPEC for 90% confidence levels (the delta fit statistic of 2.706). Uncertainties on fluxes for all models were calculated using the cflux convolution component. Our spectra contain too few photons to derive any useful constraints on the existence and the parameters of a possible Fe-line complex between 6.4 and 7 keV.

Table 1.

Spectral parameters from humps: spectral fit parameters, their uncertainties, fit statistics, and model bolometric fluxes.

The spectral shapes and temperatures of both humps are very similar, and they are compatible with each other within the error limits. The most notable difference was in the bolometric fluxes of the blackbodies. The bolometric flux of the second hump is a factor of 2 higher than that of the first hump. This is due mainly to the lower temperature found for the blackbody from the second hump, which places a larger part of the spectrum in the unobserved extreme UV (EUV) region of the spectrum. Therefore, the reliability of this calculation is debatable because we only see the extension of this blackbody component in the X-ray range. On the other hand, we note that in the 0.2–0.5 keV soft energy range, where the second hump is prominent, it has higher count numbers than the first hump (see Fig. 7, blue shaded regions).

For the distance of 758 pc, the soft blackbody emission of the first hump originates from an assumed circular region with a radius of km, that of the second hump originates from a region with a radius of km. These radii correspond to fractional areas of an assumed WD with a radius of 8000 km of 0.8% and 0.2%, respectively.

The second region is possibly larger than the first, but this is uncertain; we do not speculate about possible reasons. However, taken at face value, the implied sizes of the emission region are larger than those found for example in the prototypical object AM Herculis (about 100 km; Schwope et al. 2020), but are similar in size to the textbook object EF Eri (< 570 km Beuermann et al. 1987), and thus approximately as expected given the large uncertainties on the derived values and on the heating processes in this object. For a discussion of sizes of emission regions, see Hameury & King (1988), among others.

We also calculated hardness ratios HR = ((H − S)/(H + S)) from the counts in the two energy bands (S = 0.5−2.5 keV and H = 2.5−10 keV) from background-corrected light curves with 200 s time bins. Figure 10 shows the change in HR for the whole X-ray observation. The only significant and repetitive feature in the HR curve is a substantial increase in the dip before the first bright hump at ϕ = 0.81(1) (see Fig. 10). The dip, therefore, is naturally explained by photoelectric absorption in the intervening accretion stream lifted out of the orbital plane. To estimate the amount of absorption in the dip (ϕ = 0.81), we ran XSPEC models using the model parameter of hump 1, adding an extra TBABS component. We found a dip NH of order 1.6 × 1021 atoms cm−2.

thumbnail Fig. 10.

HR variation along the X-ray observation of V496 UMa. (a) Folded X-ray light curve of V496 UMa (0.2–0.5 keV). (b) Hardness Ratio variation of V496 UMa which corresponds to energy range between 0.5 and 2.5 keV and 2.5–10 keV. (c) shows the frequency of HR along the folded X-ray light curve.

Apart from this, no increase or significant variation in the hardness was observed during the first and second humps. In particular, we note that the hardness stays the same independently of the pronounced brightness variations of the second hump. We regard this as evidence that accretion occurs at two different accretion zones on the white dwarf surface. In other words, the system is a two-pole accretor. If there were just one accreting pole, the brightness of the two humps would change coincidentally. The occasional reduction in the brightness of the second hump would be due to absorption in an accretion curtain. Such absorption events would have been evident through an increase in the hardness ratio, which is not observed.

3.3. Spectral energy distribution

The spectral energy distribution (SED) of V496 UMa was compiled using data from XMM-Newton, the Large Binocular Telescope (LBT; Littlefield et al. 2018), the (ZTF; Masci et al. 2019; see Fig. 11), the Sloan Digital Survey (SDSS; Blanton et al. 2017), the Panoramic Survey Telescope and Rapid Response System (Pan-STARRS; Chambers et al. 2016) survey, and the Wide-field Infrared Survey (WISE; Wright et al. 2010) using effective wavelengths and zero points for each filter, as given by the Spanish Virtual Observatory2 (SVO). For the WISE observations we only used bands W1 and W2 because the data for W3 and W4 are regarded as unreliable for targets as faint as V496 UMa (Wright et al. 2010). Figure 12 shows the spectral energy distribution generated from these observation points.

thumbnail Fig. 11.

