text:
\section{Introduction}
\label{s:intro}
Luminous supersoft X-ray sources (SSSs) were discovered in the
Large Magellanic Cloud (LMC) and in the Small Magellanic Cloud
(SMC) by \cite{1981ApJ...248..925L} and \cite{1981ApJ...243..736S}.
They are characterized by very soft thermal spectra, emitting
predominantly at energies $\lesssim$0.5\,keV
\citep[][]{1991A&A...246L..17G}.
Their extremely soft spectra correspond to blackbody temperatures
of $\approx$15--80\,eV and bolometric luminosities of
$10^{36}-2\times10^{38}$$\rm\,erg\,s^{-1}$.
These objects are commonly accepted as binaries that consist
of a massive white dwarf (WD) radiating close to the Eddington
luminosity due to a steady nuclear burning on its surface, when
the hydrogen-rich material is burned as fast as it is accreted,
at rates of the order of $10^{-7}$\,$M_{\odot}\,{\rm yr}^{-1}$\
\citep[][]{1992A&A...262...97V,1997ARA&A..35...69K}.
Following multiwavelength observations have revealed a significant
excess of the radiation in the ultraviolet (UV) to near-infrared
(NIR), well above the Rayleigh-Jeans tail of the SSS radiation
itself (see Sects.~\ref{ss:0513} -- \ref{ss:0527} and \ref{s:obs}).
To explain the high luminosity of bright SSSs, and the longer
wavelength excess, \cite{1996LNP...472...65P} proposed a model,
in which a significant fraction of the WD's radiation is converted
to the UV--NIR by irradiating, (i) the flared accretion disk and
(ii) the donor star.

In this paper we selected four bright SSSs observed in the
Magellanic Clouds, RX\,J0513.9-6951, RX\,J0058.6-7135,
RX\,J0543.6-6822 and RX\,J0527.8-6954, with the aim to model
their global X-ray---NIR spectral energy distribution (SED)
by the method of multiwavelength modeling described by
\cite{2015NewA...36..116S}.
The motivation for this work is the absence of the SED model,
which would uniformly fit radiation of SSSs in both the supersoft
X-ray and the UV--NIR domains.
Further, the extreme properties of SSSs and their spectral
features indicate the presence of the nebular radiation in
the spectrum (see Appendix~\ref{s:appA}), which could explain
the observed strong UV--NIR excess as it is currently
considered for the accreting nuclear-burning WDs in symbiotic
binaries
\citep[][]{1984ApJ...279..252K,
           1991A&A...248..458M,
           2005A&A...440..995S}.
Therefore, here we are testing SED modeling, in which the UV--NIR
is dominated by the nebular emission instead of the irradiated
disk/companion radiation.

Section~\ref{s:obs} summarizes the observed supersoft X-rays
to NIR SED of our targets, while Sect.~\ref{s:analysis}
introduces the method and results of our analysis. Their
discussion is found in Sect.~\ref{s:dis}, while Sect.~\ref{s:sum}
summarizes our findings, and proposes tasks for future
investigation.
In the following subsections, we first introduce our targets.
\subsection{The LMC SSS RX\,J0513.9-6951}
\label{ss:0513}
RX\,J0513.9-6951 is a transient binary supersoft X-ray source.
Currently, it is thought that the system contains a somewhat
evolved star and a relatively massive compact object at a 0.76-day
orbit, viewed nearly pole-on
\citep[][]{1996ApJ...456..320C,1996ApJ...470.1065S}.
The system is the brightens SSS emitting a significant amount
of the radiation also in the far-UV ($\gtrsim 10^{-13}$$\,\rm erg\,cm^{-2}\,s^{-1}\,\AA^{-1}$).

