11institutetext: Leibniz-Institut für Astrophysik Potsdam (AIP), An der
Sternwarte 16, 14482 Potsdam, Germany
11email<EMAIL_ADDRESS>22institutetext: Department of Astronomy & Space Sciences,
Faculty of Science, University of Ege, 35100 Bornova, Izmir, Turkey

#  XMM-Newton and TESS observations of the highly variable polar V496
UMa††thanks: Based on observations obtained with XMM-Newton, an ESA science
mission with instruments and contributions directly funded by ESA Member
States and NASA

Samet Ok 1122 Axel Schwope 11

(Received December 2021; accepted May 2022)

###### Abstract

Aims. We aim to study the temporal and spectral behaviour of V496 UMa from the
optical to the X-ray regimes.

Methods. We used archival XMM-Newton and TESS observations obtained in 2017
and 2019, respectively, to perform a spectral and timing analysis of the
highly variable polar.

Results. The light curves of both satellites, TESS and XMM-Newton, reveal a
double-humped pattern modulated with the periodicity of $91.058467\pm 0.00001$
minutes. V496 UMa displays a two-pole accretion geometry in the high accretion
state. X-ray spectra from both regions are composed of thermal plasma
radiation and soft blackbody components with almost identical temperatures and
total accretion rate of $\dot{M}=1.4(8)\times 10^{-11}$ M⊙ yr-1. The X-ray
centers of the humps show longitudinal shifts of $-18\degr$ and $4\degr$ and
$-172\degr$ and $-186\degr$ size around photometric phase zero, for the main
hump and second hump, respectively. The long-term ZTF light curves reveal high
and low accretions states. Low-state ZTF and SDSS photometric data are
consistent with an $0.8$ M⊙ white dwarf at 10000 K and a main-sequence donor
star with a spectral type of M5.0 at a Gaia-determined distance of 758 pc.

Conclusions. V496 UMa is a very bright polar in X-rays when it is in the high
state. Due to its unusual geometric structure, mass accretion onto the second
accretion pole is interrupted occasionally. This discontinuous behavior does
not follow a certain pattern in time and is observed so far only in the high
state. The X-ray light curves display clear evidence for an accretion stream
at the photometric phase of $\phi=$0.81, which does not show up in optical
light curves. An accurate period was derived using the combined TESS and XMM-
Newton data, which differs by 3.8 $\sigma$ from published results.

###### Key Words.:

cataclysmic variable stars – binary stars – x-rays – individual: V496 UMa –
stars: fundamental parameters

##  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 named 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 will go through a strong adiabatic shock at a
certain distance above the surface which heats the infalling plasma to several
10s 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 firstly identified as a CV by
Yecheistov et al. (2012) when the system changed brightness by $\sim$2 mag
from 18.41 mag to 16.43 mag within 30 minutes. 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 TESS,
the Transiting Exoplanet Survey Satellite (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, 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 ZTF observations
obtained between 2017 and 2021, respectively, when the system was in different
accretion states. We aim to further explore the thermal, temporal, and
geometric behavior of the object by analyzing the combined data set. In
Section 2 we give the details of the observations. Section 3 contains our
analysis and results. We conclude with a discussion of our results in Section
4.

Figure 1: (a)TESS light curve of V496 UMa obtained in 2019 with 2 min time
resolution. 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 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 24x96 degrees. Each
of the 2k x 2k CCDs on the satellite has a scale of 21 arcseconds 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 Aug 15, 2019, and Sep 12, 2019, and were
carried out in the high-cadence mode with a time resolution of two minutes. We
use 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 Telescopes111https://mast.stsci.edu.

Figure 2: (a) and (b) show folded TESS light curve of V496 UMa. Black and red
dots indicate a continuous observation period of approximately 2 months. (c)
Power spectrum of V496 UMa. The highest amplitude frequency indicates the
91-minute period.

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 $\sim$10 arcsec away from our source. The coordinates of these
objects obtained by Gaia DR3 (Gaia Collaboration et al., 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 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 et al., 2018). We
used the same aperture value for sectors 16 and 15 and thus left the bright
source with GaiaID 1565396007503248000 outside of the new aperture. The newly
extracted light curve comprising the observations obtained in the two sectors
is shown in Fig. 1.

###  2.2 Gaia Observations

In Gaia DR3 (Gaia Collaboration et al., 2021), V496 UMa has the ID
1565395908719728384 and the brightness is 17.27$\pm 0.03$, 17.31$\pm 0.09$,
and 16.86$\pm 0.08$ in the G, $G_{BP}$, and $G_{RP}$ passbands, respectively.
Gaia measured the parallax of V496 UMa as 1.307$\pm$0.060 mas. We used the
distance to the system of $758\pm 33$ pc, as determined by Bailer-Jones et al.
(2021).

###  2.3 ZTF Observations

We searched the Zwicky Transient Facility (Masci et al., 2019) database for
data from V496 UMa. V496 UMa has coverage of three years (see Sec. 3.3)
between March 2018 and June 2021. All data points were obtained with 30 sec
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, respectively.

###  2.4 X-ray Observation

The XMM-Newton observations of V496 UMa took place on 2017 March 12 (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 barycentre 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 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 Sec. 3.2.2).

One observation with the OM lasted 1200 s. A total of 10 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 10
seconds time bins (see Sec. 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).

To determine periodic changes in the light curve, we firstly computed a
Fourier transformation 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 square 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 lightcurves, and its arrival
times were used to derive an improved optical ephemeris. We fit these bright
humps with a Gaussian to obtain the times $T_{max}$ of their centers and their
errors. The same process was applied to the XMM-Newton Optical Monitor light
curve (see Fig. 6). Using both XMM-Newton/OM and TESS, a weighted linear
regression between the times $T_{max}$ and the cycle numbers were used to
derive

$BJD(T_{0,max})=2458711.45213(2)+0.0632350467(7)\times E$ (1)

where the numbers in parenthesis 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 transformation is larger than that from the linear
regression. We, therefore, accept the results from the linear regression as
our final timing solution.

