# First characterization of a new High Mass X-ray Binary in LMC eRASSU
J050810.4$-$660653 with SRG/ART-XC, NuSTAR and Swift

Alexander Salganik,1,2 Sergey S. Tsygankov,3,2 Alexander A. Lutovinov,2
Alexander A. Mushtukov,4,5 Ilya A. Mereminskiy,2 Sergey V. Molkov,2 Andrei N.
Semena2
1Department of Astronomy, Saint Petersburg State University, Saint-Petersburg
198504, Russia
2Space Research Institute of the Russian Academy of Sciences, Profsoyuznaya
Str. 84/32, Moscow 117997, Russia
3Department of Physics and Astronomy, FI-20014 University of Turku, Finland
4 Astrophysics, Department of Physics, University of Oxford, Denys Wilkinson
Building, Keble Road, Oxford OX1 3RH, UK
5 Leiden Observatory, Leiden University, NL-2300RA, Leiden, The Netherlands
E-mail<EMAIL_ADDRESS>
(Accepted 2022 June 7. Received 2022 May 23; in original form 2022 February
26)

###### Abstract

We report results of the first detailed spectral and temporal studies of the
recently discovered Be/X-ray binary eRASSU J050810.4$-$660653 in LMC based on
the data from the SRG/ART-XC, NuSTAR and Swift/XRT instruments obtained in
December 2021 - May 2022 in a wide energy range of 0.5-79 keV. Pulsations with
the period of $40.5781\pm 0.0004$ s were found in the source light curve with
the pulsed fraction monotonically increasing with the energy. An estimate of
the orbital period of $\sim 38$ days was obtained based on the long-term
monitoring of the system. The source spectrum can be well approximated with a
power-law model modified by an exponential cutoff at high energies. The pulse
phase-resolved spectroscopy shows a strong variation of spectral parameters
depending on the phase of a neutron star rotation. We have not found any
features connected with the cyclotron absorption line both in the phase-
averaged and phase-resolved spectra of eRASSU J050810.4$-$660653\. However,
the neutron star magnetic field was estimated around several $10^{13}$ G using
different indirect methods. Discovered variations of the hardness ratio over
the pulse phase is discussed in terms of physical and geometrical properties
of the emitting region.

###### keywords:

accretion, accretion discs – pulsars: general – scattering – stars: magnetic
field – stars: neutron – X-rays: binaries.

††pubyear: 2022††pagerange: First characterization of a new High Mass X-ray
Binary in LMC eRASSU J050810.4$-$660653 with SRG/ART-XC, NuSTAR and
Swift–References

##  1 Introduction

On December 8, 2019 the eROSITA telescope on board the Spektrum-Roentgen-Gamma
(SRG) mission discovered a new X-ray source eRASSU J050810.4$-$660653 in the
Large Magellanic Cloud (LMC) (Haberl et al., 2020). The source was localized
at RA $=05^{\rm h}08^{\rm m}10\aas@@fstack{s}4$, Dec. $=-66\degr 06\arcmin
53\arcsec$ with an error radius of 5.1 arcsec. The source spectrum was
described by an absorbed power law with the photon index of $\Gamma\sim 1.2$
and column density of $N_{\rm H}\sim 2.1\times 10^{21}~{}\text{cm}^{-2}$ with
the flux of $3.4\times 10^{-12}$ erg s-1 cm-2 in the 0.2-10.0 keV energy band.
The source position was consistent with that of an early-type star, making
eRASSU J050810.4$-$660653 a High Mass X-ray Binary (HMXB). An optical
spectroscopy with Southern African Large Telescope (SALT) revealed single-
peaked H$\alpha$ emission line, which was found to dominate the spectrum,
indicating a Be/X-ray binary nature of the system (Haberl et al., 2020). On
March 29 and April 1, 2020 the source was observed by the XRT telescope
onboard of the Neil Gehrels Swift observatory. The measured flux of $(1.6\pm
0.3)\times 10^{-12}$ erg s-1 cm-2 (0.2-10.0 keV) turned out to be only two
times less than measured by eROSITA four month before (Haberl et al., 2020).

SRG/eROSITA observed the source again in December 2020 during the second all-
sky survey and XMM-Newton TOO observations was triggered and performed on
December 17, 2020 (Haberl et al., 2021). The power spectrum based on the EPIC-
PN detector data revealed strong X-ray pulsations with a period of 40.60254(8)
s. A detailed study of the source behaviour in the low-luminosity state based
on the XMM-Newton and SRG/eROSITA data is presented in a separate paper by
Haberl et al. (in preparation).

One year later, on December 14-15, 2021 an enhanced X-ray activity from eRASSU
J050810.4$-$660653 was detected with the Mikhail Pavlinsky ART-XC telescope on
board the SRG observatory in the harder X-ray band. The preliminary estimated
source flux of $\sim$2 mCrab ($3\times 10^{-11}$ erg s-1 cm-2) in the 4-12 keV
energy range corresponds to the luminosity of about $10^{37}$erg s-1 at the
LMC distance (Haberl et al., 2021). Follow-up NuSTAR TOO observations
confirmed the presence of the pulsations in the eRASSU J050810.4$-$660653
light curve, making it a new X-ray pulsar (XRP) in HMXB.

In this paper, we provide a detailed analysis of the spectral and temporal
properties of the eRASSU J050810.4$-$660653 based on the SRG/ART-XC, Swift/XRT
and NuSTAR data obtained during the December 2021 - January 2022 monitoring
campaign.