ZTF observations in time series with different passbands (left) and folded light curves of these time series according to Eq. (1) (right). The interval (dashed red box) in the upper left figure shows the time when TESS observations were made. The ZTF observations at this time are given by the red dots. The phase-folded figure on the right shows the location of these dots.

thumbnail Fig. 12.

The spectral energy distribution of V496 UMa. Upper panel: total spectral energy distribution of V496 UMa from the X-ray to the infrared region. White dwarf (0.8 M) (dark blue line) and main-sequence star (0.16 M) (light gray line) model spectra for 10 000 K and 3000 K, are shown combined with a red dashed line. The vertically plotted black arrow represents the amplitude of the high-state light curve in ZTF which derived from long-term g band light curve(16–18.6 mag) (see Fig. 11). Lower panel: points in the optical region and combined synthetic atmosphere models used to estimate the temperatures of the components.

The various spectroscopic and photometric observations obtained at different times reveal two fundamentally different mass accretion states, a high and a low state, as seen in many other polars. The data we analyzed from TESS and XMM-Newton can be understood in terms of a high state, but the archives (SDSS, ZTF) also document a low state. The high-state brightness at a given phase (e.g., the peak brightness of the first hump) does not seem constant, but we do not attempt to further subcategorize the state of enhanced activity.

In Fig. 12 we show one single data point representing the first hump’s brightness. The white-light filter of XMM-Newton/OM covers a broad wavelength range, ∼200−8000 Å. We use the central wavelength and flux conversion factors as given in the XMM-Newton online documentation3 to convert count rates to physical fluxes. The OM data seem to be a bit below the brightest fluxes from the ZTF, but still indicate a high state.

3.3.1. Low accretion state

The long-term light curves from the ZTF (Fig. 11) demonstrate different mass accretion states for V496 UMa. The object switched from a high to a low state in May 2020. This transition was observed in the g and r filters, the ZTF database has no i-band data point after May 2020. The faintest points from the ZTF and data points from SDSS were used in the SED and are assumed to represent upper limits for the temperatures of the naked WD and the donor star. Thus, these points became a reference for us when estimating the temperatures of the components.

We used the data of Koester (Koester 2010; Tremblay & Bergeron 2010) and the NextGen (Hauschildt et al. 1999) synthetic atmosphere models that are available online4, to represent the photospheric contributions of the WD and the donor star, which we assume to be a main-sequence star. To do this, we scale these models to the Gaia-distance of 758 pc. The distance error causes uncertainty of 200 K in the temperatures of the WD and the donor at fixed masses.

In the SED we considered two main reference points, the ZTF r band and the SDSS u band. The r-band data point has contributions from both photospheres, while the contribution of the donor star to the SDSS u band is negligible. The temperature of the white dwarf is constrained by this data point. An upper temperature for the donor is derived by establishing that the summed light of the two model components does not exceed the measured r-band brightness.

To create the synthetic flux distribution, values for the free parameters (radius Rwd and effective temperature Teff) need to be chosen. We used an 0.8 M mass WD, which is assumed to be representative of magnetic CVs (Pala et al. 2022, and references therein), and estimate Rwd using the Nauenberg (1972) mass–radius relation. The best matching temperature that we found to represent SED for this mass was 10 000 K. Taking into account the error in the u-band magnitude, we estimate the WD temperature to be in the range 8000–11 000 K (see Fig. 12). For the secondary star we used Knigge’s empirical relationship for CVs (Knigge et al. 2011). An orbital period of 91.05 min suggests a secondary star with spectral type M6.5 (2750 K). A corresponding photospheric model underpredicts the observed optical data, which are better represented with a higher temperature of the donor (see Fig. 12), but we cannot exclude that some residual non-photospheric emission is present (cyclotron radiation, stream emission). In conclusion, the most consistent temperatures with optical data points were 10 000 and 3000 K for the WD and companion, respectively. The best-fit model is given in the lower panel of Fig. 12 as 10 000 K WD + 3000 K M5 and is shown with a red dashed line. It should be noted that these temperatures represent the upper limits for the components.