The ephemeris given in Eq. 1 improves the previous period determination of
Littlefield et al. (2018) considerably. While the period they derive is
$0\aas@@fstack{d}06323520(4)$, our new value has a factor $\sim$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 $3.8\sigma$ (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.

Figure 3: The $O-C$ variation of the main photometric hump in V496 UMa with
respect to the ephemeris of Eq. 1 based on data from the OM onboard XMM-Newton
and on TESS. The inset shows the TESS residuals only.

We use our new ephemeris to create an epoch-phase diagram that shows all the
data obtained with TESS in a compact format in 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.

Fig. 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 would be affected more strongly than the first during those
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.

Fig. 5 shows the variation of both related humps in the same cycle, which
displays a linear relation. Also, this linear relationship is parallel to the
line where the flux of both 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 one and hump two is 1.89.

The linear relation nevertheless shows a large scatter, implying that the
distribution of matter onto the one or the other pole 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 a
single 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 occur. The hydrogen column density in the direction of the object
($N_{H}$) 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).

Figure 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 is obtained in sector 16. All data were folded using the
ephemeris given in Eq. 1. The wide white gaps in both graphs show where TESS
did not receive data.

Figure 5: Hump 1 vs. Hump 2 diagram. Average fluxes in the phase range of 0.92
- 1.07 (Hump 1) and 0.36 - 0.55 (Hump 2) in each cycle were calculated. The
average base corresponding between 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.

###  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 a second hump. The first hump
is a factor 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 already (after JD2458091.1) in the second full
photometric cycle, i.e. one cycle earlier than observed at X-ray wavelength.

Figure 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 sec. The OM data in the lower panel
have time bins of 10 s. In the upper panel, red (hump 1) and blue (hump 2)
filled shaded regions identify the phase intervals used to extract the X-ray
spectra of both humps.

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. It 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 $\phi$ = 0.81 with zero rates in all
covered binary cycles. The width of the dip is about $\Delta\phi$ = 0.037 (200
sec). 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.

Figure 7: Energy resolved X-ray light curves of V496 UMa. They were folded
according to the Eq. 1. The light curves were extracted using time bins of 50
seconds.

####  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 minutes 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 ${\mathrm{\chi}}^{2}$
statistics for model optimization.

Figure 8: X-ray spectrum of V496 UMa. The spectrum has been extracted from the
first bright humps and grouped with 25 counts per bin. We used TBABS(BB+MEKAL)
spectral models. The reduced chi-square value is 1.15.  Figure 9: X-ray
spectrum of V496 UMa. The spectrum has been 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. We used the same models that were applied to the first
bright hump. The reduced chi-square value is 1.20. Table 1: Spectral
parameters from humps: Spectral fit parameters, their uncertainties, fit
statistics, and model bolometric fluxes.

Model: TBABS(BBODY+MEKAL)
---
| First Hump | Second Hump
Parameters | EPIC-PN | EPIC-PN
$kT_{bb}$(eV) | $51^{+10}_{-9}$ | $43^{+10}_{-8}$
$kT_{mekal}$(keV) | $10.7^{+2.9}_{-2.0}$ | $9.8^{+4.7}_{-2.5}$
$\chi^{2}$(d.o.f) | 1.15(174/151) | 1.20(84/70)
Unabsorbed Fluxes |  |
$F_{0.5-2.5}(\mathrm{erg}\,\mathrm{cm}^{-2}\,\mathrm{s}^{-1})(10^{-12})$ | $1.50^{+0.05}_{-0.05}$ | $1.28^{+0.06}_{-0.06}$
$F_{2.5-10}(\mathrm{erg}\,\mathrm{cm}^{-2}\,\mathrm{s}^{-1})(10^{-12})$ | $2.6^{+0.2}_{-0.2}$ | $2.1^{+0.1}_{-0.1}$
$F_{bol}(\mathrm{erg}\,\mathrm{cm}^{-2}\,\mathrm{s}^{-1})(10^{-12})$ | $6.7^{+0.4}_{-0.4}$ | $7.3^{+0.4}_{-0.4}$
$F_{bb}(\mathrm{erg}\,\mathrm{cm}^{-2}\,\mathrm{s}^{-1})(10^{-12})$ | $1.2^{+0.8}_{-0.4}$ | $2.7^{+0.4}_{-0.3}$
$F_{mekal}(\mathrm{erg}\,\mathrm{cm}^{-2}\,\mathrm{s}^{-1})(10^{-12})$ | $5.4^{+0.4}_{-0.4}$ | $4.5^{+0.5}_{-0.5}$
$L_{x}(\mathrm{erg}\,\mathrm{cm}^{-2}\,\mathrm{s}^{-1})(10^{32})$ | $2.3(3)$ | $2.5(4)$

Figure 10: (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 - 2.5 keV and 2.5 - 10 keV. (c) shows the frequency of HR along the folded
X-ray light curve.

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, $N_{\rm H,gal}$
=1.23$\times 10^{20}$ atoms cm-2 (HI4PI Collaboration et al., 2016). The
combined simple model TBABS*MEKAL gave a bad fit to the data with a reduced
$\chi^{2}=2.14$ (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 model (BB) so that our new model is
TBABS(BB+MEKAL). The fit yielded a chi-square value of 174.35 for 151 degree
of freedom, $\chi_{\nu}^{2}=1.15$. The null hypothesis probability of
rejecting the model was 9%. We thus accepted this model for the first hump
(see Fig. 8).

