# A broadband X-ray study of the dwarf nova SS Cyg during quiescence and
outburst

Anirban Dutta Astronomy and Astrophysics Group, Raman Research Institute
Sadashivnagar, Bangalore, Karnataka-560094  Vikram Rana Astronomy and
Astrophysics Group, Raman Research Institute, Sadashivnagar, Bangalore,
Karnataka-560094  Koji Mukai CRESST II and X-ray Astrophysics Laboratory,
NASA/GSFC, Greenbelt, MD 20771, USA  Department of Physics, University of
Maryland Baltimore County, 1000 Hilltop Circle, Baltimore MD 21250, USA
Raimundo Lopes de Oliveira Departamento de Física, Universidade Federal de
Sergipe, Av. Marechal Rondon, S/N, 49100-000, São Cristóvão, SE, Brazil
Observatório Nacional, Rua Gal. José Cristino 77, 20921-400, Rio de Janeiro,
RJ, Brazil

###### Abstract

We present a broadband X-ray study ($\sim$ 0.3-50 keV) of the dwarf nova SS
Cyg highlighting the changes in the accretion during two phases, the
quiescence and the outburst states. The investigation was based on
simultaneous observations carried out with the XMM-Newton and NuSTAR
telescopes in two epochs, involving medium and high-resolution spectroscopy.
Spectra were harder during quiescence ($kT_{\rm high}\sim 22.8$ keV) than
outburst ($kT_{\rm high}\sim 8.4$ keV), while the mass accretion rate
increased by $\sim 35$ times in outburst ($1.7\times 10^{16}\rm g\;s^{-1}$)
than quiescence. The bolometric luminosity (0.01-100.0 keV) during the
outburst was dominated by a blackbody emission ($kT_{\rm BB}\sim 28$ eV) from
the optically thick boundary layer, and the inner edge of the accretion disk
resides very close to the WD surface. X-rays from the accretion disk boundary
layer are consistent with the white dwarf having mass $1.18_{-0.01}^{+0.02}\rm
M_{\odot}$. Our study conclusively confirms the presence of the reflection
hump in the 10-30 keV range for both phases, which arises when X-ray photons
hit colder material and undergo Compton scattering. We estimated a similarly
strong reflection amplitude during quiescence ($\sim 1.25$) and outburst
($\sim 1.31$), indicating both the WD surface and disk are contributing to
reflection. The neutral Fe Kα line, which is correlated with Compton
reflection, also showed similar strength ($\sim 80$ eV) in both phases.
Finally, X-rays also revealed the presence of a partial intrinsic absorber
during the outburst, possibly due to an outflowing accretion disk wind.

Dwarf novae(418) — Cataclysmic variable stars(203) — X-ray binary stars(1811)

††facilities: XMM-Newton, NuSTAR††software: HEASoft (Nasa High Energy
Astrophysics Science Archive Research Center (2014) (Heasarc),
https://heasarc.gsfc.nasa.gov/docs/software/heasoft/), XMM-Newton SAS (Gabriel
et al. (2004), https://www.cosmos.esa.int/web/xmm-newton/sas),

##  1 Introduction

Cataclysmic Variables (CVs) are a class of semi-detached binary systems in
which a white dwarf (WD) accretes material from the generally late-type main
sequence secondary by Roche-lobe overflow mechanism. Among the CVs are the
Dwarf Novae (DNe), consisting of ‘non-magnetic’ WD, with magnetic field
$\lesssim 10^{5}$ G, and exhibiting frequent optical outbursts (Warner, 2003;
Hellier, 2001). This is the case of our target, SS Cyg.

The most popular theory behind the outbursts in DNe is the “Disk Instability
Model” (Osaki, 1974; Bath & Pringle, 1981, 1982a, 1982b; Osaki, 1996). The
accretion disk remains calm and tranquil in the normal (quiescence) phase,
continuously receiving mass from the secondary, at a rate that is assumed to
be constant. However, the mass accretion rate onto the white dwarf is lower,
so the gradual accumulation of the material inside the disk increases the
surface density, thus temperature. After a critical density is reached, a
chain reaction kicks in, increasing temperature, viscosity, ionization, and
opacity rapidly, and a heating wave sets in. This thermal-viscous instability
increases the mass transport rate through the disk, and ultimately increases
the mass accretion rate by the WD. The increased mass accretion onto the WD
triggers the higher flux in X-rays along with the increased optical
counterpart which generally starts early with the increased mass transfer
inside the accretion disk.

DNe accretion theory suggests the presence of a boundary layer (BL) between
the inner edges of the disk and the WD surface. The properties and location of
BL and its emission are sensitive to the mass accretion rate. During the
quiescence (typical mass accretion rate is $\lesssim 10^{16}\;\rm gs^{-1}$), a
strong shock is formed in the BL due to the velocity mismatch of the WD
surface and the Keplarian velocity of the inner edge of the disk, and
Keplarian motion energy is transferred into electromagnetic radiation in the
form X-rays. The hot ($\sim 10^{8}$ K) gas in optically thin BL cools down by
thermal bremsstrahlung emission, mostly in hard X-rays. However, during
enhanced mass accretion rate of outburst ($\gtrsim 10^{16}\;\rm gs^{-1}$), the
boundary layer becomes optically thick to its own radiation, approaching a
blackbody condition, and radiates mostly in very soft X-rays with temperature
$\sim 10^{5}$ K (Pringle & Savonije, 1979; Narayan & Popham, 1993; Popham &
Narayan, 1995). This has been tested with multiple broadband observations
(Ricketts et al., 1979; Jones & Watson, 1992; Wheatley et al., 2003). Even
though the outburst phase produces mostly soft X-rays, there is clear
detection of hard X-rays with temperatures up to a few keVs. One possible
explanation is due to the vertical density gradients in the accretion disk
where a fraction of optically thin accreting materials emit hard X-rays
(Patterson & Raymond, 1985a, b). Another line of thought by Ishida et al.
(2009); Wheatley & Mauche (2005) express that hard X-rays arise from the
optically thin corona formed over the optically thick BL in outburst.

As the matter cools down before settling onto the WD surface, the X-ray
continuum is characterized by multitemperature components. Moreover, a part of
this X-ray continuum undergoes photoelectric absorption by the WD surface
and/or accretion disk and emits neutral iron Kα emission at 6.4 keV. Another
part gets reflected by WD surface and/or accretion disk via Compton reflection
(George & Fabian, 1991; Matt et al., 1991). The reflection hump is produced
mainly by the Compton scattering of hard X-ray photons to energies around
10-30 keV. This is because, at lower energies, the photoelectric absorption
dominates over Compton scattering, and at higher energies (above a few tens of
keV), the Compton scattering takes control. The dependence on photoelectric
absorption also features a prominent Fe-K edge at 7.0 keV. Since the
reflection is a geometrical effect, it is also dependent on the viewing angle
of the reflection site other than the elemental abundance of the reflecting
gas.

SS Cyg, one of brightest CV in the sky and a popular dwarf nova with WD mass
$(M_{\rm WD})$ $1.19\pm 0.02\rm M_{\odot}$, secondary mass $(M_{\rm K})$
$0.704\pm 0.002\rm M_{\odot}$ (Friend et al., 1990) ($M_{\rm WD}=0.81\pm
0.19M_{\odot}$ and $M_{\rm K}=0.55\pm 0.13M_{\odot}$ (Bitner et al., 2007)),
binary inclination angle $37\arcdeg\pm 5\arcdeg$ and orbital period
$6.603\;\rm hrs$ (Shafter, 1983; Hessman et al., 1984; Bitner et al., 2007;
Miller-Jones et al., 2013), has been subject to multiple studies in X-rays
(Ginga and ASCA (Done & Osborne, 1997), RXTE (McGowan et al., 2004), ASCA
(Baskill et al., 2005) and Suzaku (Ishida et al., 2009), NICER and NuSTAR
(Kimura et al., 2021)). The studies by Done & Osborne (1997); Ishida et al.
(2009); Kimura et al. (2021) of SS Cyg showed the presence of significant
Compton reflection during both states. However, these studies have their own
limitations arising from data quality or physical interpretation.

Now, using the simultaneous data from XMM-Newton, having good energy
resolution, and NuSTAR, having high sensitivity in hard X-rays and with
excellent cross-calibration between these two telescopes, we analysed the
broadband spectra of SS Cyg during both the quiescence and outburst phases. We
model the multi-temperature continuum with plasma emission components and
incorporate the contribution from the iron line complex, the soft X-ray
features, absorption, and directly measuring Compton reflection. We aim to
address the questions like how the accretion and nature of the X-ray emitting
plasma changes between two phases and what are the possible reflection sites
in either of the two phases.