The WISE W1 and W2 fluxes were too high to be compatible with the synthetic stellar models, which could mean that when the WISE data were collected, V496 UMa was in a high state and these points probably have cyclotron emission contribution, and is the reason why these data points are omitted here.

3.3.2. High accretion state

In the ZTF high-state data (i.e., in all data obtained before May 2020), V496 UMa varies between 16 and 18.6 in all three passbands. In Fig. 12 we show the maximum brightness in each of the bands, which always corresponds to the first hump, and indicate the photometric variability with a vertical arrow.

The Gaia and Pan-STARRS data points in the figure are averages over many individual measurements and fall within the range of the ZTF data. Hence, we assume that all these data were obtained during the high state.

The TESS observations coincide with the time frame of the ZTF observations. Figure 11 shows this interval in g-band observations when the source varied between 16.83 and 17.65 (i.e., the TESS observations were made in the high state).

In Fig. 12 we also show two optical spectra, one obtained from the SDSS database, the other obtained by Littlefield et al. (2018). The mean SDSS spectrum was obtained in January 28, 2018. The mean spectral flux density is about 3.0 × 10−16 erg cm−2 s−1 Å−1 at 5500 Å which corresponds to a V-band magnitude of 17.7 (Vega). The implied g-band magnitude is 17.9 (AB). The brightness is at the lower end, but still compatible with a high state. Because the data were obtained shortly before ZTF started observing, we have no independent confirmation for its accretion state, but the rich emission lines spectrum indicates a high state.

The mean SDSS spectrum consists of four spectra, each with 900 s exposure time. In Fig. 13 these spectra are shown separately. We calculated the phase intervals covered by the four spectra with Eq. (1). The phase intervals are ϕ1 = 0.635−0.799, ϕ2 = 0.814−0.978, ϕ3 = 0.993−1.158, and ϕ4 = 0.173−0.338. Hence, the spectra cover the phase interval showing the decrease from the second hump, the dip phase, and the rise toward the first hump. Interestingly, there is not much variability in the continuum, but a great deal of variability in the lines. The second spectrum, which covers the dip, displays the emission–absorption line reversal reported earlier by Littlefield et al. (2018). The composition of the emission line spectrum and the occurrence of the emission–absorption line reversal during the dip phase confirm that these data were obtained in a high accretion state. The SDSS spectra were obtained in an active state, although not at the highest possible level. This becomes evident from the comparison of the two spectra in Fig. 12, which shows the SDSS spectrum clearly below the LBT spectrum. To assess the energy balance in the high state, we therefore use only the LBT data.

thumbnail Fig. 13.

SDSS spectroscopy of V496 UMa. Upper panel: four SDSS spectra which covered phase intervals between ϕ1−4 = 0.635–1.338. Lower panel: wavelength region covering the Hβ and the HeII 4686 emission lines. Flux units are 10−17 erg cm−2 s−1 Å−1.

The LBT spectroscopy presented by Littlefield et al. (2018) was obtained in a high state and was used to determine the cyclotron luminosity in the high state. Their simultaneous photometry showed higher peak brightness than the reduced spectrum indicating some light loss at the spectrograph’s slit (slit width 1 arcsec in up to 1.3 arcsec ambient seeing, see their Fig. 4). We thus corrected the observed spectra by a factor of 2. The spectrum at phase ϕ = 0.99 suggests that the cyclotron component peaks at around 6000 Å, and falls off to the IR wavelength regime.