##  2 Data analysis

###  2.1 NuSTAR observatory

NuSTAR consists of two identical co-aligned X-ray telescope modules, each
equipped with focal plane detectors called FPMA and FPMB (Harrison et al.,
2013). The telescope’s optics provide X-ray data in a wide 3–79 keV energy
range with an angular resolution of 18 arcseconds (FWHM) and a uniquely high
sensitivity at high photon energies.

The effective exposure time of the utilized NuSTAR observation is 56 ks (ObsID
90701342002). We extracted spectra and light curves using nuproducts procedure
provided by the NuSTARDAS pipeline in accordance with the data analysis
manual.111https://heasarc.gsfc.nasa.gov/docs/nustar/analysis/nustar_swguide.pdf
Data for analysis were extracted from a 40 arcsec radius circle. To subtract
the background, we took data from the region with a radius of 120 arcsec.
Background-subtracted spectra were binned with the "optimal" algorithm
implemented in the ftgrouppha utility of the ftools package (Kaastra &
Bleeker, 2016). Background-subtracted light curves from two modules were added
using the lcmath utility and were barycenter-corrected using the barycorr
utility. For the analysis, we used heasoft package version 6.29 and CALDB
version 20211202.

###  2.2 Swift observatory

To study the evolution of the eRASSU J050810.4$-$660653 flux (see Fig. 1) and
spectrum during the outburst, we triggered a monitoring campaign consisting of
32 observations (ObsID 00013299003-7,9-11, 35-58, see Table 1) with the XRT
telescope (Burrows et al., 2005) on board the Neil Gehrels Swift Observatory
(Gehrels et al., 2004), covering MJD 59568-59722. Unfortunately, due to the
switch of the Swift observatory into the safe mode, there were no observations
between 59583 and 59634 MJD. All observations were made in the Photon Counting
(PC) mode. The spectra were extracted using the data analysis
software222https://www.swift.ac.uk/user_objects/ (Evans et al., 2009) provided
by the UK Swift Science Data Center. They were rebinned to have at least one
count per energy bin and W-statistics was applied (Wachter et al., 1979). The
Swift/XRT spectra were fitted in the XSPEC 12.12.0 package (Arnaud, 1996) with
a simple absorbed power-law model (the hydrogen column density $N_{\rm H}$ was
fixed at $0.27\times 10^{22}$ cm-2 for all Swift/XRT observations, the best-
fit value obtained from the broadband spectral analysis, see Sec. 3.2). All
errors are given at the 1$\sigma$ confidence level if not specified otherwise.
All luminosities within the paper were calculated assuming the distance to the
LMC of $49.97\pm 1.3$ kpc (Pietrzyński et al., 2013).

Figure 1: Light curve of eRASSU J050810.4$-$660653 based on the Swift/XRT
telescope monitoring campaign in the 0.5-10 keV energy range (red points),
NuSTAR (blue), SRG/ART-XC (green). Results of eROSITA and Swift/XRT from
Haberl et al. (2020) are shown with the gray dashed lines as well as the range
between them. The dotted line shows the approximation of the light curve by a
sinusoid with period of $\sim 38$ days.

###  2.3 SRG/ART-XC

The Spectrum Roentgen Gamma (SRG) observatory (Sunyaev et al., 2021) consists
of two X-ray telescopes: the Mikhail Pavlinsky ART-XC operating in the 4–30
keV energy range (Pavlinsky et al., 2021) and eROSITA operating in the 0.2–10
keV band (Predehl et al., 2021).

The ART-XC observed the position of the eRASSU J050810.4$-$660653 during the
ongoing all-sky survey from 14 to 19 December, 2021, for a net (i.e. not
corrected for vignetting) exposure of $\sim 0.55$ ks. The source was clearly
detected at an average flux of $(1.6\pm 0.2)\times 10^{-11}$ erg s-1 cm-2 in
the 4$-$12 keV energy band.

Assuming the same spectral shape during the NuSTAR observation (see Sec. 3.2),
scaling factor of 1.06 was used to convert ART-XC fluxes into the 0.5-10 keV
band, $F_{\rm ART,0.5-10\,keV}=1.06\times F_{\rm ART,4-12\,keV}$. Data for
spectral and timing analysis were reduced using the artproducts v0.9 pipeline
with the CALDB version 20200401. The source spectrum and light curve were
extracted with the artproducts v0.9 pipeline in the low photon statistic mode
from the 2′ vicinity of the source position.

Table 1: Observations of eRASSU J050810.4$-$660653.

ObsID | Exposure, ks | Count ratea | Bkg count rateb
---|---|---|---
Swift/XRT
00013299003 | 0.99 | 1.19 | 0.02
00013299004 | 0.31 | 1.83 | 0.06
00013299005 | 0.14 | 1.33 | 0.07
00013299006 | 0.80 | 1.70 | 0.03
00013299007 | 0.90 | 1.55 | 0.01
00013299009 | 1.20 | 1.13 | 0.02
00013299010 | 0.27 | 0.69 | 0.03
00013299011 | 0.69 | 0.62 | 0.02
00013299035 | 0.97 | 0.94 | 0.05
00013299036 | 1.32 | 1.24 | 0.11
00013299037 | 0.98 | 1.04 | 0.08
00013299038 | 0.54 | 1.95 | 0.05
00013299039 | 1.23 | 1.89 | 0.30
00013299040 | 0.53 | 1.05 | 0.04
00013299041 | 0.78 | 0.86 | 0.02
00013299042 | 0.84 | 0.36 | 0.02
00013299043 | 2.45 | 0.21 | 0.01
00013299044 | 1.00 | 0.14 | 0.01
00013299045 | 0.85 | 0.87 | 0.01
00013299046 | 0.94 | 1.13 | 0.02
00013299047 | 2.78 | 2.08 | 0.02
00013299048 | 3.08 | 1.85 | 0.02
00013299049 | 0.57 | 2.24 | 0.02
00013299050 | 0.83 | 0.69 | 0.02
00013299051 | 1.04 | 0.16 | 0.01
00013299052 | 0.87 | 0.07 | 0.01
00013299053 | 0.99 | 1.29 | 0.02
00013299054 | 2.99 | 1.32 | 0.02
00013299055 | 0.83 | 1.32 | 0.03
00013299056 | 0.48 | 1.92 | 0.02
00013299057 | 0.93 | 1.8 | 0.02
00013299058 | 1.86 | 2.02 | 0.02
NuSTAR/FPMA
90701342002 | 55.78 | 3.94 | 0.07
NuSTAR/FPMB
90701342002 | 55.37 | 3.91 | 0.08
SRG/ART-XC
| 0.55 | 0.43 | 0.02