RX\,J0513.9-6951 was discovered during the \textsl{ROSAT}
All-sky Survey (1990 July -- 1991 January) in the LMC
\citep[][]{1993A&A...270L...9S}. The authors found it to be
variable and matched its total average spectrum by a blackbody
radiation (see Table~\ref{tab:lit}).
\cite{1993A&A...278L..39P} revealed the optical counterpart as
a $B\approx 17$\,mag blue star. Its spectrum was dominated by
the hydrogen Balmer lines with a signature of a broad P-Cyg
absorption component indicating a mass-loss from the system
at $v_{\infty} \approx 3600$\kms. Absence of He\,\rm {\scriptsize I}\ lines
and the presence of highly ionized ions (O\,\rm {\scriptsize V}\rm {\scriptsize I}\,3811, 3834
doublet, He\,\rm {\scriptsize I}\I) with
$I_{\rm{He\,\rm {\scriptsize I}\I}\,4686} \gg I_{\rm{H}\beta}$ reflect
the presence of a very hot ionizing source in the binary.
They also pointed that the optical counterpart appears
fainter during the X-ray outburst.

Pronounced optical variability of RX\,J0513.9-6951 was revealed
by optical multicolor monitoring campaigns.
\cite{1996A&A...309L..11R} measured an optical low states
during February to December, 1993, lasting around 40 days with
a decrease in the continuum by $\Delta V \sim 1$\,mag and
a factor of $\approx$10 decrease in emission line fluxes.
The light curve obtained within the MACHO project specified
the occurrence of the low stages on a time-scale of
$\sim 100-200$ days
\citep[][]{1996MNRAS.280L..49A,1996ApJ...470.1065S}.
In addition, during the high-state, these authors revealed
a small ($\Delta V \sim 0.05$) light modulation with a period
of 0.763\,d, which is consistent with variations in the radial
velocities of He\,{\scriptsize II}\,$\lambda$4686 emission line, and thus
confirms a binary nature of the system
\citep[][]{1996ApJ...456..320C}.

Broad wings of the strongest emission lines (He\,\rm {\scriptsize I}\I\ and \hb)
accompanied with satellite components indicated a bipolar outflow
and thus the presence of a disk in the binary. The bipolar
outflow in the form of jets suggested that the accretor is
a WD \citep[][]{1996ApJ...470.1065S,1996ApJ...456..320C}.

Based on all previously published optical and X-ray data,
\cite{1996ApJ...470.1065S} pointed out the principal feature of
the variability: the anti-correlation between the supersoft
X-ray and the optical fluxes.
X-ray monitoring of RX\,J0513.9-6951 showed that the flux
anti-correlation is very strict: There are cyclic changes
between optical-low/X-ray-on states and optical-high/X-ray-off
states \citep[e.g.,][]{2000A&A...354L..37R,2010NewAR..54...75C}.

Based on the \textsl{HST} ultraviolet spectroscopy,
\cite{1998A&A...333..163G} derived
the neutral hydrogen density
$N_{\rm H} = (5.5\pm 1.0) \times 10^{20}$\,cm$^{-3}$.
The authors found that this value is consistent with parameters
determined by model atmosphere fits to the \textsl{ROSAT PSPC}
spectrum of July 1993 (see Table~\ref{tab:lit}).