In this paper, we have described the observation and data reduction in Section
2 , the analysis and the results in Section 3, the discussion in Section 4,
and finally, the conclusions and summary in the last section.

##  2 Observation and Data Reduction

SS Cyg was observed simultaneously (see Table 1, PI: Vikram Rana) with XMM-
Newton (Jansen et al., 2001) and NuSTAR telescopes (Harrison et al., 2013) in
both of its quiescence and outburst phases. Fig. 1 shows the X-ray
observational period of XMM-Newton and NuSTAR during quiescence and outburst
along with an optical lightcurve from the American Association of Variable
Star Observers (AAVSO). The observation was made to secure the broadband
spectra extending from 0.3 keV to 79.0 keV of the X-ray energy band. The good
energy resolution of XMM-Newton EPIC (European Photon Imaging Camera)
detectors (Strüder et al., 2001; Turner et al., 2001) in the low energy band
(0.3-10.0 keV), employed with high sensitivity of NuSTAR-FPM detectors in high
energy band (staring from 3.0 keV and extending up to 79.0 keV), offer an
excellent quality data for analysis. The high-resolution reflection grating
spectrometer, RGS (den Herder et al., 2001), onboard XMM, provides spectra in
the 0.35-2.5 keV energy band, resolving the prominent emission lines produced
in the source.

Figure 1: Optical lightcurve of SS Cyg in visual band (Source: AAVSO). The epoch of simultaneous NuSTAR and XMM-Newton observations during quiescence and outburst are marked.  Table 1: Observation log of SS Cyg  State | Telescope | Obs ID | Obs Date & Time | Exposure (s)
---|---|---|---|---
Quiescence | XMM-Newton | 0791000201 | 2016-05-16 & 07:18:26 | 30000
| NuSTAR | 80202036002 | 2016-05-16 & 06:26:08 | 49789
Outburst | XMM-Newton | 0791000101 | 2016-06-21 & 18:08:10 | 36000
| NuSTAR | 80202036004 | 2016-06-21 & 17:11:08 | 52161

###  2.1 NuSTAR

The two focusing imaging telescope modules of NuSTAR, FPMA and FPMB, capable
of focusing hard X-rays (3.0-79.0 keV) with very high sensitivity, observed
the source. These two telescopes of Wolter-I configuration employ grazing
incidence mirrors to bring the X-rays to their focus. Each of the telescope
modules is equipped with one detector module, which comprises 4 CZT-detectors.
We have selected a 50 arcsec radius circular region to include the source. The
100 arcsec radius circular background region (in the same CZT detector as that
of the source) has been selected to extract the background subtracted source
data. There are no other X-ray emitting sources present in that detector. The
NuSTAR data is devoid of any pile-up issues, thanks to its use of CZT
detectors. We have used NuSTARDAS v2.1.2 along with NuSTAR calibration files
v20221229 for data calibration, screening and science-products extraction. The
default screening criteria for attitude, dead time, orbit and instrument
parameters are used to obtain science data products, like the spectra and
detector response files. The spectra from each telescope module have been
rebinned using grppha to a minimum of 25 counts per bin to utilize $\chi^{2}$
minimization for spectral fitting. For spectral analysis involving NuSTAR
data, both the FPMA and FPMB spectra are used to improve the signal-to-noise
ratio.

###  2.2 XMM-Newton

The XMM-Newton satellite consists of three X-ray telescopes. The EPIC-PN
detector is placed behind one telescope, receiving X-ray photons with PN-CCD
arrays. The EPIC-MOS detectors are two in number and utilize other telescopes
for receiving the X-ray photons using Metal Oxide Semiconductor CCD arrays.
These three EPIC detectors (one PN, two MOS) have been used to observe the
source in 0.3-10.0 keV energy band. The two telescopes, working for MOS1 and
MOS2, are also equipped with two grating spectrometers, RGS1 and RGS2. Nearly
half of the X-ray flux received by those two telescopes are sent to MOS
detectors whereas, other half is used by the RGS. We have used the first order
spectra from the grating spectroscope, which can resolve emission and
absorption lines in 0.35-2.5 keV band (5-38 Å), comprising the important
$K_{\alpha}$ transition from ionised C, N, O, Ne, Mg, Si elements as well as
Fe L-Shell emission lines.

We have used XMMSAS (Gabriel et al., 2004) software (version 20.0.0) for data
reduction and extracting science products like the spectra and the detector
response files. For the latest calibration files, we have used XMMSAS ccf
repository 111https://www.cosmos.esa.int/web/xmm-newton/current-calibration-
files. The observation was taken in Small Window mode for both PN and MOS
detectors. Since SS Cyg is a fairly bright source, we have checked for pile-up
in all three detectors using the epatplot tool. We have found that the
outburst phase data suffers from pile-up, most strongly in PN. The pile-up
effect has been reduced by selecting annular regions to include the source.
Since the central core pixels contain maximum counts, thus having maximum
impact on pile-up, we have excised those pixels to eliminate the pile-up
issue. Running some trials on the annular region size, we have finalized on
(15,30) arcsec radii annular region for source selection (for PN, MOS1, MOS2),
which minimizes the pile-up without sacrificing the number of counts too much.
The background is selected from a circular region in the same CCD as that
source, with a radius of 40 arcsec (for PN, MOS1, MOS2). However, since RGS
detectors get only 50% of the received flux, the pile-up is not noticeable in
the RGS data of the outburst phase. This has been cross-checked by comparing
the RGS 1st order and 2nd-order spectra. We have checked the quiescence phase
data from EPIC and RGS detectors for pile-up, and we didn’t notice a
significant pile-up there. However, to have a conservative approach, we
performed the core-excising technique for the quiescence phase data from EPIC
(PN, MOS1, MOS2) detectors as well – by choosing an annular region of (15,30)
arcsec radii for the source and selected a circular background region of 40
arcsec radius in the same CCD as that of the source. The pile-up correction is
done following the SAS analysis thread (for EPIC
222https://www.cosmos.esa.int/web/xmm-newton/sas-thread-epatplot and for RGS
333https://www.cosmos.esa.int/web/xmm-newton/sas-thread-pile-up-in-the-rgs).

We have also checked for any high background flares present in the data,
occurring due to unpredictable solar soft protons. Fortunately, our data does
not include any such flaring backgrounds. After employing the necessary
selection criteria, we screened and reduced the final science products eg. the
spectra and the detector response files. We have applied corrections to the
effective area to remove residuals between simultaneous fits of EPIC and
NuSTAR observations by applying the command applyabsfluxcorr=yes with the tool
arfgen. The spectral data from all the detectors have been re-binned using
specgroup to minimum counts of 25 and the oversample parameter of 3.

##  3 Data Analysis and Results

In this section, we describe the spectral analysis of the data, performed
using XSPEC v12.12.1 (Arnaud, 1996). First, we discuss the analysis of the
data obtained during the quiescence phase from NuSTAR and XMM-Newton
separately and proceed to simultaneous broadband fitting. Next, we discuss the
same for the observations during the outburst. Here, we want to mention that
while both XMM observations were carried out entirely with the time interval
covered by the respective NuSTAR observations, the latter have data gaps and
cover longer periods. We have also analyzed strictly simultaneous portion of
the data and confirm that this did not unduly influence our results. This
appears to be because the random varaibility within these observing periods
largely averaged out. The only minor exception is in the cross-normalization
factor for NuSTAR data for the quiescence observation: the flux was somewhat
higher during the first half (with XMM overlap) than during the second half
(without). Even so, we do not observe any statistically significant changes in
the best-fit model parameters.