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 degrees of freedom ($\chi^{2}$=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 degrees of freedom. Our
reduced $\chi^{2}$ value decreased to $\chi^{2}=1.19$. The probability of
rejecting the null hypothesis is 12%, and we thus accept the emission model
with a blackbody and a thermal component. The spectrum, the best-fit model and
the residuals are shown in Fig. 9.

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 constraint on the existence and
the parameters of possible Fe-line complex between 6.4 and 7 keV.

The spectral shapes and temperatures of both humps are very similar and
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 2 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 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 emphasize 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 $690^{+620}_{-300}$
km, that of the second hump with a radius $1450^{+1350}_{-430}$ 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 and
we do not speculate about possible reasons. However, taking at face value, the
implied sizes of the emission region are larger than those found e.g. in the
prototypical object AM Herculis (about 100 km, Schwope et al., 2020) but of
similar size as in the textbook object EF Eri ($<$ 570 km Beuermann et al.,
1987) and thus approximately as expected given the large uncertainties of the
derived values and on the heating processes in this object. For a discussion
of sizes of emission regions, see e.g. Hameury & King (1988).

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 of HR
for the whole X-ray observation. The only significant and repetitive feature
in the hardness ratio curve is a substantial increase in the dip before the
first bright hump at $\phi$=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 ($\phi$=0.81), we ran XSPEC models using the model parameter of
hump 1, adding an extra TBABS component. We found a dip $N_{H}$ of order
$1.6\times 10^{21}$ atoms cm-2.

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 independent 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 of 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.

Figure 11: The three figures from top to bottom on the left show the ZTF
observations in time series with different passbands. The figures on the right
side show that folded light curves of these time series according to Eq. 1.
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.  Figure 12: Upper panel: Total spectral energy distribution of V496 UMa
from the X-ray to the infrared region. White dwarf (0.8 $M_{\odot}$) (dark
blue line) and main-sequence star (0.16 $M_{\odot}$) (light gray line) model
spectra for 10000 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 g-band (16 - 18.6 mag). Lower panel: This graph focuses on
the points in the optical region and combined synthetic atmosphere models that
we use to estimate the temperatures of the components.

###  3.3 Spectral Energy Distribution

The spectral energy distribution (SED) of V496 UMa which was compiled using
data from XMM-Newton, the Large Binocular Telescope (LBT) (Littlefield et al.,
2018), the Zwicky Transient Facility (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 in the Spanish Virtual
Observatory222http://svo2.cab.inta-csic.es/theory/fps/ (SVO). For the WISE
observations, we used bands W1 and W2 only, because the W3 and W4 band data
are regarded as unreliable for targets as faint as V496 UMa (Wright et al.,
2010). Fig. 12 shows the spectral energy distribution generated from these
observation points.

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 analyzed by us 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 subcategorize the state of enhanced activity further.

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, $\sim 200-8000$ Å. We use the central wavelength and flux conversion
factors as given in the XMM-Newton online documentation333https://xmm-
tools.cosmos.esa.int/external/xmm_user_support/documentation/uhb/omfilters.html
to convert count rates to physical fluxes. The OM data seems to stay a bit
below the brightest fluxes from the ZTF but still indicates 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 online444Synthetic atmosphere data available at
http://svo2.cab.inta-csic.es/theory/newov2, 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 requesting that the
summed light of both model components shall not exceed the measured $r$-band
brightness.

To create the synthetic flux distribution, values for the free parameters, the
radius $R_{\rm wd}$ and the effective temperature, $T_{\mathrm{eff}}$, need to
be chosen. We used an 0.8 $M_{\odot}$ mass WD, which is assumed to be
representative of magnetic CVs (Pala et al., 2021, and references therein),
and estimate $R_{\rm wd}$ using the Nauenberg (1972) mass-radius relation. The
best matching temperature that we found to represent SED for this mass was
10000 K. Taking into account the error in the $u$ band magnitude, we estimate
the WD temperature to be in the range 8000 and 11000 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 10000${}^{+1000}_{-2000}$ and 3000${}^{+100}_{-250}$ K for the WD
and companion, respectively. The best-fitted model is given in the lower panel
of Figure 12 as 10000 K WD + 3000 K M5 and is shown with a red dashed line. On
a side note, we would like to emphasize that these temperatures represent the
upper limits for the components.

The WISE W1 and W2 band 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. Because of that, 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.
Fig. 11 shows this interval in g-band observations when the source varied
between 16.83 - 17.65, i.e. 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 28-JAN-2018. The mean spectral flux density is about
3.0$\times$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 sec exposure
time. In Fig. 13, these are shown separately. We calculated the phase
intervals covered by the four spectra with Eq. 1. The phase intervals are
$\phi_{\rm 1}=0.635-0.799$, $\phi_{\rm 2}=0.814-0.978$, $\phi_{\rm
3}=0.993-1.158$, and $\phi_{\rm 4}=0.173-0.338$, respectively. 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 lot 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.

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
correct the observed spectra by a factor of 2. The spectrum at phase
$\phi=0.99$ 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 bright
(first bright hump) and faint phase was regarded as the cyclotron spectrum
proper and integrated. One may assume to have sampled a good fraction of the
total cyclotron spectrum, which stretches further into the unobserved
neighboring wavelength regions. By integrating the spectrum, we calculated the
cyclotron flux as a $F_{\rm cyc}\sim 2.8\times 10^{-12}$ ergs cm2 s-1 with a
considerable but difficult to specify uncertainty. The $F_{\rm cyc}$ flux that
we have obtained here is almost a factor 2 above the blackbody flux $F_{\rm
bb}$ 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 ($L_{\rm
acc}\sim L_{\rm x}+L_{\rm cyc}$). However, one needs 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 $L_{\rm cyc}=\pi F_{\rm
cyc}D^{2}$ to get $L_{\rm cyc}=4.8(2)\times 10^{31}$ erg s-1) at a distance of
758 pc. The bolometric X-ray luminosity which we obtained from the first hump
is $L_{\rm x}=2.3(3)\times 10^{32}$ erg s-1 so that the accretion luminosity
from the first hump becomes $L_{\rm acc}=7.1(5)\times 10^{32}$ erg s-1.