a $10^{-1}$ cnt s-1 (total source region count rate)
b $10^{-1}$ cnt s-1 (background count rate renormalised to the source region)

##  3 Results

Using the available data described above we were able to study temporal and
spectral properties of eRASSU J050810.4$-$660653 at different time scales.
Fig. 1 shows a light curve of the source based on observations by the
Swift/XRT, NuSTAR, and SRG/ART-XC instruments between 59562 and 59722 MJD,
clearly demonstrating an enhanced (about one order of magnitude) flux compared
to the discovery value. The source is demonstrating a sinusoidal variability
of the flux, which may point to the orbital periodicity in the system (for
details see below). About one year before the considered outburst, in the end
of 2019–beginning of 2020 eRASSU J050810.4$-$660653 was observed with
SRG/eROSITA and Swift/XRT (Haberl et al., 2020). The measured luminosities at
that time fall into a narrow range of values around $0.5-1.0\times 10^{36}$
erg s-1 (see grey shaded area at Fig. 1), which can be associated with the low
state luminosity of the source. During the entire observation campaign, the
source flux does not fall below this area.

###  3.1 Timing analysis

Preliminary results of the timing analysis performed on a part of the NuSTAR
data were published by Haberl et al. (2021). To refine the period of
pulsations we used the full set of the NuSTAR data in the energy range 3-79
keV. For that we used method based on a linear approximation of pulse arrival
times (see e.g. Deeter et al., 1981), resulted in the value $P_{\rm
spin}=40.5781\pm 0.0004$ s. The spin period value was not corrected for binary
motion, since the orbital parameters of the system are unknown except for the
orbital period estimated in this work (see below). The NuSTAR wide energy
range 3-79 keV, combined with high count statistics allowed us to study the
dependence of the eRASSU J050810.4$-$660653 pulse profile on the energy (Fig.
2). Pulse profiles in different energy ranges were obtained by folding energy-
resolved light curves with the measured period $P_{\rm spin}$ and normalized
by the average intensity in a given energy band. Formally, we do not register
pulsations from eRASSU J050810.4$-$660653 in the ART-XC data due to the short
exposure and insufficient statistics. Nevertheless, if we fold the light curve
obtained by ART-XC in the 4-12 keV energy range with the period measured
above, then the corresponding pulse profile will be generally similar to that
obtained from the NuSTAR data (see Fig. 2). Pulse profiles in all bands have a
broad single-peaked profile with asymmetric wings. The intensity of the right
wing relative to the left one increases with the energy.

Figure 2: eRASSU J050810.4$-$660653 pulse profile as a function of the energy
based on the NuSTAR and SRG/ART-XC data. Pulse profiles are repeated at phases
1.0-2.0 and spaced along the y-axis for the better visualization convenience.
Intensities for each profile were normalized by the profile’s average
intensity. Zero phase values are different for NuSTAR and SRG/ART-XC.

We also studied a dependence of the pulsed fraction (PF)333PF is defined as
[max (rate) - min (rate)] / [max (rate) + min (rate)], where max (rate) and
min (rate) are maximum and minimum count rates in the profile, respectively.
on the energy (Fig. 3). The PF was calculated from the energy-resolved pulse
profile with 15 phase bins. It demonstrates a monotonic increase in the entire
energy range with the lowest value $\sim$ 30 per cent, that is typical for
most bright XRPs (Lutovinov & Tsygankov, 2009).

Based on the conducted long-term monitoring of eRASSU J050810.4$-$660653, we
were able to estimate the orbital period of the system. From the approximation
of the light curve by a sinusoid we obtained a value of a possible orbital
period of $38.0\pm 0.1$ days (see Fig. 1). At the moment, a more accurate and
detailed determination of the orbital parameters is not possible and
additional observations are required.

Figure 3: Pulsed fraction of eRASSU J050810.4$-$660653 as a function of the
energy based on the NuSTAR data.

###  3.2 Spectral analysis

To study the spectral properties of eRASSU J050810.4$-$660653 in a wide energy
range we jointly approximated data from the FPMA, FPMB, XRT and ART-XC
telescopes. To get better statistics at a low-energy part of the source
spectrum, we decided to use the averaged spectrum of several Swift/XRT
observations, which did not differ significantly in the flux (ObsID
00013299003, 00013299004, 00013299005, 00013299006, 00013299007), covering MJD
59568-59575 The resulting phase averaged energy spectrum of eRASSU
J050810.4$-$660653 is shown in Fig. 4. In order to take into account the non-
simultaneity of observations as well as possible inaccuracies in calibrations
between FPMA, FPMB, XRT and ART-XC, the cross-calibration multiplicative
factors were used (the const model in xspec). All models were also modified by
the photoabsorption model using the tbabs component with the abundances from
Wilms et al. (2000).