The spectral models used in this work are part of the XSPEC: mkcflow (after
Mushotzky & Szymkowiak, 1988), a multi-temperature model assuming cooling flow
from a hot optically thin plasma to account for the primary X-ray emission
arising from the boundary layer; reflect (Magdziarz & Zdziarski, 1995),
describing Compton hump expected by reflection; tabs (Wilms et al., 2000),
responding for the photoelectric absorption features of the ISM and local
absorbers, eventually associated to the partcov model to partial coverage;
bbody to consider the soft X-ray emission from optically thick boundary layer
during outburst; gaussian to describe the iron fluorescence line at 6.4 keV;
and constant to accommodate and evaluate cross-correlation issues between XMM-
Newton and NuSTAR cameras We have set the abundance table as Wilms (Wilms et
al., 2000) and chosen the Verner photo-electric absorption cross-section
(Verner et al., 1996). As for the mkcflow model, the switch parameter was set
to 2 to follow the AtomDB database and the redshift parameter was fixed at
$2.67\times 10^{-8}$ – corresponding to the GAIA DR2 distance to SS Cyg
adopted in this work, of $114.62$ pc (Gaia Collaboration et al., 2018).444We
are aware of the geometric distance determined by Bailer-Jones et al. (2021)
from GAIA data of 112.35${}^{+0.39}_{-0.35}$ pc, which is only 2% less than
the adopted distance and as such has no impact on the results presented here.
The model flux has been calculated using cflux component from the broadband
models. We have extended the range of energy response for all spectral groups
in the range 0.01 keV-100.0 keV using energies extend command.

###  3.1 Quiescence Phase

First, we have looked into the NuSTAR spectra to get an idea of the hard X-ray
properties of SS Cyg in quiescence. The data are used in the 3.0-50.0 keV band
since photon counts are very low above 50.0 keV and dominated by background.
The multi-temperature emission from hot optically thin plasma of the boundary
layer has been modelled using cooling flow component mkcflow. The lower
temperature of this component is fixed at the lowest value allowed, 0.0808
keV, since it is closer to the expected lower temperature of the boundary
layer plasma while not constrained from the data. The ISM absorption is
incorporated using tbabs. Since the NuSTAR data cannot constrain the column
density of the ISM, which influences the spectra below a few hundred of eV, we
have fixed its value at $3.5\times 10^{19}\>cm^{-2}$ (Mauche et al., 1988). We
have kept the abundance of the cooling flow model free, to reproduce the
necessary strength of Fe H-like and He-like $K_{\alpha}$ emission lines. We
introduce a narrow gaussian ($\sigma=0$ eV) for the neutral Fe Kα line. The
resultant best-fit ($\chi^{2}/DOF=719/657$) returns a upper temperature of
$\sim 33$ keV. However, excess residual for the Compton reflection hump in the
hard X-rays ($\sim 10-30$ keV) is evident, and we convolve the reflect
component with the plasma emission component to consider Compton reflection.
Since the possible reflection sites are regions of white dwarf surface which
has freshly accreted material and/or the accretion disk surface, we can assume
the same elemental abundance between the Compton reflection component and the
plasma emission component. The viewing angle ($i$) of the reflection site is
fixed at the default value ($\mu=cosi$ = 0.45, which is the ensemble average
of the viewing angles of the accreting binary systems) of the reflection
component. The final best-fit model ($\chi^{2}/DOF=666/657$) gives upper
temperature $21.3_{-1.3}^{+1.5}$ keV, which is in agreement with the finding
of Done & Osborne (1997) ($21.0_{-5.7}^{+11.0}$ keV) and Ishida et al. (2009)
($20.4_{-2.6}^{+4.0}$ keV). The abundance comes out to be
$0.53_{-0.08}^{+0.09}$ w.r.t solar. The reflection amplitude is obtained as
$1.18_{-0.25}^{+0.26}$, validating the presence of reflection as noticed from
the excess residual. However, this component may have degeneracy with a
complex intrinsic absorber, which can affect even beyond 10 keV for a strong
absorber (Fig. 8 of Dutta & Rana (2022)), thereby, the measured value of
reflection amplitude can change. Now, in order to probe the effect of the
intrinsic absorber in the soft X-rays, we next perform the analysis of the
XMM-Newton EPIC spectra.

For the XMM-Newton EPIC data (PN, MOS1, and MOS2), initially, we probed the
spectra in 5-9 keV which include the Fe line complex in 6-7 keV. We have used
an absorbed bremsstrahlung component to model the continuum and three Gaussian
components for the neutral, H-like and He-like Fe Kα lines. The column density
of the absorber is fixed at the literature value. The fit resulted in a fit-
statistic of $\chi^{2}/DOF=110/91$, and the best-fit parameters are quoted in
Table 4. A spectral plot comparing three iron lines in quiescence and outburst
phases are shown in Fig. 4. We noticed that the $\sigma$ of all three lines
are consistent with EPIC instrument resolution ($\Delta E\sim 120$ eV at $\sim
6$ keV), and the line widths could not be constrained, so fixed at zero. The
line central energies appear at the theoretically expected values, within
statistical uncertainty, and the strength of the neutral line is weaker
($82_{-30}^{+34}$eV) compared to the H-like ($102_{-31}^{+62}$eV) and He-like
($131_{-28}^{+46}$eV).

We next model the EPIC spectra in 0.3-10.0 keV energy range. The spectra are
described with the cooling flow component (mkcflow) and an absorption
component tbabs). The lower temperature is fixed at 0.0808 keV, whereas the
upper temperature of the cooling flow component is kept free. We added one
narrow Gaussian component for the neutral Fe line. The resultant fit
statistics is $\chi^{2}/DOF=530/417$. However, the column density is not
constrained, and we obtained an upper limit of $5\times 10^{19}\;cm^{-2}$. At
this point, to probe the presence of the intrinsic absorber, we included a
partial covering photo-electric absorption model (partcov*tbabs), and obtained
an improved fit-statistic of $\chi^{2}/DOF=511/415$. The covering fraction of
the intrinsic absorber is $0.21_{-0.07}^{+0.09}$ with a column density of
$4.2_{-1.5}^{+2.7}\times 10^{23}\;cm^{-2}$ indicating that the intrinsic
absorber is quite strong. The overall absorber column density, which includes
the ISM absorption along the line of sight, is now constrained (
$8.8_{-4.3}^{+5.1}\times 10^{19}\;cm^{-2}$). The upper temperature and the
elemental abundance of the cooling flow component are found to be
$30.7_{-4.0}^{+3.8}$ keV and $0.61_{-0.15}^{+0.16}$ as that of solar values,
respectively.

Now, to check the effect of the reflection and degeneracy with the partial
absorber, we introduced the Compton reflection component instead of the
partial covering absorber. We obtained a similar fit statistic
($\chi^{2}/DOF=514/416$), with a reflection amplitude of
$1.07_{-0.43}^{+0.32}$. The parameter values of the other components are
similar (within statistical uncertainty) to that of partial absorber fit. This
points to the delicate degeneracy between the partial absorber and the
reflection present in the modelling of the EPIC spectra.

In the final stage, guided by the individual modelling of the NuSTAR and EPIC
spectra, we proceed towards jointly fitting the simultaneous spectra.
Considering the possibility of an intrinsic absorber, we used two model
variants - one including the partial absorber and another without it. In XSPEC
notations the models are (Q1) constant* tbabs* (partcov* tbabs)* (reflect*
mkcflow+ gaussian) and (Q2) constant* tbabs* (reflect* mkcflow+ gaussian). The
best-fit parameter values are quoted in Table 2 and the spectra are plotted in
Fig. 2. In the first model, Q1, both the partial absorber and the Compton
reflection are considered, where we obtain a reflection amplitude
$0.40_{-0.19}^{+0.47}$ and intrinsic absorber column density of
$2.6_{-0.6}^{+1.2}\times 10^{23}\;cm^{-2}$ with covering fraction of
$0.16_{-0.05}^{+0.05}$. For the second model, Q2, the reflection amplitude
comes out to be $1.25_{-0.20}^{+0.27}$, which is close to the value obtained
from individual EPIC or NuSTAR analysis when intrinsic absorber was not
considered. All other parameter values agree within statistical confidence
between the models Q1 and Q2. Also, the cross normalisation parameters for
model Q2 are: CMOS1=$1.02_{-0.01}^{+0.01}$, CMOS2=$1.05_{-0.01}^{+0.01}$,
CFPMA=$1.13_{-0.02}^{+0.02}$, CFPMB=$1.09_{-0.02}^{+0.02}$, while CPN is fixed
to 1.

At this point, we argue that, since statistically, both these models are
equally acceptable, we need to favour one model over another based on physical
considerations. This has been discussed in the Section 4.2.