We found the mass accretion rate ($\dot{M}=L_{\rm acc}R_{\rm wd}/M_{\rm wd}G$)
in the high state of the V496 UMa for the first bright hump as $\dot{M}_{\rm
hump1}=$ $7.4(3)\times 10^{-12}$ $M_{\odot}$ yr-1. We used the same method for
the second hump. The X-ray luminosity for second hump is $L_{\rm
x}=2.5(4)\times 10^{32}$ erg s-1 and the estimated cyclotron flux $L_{\rm
cyc}=2.9(2)\times 10^{31}$ erg s-1 which estimated from 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 as $\dot{M}_{\rm
hump2}=6.8(5)\times 10^{-12}$ $M_{\odot}$ yr-1. Finally, the total accretion
rate at the time of the XMM-Newton observation was $\dot{M}_{\rm
tot}=\dot{M}_{\rm hump2}+\dot{M}_{\rm hump1}=1.4(8)\times 10^{-11}$ M⊙ yr-1.

Figure 13: The upper panel shows four SDSS spectra which covered between
$\phi_{\rm 1-4}$=0.635 - 1.338 phase intervals. The lower panel shows the
wavelength region, which covers the H$\beta$ and the HeII 4686 emission lines.
Flux units are 10-17 erg cm-2 s-1 Å-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, 5 data points) has centroids at phases $\phi_{\rm
phot}=0.949,0.982,0.956,1.012,$ and 0.995, respectively. 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 $\phi_{phot}=0.0$) between
$-18\degr$ and $+4\degr$ and the second hump between $172\degr$ to $186\degr$.
In sum, the two regions are separated by about 0.5 phase units. This is
particularly interesting because both 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 $\sim$0.9, when
the line-of-sight crosses the accretion stream.

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

In other polars such a dip occurs between binary phases $\sim$0.93 and
$\sim$0.8 (Worpel & Schwope, 2015, V808 Aur, ; Schwope et al., 2020, AM Her,
). If this applies to V496 UMa, we may expect the orbital phase of hump1
between phases 0.0 and 0.12. Hence, the spot faces the donor star directly or
trailing the donor in phase by almost 45°. In any 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
$\sim 0.5-0.6$.

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-eclipse (or alternatively
their visibility) individually because of apparent phases of visibility of
both 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 visibility of $\Delta\phi\simeq 0.55$, i.e. the first region lies above
the orbital plane (’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 is a southern region, i.e. 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.

Figure 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.
$\phi_{phot}$ indicates photometric phase zero (center of the main hump).
Phase is counted clockwise. $\phi_{1}$, $\phi^{{}^{\prime}}_{1}$ and
$\phi_{2}$, $\phi^{{}^{\prime}}_{2}$ represent the longitude range where the
first and second column can be found on the WD surface in the XMM-Newton
observations, respectively. The blue line indicates the phase, $\phi_{dip}$,
of the X-ray absorption dip.

##  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 3.8$\sigma$ 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, an instrumental or a systematic error).

Also, the X-ray light curve is double-humped and shows a pronounced dip. Our
analysis revealed that the dip at photometric phase $\phi_{\rm phot}=0.81$ 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
which 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 which 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 $\Delta\phi$=0.13 to
0.19. Such a 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 further ahead in phase by up to $\sim$0.1
phase units. Humps are mobile in the light curve, and the hump centers show
some phase, 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 both 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
shirt-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 the 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 black body ($kT_{\rm bb}$) temperature in polars spread
between 5 - 30 eV (Kuulkers et al., 2010). V496 UMa has a hotter $kT_{\rm bb}$
($\sim$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, 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 ($\approx 5\times 10^{32}$) lies
upper energy limits which 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 with a typically 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 (Schwope & Beuermann, 1997, UZ For, ;
Campbell et al., 2008a, AM Her, ; Campbell et al., 2008b, VV Pup, ). 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 ($\beta<i$). 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 $\phi_{phot}\sim 0.1$. 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 spectral energy distribution.
Significantly, the reference of optical data points, with the distance from
Gaia, the SED tells us the upper-temperature limit of the white dwarf can be
in the range of 11000 - 9000 K with the mass of 0.8 $M_{\odot}$. It would be
possible to obtain similar SED distribution 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 $M_{\odot}$ white dwarf and the
temperature of 10000 K, represented quite well the spectral energy
distribution 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 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 be 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.

———————————————

###### Acknowledgements.

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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# Enhanced optical properties of MoSe2 grown by molecular beam epitaxy on
hexagonal boron nitride

C. Vergnaud  Univ. Grenoble Alpes, CEA, CNRS, Grenoble INP, IRIG-Spintec,
38000 Grenoble, France  V. Tiwari  Univ. Toulouse, INSA-CNRS-UPS, LPCNO, 31077
Toulouse, France  L. Ren  Univ. Toulouse, INSA-CNRS-UPS, LPCNO, 31077
Toulouse, France  T. Taniguchi  National Institute for Materials Science,
Tsukuba 305-0047, Ibaraki, Japan  K. Watanabe  National Institute for
Materials Science, Tsukuba 305-0047, Ibaraki, Japan  H. Okuno  Univ. Grenoble
Alpes, CEA, IRIG-MEM, 38000 Grenoble, France  I. Gomes de Moraes  Univ.
Grenoble Alpes, CEA, CNRS, Grenoble INP, IRIG-Spintec, 38000 Grenoble, France
A. Marty  Univ. Grenoble Alpes, CEA, CNRS, Grenoble INP, IRIG-Spintec, 38000
Grenoble, France  C. Robert  Univ. Toulouse, INSA-CNRS-UPS, LPCNO, 31077
Toulouse, France  X. Marie  Univ. Toulouse, INSA-CNRS-UPS, LPCNO, 31077
Toulouse, France  M. Jamet  Univ. Grenoble Alpes, CEA, CNRS, Grenoble INP,
IRIG-Spintec, 38000 Grenoble, France<EMAIL_ADDRESS>
###### Abstract