Figure 4: Unfolded spectrum of eRASSU J050810.4$-$660653 and its approximation with the model const $\times$ tbabs $\times$ cutoffpl (solid lines in panel a). Red and black dots are for the FPMA and FPMB telescopes of the NuSTAR observatory, blue for the Swift/XRT telescope and dark green for the SRG/ART-XC telescope. The bottom three panels show the residuals for different continuum models: cutoffpl (panel b), po $\times$ highecut (panel c), compTT (panel d). Table 2: Results of approximation of the eRASSU J050810.4$-$660653 spectrum by various continuum models.  Parameter | cutoffpl | po $\times$ highecut $\times$ gabs | compTT
---|---|---|---
${\rm const}_{\rm FPMA}$ | 1.00 (frozen) | 1.00 (frozen) | 1.00 (frozen)
${\rm const}_{\rm FPMB}$ | $1.05\pm 0.01$ | $1.05\pm 0.01$ | $1.05\pm 0.01$
${\rm const}_{\rm XRT}$ | $0.79\pm 0.04$ | $0.73\pm 0.04$ | $0.95\pm 0.05$
${\rm const}_{\rm ART-XC}$ | $1.0\pm 0.1$ | $1.1\pm 0.1$ | $1.0\pm 0.1$
$N_{\rm H}$, $10^{22}$ cm-2 | $0.27\pm 0.07$ | $0.6\pm 0.1$ | $0.25\pm 0.25$
$E_{\rm cut}$, keV |  | $19.5\pm 0.8$ |
$E_{\rm fold}$, keV | $17.1\pm 0.6$ | $17\pm 1$ |
$\Gamma$ | $0.68\pm 0.03$ | $1.16\pm 0.02$ |
$T_{0}$, keV |  |  | $0.87\pm 0.04$
$T$, keV |  |  | $7.0\pm 0.1$
$\tau$ |  |  | $5.7\pm 0.1$
${\rm Norm}_{\rm continuum}$, ph keV-1 s-1 cm-2 | $(1.14\pm 0.04)\times 10^{-3}$ | $(1.87\pm 0.06)\times 10^{-3}$ | $(0.66\pm 0.02)\times 10^{-3}$
$E_{\rm smoothgabs}$, keV |  |  $19.5$ (=$E_{\rm cut}$) |
$\sigma_{\rm smoothgabs}$, keV |  |  $1.95$ (=$0.1\times E_{\rm cut}$) |
$\tau_{\rm smoothgabs}$ |  | $0.20\pm 0.05$ |
Flux0.5-79keV, erg s-1 cm-2 | $(6.56\pm 0.09)\times 10^{-11}$ | $(6.52\pm 0.09)\times 10^{-11}$ | $(6.19\pm 0.07)\times 10^{-11}$
Luminosity0.5-79keV, erg s-1 | $(1.96\pm 0.03)\times 10^{37}$ | $(1.95\pm 0.03)\times 10^{37}$ | $(1.85\pm 0.02)\times 10^{37}$
W-statistic/d.o.f. | 684/680 | 681/678 | 689/679
Figure 5: The hardness ratio for eRASSU J050810.4$-$660653 pulse profiles and
the spectral model parameters as a function of the spin phase. The averaged
pulse profile in a wide energy range (3-79 keV) is superimposed in gray for
visual comparison. Hardness is defined as the ratio of unnormalized pulse
profiles in the corresponding energy bands (10-20 keV / 3-10 keV and 20-30 keV
/ 10-20 keV).

To approximate the spectrum, we used the cutoff power-law continuum models
cutoffpl and powerlaw $\times$ highecut as well as the Comptonized radiation
model compTT (Titarchuk, 1994) from the xspec package. To smooth out the
discontinuity in the powerlaw $\times$ highecut continuum that forms
artificial absorption-like residuals near the cutoff energy $E_{\rm cut}$, we
have added a smoothing Gaussian absorption line gabs at energy $E_{\rm
smoothgabs}$ = $E_{\rm cut}$, with the width of $\sigma_{\rm smoothgabs}$ =
0.1 $E_{\rm cut}$ and the optical depth $\tau_{\rm smoothgabs}$ (see Coburn et
al., 2002, for details).

The source spectrum has a typical shape for XRPs (Coburn et al., 2002;
Filippova et al., 2005). All three above mentioned models describe it with
similar quality, however cutoff power-law continuum models make it slightly
better (see Table 2). Note that there is some spread in the value of a neutral
hydrogen column density $N_{\rm H}$ depending on the selected continuum model
and it is poorly defined in the model with the compTT continuum. The value of
$N_{\rm H}$ from the const $\times$ tbabs $\times$ cutoffpl model is mostly
close to the absorption value in the source direction $1.18\times 10^{21}$
cm-2 obtained by HI4PI Collaboration et al. (2016). Some excess of the value
measured in X-rays is probably due to an additional absorption in the binary
system. None of the continuum models revealed a significant presence of the Fe
K$\alpha$ line. The $3\sigma$ upper limit flux for an narrow ($\sigma=0.1$
keV) iron line at 6.4 keV is $F_{\rm iron}=1.2\times 10^{-5}\text{ photons
cm}^{-2}\text{ s}^{-1}$, which corresponds to an equivalent width of 0.05 keV.
In the further analysis we will use the exponential cutoff power-law model
const $\times$ tbabs $\times$ cutoffpl as it has the smallest number of
parameters.