###  3.2 Outburst Phase

The outburst NuSTAR spectra in the 3.0-40.0 keV range are fitted with the
cooling flow model mkcflow and the ISM absorption model tbabs. We restrict the
analysis to energies up to 40 keV, after which the background begins to
dominate over source counts. We kept the lower temperature of the cooling flow
model fixed at 0.0808 keV (for the same reasons explained in Section 3.1) and
the column density of the ISM absorber at the literature value, not
constrained from the data. We included a gaussian component with free sigma to
consider the iron line complex in 6-7 keV, which appears to be a broad peak
and could not be resolved by NuSTAR. The fit statistic is
$\chi^{2}/DOF=668/554$ with an upper temperature of $10.9_{-0.2}^{+0.2}$ keV,
which is expected for the softer spectra in the outburst phase. For the
Compton reflection hump, we next included the reflect component with its
abundance linked to the cooling flow component, and viewing angle fixed at
default value as mentioned in the quiescence phase analysis. We now obtain an
improved fit statistic of $\chi^{2}/DOF=650/553$, with reflection amplitude of
$0.74_{-0.31}^{+0.39}$. The upper temperature is now $9.3_{-0.6}^{+0.6}$ keV,
and the abundance is $0.43_{-0.11}^{+0.09}$ w.r.t solar values.

Next, we attempted fitting the iron line complex in 6-7 keV using the XMM-
Newton EPIC spectra in the 5.0-9.0 keV range, as done for quiescence phase
analysis. The best-fit parameters are quoted in Table 4. We notice that all
line widths are consistent with the EPIC instrument resolution, and therefore
$\sigma$ was fixed at zero. The strength of the He-like Fe Kα line is maximum
($263_{-36}^{+43}$eV) among the three dominant lines. The neutral Fe Kα line
has similar strength as that during the quiescence phase, whereas the He-like
line is much stronger than quiescence. We notice the apparent blueshift
($6.46_{-0.03}^{+0.03}$ keV) of the neutral line. The reason behind is that
the K shell lines from the lower ionisation states - Fe XVII through Fe XXII
(which are certainly present, as the corresponding L-shell emissions are
strongly detected in the RGS spectra of outburst phase, Fig. 5) - have
intrinsic centroid around 6.5 keV, which are blended with the neutral line.

We then proceeded to model the entire EPIC spectra (PN, MOS1 and MOS2) in
0.3-10.0 keV. We introduced the cooling flow model to consider the emission
from the multi-temperature boundary layer, along with the ISM absorption
model. The lower temperature is fixed at 0.0808 keV and the ISM column density
is at the literature value. The fit statistic is extremely poor with
$\chi^{2}/DOF=6871/438$. We notice that outburst EPIC spectra are
significantly complex with an evident signature of blackbody emission, which
presents itself as excess in residual in soft X-ray below 0.5 keV. We added
the blackbody component, which improved the fit statistic to
$\chi^{2}/DOF=4574/437$. There are multiple strong emission line features as
expected during the outburst phase of a dwarf nova, like SS Cyg (Mauche, 2004;
Okada et al., 2008). Though many lines can be resolved in RGS spectra (see Fig
5), EPIC only detect those as narrow or broad peaks in the soft X-rays below
and around $\sim 2$ keV. Therefore, we needed to carefully add multiple
emissions components to bring down the fit statistic to an acceptable value.
We introduced five Gaussian components to consider the line emission features
and obtained an improved fit statistic of $\chi^{2}/DOF=604/426$. Three narrow
Gaussian components consider the emission features due to the O-VII line, Si
lines and Mg lines. One broad Gaussian accounts for a strong O-VIII line and
few neighbouring Fe L-shell emissions, and another broad Gaussian incorporates
Ne-lines. At this stage, we include the partial covering component
(partcov*tbabs) to probe the presence of the complex intrinsic absorber. The
improved fit statistic is now $\chi^{2}/DOF=581/421$, with a column density of
the intrinsic absorber $3.2\times 10^{22}\;cm^{-2}$ and covering fraction of
$0.14_{-0.04}^{+0.04}$.

After receiving the clues regarding model components from analysing individual
EPIC and NuSTAR spectra, we attempted simultaneous broadband spectral
modelling. In XSPEC notation, our model is constant* tbabs* (partcov* tbabs)*
(reflect* mkcflow+ gauss+ gauss+ gauss+ gauss+ gauss+ gauss+ bbody). The fit
statistic comes out to be $\chi^{2}/DOF=1257/979$ and best-fit parameter
values are quoted in Table 3. The spectra are plotted in Fig. 3 The fit
statistic is acceptable for the purpose of our study, where we focus on
obtaining the overall description of the continuum. The cross normalisation
parameters are: CMOS1=$1.04_{-0.01}^{+0.01}$, CMOS2=$1.11_{-0.01}^{+0.01}$,
CFPMA=$1.21_{-0.02}^{+0.02}$, CFPMB=$1.18_{-0.01}^{+0.02}$, while CPN is fixed
to 1. In this broadband modelling, we considered similar five Gaussian
components, as that of EPIC only fit, to consider the excess residual due to
line emission features in soft X-rays. The strong blackbody emission is also
modelled in the broadband spectra. The reflection amplitude is constrained at
$1.31_{-0.30}^{+0.30}$. The abundance ($0.51_{-0.02}^{+0.03}$) is
statistically consistent with the corresponding value of that parameter during
quiescence. We have also checked that fitting the broadband quiescence and
outburst data together with a tied abundance value recovers, to within
statistical uncertainties, the results from individual broadband fits, in
terms of all the parameters including the abundance ($0.46^{+0.06}_{-0.01}$)
and the reflection amplitudes ($1.18^{+0.13}_{-0.12}$ in quiescence and
$1.49^{+0.17}_{-0.24}$ in outburst). We could not constrain the overall
absorber column density, whose fit value was reaching the lowest limit allowed
for that component; so was fixed at the ISM column density from the
literature. The intrinsic absorber is evidently required in our fitting, which
if not considered, produces a much worse fit statistic of
$\chi^{2}/DOF=1358/980$ along with an unphysically high value of reflection
amplitude ($\sim 2.5$). The upper temperature of the cooling flow component is
$\sim 8.4$ keV, less than the quiescence phase (temperature $\sim 22.8$ keV),
indicating softer spectra during the outburst.

###  3.3 High resolution RGS spectra during quiescence and outburst Phase

To verify the line emission features that appeared in the soft X-rays obtained
from EPIC, we further checked the RGS spectra. The RGS spectra in 0.35-2.5 keV
range for both phases are shown in Fig. 5. We notice that during the
quiescence phase, the O-VIII line appears to be the strongest with other weak
emission lines. During the outburst, multiple strong emission lines are
present, including Kα lines of highly ionised states of several low Z
elements, e.g., C, N, O, Ne, Mg, Si, and Fe L shell emissions. However, given
the complexity involved in modelling the line emissions from the dwarf nova
systems, particularly in the outburst phase, we did not attempt robust
modelling of the RGS spectra, which is out of scope for this work.

Table 2: Best-fit parameter values from quiescence joint XMM-EPIC and NuSTAR fit (0.3-50.0 keV)  Parameters | Unit | Q${}_{1}^{\hskip 2.84544pt\dagger c}$ | Q${}_{2}^{\hskip 2.84544pt\dagger d}$
---|---|---|---
nHtb |  $10^{19}$cm-2 | $12.5_{-2.2}^{+4.0}$ | $15.8_{-2.7}^{+2.8}$
nHpcf |  $10^{22}$cm-2 | $25.7_{-5.8}^{+11.9}$ |
pcf |  | $0.16_{-0.05}^{+0.05}$ |
Tlow | keV | $0.0808_{f}$ | $0.0808_{f}$
Thigh | keV | $25.9_{-2.3}^{+1.1}$ | $22.8_{-1.1}^{+1.5}$
N${}_{C}^{\hskip 2.84544pt\dagger a}$ | $10^{-11}$ | $1.46_{-0.06}^{+0.13}$ | $1.32_{-0.04}^{+0.05}$
Z | Z⊙ | $0.56_{-0.13}^{+0.04}$ | $0.44_{-0.04}^{+0.06}$
relrefl |  | $0.40_{-0.19}^{+0.47}$ | $1.25_{-0.20}^{+0.27}$
EL | keV | $6.40_{-0.02}^{+0.04}$ | $6.42_{-0.04}^{+0.02}$
$\sigma$ | eV | $0_{f}$ | $0_{f}$
N${}_{L}^{\hskip 2.84544pt\dagger b}$ |  | $2.5_{-0.4}^{+0.4}$ | $2.4_{-0.4}^{+0.4}$
$\chi^{2}/DOF$ |  | $1189/1076$ | $1202/1078$