Transition metal dichalcogenides (TMD) like MoSe2 exhibit remarkable optical
properties such as intense photoluminescence (PL) in the monolayer form. To
date, narrow-linewidth PL is only achieved in micrometer-sized exfoliated TMD
flakes encapsulated in hexagonal boron nitride (hBN). In this work, we develop
a growth strategy to prepare monolayer MoSe2 on hBN flakes by molecular beam
epitaxy in the van der Waals regime. It constitutes the first step towards the
development of large area single crystalline TMDs encapsulated in hBN for
potential integration in electronic or opto-electronic devices. For this
purpose, we define a two-step growth strategy to achieve monolayer-thick MoSe2
grains on hBN flakes. The high quality of MoSe2 allows us to detect very
narrow PL linewidth down to 5.5 meV at 13 K, comparable to the one of
encapsulated exfoliated MoSe2 flakes. Moreover, sizeable PL can be detected at
room temperature as well as clear reflectivity signatures of A, B and charged
excitons.

††preprint: AIP/123-QED

Hexagonal boron nitride (hBN) has been identified as a key material to
encapsulate 2D materials and enhance their electronic properties such as
carrier mobility Mayorov  _et al._ (2011) or photoluminescence (PL) Cadiz  _et
al._ (2017). Moreover, for its flatness, inertness and large bandgap, hBN
constitutes an ideal substrate for the van der Waals epitaxy of other 2D
materials like transition metal dichalcogenides (TMD) of general formula MX2
with M=Mo, W and X=S, Se. It also exhibits a 3-fold symmetry matching the one
of TMDs in the 2H phase, which could prevent the formation of twin domains and
boundaries to reach high quality TMD monolayers. Previous works reported the
molecular beam epitaxy (MBE) growth of MoSe2 monolayers on hBN flakes
exfoliated from the bulk crystal Poh  _et al._ (2018); Pacuski  _et al._
(2020). In Ref.3, Poh et al. have grown MoSe2 monolayer on hBN at two
different temperatures 250°C and 500°C, at deposition rates of 0.6 and 1.3
ML/h respectively while keeping a constant Se:Mo ratio of 20. They found that
the film grown at 500°C exhibit highly oriented large grains that coalesced to
form continuous film. They could measure the photoluminescence at room
temperature showing the neutral exciton line with a full width at half maximum
(FWHM) of $\approx$60 meV at room temperature. In Ref.4, Pacuski et al. have
shown very narrow photoluminescence lines of MBE grown MoSe2 monolayer (6.6
meV for the neutral exciton line at 10 K) demonstrating the ability of MBE to
synthesize high quality TMD monolayers with electronic properties comparable
to or even better than that of exfoliated TMD flakes. In this work, the
authors proceeded in multi-steps alternating growths at 300°C to favor
nucleation and annealings at 750°C to improve the crystal quality and clean
the surface from the second layer. The Se:Mo ratio was between 100 and 1000.
Here, we adopted another growth strategy. The full growth of one MoSe2 layer
on exfoliated hBN flakes was achieved at high temperature (800°C) in order to
target both high crystalline quality and a limited formation of bilayers.
However, due to the ultralow surface energy of hBN, the nucleation rate is
negligible at such high temperature. To circumvent this issue, we optimized
the nucleation step at 300°C with a low deposition rate. By this, we obtained
a reasonable density of monolayer-thick nuclei at the hBN surface and we could
proceed with the growth of the MoSe2 monolayer at 800°C at very low deposition
rate. We obtained neutral exciton photoluminescence linewidths of the order of
5.5 meV at 13 K, comparable to the one obtained in Ref.4 as well as clear
signature of A, B and charged excitons in the reflectivity spectrum. Finally,
we detected a sizeable photoluminescence signal at room temperature comparable
to the one of mechanically exfoliated flakes with a FWHM of the order of 40
meV Cadiz  _et al._ (2017). This work demonstrates the potential of MBE to
grow high quality TMD monolayers on large areas constituting model systems to
further study optically proximity effects.

The sample preparation starts with the mechanical exfoliation of hBN flakes
from high quality crystals (NIMS Tsukuba) using a dry-stamping technique
Castellanos-Gomez  _et al._ (2014) onto a 4$\times$4 mm SiO2(90nm)/Si
substrate. The surface is covered with tens of hBN flakes in average with
varying thickness (few nm up to 100 nm) and size (few $\mu$m up to 200
$\mu$m). Prior to the growth, the substrate is heated in ultrahigh vacuum
(UHV) at 800°C during one hour to desorb all the contaminations from the
surface, in particular the organic ones left by the mechanical exfoliation
process. The base pressure in the molecular beam epitaxy reactor is in the low
10-10 mbar range. Molybdenum is evaporated using an electron gun. The
deposition rate of Mo controlled by a quartz balance monitor is kept in the
0.0025-0.005 Å/s range. The Se partial pressure (measured at the sample
position thanks to a retractable gauge) is 10-6 mbar giving a Se:Mo ratio in
the 20-40 range. Considering this large Se:Mo ratio and the volatile character
of Se, the deposition rate of Mo mostly determines the deposition rate of
MoSe2. The deposited MoSe2 films grown at low temperature ($<$800°C) are
systematically annealed at 800°C under Se flux (at 10-6 mbar) to improve the
crystalline quality. The deposition temperature is varied between 200°C and
800°C. After the MBE growth, a second hBN layer (top hBN, a few nm thick) is
transferred on top of the structure by repeating the dry-stamping exfoliation
technique. Tens of samples of encapsulated MoSe2 monolayers have been
fabricated and their properties were investigated by optical spectroscopy.
Photoluminescence (PL) and differential reflectivity measurements were
performed in a home built micro-spectroscopy set-up around a closed-cycle, low
vibration attoDry cryostat with a temperature controller (T = 4–300 K). For
PL, a HeNe laser ($\lambda$=633 nm) was used for excitation with a typical
power of 30 $\mu$W and integration time of 30 seconds. The white light source
for reflectivity measurements is a halogen lamp with a stabilized power
supply. The emitted and/or reflected light was dispersed in a spectrometer and
detected by a Si-CCD camera. The excitation spot diameter is of the order of 1
$\mu$m.