Thanks to the high counting statistics we were able to study an evolution of
the source spectral parameters over the pulse phase using a pulse phase-
resolved spectroscopy. The NuSTAR spectral data were divided into five evenly
distributed phases, each of which was described by the model used to describe
the phase-averaged spectrum: const $\times$ tbabs $\times$ cutoffpl with the
$N_{\rm H}$ value fixed at 0.27. Despite the fact that the model is
phenomenological and makes it difficult to draw unambiguous conclusions about
the ongoing physical processes, one can notice some characteristic features of
the evolution of spectral parameters with a rotation phase. A remarkable
correlation (linear cross-correlation coefficient $\simeq 0.93$) between the
energy flux and the hardness ratio over the pulse was revealed in our analysis
(see Fig. 5). The spectrum hardness is defined as the ratio of non-normalized
count rate pulse profiles in two adjacent energy bands. There is also some
correlation between the folding energy $E_{\rm fold}$ and the pulse profile
intensity, and an anti-correlation between the photon index $\Gamma$ and the
pulse profile intensity. The latter one is generally agreed with the above
mentioned correlation of the hardness with the pulse profile intensity.

##  4 Discussion

In this paper, we investigated properties of the recently discovered Be/X-ray
binary eRASSU J050810.4$-$660653\. Below we discuss our observational results
in framework of theoretical models of the accretion onto the magnetised NSs.

###  4.1 eRASSU J050810.4$-$660653 on the Corbet diagram

Conventionally, it is believed that the main factor influencing the observed
properties of pulsars is the angular momentum evolution of the NS as a result
of accretion of matter (see, e.g., Mushtukov & Tsygankov, 2022). This leads to
an observational correlation between the pulsar spin period $P_{\rm spin}$ and
the orbital period $P_{\rm orb}$ (Corbet, 1984, 1985, 1986). This correlation
clearly distinguishes between three main HMXB groups: Roche lobe-filling
supergiants, wind accretion supergiants, and Be-HMXB.

The orbital 38-day and spin 40.6 s periods we measured allow us to study the
position of eRASSU J050810.4$-$660653 on the pulse period - orbital period
Corbet diagram (see Fig 6). eRASSU J050810.4$-$660653 is in the middle of Be-
star systems on the Corbet diagram, which confirms its Be nature deduced from
the SALT spectroscopy (Haberl et al., 2020).

Figure 6: Pulse period - orbital period diagram adopted from Corbet et al.
(2017). eRASSU J050810.4$-$660653 is superimposed and marked as a red circle.
"B” is for Be-star systems, “W” is for stellar wind acrretion, “R” is for
Roche lobe-filling supergiants candidates.

###  4.2 Magnetic field estimation

In order to interpret the observed behaviour of a new XRP, some knowledge of
the NS magnetic field is required. The most accurate and only direct method
for measuring XRP magnetic fields is to detect the cyclotron resonant
scattering feature (CRSF) in its energy spectrum (see Staubert et al., 2019;
Mushtukov & Tsygankov, 2022, for a recent review). The analysis of the phase-
averaged spectrum of eRASSU J050810.4$-$660653 did not reveal the presence of
CRSF in the energy range from 5 to 50 keV (see Tsygankov & Lutovinov, 2005,
for a brief description of the technique). It is important to note that in
some cases, such spectral features appear only at some specific phases of the
NS rotation (Molkov et al., 2019; Molkov et al., 2021). However, in the case
of eRASSU J050810.4$-$660653, the pulse phase-resolved spectroscopy did not
reveal a phase-transient CRSF as well. An absence of the CRSF in the source
energy spectrum allows us to constrain the XRP’s magnetic field strength. For
the energy range 5-50 keV and the canonical NS parameters ($M=1.4M_{\sun}$,
$R=10^{6}$ cm), it points either to a low value $B<5\times 10^{11}$ G or quite
strong one $B>5\times 10^{12}$ G. It is important to note that despite the
absence of significant CRSF detection in the spectrum, an unusually shallow
line can never be excluded.

If the direct measurement of the magnetic field strength using the CRSF energy
is not possible, indirect methods can be applied. When the accretion rate
drops to very low values, the so-called propeller effect may take place
(Illarionov & Sunyaev, 1975), causing a sharp drop in the observed luminosity.
As previously noted, eRASSU J050810.4$-$660653 observations by SRG/eROSITA and
Swift/XRT, performed in 2019-2020, when the source was not in the outburst,
demonstrated relatively high luminosities, $1.0\times 10^{36}$ and $4.8\times
10^{35}$ erg s-1, respectively (Haberl et al., 2020). Since such a luminosity
is much higher than the typical quiescent luminosity of transient Be/XRPs
(Tsygankov et al., 2017a), it indicates the absence of a transition of the
source to the propeller regime. The observed luminosity can rather be
associated with the accretion from the cold recombined accretion disc,
observed in several XRPs with relatively long spin periods (Tsygankov et al.,
2017a; Tsygankov et al., 2017b; Tsygankov et al., 2019; Rouco Escorial et al.,
2018; Reig & Zezas, 2018). In this case, the magnetic field can be estimated
using formula (12) from Tsygankov et al. (2017b) as $B\sim 10^{13}$ G. This
estimate should be treated with caution, since it was obtained under the
assumption that accretion in the low state occurs from the “cold” recombined
accretion disc. In the case of another accretion mechanism in the low state,
this model is not applicable.

The NS magnetic field can also be indirectly estimated from an evolution of
the pulsar’s spin period. Measuring the spin-up and spin-down rates as a
function of the mass accretion rate allows to study the interaction of the
accreting plasma with the magnetosphere and estimate the magnetic field (see,
e.g., Ghosh & Lamb, 1979). Unfortunately, the absence of a long observational
history and, consequently, the absence of the orbital parameters of the system
do not give us such a possibility yet.