Figure 2: Spectrum and ratio (data/model) plot of the quiescence phase joint XMM-EPIC and NuSTAR data including partial covering absorber and Compton reflection, model Q1 (top) and including only the Compton reflection component, model Q2 (bottom) Table 3: Best-fit parameter values from joint outburst XMM-EPIC and NuSTAR fit (0.3-40.0 keV)  Parameters | Unit | Values
---|---|---
nHtb |  $10^{19}$cm-2 | $3.5_{f}$
nHpcf |  $10^{22}$cm-2 | $3.4_{-0.9}^{+1.0}$
$\rm pcf$ |  | $0.23_{-0.02}^{+0.02}$
relrefl |  | $1.31_{-0.30}^{+0.30}$
TBB | eV | $27.9_{-1.7}^{+1.2}$
N${}_{BB}^{\hskip 2.84544pt\dagger a}$ | $10^{-3}$ | $24.2_{-7.2}^{+18.1}$
Tlow | keV | $0.0808_{f}$
Thigh | keV | $8.4_{-0.3}^{+0.3}$
N${}_{C}^{\hskip 2.84544pt\dagger b}$ | $10^{-11}$ | $5.2_{-0.1}^{+0.1}$
Z | Z⊙ | $0.51_{-0.02}^{+0.03}$
E1 | keV | $0.563_{-0.002}^{+0.006}$
$\sigma_{1}$ | eV | $0_{f}$
N${}_{1}^{\hskip 2.84544pt\dagger c}$ | $10^{-3}$ | $2.1_{-0.2}^{+0.1}$
E2 | keV | $0.647_{-0.029}^{+0.016}$
$\sigma_{2}$ | eV | $135_{-19}^{+32}$
N${}_{2}^{\hskip 2.84544pt\dagger c}$ | $10^{-3}$ | $3.3_{-0.4}^{+1.0}$
E3 | keV | $1.89_{-0.01}^{+0.01}$
$\sigma_{3}$ | eV | $0_{f}$
N${}_{3}^{\hskip 2.84544pt\dagger c}$ | $10^{-3}$ | $6.8_{-1.6}^{+1.6}$
E4 | keV | $1.34_{-0.01}^{+0.01}$
$\sigma_{4}$ | eV | $0_{f}$
N${}_{4}^{\hskip 2.84544pt\dagger c}$ | $10^{-3}$ | $7.6_{-1.8}^{+1.8}$
E5 | keV | $0.958_{-0.016}^{+0.015}$
$\sigma_{5}$ | eV | $58_{-14}^{+15}$
N${}_{5}^{\hskip 2.84544pt\dagger c}$ | $10^{-3}$ | $0.6_{-0.2}^{+0.2}$
EL | keV | $6.44_{-0.01}^{+0.01}$
$\sigma$ | eV | $0_{f}$
N${}_{L}^{\hskip 2.84544pt\dagger d}$ | $10^{-5}$ | $4.2_{-0.4}^{+0.5}$
$\chi^{2}/DOF$ |  | $1257/979$
Table 4: Iron line comparison from outburst and quiescence XMM-EPIC data in 5-9 keV  | Parameters | Unit | Quiescence | Outburst
---|---|---|---|---
| nHtb |  $10^{19}$cm-2 | $3.5_{f}$ | $3.5_{f}$
| TBrems | keV | $11.6_{-3.0}^{+5.6}$ | $7.1_{-0.5}^{+1.7}$
Neutral | EL | keV | $6.42_{-0.03}^{+0.03}$ | $6.46_{-0.03}^{+0.03}$
line | $\sigma$ | eV | $0_{f}$ | $0_{f}$
| eqw | eV | $82_{-30}^{+34}$ | $81_{-22}^{+23}$
| N${}_{L}^{\hskip 2.84544pt\dagger a}$ | $10^{-5}$ | $2.4_{-0.8}^{+0.8}$ | $3.0_{-0.5}^{+1.1}$
He-like | EL | keV | $6.68_{-0.02}^{+0.03}$ | $6.69_{-0.01}^{+0.01}$
line | $\sigma$ | eV | $0_{f}$ | $0_{f}$
| eqw | eV | $131_{-28}^{+46}$ | $263_{-33}^{+42}$
| N${}_{L}^{\hskip 2.84544pt\dagger a}$ | $10^{-5}$ | $3.7_{-0.8}^{+0.9}$ | $8.4_{-1.0}^{+1.1}$
H-like | EL | keV | $6.99_{-0.03}^{+0.03}$ | $6.93_{-0.02}^{+0.03}$
line | $\sigma$ | eV | $0_{f}$ | $0_{f}$
| eqw | eV | $102_{-31}^{+62}$ | $86_{-28}^{+36}$
| N${}_{L}^{\hskip 2.84544pt\dagger a}$ | $10^{-5}$ | $2.5_{-0.9}^{+0.8}$ | $2.8_{-0.7}^{+0.8}$
| $\chi^{2}/DOF$ |  | $110/91$ | $118/97$
Figure 3: Spectrum and ratio (data/model) plot of the outburst phase joint
XMM-EPIC and NuSTAR data Figure 4: Comparison of three iron lines in
quiescence and outburst phase. The spectrum and ratio (data/model) plot is
shown for PN data only. Quiescence phase data is shown with black, and
outburst phase data is shown in red.

Figure 5: Multiple strong line emission features seen in the RGS spectra
during quiescence(top) and outburst (bottom) phase.

##  4 Discussion

###  4.1 Quiescence vs Outburst X-ray : Hard vs Soft

In dwarf novae systems like SS Cyg, where the material is accreted via an
accretion disk, the kinetic energy of the accreting material in the boundary
layer is equal to half of the gravitational potential energy of the WD.
Following the formation of a strong shock, a fraction of this kinetic energy
is transformed into thermal energy, and the remaining kinetic energy gradually
converts into thermal energy as the matter cools down, giving rise to the
multi-temperature nature of the plasma. If we assume model Q2 during
quiescence (the reason discussed in the Sec. 4.2), the upper temperature of
the cooling flow component ($22.8_{-1.1}^{+1.5}$ keV) is related to the shock
temperature of the optically thin plasma in the boundary layer (Pandel et al.,
2005). By relating the thermal energy of the accreting material with the
gravitational potential energy of WD and incorporating the empirical
correction factor ($\alpha=T_{\rm high}/T_{\rm s,k}$, where $T_{\rm high}$ is
the maximum temperature obtained from plasma emission model, $T_{\rm s,k}$ is
the Keplerian shock temperature) of 0.611 (Mukai & Byckling, 2022); we can
write the following equation (Yu et al., 2018; Byckling et al., 2010):

$KT_{high}=\alpha\times\frac{3}{16}\times\frac{GM_{\text{WD}}\mu
m_{\text{P}}}{R_{\text{WD}}}$ (1)

where K, G, $\mu$ and m${}_{\text{P}}$ represents the Boltzmann constant,
gravitational constant, mean molecular weight ( assumed to be 0.615) of the
accreting material, and mass of proton, respectively. $M_{\text{WD}}$ and
$R_{\text{WD}}$ denote mass and radius of WD respectively. Coupling this
equation with the mass-radius relationship for WD (Nauenberg, 1972), we obtain
a WD mass of $1.18_{-0.01}^{+0.02}M_{\odot}$ and a WD radius of
$0.40_{-0.02}^{+0.01}\times 10^{9}$cm. Our measured mass value agrees very
well with the value obtained by Friend et al. (1990)
($1.19_{-0.02}^{+0.02}M_{\odot}$) using radial velocity study of sodium
doublet line. On the other hand, the mass measurement by Bitner et al. (2007)
using absorption line based optical spectroscopic study is smaller ($0.81\pm
0.19M_{\odot}$) than ours. However, we should note that the above two methods
rely on the indirect way of measuring the WD mass by performing the difficult
task of precise measurement of the inclination angle and mass ratio of SS Cyg.
Whereas our X-ray spectroscopy method of WD mass estimate is more direct; by
measuring the shock temperature obtained from broadband X-ray spectra which is
directly linked to the accretion onto the WD (thereby, linked to its mass).
However, we want to caution the reader that the empirical correction factor,
which we have used and definitely needed, may not be universal for all DNe
(Mukai & Byckling, 2022).