Following Littlefield et al. (2018) the difference spectrum between the bright (first bright hump) and the faint phase was regarded as the cyclotron spectrum proper and integrated. We are able to assume to have sampled a good fraction of the total cyclotron spectrum, which stretches farther into the unobserved neighboring wavelength regions. By integrating the spectrum, we calculated the cyclotron flux as a Fcyc ∼ 2.8 × 10−12 ergs cm2 s−1 with a considerable but difficult-to-specify uncertainty. The Fcyc flux that we obtained is almost a factor of 2 above the blackbody flux Fbb observed with XMM-Newton.

The cyclotron luminosity and the X-ray luminosity are accretion-induced, and their sum is regarded as a fair estimate of the accretion luminosity (Lacc ∼ LX + Lcyc). However, it is necessary to recognize that the cyclotron luminosity is poorly constrained. Uncertainties arise from the unknown bolometric correction factor for the flux and the unknown geometry factor to convert the flux to a luminosity. We assume Lcyc = πFcycD2 to get (Lcyc = 4.8(2) × 1031 erg s−1) at a distance of 758 pc. The bolometric X-ray luminosity that we obtained from the first hump is LX = 2.3(3) × 1032 erg s−1 so that the accretion luminosity from the first hump becomes Lacc = 7.1(5) × 1032 erg s−1.

We found the mass accretion rate ( = LaccRwd/MwdG) in the high state of the V496 UMa for the first bright hump to be hump1 = 7.4(3) × 10−12 M yr−1. We used the same method for the second hump. The X-ray luminosity for the second hump was LX = 2.5(4) × 1032 erg s−1 and the estimated cyclotron flux is Lcyc = 2.9(2) × 1031 erg s−1, which was estimated by scaling the brightness of the first and the second humps and assuming the same spectral shape. The mass accretion rate was estimated for the second hump to be hump2 = 6.8(5) × 10−12M yr−1. Finally, the total accretion rate at the time of the XMM-Newton observation was tot = hump2 + hump1 = 1.4(8) × 10−11M yr−1.

3.4. Accretion geometry

In the following we discuss constraints on the accretion geometry, which means the possible locations of the accretion spots, and the orbital inclination. We base the analysis and discussion on the phase difference of the humps in the light curves, the visibility of the two regions (or their self-eclipses), the existence of an X-ray absorption dip, and the non-existence of a binary eclipse.

The X-ray observations revealed two bright phases per photometric cycle, to which we assign two accretion regions. We determined their centroids by applying Gaussian fits to the original light curve data. The first hump (red regions in Fig. 6, five data points) has centroids at phases ϕphot = 0.949, 0.982, 0.956, 1.012, and 0.995. The first two of the second humps are centered on phases of 0.479 and 0.515 with a mean of 0.497 (blue regions in Fig. 6). These hump centroids scatter around the mean centroid phase of the first hump (given by phase ϕphot = 0.0) between −18° and +4° and the second hump between 172° to 186°. In summary, the two regions are separated by about 0.5 phase units. This is particularly interesting because the two regions have comparable X-ray luminosities and possibly similar accretion rates. Since there is no eclipse in the light curve, we do not know their absolute phase zero. The same problem was described by Littlefield et al. (2018) who argue, based on expectation and similarity with other polars, that the phase of their observed emission–absorption line reversal is expected at binary phase ∼0.9, when the line of sight crosses the accretion stream.

The X-ray data reveal an absorption dip at photometric phase ϕphot = 0.81. The existence of a dip requires i >  β, with i being the orbital inclination and β the co-latitude of the corresponding accretion spot which is fed by this stream (see Fig. 14).

thumbnail Fig. 14.

Schematic view of the two-pole accreting WD. The big black circles show the photosphere of the WD. (a) Side view of the WD. The red line represents the orbital plane. The dashed blue line shows the observer’s line of sight. The magnetic accretion regions B1 (primary) and B2 (secondary) are almost diametrically opposed. (b) Top view, projection onto the orbital plane. ϕphot indicates photometric phase zero (center of the main hump). The phase is counted clockwise. ϕ1, and ϕ2, respectively represent the longitude range where the first and second column can be found on the WD surface in the XMM-Newton observations. The blue line indicates the phase ϕdip of the X-ray absorption dip.