\subsection{The SMC SSS RX\,J0058.6-7135 (LIN~333)}
\label{ss:0058}
\cite{1956ApJS....2..315H} labeled this object in his
``Catalog of Emission Nebulae in the Small Cloud'' as
LH$\alpha$-115~N67. Independently, \cite{1961AJ.....66..169L}
put it in his catalog
under the number 333, remarking features of a planetary nebula in
its spectrum. Therefore, the identifier LIN~333 is frequently
used for this object. \cite{1987ApJ...320..159A} analyzed its
\textsl{IUE} spectra, and revealed a strong nebular emission
produced by the object, characterized with the emission measure
of $\sim 1.4\times 10^{60}$\,cm$^{-3}$\ (see Appendix~\ref{s:appA})
and a high electron temperature of $\sim 30\,000$\,K.
They also measured the optical position of the nebula, which
helped \cite{1991MNRAS.252P..47W} to identify
LH$\alpha$-115~N67 with the strong SSS 1E0056.8-7154, which
is also named as SMP~SMC 22 \citep[][]{1978PASP...90..621S}.
\cite{1991MNRAS.252P..47W} suggested that 1E0056.8-7154
is the single hot nucleus of the planetary nebula
LH$\alpha$-115~N67.
The X-ray detection of this source was first reported by
\cite{1981ApJ...243..736S} on the basis of observations with
the \textsl{Einstein} satellite.
Following X-ray observations were carried out by the
\textsl{ROSAT} and \textsl{XMM-Newton} satellites, see
\cite{1994A&A...288..538K} and \cite{2010A&A...519A..42M},
respectively.
Modeling the X-ray SED of LIN~333 was performed by
\cite{1994A&A...288..538K}, \cite{1994A&A...288L..45H},
and \cite{2010A&A...519A..42M}. Corresponding parameters
are introduced in Table~\ref{tab:lit}.
Based on their models, \cite{1994A&A...288L..45H} found
that accreting WD in a binary is consistent with the
\textsl{ROSAT} spectrum of 1E0056.8-7154, but also admitted
a possibility that the SSS is an exceptionally hot single
central star of a planetary nebula.
Comparing all X-ray data and their models, spanning almost
30 years, \cite{2010A&A...519A..42M} did not find any apparent
long-term variability in the luminosity or spectrum of LIN~333.
The authors pointed out that the lack of variability, typical
for other SSSs, and too low upper limit to the optical
counterpart \citep[$V\sim 21$,][]{2004ApJ...614..716V} do not
favor a binary nature of LIN~333. Therefore, they supported
the interpretation that it is a single, very hot star on its
way to becoming a relatively massive ($\sim$1\,$M_{\odot}$) WD.
Using the \textsl{Spitzer Space Telescope} infrared spectra,
\cite{2009ApJ...699.1541B} classified SMP~SMC~22 as
a high-excitation planetary nebula with high excitation
lines ([O\,{\small IV}] and [Ne\,{\small V}]). The absence of
dust-related features in the spectrum was ascribed to the high
temperature and luminosity of SMP~SMC~22.