Our spectral model during the quiescence measures an unabsorbed bolometric
flux of $5.9_{-0.1}^{+0.1}\times 10^{-11}\;erg\;cm^{-2}\;s^{-1}$ in 0.01-100.0
keV energy range. Considering a distance of $114.62$pc to the source, this
flux value corresponds to a luminosity of $\sim 9.3\times 10^{31}\;\rm
erg\;s^{-1}$. Now, relating the luminosity with the mass accretion rate as
follows,

$L=\frac{GM_{\text{WD}}\dot{m}}{2R_{\text{WD}}}$ (2)

we obtain a mass accretion rate ($\dot{m}$) of $\sim 4.7\times 10^{14}\;\rm
g\;s^{-1}$ $\sim 7.5\times 10^{-12}\;M_{\odot}\;yr^{-1}$. This value is
consistent with the mass accretion rate obtained from the mkcflow
normalisation parameter after incorporating the empirical correction factor
(actual mass accretion rate = empirical correction factor $\times$ cooling
flow normalization; since cooling flow $T_{\rm high}$ is empirical factor
times the actual shock temperature, therefore $T_{\rm high}$ gives an
apparently lower $M_{\rm WD}/R_{\rm WD}$ ratio, thus apparently higher mass
accretion rate).

Now, for the outburst phase, broadband spectral analysis indicates an upper
temperature of the optically thin plasma to be $8.4_{-0.3}^{+0.3}$ keV. This
result points out the spectral softness during the outburst than quiescence.
The possible origin of this hard X-ray emitting plasma is the optically thin
corona instead of the boundary layer, which is optically thick during this
phase. The outburst model results in an unabsorbed bolometric flux (0.01-100.0
keV) of $2.1_{-0.6}^{+0.2}\times 10^{-9}\;erg\;cm^{-2}\;s^{-1}$ and a
corresponding luminosity of $\sim 3.3\times 10^{33}\;erg\;s^{-1}$. Using eqn.
2, we obtain $\dot{m}$ $\sim 1.7\times 10^{16}\;g\;s^{-1}$ $\sim 2.7\times
10^{-10}\;M_{\odot}\;yr^{-1}$ during the outburst. This enhanced $\dot{m}$
during outburst ($\sim 35$ times of quiescence phase) is expected for an
optically thick boundary layer (Patterson & Raymond, 1985b). We clearly notice
the signs of the blackbody emission in the soft X-rays from our modelling,
which is consistent with an optically thick boundary layer. The temperature of
the blackbody ($T_{\text{BL}}$) is $28_{-2}^{+1}$ eV, along with an unabsorbed
blackbody flux (0.01-100.0 keV) of $2.0_{-0.2}^{+0.8}\times
10^{-9}\;erg\;cm^{-2}\;s^{-1}$ and a corresponding luminosity
($L_{\text{BL}}$) of $\sim 3.2\times 10^{33}\;erg\;s^{-1}$. This agrees with
the expectation that the increased luminosity in X-rays during outburst emits
almost entirely ($\sim 97\%$) in the very soft X-rays in the form of blackbody
from the optically thick BL. Following Frank et al. (2002), we can relate the
blackbody luminosity to the area of the emitting region as follows,

$L_{\text{BL}}=4\pi R_{\text{WD}}H\sigma T_{\text{BL}}^{4}$ (3)

where $\sigma$ is the Stefan–Boltzmann constant, and H denotes the radial
extent of the emitting region. Substituting for $L_{\text{BL}},T_{\text{BL}}$
and $R_{\text{WD}}$, we obtain $H\sim 1.0\times 10^{6}\;\text{cm}\sim
2.6\times 10^{-3}R_{\text{WD}}$. This result shows that the optically thick BL
is very close to the WD surface, which is consistent with the picture that the
disk’s inner edge reaches almost near the WD surface.

###  4.2 Clues from Reflection and Partial absorber: Location of X-ray
emitting plasma

The Compton reflection is undoubtedly confirmed during both phases from our
broadband spectral analysis. During quiescence, there is a degeneracy between
the intrinsic partial absorber and the Compton reflection, which influence an
overlapping energy band. Considering model Q1 involving both of those two
components, we obtain a reflection amplitude of $0.40_{-0.19}^{+0.47}$.

In a simplistic geometry, the reflection from cold neutral material is $\sim
1$ when a point source emitter subtends a $2\pi$ solid angle over the
reflector, i.e. emitter is just above the reflector. The reflection amplitude
($\Omega/2\pi$, where $\Omega$ is the solid angle subtended by the emitter on
the reflector) thus can be related to the height of the emitter ($h$) from the
reflector as (see Lopes de Oliveira & Mukai (2019)),
$h/(R_{\text{WD}})=\sqrt{1/(1-(1-\Omega/2\pi)^{2})}-1$. We visualise a
scenario in which the hard X-rays from optically thin BL plasma get reflected
by the WD surface. Assuming a point like plasma and using the obtained value
of the solid angle subtended by the optically thin BL on the surface of the
WD, we calculate a height, $0.25_{-0.24}^{+0.38}\;R_{\text{WD}}$, of the
plasma from the WD surface. Though this quantity is very poorly constrained,
the central value represents that the inner edge of the disk is quite far away
from WD surface compared to the typical values obtained for other dwarf nova.
For example, eclipsing dwarf nova Z Cha (Nucita et al., 2011), HT Cas (Nucita
et al., 2009; Mukai et al., 1997), OY Car (Ramsay et al., 2001; Wheatley et
al., 2003) shows that extent of the X-ray emission region is slightly smaller
than that the WD radius or almost comparable within few per cent more than WD
radius. This makes the large value of the height of the X-ray emitting
boundary layer from the WD surface ($\sim 25\%R_{\rm WD}$) doubtful, which
deviates from the typical picture of dwarf nova. The next concern of this
scenario is that the inner edge of the disk, which is considerably far away
from the WD surface, cannot be contributing to the partial absorber,
especially when the binary inclination angle is relatively small $\sim
37\arcdeg$. As a consequence, it becomes difficult to explain such a strong
($\sim 10^{23}\;cm^{-2}$) partial absorber during the quiescence phase. Due to
these ambiguities, we do not favour the scenario based on model Q1.

For the model Q2 in quiescence, the reflection amplitude is more than 1 ($\sim
1.25$) and demands multiple sites of reflection. In this scenario, the photons
emitted from the X-ray emitting plasma will get Compton scattered by both the
WD surface as well as the accretion disk.

For the outburst phase, the reflection amplitude is almost similar ($\sim
1.31$), within statistical uncertainty, to that of the quiescence phase value
and a similar reflection geometry can be envisaged. We assume a picture where
the hard X-ray emitting corona is present above the optically thick BL. Since
the disk’s inner edge is almost near the WD surface (as supported by the
calculation in Section 4.1), the X-rays from the emitted source can be
reflected by both the WD surface and the cold accretion disk. Also, our
spectral analysis showed that the outburst exhibit presence of a partial
absorber (column density of $3.4_{-0.9}^{+1.0}\times 10^{22}\;cm^{-2}$ with a
covering fraction of $0.23^{+0.02}_{-0.02}$), intrinsic to the source. During
the outburst, the accretion disk remains turbulent. The partial absorber we
see during this phase may originate from the outflowing accretion disk wind.

Done & Osborne (1997) found that the reflection amplitude is higher ($\sim
2.2$) during the outburst than the quiescence ($\sim 0.7$). They conclude that
in outburst, the BL extends over the WD surface, thus providing more
reflection site - WD surface as well as the inner disk. In contrast, in the
quiescence phase, the inner disk is truncated or optically thin, so no
reflection from the disk. But we should note that this conclusion on the value
of reflection amplitudes has limitations. Their spectral analysis, based on
GINGA observation, already fits a simpler continuum model with reasonably good
statistics even without considering reflection.

On the other hand, Ishida et al. (2009) obtained much higher reflection
amplitude in quiescence ($\sim 1.7$) than in outburst ($\sim 0.9$). Their
explanation is quite the opposite to Done & Osborne (1997), where they
describe the reflection of the emission by BL from both the accretion disk and
the WD surface in quiescence. But, in the outburst, the optically thin thermal
plasma is distributed as corona over an optically thick accretion disk,
thereby getting reflected only from the accretion disc. But the difficulty
with their measured reflection amplitudes is that either the data is not
directly extended till Compton reflection hump (in outburst, using only Suzaku
XIS data extended till 10 keV), or the complications due to systematic
uncertainties in the HXD/PIN background level and/or cross-calibration between
XIS and HXD/PIN (in quiescence, using simultaneous XIS and HXD/PIN data in
4.2-40 keV).