We first calibrate the MoSe2 deposition rate on graphene/SiC since we
thoroughly studied this system in previous works Khalil  _et al._ (2022);
Alvarez  _et al._ (2018); Quang  _et al._ (2018); Dau  _et al._ (2018). In
this case, the deposition temperature was 300°C followed by in situ annealing
during 15 minutes at 800°C under Se flux. The Mo deposition rate is 0.005 Å/s
and the Se partial pressure 10-6 mbar. The completion of one monolayer of
MoSe2 (1 MLGr) with 100% coverage corresponds to an equivalent Mo thickness of
2.8 Å. Using the exact same growth conditions on hBN flakes, we obtain the
layer morphology shown in Fig. 1a (resp. Fig. 1b-c) for 1 MLGr on SiO2 (resp.
hBN).

Figure 1: Atomic force microscopy (AFM) image of 1 MLGr deposited on (a) SiO2
and (b),(c) on hBN. (d) AFM image of 4.5 MLGr deposited on hBN. The inset in
(c) shows the height profile along the blue line, 0.7 nm corresponds to 1 ML
of MoSe2 on hBN including the thickness of the MoSe2 triatomic layer and the
vdW gap between MoSe2 and hBN.

On SiO2, we find 100 % coverage as expected with very small MoSe2 grains with
diameters ranging from 10 to 20 nm. However, the coverage on hBN flakes is
only $\approx$42 % with monolayer MoSe2 grains of $\approx$170 nm in diameter.
A small fraction of second layer can also be observed in Fig. 1c on top of the
monolayer grains. Taking into account the first and second layers, the total
amount of deposited MoSe2 on hBN flakes as measured by AFM is only
$\approx$0.55 MLGr. Hence, the sticking coefficient of MoSe2 monomers (if the
reaction between Mo and Se atoms occurs in the gas phase) and/or the residence
time of MoSe2 monomers on hBN are clearly less than on graphene and SiO2.
Moreover, the low nucleation density demonstrates the much higher monomers
mobility on hBN than on graphene or SiO2. In order to reach 100 % coverage, we
deposited 4.5 MLGr as shown in Fig. 1d. In this case, MoSe2 grains coalesce
but they are 5 monolayers thick and exhibit a "pyramid" like shape. Based on
this result, we then vary the growth temperature Tg with the objective to
obtain 100 % coverage of monolayer MoSe2. First, in order to improve the
coverage, we lowered Tg from 300°C down to 200°C keeping the same Mo
deposition rate and Se flux to increase the nucleation density. However, as
shown in the inset of Fig. 2a, as-grown MoSe2 grains exhibit highly dendritic
shape which is detrimental to reach 100 % coverage. Annealing up to 800°C does
not change drastically the dendritic shape of the grains. In comparison, as
grown grains at 300°C show a compact shape in Fig. 2a. We thus consider that
Tg=300°C is the minimum growth temperature to obtain compact MoSe2 grains.

Figure 2: (a) AFM image of 2.25 MLGr MoSe2 deposited on hBN at 300°C. The
inset shows the same deposition but at 200°C. (b) AFM image of the sample in
(a) annealed at 800°C during 15 minutes.

The second objective is to stabilize a single layer of MoSe2 on hBN to study
optical properties (only monolayer exhibits direct bandgap). Starting from
Tg=300°C, we first study the effect of annealing to suppress the second and
third MoSe2 layers in Fig. 2a. The result is shown in Fig. 2b: annealing only
smoothens the grain edges thanks to higher monomer mobility but the second and
third MoSe2 layers remain on top of the grains. The second strategy consists
then to increase Tg to avoid the formation of multilayers during the growth.
However, when increasing the growth temperature above 400°C, the nucleation
density decreases down to zero and hBN flakes are no more covered with MoSe2
after depositing 1 MLGr (not shown). Finally, we followed a two-step method
consisting in depositing 1 ML-thick compact MoSe2 grains at 300°C (nucleation
step) and growing the rest of the film up to 1 ML MoSe2 at higher temperature
to avoid the formation of multilayers (growth step). For this purpose, we
carried out a thorough study of MoSe2 nucleation at Tg=300°C varying the
content of deposited MoSe2 in MLGr as shown in Fig. 3. It should be noted that
all the samples of Fig. 3 were grown at 300°C and annealed at 800°C during 15
minutes to smoothen the grain edges.

Figure 3: AFM images of (a) 0.5 MLGr; (b) 1.125 MLGr; (c) 1.4 MLGr and 2.25
MLGr MoSe2 deposited on hBN at 300°C. (e) Average grain diameter as a function
of the deposited thickness in MLGr extracted from AFM images in (a-d). Based
on the observed grain thickness, the graph has been divided into three zones
with arbitrary boundaries for 1 ML-thick; 2 ML-thick and 3 ML-thick MoSe2
grains.