In spite of these arguments, we interpret the results of our
multiwavelength modeling of the LIN~333 SED within a binary-star
model, in which a WD accretes from its companion at a high
rate (Sect.~\ref{ss:lum}). The main reason for this assumption is
the exceptionally high luminosity of LIN~333 compared to other
planetary nebulae, indication of a compact unresolved nebula
in its spectrum -- common main features of all our targets
(Fig.~\ref{fig:seds}, Sect.~\ref{ss:ducn}, Appendix~\ref{s:appA}),
and possible presence of the binary companion indicated by
the optical fluxes (see Appendix~\ref{s:appC}).
\begin{table*}[t]
\caption{Physical parameters of our targets from the
literature (designation as in Sect.~\ref{ss:sed})}
\label{tab:lit}
\begin{center}
\begin{tabular}{rcccccc}
\hline
\hline
\noalign{\smallskip}
Object                          &
$N_{\rm H}$                     &
$R_{\rm SSS}^{\rm eff}$         &
$T_{\rm BB}/T_{\rm eff}$        &
$\log(L_{\rm SSS})$             &
Model                           &
Ref.                            \\
                                &
[$10^{20}\,{\rm cm^{-2}}$]      &
[ $R_{\odot}$ ]                 &
[ K ]                          &
[ ${\rm erg\,s^{-1}}$ ]         &
BB/Atm.                         &
                                \\
\noalign{\smallskip}
\hline
\noalign{\smallskip}
RX\,J0513 & 9.4 & $\sim$0.039 & 456000$\pm 78000$ & $\sim$38.37
          & BB$^{a}$ & 1 \\
RX\,J0513 & 4--7  & 0.009--0.017 & $\approx$560000 & 37.40--37.95
          & Atm.$^{b}$ & 2 \\
LIN~333   & 5.2 - 16   & 0.086   & 160000 - 400000 &  38.28
          & BB$^{l}$   & 9 \\
LIN~333   & 5   & 0.012       & 440000      &       37.30
          & Atm.$^{c}$ & 3 \\
LIN~333   & 8   & 0.072       & 360000      &       38.48
          & BB$^{c}$   & 3 \\
LIN~333   & 2.8--3.2 & 0.19--0.22 & 154000  &  37.81--37.93
          & Atm.$^{d}$ & 4 \\
LIN~333   & 5.2      & 0.049      & 313000  &       37.91
          & BB$^{d}$ & 4 \\
CAL~83    & 17       & $>0.06$ & 302000 & $L_{\rm SSS}> L_{\rm Edd}$
          & BB$^{e}$ & 5 \\
CAL~83    & 8        & 0.022   & 500000 & $L_{\rm SSS}\equiv L_{\rm Edd}$
          & BB$^{f}$ & 5 \\
CAL~83    & 8.87     & 0.014--0.016 & 516000 &       37.76
          & Atm.$^{g}$ & 6 \\
CAL~83    & 6.07     & $\gtrsim$0.015 & $\lesssim$403000 & $\gtrsim$37.30
          & Atm.$^{g}$ & 6 \\
CAL~83    & 6.5      & 0.012$\pm 0.003$  & 539000$\pm 16000$ & 37.40$\pm 0.03$
          & BB$^{h}$ & 7 \\
CAL~83    & 6.5      & 0.018$\pm 0.001$  & 378000$\pm 9000$ & 37.37$\pm 0.01$
          & Atm.$^{h}$ & 7 \\
CAL~83    & 6.5$\pm 1.0$ & 0.01$\pm 0.001$ & 550000$\pm 25000$ & 37.54$\pm 0.13$
          & Atm.$^{i}$ & 8 \\
RX\,J0527 & 14       & $>0.16$  & 209000 & $L_{\rm SSS}> L_{\rm Edd}$
          & BB$^{j}$ & 5 \\
RX\,J0527 & 8.5      & 0.043    & 348000 & $L_{\rm SSS}\equiv L_{\rm Edd}$
          & BB$^{k}$ & 5 \\
\noalign{\smallskip}
\hline
\end{tabular}
\end{center}
$^{a}$ \textsl{ROSAT}, October 30, 1990;
1 - \cite{1993A&A...270L...9S};
$^{b}$ \textsl{ROSAT}, July 1993;
2 - \cite{1998A&A...333..163G};
$^{c}$ \textsl{ROSAT}, October 8, 1991;
3 - \cite{1994A&A...288L..45H};
$^{d}$ \textsl{XMM-Newton}, dates in Table~\ref{tab:log};
4 - \cite{2010A&A...519A..42M};
$^{e}$ \textsl{ROSAT}, June 20, 1990 - best fit;
5 - \cite{1991A&A...246L..17G};
$^{f}$ as in $^{e}$, but for the Eddington luminosity ($L_{\rm Edd}$);
$^{g}$ \textsl{ROSAT}, observation No. 500131p;
6 - \cite{1998A&A...331..328K};
$^{h}$ \textsl{BeppoSAX}, $N_{\rm H}$ fixed, March 7-8, 1997;
7 - \cite{1998A&A...332..199P};
$^{i}$ \textsl{Chandra, XMM-Newton}, $N_{\rm H}$ fixed,
       dates in Table~\ref{tab:log};
8 - \cite{2005ApJ...619..517L};
$^{j}$ \textsl{ROSAT}, June 16-25, 1990 - best fit;
$^{k}$ as in $^{j}$, but for $L_{\rm Edd}$;
$^{l}$ \textsl{ROSAT}, October 27-31, 1990;
9 - \cite{1994A&A...288..538K}.
\normalsize
\end{table*}
\subsection{The LMC SSS RX\,J0543.6-6822 (CAL~83)}
\label{ss:cal83}
The bright SSS CAL~83 was discovered in the {\em Einstein}
survey of the LMC \citep[][]{1981ApJ...248..925L}. Subsequent
observations with \textsl{EXOSAT} from November 1983 confirmed
its very soft X-ray spectrum with an upper limit of 0.3 count/s
\citep[][]{1985SSRv...40..229P}. The optical spectrum from May 1984
revealed its similarity to that of the low mass X-ray binaries
LMC~X-2 and Sco~X-1. From radial velocity variations of the
optical emission lines (H and He\,{\scriptsize II}\,$\lambda$4686),
\cite{1987ApJ...321..745C} discovered that CAL~83 is a binary
system with a period of $\sim 1$ day. Orbital elements from radial
velocities of the He\,{\scriptsize II}\,$\lambda$4686 line were improved by
\cite{2004AJ....127..469S}.