A recent study (Kimura et al., 2021) of anomalous outburst event of SS Cyg in
2021 using simultaneous NICER and NuSTAR data showed a weak reflection ($\sim
0.2$) amplitude during the anomalous outburst event as well as during the
quiescence phase before it. They proposed a large shock height where the hard
X-ray emitting corona is expanded in the vertical direction greatly, similar
to a coronal siphon flow scenario, to an extent which is more than the WD
radius and resulting in a weak reflection (their Figure 10). However, it would
be unusual (see the results on eclipsing dwarf novae mentioned earlier) for
the inner edge of the disk to be truncated so far away from the WD radius
($\sim 10R_{\rm WD}$) during quiescence, and the X-ray emitting plasma is
extended till such a great distance. Note also that the maximum plasma
temperature during quiescence epochs T1 and T2 derived by Kimura et al. are
higher ($\sim 33$ keV) than our value. More importantly, the Fe abundance
value obtained by Kimura et al. of $\sim 0.10$ is significantly lower than our
value ($\sim 0.5$) or that of Ishida et al. ($\sim$0.37). Harrison & Hamilton
(2015), using infrared spectroscopy of the secondary, also found a Fe abundace
of $\sim 0.3-1.0Z_{\odot}$, even though they noted the potential degeneracy
between the secondary temperature and abundance. We note that there is
correlation among the reflection amplitude, the plasma upper temperature and
the Fe abundance, and thereby the measurement of reflection amplitude can be
impacted by the other two parameter values. In particular, while the
reflection amplitude and the maximum temperature can change from one state to
another, the abundance is expected to remain constant, so it is essential to
reconcile the discrepant abundance values. Finally, we note the possibility
that the result of Kimura et al. potentially depends on perfect cross-
calibration between NICER and NuSTAR, which may be unrealistic considering the
relatively young age of the NICER mission.

At this point, our study, based on the simultaneous XMM-Newton and NuSTAR data
having good cross-calibration among the instruments and extended broadband
coverage, securely proves the existence of the reflection. Our measured
reflection amplitudes are similar and higher than 1, indicating that both the
disk and the WD surface are responsible for the reflection in both phases. We
agree that there are disagreements of our results with the previous studies.
Although we have our reasons to believe our modelling is correct, the
disagreements should be resolved in future studies.

Now, another important feature is the neutral Fe $K_{\alpha}$ line, whose
parameters agree within statistical uncertainty (see Table 4) in both phases.
This is expected because the strength of the neutral iron is correlated with
the reflection amplitude as both the fluorescence emission and the Compton
reflection originate from the cold material like the WD surface or accretion
disk. The Gaussian line width of the neutral line is consistent with the
instrument resolution during both the quiescence and outburst phases. We
should note that the actual widths of the Fe lines are limited by the
instrument resolution of the EPIC detectors ($\Delta E\sim 128$ eV at 6.4
keV). Therefore, it is hard to distinguish from the EPIC data whether an
actual narrow component of this line is contributed from the WD surface and a
relatively broader component is contributed from the accretion disk. As a
matter of fact, the disk contribution is unlikely to be resolved with EPIC
data, given the possible Keplarian velocity near WD surface along the line of
sight ($v_{\rm k}\sin{i}\sim 3700\rm km\,s^{-1}$, for the given WD mass and
radius of SS Cyg and its binary inclination ($i$)) can at most produce a line
width of $\sim 80$eV. Also, the high-resolution spectroscopic study (Rana et
al., 2006) of neutral Fe line of SS Cyg in both the quiescence and outburst
phase using HETG data suggest that the lines are of similar width ($\sim 60$
eV). The relative contribution of WD surface and the disk to Compton
reflection can be calculated based on the strength of the narrow and broad
components of the neutral Fe Kα line. In that regard, future observations with
high-resolution instruments, e.g., XRISM, has the potential to determine this
via a secure deconvolution of the neutral Fe Kα line into a narrow and broad
component.

##  5 Summary

In this work, we have investigated the dwarf nova SS Cyg during quiescence and
outburst using broadband X-ray spectroscopy carried out by XMM-Newton and
NuSTAR. Thanks to the good cross-calibration between the two telescopes and
excellent sensitivity in broad energy bands - in soft X-rays (XMM-Newton) and
hard X-rays (NuSTAR), we have distinguished spectral features and thus
physical conditions in both phases, and constrained the WD mass. In summary,
we found that:

  * •

The spectral modelling showed that the spectra were harder during quiescence
(upper temperature of the plasma emission component is $\sim 22.8$ keV) than
the outburst phase ($\sim 8.2$ keV).

  * •

The bolometric (0.01-100.0 keV) luminosity (as well as the mass accretion
rate) during outburst is $\sim 35$ times more than quiescence. The major
contribution to flux during outburst appears from the optically thick boundary
layer in the form of blackbody emission ($T_{\rm BL}\sim 28\;\rm eV$). During
the outburst, the inner edge of the disc resides very close to the WD surface
($\sim 0.0026R_{\rm WD}$).

  * •

Both the quiescence and outburst spectra showed similarly strong reflection
amplitude, demanding both the disk and the WD surface to contribute to the
reflection in both phases. The strengths of the neutral iron Kα lines are also
similar between both phases. Our current data have limitations to resolve in
the broad and narrow components of the line, which could potentially reveal
the relative contribution of the disk and the WD surface to Compton
reflection.

  * •

Partial intrinsic absorber ($\sim 3\times 10^{22}\;\rm cm^{-2}$ with covering
fraction $\sim 0.23$), possibly arising from outflowing accretion disk wind,
is present during the outburst. For quiescence, our modelling exhibited a
delicate statistical degeneracy between the partial absorber and the
reflection component. However, we could not physically justify the presence of
the partial intrinsic absorber during this phase.

  * •

The WD mass is consistent with $1.18_{-0.01}^{+0.02}\rm M_{\odot}$, as
inferred from the X-ray broadband spectral modelling of the quiescence phase.

RLO was partially supported by the Brazilian institution CNPq
(PQ-312705/2020-4). This research has used the data obtained from the NuSTAR
telescope, operated jointly by Caltech and NASA, and the XMM-Newton telescope,
operated by ESA. We thank the NuSTAR science operation team and the XMM-Newton
science operation team for providing the data. We acknowledge the members at
the helpdesk maintained by the High Energy Astrophysics Science Archive
Research Center (HEASARC) and the XMM-Newton helpdesk team members for
providing necessary support. The data used for analysis in this article are
publicly available in NASA’s High Energy Astrophysics Science Archive Research
Center (HEASARC) archive (https://heasarc.gsfc.nasa.gov/docs/archive.html) and
XMM-Newton Science archive (http://nxsa.esac.esa.int/nxsa-web/#search). We
also acknowledge the variable star observations from the AAVSO International
Database contributed by observers worldwide and used in this research.