At the same time, it is generally accepted that stably accreting XRPs, in the
course of their evolution, come to an equilibrium of spin-up and spin-down
torques, which is achieved at the so-called equilibrium period. As previously
noted, eRASSU J050810.4$-$660653 observations by SRG/eROSITA and Swift/XRT in
2019-2020 demonstrated quite high luminosities. These values differ only by a
factor of 2 despite a significant gap of $\sim 100$ days between observations,
which allows us to assume the relative stability of the mass accretion rate in
the low state (see gray strip in Fig. 1). Although the source exhibits flux
variability similar to the one discussed in this work, the dynamic range of
the observed luminosity is still about one order of magnitude. This fact
allows us to assume an equilibrium regime of accretion and roughly estimate
the NS magnetic field considering the observed spin period as equilibrium one
(see, e.g., Chapter 5 in Lipunov 1992):

$P_{\rm eq}\simeq 5.7\,\Lambda^{3/2}B_{12}^{6/7}L_{37}^{-3/7}M_{\rm
s}^{-2/7}R_{6}^{15/7}~{}\text{s,}$ (1)

where $\Lambda$ is the coefficient of proportionality between the Alfven
radius and the radius of neutron star magnetosphere $R_{\rm m}$ (in the case
of the accretion from gas pressure dominated disc, the coefficient is taken to
be $\Lambda=0.5$), $B_{12}$ is the magnetic field strength $B$ at the NS
surface in units of $10^{12}\,{\rm G}$, $L_{37}$ is the accretion luminosity
$L$ in units of $10^{37}\,{\rm erg\,s^{-1}}$, $M_{\rm s}$ is the mass of a NS
in units of solar masses $M_{\sun}$, and $R_{6}$ is the radius of a NS in
units of $10^{6}\,{\rm cm}$.

The numerical factor in the right hand side of eq. (1) is determined by the
critical fastness parameter $\omega_{\rm s}=({R_{\rm m}}/{R_{\rm cor}})^{3/2}$
(at which the total torque becomes zero), where $R_{\rm cor}$ is the
corotation radius. The critical fastness parameter takes different values
depending on the assumptions of the theoretical model. In particular, the
model by Ghosh & Lamb (1979) suggests $\omega_{\rm s}$=0.35, that corresponds
to the factor value of 5.7 and magnetic field $B\sim 1.5\times 10^{13}$ G,
whereas the model by Wang (1995) suggests $\omega_{\rm s}$=0.95 (factor value
is 2.1) resulting in $B\sim 5\times 10^{13}$ G. Both values are in agreement
with estimates obtained from the accretion from the cold disc and point to the
relatively strong magnetic field in eRASSU J050810.4$-$660653\. However, such
a magnetic field estimation should be treated with the caution since there is
no sufficiently long and detailed history of observations of eRASSU
J050810.4$-$660653 in the quiescent state to claim the presence of the spin
equilibrium confidently.

###  4.3 Emission mechanism

The pulse profile of eRASSU J050810.4$-$660653 in all energy ranges
demonstrates a single-peak structure, which indicates that the pulsar is
probably turned towards the observer by one of its poles, while another one is
practically invisible. As previously noted, there is a strong correlation
between the energy flux and the hardness ratio over the pulse (see Sec. 3.2).
Such an unusually strong correlation may indicate the dominant nature of the
pencil beam pattern in the NS radiation. As shown below, it can be caused,
depending on the NS’s magnetic field, either by the features of the energy
release in the atmosphere or by the details of photons propagation above its
surface.

If the magnetic field strength at the NS surface is extremely high, the
critical luminosity is well above the observed luminosity level of $\sim
2\times 10^{37}\,{\rm erg\,s^{-1}}$ (Basko & Sunyaev, 1976; Mushtukov et al.,
2015). Then the correlation between the flux and hardness ratio may be a
result of temperature structure in the atmosphere and dependence of Compton
scattering cross section on the photon momentum direction. The beam pattern
produced by the hot spots at the stellar surface is close to the pencil beam.
Most photons leaving the surface do not experience scattering by the accreting
matter. Photons propagating closer to the normal to the NS surface are
originated from deeper layers in the atmosphere due to the geometrical reason
and strong dependence of the scattering cross section on the angle between the
magnetic field direction and photon momentum (Basko & Sunyaev, 1975). The
deeper atmospheric layers are expected to be hotter than the upper ones at the
considered mass accretion rates. As a result, the photons propagating close to
the perpendicular to the NS surface experience a thermal Comptonization by the
electron gas of the higher temperature and, thus, have harder spectra. This
scenario was utilised earlier by Klochkov et al. (2008) to explain a similar
correlation between the flux and hardness ratio in XRP EXO 2030+375.

In the case of the moderate magnetic field strength, the observed luminosity
$\sim 2\times 10^{37}\,{\rm erg\,s^{-1}}$ is close to the critical value. In
this case, a significant fraction of X-ray photons leaving the NS surface
experience a Compton scattering in the accretion channel above the hot spots,
and the bulk Comptonization becomes important (Becker & Wolff, 2007). The
Compton scattering by the accreting plasma is strongly anisotropic due to the
high free-fall velocity of the accretion flow. Momenta of the majority of
scattered photons are directed close to the direction of the accretion flow
motion. The closer the direction of the scattered photon momenta is to the
direction of the accretion flow, the energy of the scattered photons is
higher. As a result, one would expect that the direction of predominant photon
scattering is correlated with the direction of the hard emission. The photons
experienced scattering in the accretion channel can undergo a following
reflection from the NS surface, which makes the spectra even harder (Postnov
et al., 2015) and conserves a correlation between the predominant direction of
the photon motion and hardness ratio. Thus, one would expect a correlation
between the flux and hardness ratio during the pulse period at accretion
luminosities close to the critical value.