In other polars such a dip occurs between binary phases ∼0.93 and ∼0.8 (V808 Aur, Worpel & Schwope 2015; AM Her, Schwope et al. 2020). If this applies to V496 UMa, we can expect the orbital phase of hump 1 between phases 0.0 and 0.12. Hence, the spot faces the donor star directly or trails the donor in phase by almost 45°. In either case, if the stream feeding the first region initially follows a ballistic trajectory in the WD’s Roche lobe, it must be bent considerably so that the stream advances in the orbital phase. In such a geometry, the second region has its maximum at binary phase ∼0.5−0.6.

The X-ray light curve is modulated according to the visibility of the two accretion spots, which both seem to undergo self-eclipses by the white dwarf. It is difficult to determine the length of self-eclipses (or alternatively their visibility) individually because of apparent phases of visibility of the two spots simultaneously. We roughly determined the visibility of the first hump when the second region was faint (i.e., after cycle 2.5 in Fig. 7). We derive a visibility of Δϕ ≃ 0.55, which means that the first region lies above the orbital plane (the northern spot). It thus appears likely that the X-ray absorption dip belongs to the stream feeding this region. However, we cannot safely determine the visibility of the second region; we assume nevertheless that it is a southern region (i.e., it lies below the orbital plane). If this interpretation is correct, the dip lies at the beginning of the first bright phase, which is somewhat unusual. In other systems showing a dip like EK UMa (Clayton & Osborne 1994) and HU Aqr (Schwope et al. 2001), the dip is located closer to the centers of the bright phase. A possible accretion geometry in projection onto the orbital plane (xy-plane) and a plane orthogonal to it (xz-plane) is sketched in Fig. 14.

4. Discussion and conclusion

This study investigates the thermal, temporal, and geometric behavior of V496 UMa in the X-ray and optical regime. Unfortunately, the system does not show any eclipse. However, we have obtained the photometric period precisely from the extended TESS data connected without cycle count alias to data obtained with XMM-Newton obtained two years earlier. The improved period is based on the repetitive double hump structure.

There is a 3.8σ difference between the period derived by Littlefield et al. (2018) and our newly derived period. Precise (spectroscopic) observations are needed to understand better the reasons for this difference (a true period shift, or an instrumental or systematic error).

In addition, the X-ray light curve is double-humped and shows a pronounced dip. Our analysis revealed that the dip at photometric phase ϕphot = 0.81 is shaped by photoelectric absorption due to the accretion stream crossing the line of sight. As a result, the second hump displays considerable brightness but no hardness variations. We interpret this behavior in a scenario with two different accretion poles. The brightness changes at the second pole are thus interpreted as accretion rate changes and, for example, not due to an intervening accretion curtain.

Littlefield et al. (2018) described an emission-to-absorption line reversal that occurred at their photometric phase 0.87. We assume that the line reversal and the X-ray absorption dip are due to the same underlying effect, namely radiation interaction with the accretion stream that has left the orbital plane. We measured the X-ray absorption dip at our photometric phase of 0.81. Compared to Littlefield et al. (2018) the phase difference between the dip and the center of the main hump changed from Δϕ = 0.13 to 0.19. This variation is thought to be dependent on the mass accretion rate. The accreted matter may penetrate the magnetosphere deeper at high accretion rates, and the region where the material couples onto the magnetic field move away from the line connecting the WD and the donor star, causing the dip to occur at earlier orbital phases. A similar event was measured on eclipsing polar HU Aqr at different mass accretion states (Schwope et al. 2001).

Using XMM-Newton, we determined the relative longitudes of the two accretion regions. We assumed that the main accretion column (first hump) is in the direction of the secondary star or farther ahead in phase by up to ∼0.1 phase units. Humps are mobile in the light curve, and the hump centers show some phase variability, hence azimuthal variability.