## References

  * Arnaud (1996) Arnaud, K. A. 1996, in Astronomical Society of the Pacific Conference Series, Vol. 101, Astronomical Data Analysis Software and Systems V, ed. G. H. Jacoby & J. Barnes, 17
  * Bailer-Jones et al. (2021) Bailer-Jones, C. A. L., Rybizki, J., Fouesneau, M., Demleitner, M., & Andrae, R. 2021, AJ, 161, 147, doi: 10.3847/1538-3881/abd806
  * Baskill et al. (2005) Baskill, D. S., Wheatley, P. J., & Osborne, J. P. 2005, MNRAS, 357, 626, doi: 10.1111/j.1365-2966.2005.08677.x
  * Bath & Pringle (1981) Bath, G. T., & Pringle, J. E. 1981, MNRAS, 194, 967, doi: 10.1093/mnras/194.4.967
  * Bath & Pringle (1982a) —. 1982a, MNRAS, 199, 267, doi: 10.1093/mnras/199.2.267
  * Bath & Pringle (1982b) —. 1982b, MNRAS, 201, 345, doi: 10.1093/mnras/201.2.345
  * Bitner et al. (2007) Bitner, M. A., Robinson, E. L., & Behr, B. B. 2007, ApJ, 662, 564, doi: 10.1086/517496
  * Byckling et al. (2010) Byckling, K., Mukai, K., Thorstensen, J. R., & Osborne, J. P. 2010, MNRAS, 408, 2298, doi: 10.1111/j.1365-2966.2010.17276.x
  * den Herder et al. (2001) den Herder, J. W., Brinkman, A. C., Kahn, S. M., et al. 2001, A&A, 365, L7, doi: 10.1051/0004-6361:20000058
  * Done & Osborne (1997) Done, C., & Osborne, J. P. 1997, MNRAS, 288, 649, doi: 10.1093/mnras/288.3.649
  * Dutta & Rana (2022) Dutta, A., & Rana, V. 2022, ApJ, 940, 100, doi: 10.3847/1538-4357/ac9587
  * Frank et al. (2002) Frank, J., King, A., & Raine, D. J. 2002, Accretion Power in Astrophysics: Third Edition
  * Friend et al. (1990) Friend, M. T., Martin, J. S., Smith, R. C., & Jones, D. H. P. 1990, MNRAS, 246, 654
  * Gabriel et al. (2004) Gabriel, C., Denby, M., Fyfe, D. J., et al. 2004, in Astronomical Society of the Pacific Conference Series, Vol. 314, Astronomical Data Analysis Software and Systems (ADASS) XIII, ed. F. Ochsenbein, M. G. Allen, & D. Egret, 759
  * Gaia Collaboration et al. (2018) Gaia Collaboration, Brown, A. G. A., Vallenari, A., et al. 2018, A&A, 616, A1, doi: 10.1051/0004-6361/201833051
  * George & Fabian (1991) George, I. M., & Fabian, A. C. 1991, MNRAS, 249, 352, doi: 10.1093/mnras/249.2.352
  * Harrison et al. (2013) Harrison, F. A., Craig, W. W., Christensen, F. E., et al. 2013, ApJ, 770, 103, doi: 10.1088/0004-637X/770/2/103
  * Harrison & Hamilton (2015) Harrison, T. E., & Hamilton, R. T. 2015, AJ, 150, 142, doi: 10.1088/0004-6256/150/5/142
  * Hellier (2001) Hellier, C. 2001, Cataclysmic Variable Stars (Springer)
  * Hessman et al. (1984) Hessman, F. V., Robinson, E. L., Nather, R. E., & Zhang, E. H. 1984, ApJ, 286, 747, doi: 10.1086/162651
  * Ishida et al. (2009) Ishida, M., Okada, S., Hayashi, T., et al. 2009, PASJ, 61, S77, doi: 10.1093/pasj/61.sp1.S77
  * Jansen et al. (2001) Jansen, F., Lumb, D., Altieri, B., et al. 2001, A&A, 365, L1, doi: 10.1051/0004-6361:20000036
  * Jones & Watson (1992) Jones, M. H., & Watson, M. G. 1992, MNRAS, 257, 633, doi: 10.1093/mnras/257.4.633
  * Kimura et al. (2021) Kimura, M., Yamada, S., Nakaniwa, N., et al. 2021, PASJ, 73, 1262, doi: 10.1093/pasj/psab073
  * Lopes de Oliveira & Mukai (2019) Lopes de Oliveira, R., & Mukai, K. 2019, ApJ, 880, 128, doi: 10.3847/1538-4357/ab2b41
  * Magdziarz & Zdziarski (1995) Magdziarz, P., & Zdziarski, A. A. 1995, MNRAS, 273, 837, doi: 10.1093/mnras/273.3.837
  * Matt et al. (1991) Matt, G., Perola, G. C., & Piro, L. 1991, A&A, 247, 25
  * Mauche (2004) Mauche, C. W. 2004, ApJ, 610, 422, doi: 10.1086/421438
  * Mauche et al. (1988) Mauche, C. W., Raymond, J. C., & Cordova, F. A. 1988, ApJ, 335, 829, doi: 10.1086/166971
  * McGowan et al. (2004) McGowan, K. E., Priedhorsky, W. C., & Trudolyubov, S. P. 2004, ApJ, 601, 1100, doi: 10.1086/380758
  * Miller-Jones et al. (2013) Miller-Jones, J. C. A., Sivakoff, G. R., Knigge, C., et al. 2013, Science, 340, 950, doi: 10.1126/science.1237145
  * Mukai & Byckling (2022) Mukai, K., & Byckling, K. 2022, Research Notes of the American Astronomical Society, 6, 65, doi: 10.3847/2515-5172/ac618b
  * Mukai et al. (1997) Mukai, K., Wood, J. H., Naylor, T., Schlegel, E. M., & Swank, J. H. 1997, ApJ, 475, 812, doi: 10.1086/303571
  * Mushotzky & Szymkowiak (1988) Mushotzky, R. F., & Szymkowiak, A. E. 1988, in NATO Advanced Study Institute (ASI) Series C, Vol. 229, Cooling Flows in Clusters and Galaxies, ed. A. C. Fabian, 53, doi: 10.1007/978-94-009-2953-1_6
  * Narayan & Popham (1993) Narayan, R., & Popham, R. 1993, Nature, 362, 820, doi: 10.1038/362820a0
  * Nasa High Energy Astrophysics Science Archive Research Center (2014) (Heasarc) Nasa High Energy Astrophysics Science Archive Research Center (Heasarc). 2014, HEAsoft: Unified Release of FTOOLS and XANADU, Astrophysics Source Code Library, record ascl:1408.004.  http://ascl.net/1408.004
  * Nauenberg (1972) Nauenberg, M. 1972, ApJ, 175, 417, doi: 10.1086/151568
  * Nucita et al. (2011) Nucita, A. A., Kuulkers, E., Maiolo, B. M. T., et al. 2011, A&A, 536, A75, doi: 10.1051/0004-6361/201117572
  * Nucita et al. (2009) Nucita, A. A., Maiolo, B. M. T., Carpano, S., et al. 2009, A&A, 504, 973, doi: 10.1051/0004-6361/200811461
  * Okada et al. (2008) Okada, S., Nakamura, R., & Ishida, M. 2008, ApJ, 680, 695, doi: 10.1086/587161
  * Osaki (1974) Osaki, Y. 1974, PASJ, 26, 429
  * Osaki (1996) —. 1996, PASP, 108, 39, doi: 10.1086/133689
  * Pandel et al. (2005) Pandel, D., Córdova, F. A., Mason, K. O., & Priedhorsky, W. C. 2005, ApJ, 626, 396, doi: 10.1086/429983
  * Patterson & Raymond (1985a) Patterson, J., & Raymond, J. C. 1985a, ApJ, 292, 535, doi: 10.1086/163187
  * Patterson & Raymond (1985b) —. 1985b, ApJ, 292, 550, doi: 10.1086/163188
  * Popham & Narayan (1995) Popham, R., & Narayan, R. 1995, ApJ, 442, 337, doi: 10.1086/175444
  * Pringle & Savonije (1979) Pringle, J. E., & Savonije, G. J. 1979, MNRAS, 187, 777, doi: 10.1093/mnras/187.4.777
  * Ramsay et al. (2001) Ramsay, G., Poole, T., Mason, K., et al. 2001, A&A, 365, L288, doi: 10.1051/0004-6361:20000039
  * Rana et al. (2006) Rana, V. R., Singh, K. P., Schlegel, E. M., & Barrett, P. E. 2006, ApJ, 642, 1042, doi: 10.1086/500316
  * Ricketts et al. (1979) Ricketts, M. J., King, A. R., & Raine, D. J. 1979, MNRAS, 186, 233, doi: 10.1093/mnras/186.2.233
  * Shafter (1983) Shafter, A. W. 1983, PhD thesis, California Univ., Los Angeles.
  * Strüder et al. (2001) Strüder, L., Briel, U., Dennerl, K., et al. 2001, A&A, 365, L18, doi: 10.1051/0004-6361:20000066
  * Turner et al. (2001) Turner, M. J. L., Abbey, A., Arnaud, M., et al. 2001, A&A, 365, L27, doi: 10.1051/0004-6361:20000087
  * Verner et al. (1996) Verner, D. A., Ferland, G. J., Korista, K. T., & Yakovlev, D. G. 1996, ApJ, 465, 487, doi: 10.1086/177435
  * Warner (2003) Warner, B. 2003, Cataclysmic Variable Stars (Cambridge University Press), doi: 10.1017/CBO9780511586491
  * Wheatley & Mauche (2005) Wheatley, P. J., & Mauche, C. W. 2005, in Astronomical Society of the Pacific Conference Series, Vol. 330, The Astrophysics of Cataclysmic Variables and Related Objects, ed. J. M. Hameury & J. P. Lasota, 257.  https://arxiv.org/abs/astro-ph/0412166
  * Wheatley et al. (2003) Wheatley, P. J., Mauche, C. W., & Mattei, J. A. 2003, MNRAS, 345, 49, doi: 10.1046/j.1365-8711.2003.06936.x
  * Wilms et al. (2000) Wilms, J., Allen, A., & McCray, R. 2000, ApJ, 542, 914, doi: 10.1086/317016
  * Yu et al. (2018) Yu, Z.-l., Xu, X.-j., Li, X.-D., et al. 2018, ApJ, 853, 182, doi: 10.3847/1538-4357/aaa47d