Based on the estimates of the magnetic field strength obtained above (several
$10^{13}$ G), we consider the second scenario as the most probable one. We
emphasize that even in this situation, the pulsar’s beam function is expected
to have a pencil configuration due to the reflection of scattered emission
from the NS surface.

##  5 Conclusion

This paper presents results of the first spectral and temporal analysis in a
wide energy range of recently discovered Be/X-ray binary eRASSU
J050810.4$-$660653\. The investigation is based on the data from the SRG,
NuSTAR, and Swift observatories obtained during the December 2021 – May 2022
monitoring of the source. Timing analysis revealed pulsations with a period of
$40.5781$ s and a monotonic increase in PF over the entire energy range. Based
on the long-term Swift/XRT monitoring of the system, we obtained an estimate
for the system’s orbital period of 38 days. The eRASSU J050810.4$-$660653
spectrum has the form of a power law with an exponential cutoff at high
energies. We did not detect the presence of CRSF both in the phase-averaged
and phase-resolved spectra. Based on indirect methods, estimates were given
for the magnetic field about several $10^{13}$ G. The hardness ratio and pulse
profile intensity demonstrate a strong correlation, which we interpret as a
consequence of the bulk Comptonization of the emission by the accretion flow.

The high sensitivity of the instruments of the SRG observatory and the
possibility of surveying large sky areas allow it to discover many faint
transient or quasi-permanent objects, including X-ray pulsars, both in our
Galaxy (see, e.g., Doroshenko et al., 2021; Lutovinov et al., 2021) and
neighboring galaxies, primarily in the Large Magellanic Cloud (see, e.g.,
Maitra et al., 2021; Haberl et al., 2022). The latter is most likely due to
the fact that the LMC is too large to be completely covered by the relatively
small field of view of other sensitive instruments, like Chandra or XMM-
Newton. The SRG observatory survey strategy, as well as deep observations
during the CalPV phase, have significantly increased the coverage of this
region of the sky with a high sensitivity. This has already led to the
discovery of several new pulsars, including eRASSU J050810.4$-$660653, which
is the subject of this paper. It is noteworthy that most of the new pulsars,
discovered by SRG both in our Galaxy and in the LMC, reside in systems with Be
stars.

## Acknowledgements

This work is based on data from Mikhail Pavlinsky ART-XC X-ray telescope
aboard the SRG observatory. The SRG observatory was built by Roskosmos in the
interests of the Russian Academy of Sciences represented by its Space Research
Institute (IKI) in the framework of the Russian Federal Space Program, with
the participation of the Deutsches Zentrum für Luft- und Raumfahrt (DLR). The
SRG spacecraft was designed, built, launched and is operated by the Lavochkin
Association and its subcontractors. The science data are downlinked via the
Deep Space Network Antennae in Bear Lakes, Ussurijsk, and Baykonur, funded by
Roskosmos. The ART-XC team thank the Russian Space Agency, Russian Academy of
Sciences and State Corporation Rosatom for the support of the SRG project and
ART-XC telescope and the Lavochkin Association (NPOL) with partners for the
creation and operation of the SRG spacecraft (Navigator). We are grateful to
the NuSTAR team for approving and rapid scheduling of the follow-up
observation. This work is based on data from Mikhail Pavlinsky ART-XC X-ray
telescope aboard the SRG observatory. We are grateful to the Swift team for
approving and rapid scheduling of the monitoring campaign. This work made use
of data supplied by the UK Swift Science Data Centre at the University of
Leicester and data obtained with NuSTAR mission, a project led by Caltech,
funded by NASA and managed by JPL. This research also has made use of the
NuSTAR Data Analysis Software (NUSTARDAS) jointly developed by the ASI Science
Data Center (ASDC, Italy) and Caltech. This research has made use of data and
software provided by the High Energy Astrophysics Science Archive Research
Center (HEASARC), which is a service of the Astrophysics Science Division at
NASA/GSFC and the High Energy Astrophysics Division of the Smithsonian
Astrophysical Observatory. This work was supported by the grant 19-12-00423 of
the Russian Science Foundation. SST also acknowledges the support from the
Academy of Finland travel grant 349373.

##  6 Data availability

NuSTAR and Swift data can be accessed from corresponding online archives. At
this moment SRG/ART-XC data have a private status. They will be open for the
scientific community after a special decision of the Roscosmos.