Increasing the total amount of deposited MoSe2 up to 2 MLGr in Fig. 3a-d
clearly increases the thickness of the grains from 1 to 3 ML as plotted in
Fig. 3e. We conclude that a deposited thickness less than $\approx$0.7 MLGr is
necessary to obtain monolayer thick grains even though their density is very
low (2 per 500$\times$500 nm2 in Fig. 3a). To ensure monolayer thick MoSe2
grains, we first deposited 0.1 MLGr of MoSe2 at 300°C and study the effect of
growth temperature Tg on the grain thickness and morphology in Fig. 4.

Figure 4: (a), (b) AFM images of 6.1 MLGr MoSe2 grown at 600°C on hBN. (c),
(d) AFM images of 6.5 MLGr MoSe2 grown at 750°C on hBN. (e) FWHM of the A1g
Raman peak of MoSe2 as a function of growth temperature. (f) Raman A1g peak of
MoSe2 grown at 800°C.

The results are shown in Fig. 4a-b (resp. Fig. 4c-d) for Tg=600°C (resp.
750°C). Considering the very low sticking coefficient and/or residence time of
MoSe2 monomers at the hBN surface at these temperatures, we deposited thicker
films of 6.1 MLGr at 600°C and 6.5 MLGr at 750°C respectively. For Tg=600°C
(resp. 750°C), the grains exhibit an average thickness of 5 ML (resp. 4 ML).
In order to still reduce the grain thickness down to 1 ML, we selected the
highest growth temperature of 800°C. The first remarkable observation is the
sharp decrease of the Raman A1g peak full width at half maximum (FWHM) above
Tg=600°C down to $\approx$1.1 cm-1 for Tg=800°C as shown in Fig. 4e-f. It
demonstrates the superior crystalline quality of MoSe2 grains grown at 800°C
on hBN flakes. The results for Tg=800°C are summarized in Fig. 5.

Figure 5: (a) AFM images of 12 MLGr deposited on hBN at 800°C during 1.5 hours
after a nucleation step of 0.1 MLGr at 300°C (sample 1). (b) Height profile
along the blue line in (a) demonstrating the monolayer thickness of the MoSe2
grain. (c) Same MoSe2 deposition but imaged on a second hBN flake. (d) AFM
image of 24 MLGr deposited on hBN at 800°C during 3 hours after a nucleation
step of 0.2 MLGr at 300°C (sample 2). (e-h) AFM images of 3.5 MLGr deposited
on different hBN flakes at 800°C during 55 minutes after a nucleation step of
0.7 MLGr at 300°C. The insets are optical images of the hBN flakes.

The AFM image of Fig. 5a-c (resp. Fig. 5d) corresponds to sample 1 (resp.
sample 2). In sample 1 (resp. sample 2), MoSe2 was deposited during 1.5 hour
(resp. 3 hours) corresponding to a total thickness of 12 MLGr (resp. 24 MLGr)
after 0.1 MLGr (resp. 0.2 MLGr) nucleation step. The growth step was carried
out at Tg=800°C with a Mo deposition rate of 0.0025 Å/s and a Se flux of 10-6
mbar. In Fig. 5a and 5d, we observe 500 nm and 1 $\mu$m large monolayer thick
MoSe2 grains on hBN flakes. They are covered with clusters (bright spots) and
lines of height 8 nm and 1 nm respectively which most probably correspond to
Mo-rich nanostructures forming due to the low Se:Mo atomic ratio at the
surface of hBN flakes at 800°C. However, we could not decrease (resp.
increase) the Mo deposition rate (resp. Se flux) any further with our setup.
Averaging over larger areas, the coverage is $\approx$5 % for sample 1 and
$\approx$10 % for sample 2 meaning that the full coverage with 1 ML thick
MoSe2 would take approximately 30 hours. In Fig. 5c, we show the AFM image of
a second flake of sample 1 where the coverage is clearly higher with the
coexistence of MoSe2 mono- and bilayers along with Mo-rich nanoclusters and
nanowires. This illustrates the coverage and thickness dispersion observed
from flake to flake. At this stage, we can only speculate that this is due to
the hBN flake surface quality in terms of point defects or steps. Fig. 5e-h
illustrate the effect of increasing the deposited thickness at the nucleation
step to 0.7 MLGr corresponding to the 1 ML-2 ML thickness transition in the
graph of Fig. 3e as well as the dispersion of coverage from flake to flake.
The MoSe2 grain thickness varies from 1 to 3 ML and the coverage from
$\approx$34 % to almost 100 %. In summary, ultralow thickness at the
nucleation step (0.1-0.2 MLGr) and high temperature growth of 800°C are
necessary to stabilize monolayer thick MoSe2 grains on hBN flakes. In the
following, we study the optical properties of the samples grown in these
conditions.

Figure 6: (a) Photoluminescence spectra at T=13 K of hBN/MoSe2/hBN in sample 2
recorded at two different positions in red and black of the hBN flake shown in
(b). (c) Photoluminescence spectra at T=300 K of hBN/MoSe2/hBN in sample 1
recorded at two different positions in red and black of the hBN flake shown in
(d). (e) PL spectrum recorded at T=5 K on hBN/MoSe2/hBN (shown in (f)) for 1
MLGr of MoSe2 grown at 300°C and annealed at 800°C. (g) FWHM of PL spectra as
a function of temperature for three different samples: sample 2 corresponding
to hBN encapsulated MoSe2 grown at 800°C (blue) on two different hBN flakes
and different laser spot positions, hBN encapsulated MoSe2 grown at 300°C and
annealed at 800°C (red) and MoSe2 directly grown on SiO2/Si Vergnaud  _et al._
(2019) (green). (h) Differential reflectivity of hBN/MoSe2/hBN in sample 1
(shown in (d)) recorded at T=5 K. Inset: corresponding photoluminescence
spectrum.