The accretion geometry of V496 UMa thus seems to be unusual and peculiar. The main spot seems to be ahead in phase. It is fed by a stream that gives rise to the absorption dip, which must be bent profoundly to reach the main pole. The secondary pole might be similarly bright or even brighter in soft X-ray energies (see Fig. 6, top panel) than the putative prime pole, but is located in the hemisphere away from the donor star.

The previously reported cessation of mass accretion flow to the second column was seen in TESS and XMM-Newton observations. The weakening of the second column occurs randomly. We did not find any evidence that it followed a particular pattern. The TESS observations show that the two poles seem to be equally affected by the change in the overall mass accretion rate. The TESS observations were obtained in a high accretion state, but also included mass accretion cessations in some cycle intervals and their transitions. A general transition from a high to a low state was not observed with TESS. During these short-term transitions to a reduced state, no overall change in the shape of the light curve was detected. The second accretion pole also weakly represents itself in the TESS low state. Although there are cases where the second pole is mainly weak in the low state, this situation has also been encountered in the high state. The location of the second pole, which is far from the secondary, and the partial mass accretion may be causing the interruption of the accretion to the second pole.

V496 UMa exhibits a multi-temperature spectrum in X-rays. The system has a prominent blackbody emission at soft X-ray energy, which is typical for polars (Mukai 2017). The blackbody (kTbb) temperature in polars spread between 5 and 30 eV (Kuulkers et al. 2010). V496 UMa has a hotter kTbb (∼40 eV) component than this for both poles and both models with high error values. Since these temperature values are outside the detection limits of XMM-Newton (< 0.2 keV), the peak temperature of the soft component comes with high error values. Nevertheless, the lower limits in errors are still within this temperature range.

The system shows two different mass accretion states in the spectral energy distribution, an active state at different brightness levels and an inactive or low state. V496 UMa was in a high state during XMM-Newton observation. In a high state, the bolometric X-ray luminosity (≈5 × 1032) lies within the upper energy limits specified for polars (Verbunt et al. 1997; Reis et al. 2013). This value corresponds to the average X-ray luminosity of the intermediate polars (Patterson 1994). This luminosity is of particular interest given the short orbital period of the system (which would imply a lower accretion rate than systems with a longer orbital period) if our photometric period is the proper orbital period. Perhaps measuring such high luminosity may be due to the two-pole accretion. Other polars usually have one main pole typically with a lower field strength that is more or less facing the donor star and a second weakly accreting pole found at odd locations, and often has the higher field strength (UZ For, Schwope & Beuermann 1997; AM Her, Campbell et al. 2008a; VV Pup, Campbell et al. 2008b). However, the most significant property that makes V496 UMa different from other polars is the almost equal contribution of the two emission regions to the overall energy budget. Considering the variable second hump, it is curious how the same amount of matter was carried to the second column. In the case of the self-eclipse of columns, the co-latitude angle should be smaller than the inclination (β <  i). The second column is located quite far from the stagnation region in such a geometry. In order for the matter to reach the second pole, it should be considered that the orbital phase zero must be in a later phase, likely ϕphot ∼ 0.1. Thus, it can be ensured that a sufficient amount of mass can be conveyed from the stagnation region to both poles, and certain interruptions may occur on the second pole with the change in the mass accretion rate. Similar mass accretion rate variations onto a second pole were also observed in a similar system, V808 Aur (Worpel & Schwope 2015).

We tried to constrain the parameters of the components that make up the system with synthetic spectra that we used in the SED. Significantly, using the reference of optical data points, with the distance from Gaia, the SED tells us that the upper temperature limit of the white dwarf can be in the range 11 000–9000 K with a mass of 0.8 M. It would be possible to obtain similar SED distributions for different white dwarf masses at different temperatures. Since we do not have direct observational evidence to determine the mass of the WD, we used the currently accepted mean mass of WDs in polars.

Our attempt to find the spectral type of the secondary was based on the empirical relationship of Knigge et al. (2011). A main-sequence star of the M5.0 spectral type, together with a 0.8 M white dwarf and the temperature of 10 000 K, represented quite well the SED in the low accretion state.