## References

  * Arnaud (1996) Arnaud K. A., 1996, in Jacoby G. H., Barnes J., eds, ASP Conf. Ser. Vol. 101, Astronomical Data Analysis Software and Systems V. p. 17
  * Basko & Sunyaev (1975) Basko M. M., Sunyaev R. A., 1975, A&A, 42, 311
  * Basko & Sunyaev (1976) Basko M. M., Sunyaev R. A., 1976, MNRAS, 175, 395
  * Becker & Wolff (2007) Becker P. A., Wolff M. T., 2007, ApJ, 654, 435
  * Burrows et al. (2005) Burrows D. N., et al., 2005, Space Sci. Rev., 120, 165
  * Coburn et al. (2002) Coburn W., Heindl W. A., Rothschild R. E., Gruber D. E., Kreykenbohm I., Wilms J., Kretschmar P., Staubert R., 2002, ApJ, 580, 394
  * Corbet (1984) Corbet R. H. D., 1984, A&A, 141, 91
  * Corbet (1985) Corbet R., 1985, Space Sci. Rev., 40, 409
  * Corbet (1986) Corbet R. H. D., 1986, MNRAS, 220, 1047
  * Corbet et al. (2017) Corbet R. H. D., Coley J. B., Krimm H. A., 2017, ApJ, 846, 161
  * Deeter et al. (1981) Deeter J. E., Boynton P. E., Pravdo S. H., 1981, ApJ, 247, 1003
  * Doroshenko et al. (2021) Doroshenko V., et al., 2021, arXiv e-prints, p. arXiv:2106.14539
  * Evans et al. (2009) Evans P. A., et al., 2009, MNRAS, 397, 1177
  * Filippova et al. (2005) Filippova E. V., Tsygankov S. S., Lutovinov A. A., Sunyaev R. A., 2005, Astronomy Letters, 31, 729
  * Gehrels et al. (2004) Gehrels N., et al., 2004, ApJ, 611, 1005
  * Ghosh & Lamb (1979) Ghosh P., Lamb F. K., 1979, ApJ, 234, 296
  * HI4PI Collaboration et al. (2016) HI4PI Collaboration et al., 2016, A&A, 594, A116
  * Haberl et al. (2020) Haberl F., et al., 2020, The Astronomer’s Telegram, 13609, 1
  * Haberl et al. (2021) Haberl F., et al., 2021, The Astronomer’s Telegram, 15133, 1
  * Haberl et al. (2022) Haberl F., Maitra C., Vasilopoulos G., Maggi P., Udalski A., Monageng I. M., Buckley D. A. H., 2022, arXiv e-prints, p. arXiv:2203.00625
  * Harrison et al. (2013) Harrison F. A., et al., 2013, ApJ, 770, 103
  * Illarionov & Sunyaev (1975) Illarionov A. F., Sunyaev R. A., 1975, A&A, 39, 185
  * Kaastra & Bleeker (2016) Kaastra J. S., Bleeker J. A. M., 2016, A&A, 587, A151
  * Klochkov et al. (2008) Klochkov D., Santangelo A., Staubert R., Ferrigno C., 2008, A&A, 491, 833
  * Lipunov (1992) Lipunov V. M., 1992, Astrophysics of Neutron Stars. Springer Berlin Heidelberg
  * Lutovinov & Tsygankov (2009) Lutovinov A. A., Tsygankov S. S., 2009, Astronomy Letters, 35, 433
  * Lutovinov et al. (2021) Lutovinov A. A., et al., 2021, arXiv e-prints, p. arXiv:2107.05587
  * Maitra et al. (2021) Maitra C., Haberl F., Maggi P., Kavanagh P. J., Vasilopoulos G., Sasaki M., Filipović M. D., Udalski A., 2021, MNRAS, 504, 326
  * Molkov et al. (2019) Molkov S., Lutovinov A., Tsygankov S., Mereminskiy I., Mushtukov A., 2019, ApJ, 883, L11
  * Molkov et al. (2021) Molkov S., Doroshenko V., Lutovinov A., Tsygankov S., Santangelo A., Mereminskiy I., Semena A., 2021, ApJ, 915, L27
  * Mushtukov & Tsygankov (2022) Mushtukov A., Tsygankov S., 2022, arXiv e-prints, p. arXiv:2204.14185
  * Mushtukov et al. (2015) Mushtukov A. A., Suleimanov V. F., Tsygankov S. S., Poutanen J., 2015, MNRAS, 447, 1847
  * Pavlinsky et al. (2021) Pavlinsky M., et al., 2021, A&A, 650, A42
  * Pietrzyński et al. (2013) Pietrzyński G., et al., 2013, Nature, 495, 76
  * Postnov et al. (2015) Postnov K. A., Gornostaev M. I., Klochkov D., Laplace E., Lukin V. V., Shakura N. I., 2015, MNRAS, 452, 1601
  * Predehl et al. (2021) Predehl P., et al., 2021, A&A, 647, A1
  * Reig & Zezas (2018) Reig P., Zezas A., 2018, A&A, 613, A52
  * Rouco Escorial et al. (2018) Rouco Escorial A., van den Eijnden J., Wijnands R., 2018, A&A, 620, L13
  * Staubert et al. (2019) Staubert R., et al., 2019, A&A, 622, A61
  * Sunyaev et al. (2021) Sunyaev R., et al., 2021, A&A, 656, A132
  * Titarchuk (1994) Titarchuk L., 1994, ApJ, 434, 570
  * Tsygankov & Lutovinov (2005) Tsygankov S. S., Lutovinov A. A., 2005, Astronomy Letters, 31, 88
  * Tsygankov et al. (2017a) Tsygankov S. S., Wijnands R., Lutovinov A. A., Degenaar N., Poutanen J., 2017a, MNRAS, 470, 126
  * Tsygankov et al. (2017b) Tsygankov S. S., Mushtukov A. A., Suleimanov V. F., Doroshenko V., Abolmasov P. K., Lutovinov A. A., Poutanen J., 2017b, A&A, 608, A17
  * Tsygankov et al. (2019) Tsygankov S. S., Doroshenko V., Mushtukov A. A., Lutovinov A. A., Poutanen J., 2019, A&A, 621, A134
  * Wachter et al. (1979) Wachter K., Leach R., Kellogg E., 1979, ApJ, 230, 274
  * Wang (1995) Wang Y. M., 1995, ApJ, 449, L153
  * Wilms et al. (2000) Wilms J., Allen A., McCray R., 2000, ApJ, 542, 914