Fig. 6a presents the photoluminescence spectrum for a hBN/MoSe2/hBN structure
at T=13 K. It evidences clearly two peaks corresponding respectively to the
recombination of neutral exciton (X0) and charged exciton (XT), in agreement
with previous results Cadiz  _et al._ (2017); Ajayi  _et al._ (2017).
Remarkably the neutral exciton PL shows a narrow linewidth. The Full Width at
Half Maximum (FWHM) of the neutral exciton line is $\approx$5.5 meV,
demonstrating the high quality of the structure. Although a little larger,
this line width is comparable with that obtained with hBN encapsulated MoSe2
monolayer obtained by mechanical exfoliation Rogers  _et al._ (2020); Zhou
_et al._ (2020). The PL spectra do not change much for different points of the
sample (see two typical points in Fig. 6a). This demonstrates the good growth
homogeneity on this hBN flake. Note that the slight change of the PL peak of
the neutral and charged exciton observed in Fig. 6a also occurs in exfoliated
samples (probably induced by small local strain variations). Using the same
excitation conditions, ML MoSe2 flakes exfoliated from the bulk crystal
exhibit almost two orders of magnitude larger PL intensity. However, as shown
in Fig. 5, the monolayer coverage is very low in our samples, of the order of
few percents, which can partly explain this difference in PL intensity. In
Fig. 6c, a reasonable PL intensity at room temperature is obtained and shown
at two different positions on the hBN flake. The FWHM is typically 40 meV. For
comparison, we show in Fig. 6e the PL spectrum at T=5 K of hBN encapsulated
MoSe2 grown at 300°C and annealed at 800°C corresponding to the sample of Fig.
3b. This spectrum was recorded with a laser energy of 100 $\mu$W and an
integration time of 60 seconds. The PL spectrum FWHM for the neutral exciton
is $\approx$20 meV demonstrating that growth at high temperature greatly
narrows the PL spectrum following the same trend as the FWHM of the A1g Raman
peak in Fig. 4e. PL spectra FWHM as a function of temperature for three
different samples are shown in Fig. 6g. For hBN encapsulated MoSe2 grown at
800°C (in blue), the FWHM varies from 5.5 meV at 13 K to 40 meV at room
temperature. For hBN encapsulated MoSe2 grown at 300°C and annealed at 800°C
(in red), the FWHM varies from 20 meV at 5 K to 70 meV at 250 K. Finally, for
non-encapsulated MoSe2 monolayer directly grown on SiO2/Si Vergnaud  _et al._
(2019) (in green), the PL FWHM varies from 45 meV at 5 K to 80 meV at room
temperature. We can conclude that high temperature growth on hBN flakes
drastically improves the optical properties of MoSe2. Fig. 6h displays the
differential reflectivity spectrum of a sample grown at high temperature. The
peaks corresponding to the absorption of A and B neutral exciton are observed
together with the absorption of the charged exciton at lower energy
(oscillation below 1.65 eV). The PL peaks of both the neutral and charged
exciton are shown in the inset. This confirms that the MoSe2 monolayer is
doped.

In summary, we studied the growth of MoSe2 on hBN flakes by van der Waals
epitaxy in order to obtain monolayer coverage and intense and narrow-linewidth
photoluminescence. We found a PL FWHM of 5.5 meV at 13 K and 40 meV at 300 K
for the neutral exciton line. These results represent an improvement compared
to previous works by MBE. MoSe2 grown by MBE at low temperature (300°C-500°C)
shows PL FWHM of 6.6 meV at 10 K (Ref. 4) and 60 meV at 300 K (Ref. 3). The
linewidth is comparable to the one of MoS2 grown by chemical vapor deposition
with a PL FWHM of 5 meV at 4 K (Ref. 14) but still remains a factor two larger
than the one of exfoliated MoSe2 flakes encapsulated in hBN ($\approx$2 meV at
4 K in Refs. 2; 11). To obtain these results, we had to address two main
constraints. First, the very low sticking coefficient and/or residence time of
MoSe2 monomers at the surface of hBN flakes during the growth leads to very
low or even zero nucleation density. To circumvent this issue, we
systematically started with a nucleation step at low substrate temperature to
obtain monolayer-thick MoSe2 grains. Second, the growth mainly proceeds in a
multilayer mode at low and medium substrate temperatures. In order to limit
the formation of MoSe2 bilayers, we thus carried out the growth step at very
high temperature (800°C). Following this two-step method, we achieved the
growth of high quality MoSe2 monolayers with partial coverage exhibiting
narrow-linewidth photoluminescence spectra at low temperature and sizeable
signal at room temperature. We also demonstrated clear A and B neutral exciton
and charged exciton signatures in reflectivity measurements at low
temperature. This work demonstrates that molecular beam epitaxy in the van der
Waals regime of TMDs on hBN provides high quality crystals comparable to
exfoliated ones over large areas. It paves the way for the study of proximity
effects in large area and high crystalline quality van der Waals
heterostructures.

The authors acknowledge the support from the European Union’s Horizon 2020
research and innovation Programme under grant agreement No 881603 (Graphene
Flagship), No 829061 (FET-OPEN NANOPOLY) and No 101079179 (DYNASTY). The
French National Research Agency (ANR) is acknowledged for its support through
the ANR-18-CE24-0007 MAGICVALLEY and ESR/EQUIPEX+ ANR-21-ESRE-0025 2D-MAG
projects. The LANEF framework (No. ANR-10-LABX-0051) is acknowledged for its
support through the project 2DMAT.

## Data Availability Statement

The data that support the findings of this study are available from the
corresponding author upon reasonable request.

## References

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