The parameters of the WD in V496 UMa would benefit from a dedicated spectroscopic UV observation in the low state. This is so because the contribution of the donor is negligible in the UV. Hence the temperature of the WD and its radius would be much better constrained if the WD could be unequivocally identified and traced spectroscopically in the UV.

Finally, we emphasize the importance of spectroscopic observations to identify features from the secondary star (either in emission or absorption) to constrain the orbital motion of the secondary and orbital phase zero. This would be particularly useful in the low state where the photospheric absorption lines should be easier to detect.


4

Synthetic atmosphere data available at http://svo2.cab.inta-csic.es/theory/newov2

Acknowledgments

This research has made use of data, software and/or web tools obtained from the High Energy Astrophysics Science Archive Research Center (HEASARC), a service of the Astrophysics Science Division at NASA/GSFC and of the Smithsonian Astrophysical Observatory’s High Energy Astrophysics Division. This paper includes data collected by the TESS mission. Funding for the TESS mission is provided by the NASA’s Science Mission Directorate. Funding for the Sloan Digital Sky Survey IV has been provided by the Alfred P. Sloan Foundation, the U.S. Department of Energy Office of Science, and the Participating Institutions. SDSS-IV acknowledges support and resources from the Center for High Performance Computing at the University of Utah. The SDSS website is www.sdss.org. SDSS-IV is managed by the Astrophysical Research Consortium for the Participating Institutions of the SDSS Collaboration including the Brazilian Participation Group, the Carnegie Institution for Science, Carnegie Mellon University, Center for Astrophysics | Harvard & Smithsonian, the Chilean Participation Group, the French Participation Group, Instituto de Astrofísica de Canarias, The Johns Hopkins University, Kavli Institute for the Physics and Mathematics of the Universe (IPMU)/University of Tokyo, the Korean Participation Group, Lawrence Berkeley National Laboratory, Leibniz Institut für Astrophysik Potsdam (AIP), Max-Planck-Institut für Astronomie (MPIA Heidelberg), Max-Planck-Institut für Astrophysik (MPA Garching), Max-Planck-Institut für Extraterrestrische Physik (MPE), National Astronomical Observatories of China, New Mexico State University, New York University, University of Notre Dame, Observatário Nacional/MCTI, The Ohio State University, Pennsylvania State University, Shanghai Astronomical Observatory, United Kingdom Participation Group, Universidad Nacional Autónoma de México, University of Arizona, University of Colorado Boulder, University of Oxford, University of Portsmouth, University of Utah, University of Virginia, University of Washington, University of Wisconsin, Vanderbilt University, and Yale University. Samet Ok is supported by TUBITAK 2219-International Postdoctoral Research Fellowship Program for Turkish Citizens. We are grateful to the anonymous referee, whose comments led to large improvements in the clarity of the paper.

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All Tables

Table 1.

Spectral parameters from humps: spectral fit parameters, their uncertainties, fit statistics, and model bolometric fluxes.

All Figures

thumbnail Fig. 1.

TESS light curve of V496 UMa obtained in 2019 with 2 min time resolution. (a) The red line displays the binning time of 45 min. In the range of JD 2458739.1 and JD 2458741.4, the brightness of V496 UMa displays increases and decreases suddenly. (b) shows the sudden decrease in brightness, while (c) focuses on the increase.

In the text
thumbnail Fig. 2.

TESS light curves of V496 UMa. (a) and (b) show folded TESS light curve of V496 UMa. The black and red dots indicate a continuous observation period of approximately two months. (c) Power spectrum of V496 UMa. The highest amplitude frequency indicates the 91-min period.

In the text
thumbnail Fig. 3.

O − C variation of the main photometric hump in V496 UMa with respect to the ephemeris of Eq. (1), based on data from the OM on board XMM-Newton and on TESS. The inset shows the TESS residuals only.

In the text
thumbnail Fig. 4.

Cycle–Cycle Mod 2 diagram of V496 UMa for all high-cadence TESS data. Two consecutive cycles are drawn consecutively from the beginning. The color bar shows the flux density. The left panel shows data obtained in sector 15; the right panel shows data obtained in sector 16. All data were folded using the ephemeris given in Eq. (1). The wide white gaps in the two graphs show where TESS did not receive data.

In the text
thumbnail Fig. 5.

Diagram of hump 1 vs. hump 2. The average fluxes in the phase range 0.92–1.07 (hump 1) and 0.36–0.55 (hump 2) in each cycle were calculated. The average base corresponding between the 0.68–0.74 phase in each cycle was subtracted from the related humps. The red line shows the linear fit corresponding to the humps. The dashed line shows where the flux in both humps are equal.

In the text
thumbnail Fig. 6.

X-ray and optical light curves of V496 UMa obtained XMM-Newton. The top two panels show the light curves obtained in the 0.2−0.5 keV and 0.5−10 keV ranges with time bins of 50 s. The OM data in the lower panel have time bins of 10 s. In the upper panel, red (hump 1) and blue (hump 2) shaded regions identify the phase intervals used to extract the X-ray spectra of the two humps.

In the text
thumbnail Fig. 7.

Energy resolved X-ray light curves of V496 UMa. They were folded according to Eq. (1). The light curves were extracted using time bins of 50 s.

In the text
thumbnail Fig. 8.

X-ray spectrum of V496 UMa. The spectrum was extracted from the first bright humps and grouped with 25 counts per bin using TBABS(BB+MEKAL) spectral models. The reduced chi-square value is 1.15.

In the text
thumbnail Fig. 9.

X-ray spectrum of V496 UMa. The spectrum was extracted from the first two peaks of the second hump, which can be seen in the light curve in Fig. 6, and grouped with 25 counts per bin. The same models as applied to the first bright hump were used. The reduced chi-square value is 1.20.

In the text
thumbnail Fig. 10.

HR variation along the X-ray observation of V496 UMa. (a) Folded X-ray light curve of V496 UMa (0.2–0.5 keV). (b) Hardness Ratio variation of V496 UMa which corresponds to energy range between 0.5 and 2.5 keV and 2.5–10 keV. (c) shows the frequency of HR along the folded X-ray light curve.

In the text
thumbnail Fig. 11.

ZTF observations in time series with different passbands (left) and folded light curves of these time series according to Eq. (1) (right). The interval (dashed red box) in the upper left figure shows the time when TESS observations were made. The ZTF observations at this time are given by the red dots. The phase-folded figure on the right shows the location of these dots.

In the text
thumbnail Fig. 12.

The spectral energy distribution of V496 UMa. Upper panel: total spectral energy distribution of V496 UMa from the X-ray to the infrared region. White dwarf (0.8 M) (dark blue line) and main-sequence star (0.16 M) (light gray line) model spectra for 10 000 K and 3000 K, are shown combined with a red dashed line. The vertically plotted black arrow represents the amplitude of the high-state light curve in ZTF which derived from long-term g band light curve(16–18.6 mag) (see Fig. 11). Lower panel: points in the optical region and combined synthetic atmosphere models used to estimate the temperatures of the components.

In the text
thumbnail Fig. 13.

SDSS spectroscopy of V496 UMa. Upper panel: four SDSS spectra which covered phase intervals between ϕ1−4 = 0.635–1.338. Lower panel: wavelength region covering the Hβ and the HeII 4686 emission lines. Flux units are 10−17 erg cm−2 s−1 Å−1.

In the text
thumbnail Fig. 14.

Schematic view of the two-pole accreting WD. The big black circles show the photosphere of the WD. (a) Side view of the WD. The red line represents the orbital plane. The dashed blue line shows the observer’s line of sight. The magnetic accretion regions B1 (primary) and B2 (secondary) are almost diametrically opposed. (b) Top view, projection onto the orbital plane. ϕphot indicates photometric phase zero (center of the main hump). The phase is counted clockwise. ϕ1, and ϕ2, respectively represent the longitude range where the first and second column can be found on the WD surface in the XMM-Newton observations. The blue line indicates the phase ϕdip of the X-ray absorption dip.

In the text

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