Following X-ray observations of CAL~83 were carried out with
the \textsl{ROSAT}, \textsl{BeppoSAX}, \textsl{Chandra} and
\textsl{XMM-Newton} satellites.
\cite{1998A&A...331..328K} presented a 1.5-year
X-ray light curve of CAL~83 as measured with the \textsl{ROSAT/HRI}
from July 1995 to December 1996.
The authors also indicated the first short-term X-ray-off state
of CAL~83 on JD~2\,450\,200 (April 26, 1996). The second and
the third  X-ray-off state was reported by
\cite{2002A&A...387..944G} and \cite{2005ApJ...619..517L} on
the basis of \textsl{Chandra} observations from November 1999
and October 2001, respectively. This demonstrates recurrent nature
for CAL~83.
Modeling the X-ray SED of CAL~83 was carried out by
\cite{1991A&A...246L..17G},
\cite{1998A&A...331..328K},
\cite{1998A&A...332..199P},
\cite{2001A&A...365L.308P} and
\cite{2005ApJ...619..517L}.
Corresponding parameters are found in Table~\ref{tab:lit}.

The prototypical SSS CAL~83 was also intensively studied
in the ultraviolet and optical. It was identified with
a variable, blue, $V \approx 17$, point like source with an
orbital period of 1.047 days
\citep[][]{1984ApJ...286..196C,
1985SSRv...40..229P,
1988MNRAS.233...51S,
2004AJ....127..469S,
2013MNRAS.432.2886R}.
Optical 3900--6800\,\AA\ spectrum from May 1984 showed relatively
weak Balmer emission lines and a high He\,{\scriptsize II}\,$\lambda$4686/\hb\
ratio ($> 5$). The nebular [O\rm {\scriptsize I}\I\rm {\scriptsize I}]\,5007\,\AA\ line was also
present. The blue-shifted He\,{\scriptsize II}\,$\lambda$4686 emission component
suggested a mass outflow with velocities at 1500--2300\,\kms\
\citep[][]{1985SSRv...40..229P}.
CAL~83 is known to show irregular brightness variations
of more than a magnitude over timescales of months. Using
the MACHO $V$ and $R$ light curves (1993--1999),
\cite{2002A&A...387..944G} indicated that CAL~83 exhibits
distinct and well-defined low, intermediate, and high optical
states, characterized with no color changes during transition
phases. They also found that X-ray-off states were observed
during optical high states. A variability has also been found
in the ultraviolet by \cite{1996LNP...472..107G}, who observed
CAL~83 during high and low states.
More recent optical and X-ray observations revealed
a quasi-periodic variation on a time-scale of 450\,d with
the optical low and high states lasting for $\sim$200 and
$\sim$250\,d \citep[][]{2013MNRAS.432.2886R}. The authors also
clearly established the X-ray/optical flux anticorrelation.
It was found that the X-ray light curve exhibits significant
modulations with periodicities from 67\,s to hours
\citep[][]{2014MNRAS.437.2948O,2017MNRAS.467.2797O}.
It is generally assumed that variations in the optical flux
are most likely associated with changes in the accretion disk
\citep[e.g.,][]{2002A&A...387..944G}.

Optical imaging of CAL~83 revealed the presence of an extended
ionized nebula surrounding CAL~83, first recognized by
\cite{1989ESOC...32..285P} on the [O\,{\scriptsize III}]\,$\lambda$5007 CCD
image with a diameter of $\sim50\arcsec$.
\cite{1995ApJ...439..646R} reported that the nebula is caused by
the illumination of the local ISM by the central SSS CAL~83 with
the time-averaged X-ray luminosity $>3\times10^{37}$$\rm\,erg\,s^{-1}$.
The authors inferred that the nebula has a bright inner zone with
a characteristic radius, particle density and mass of $\sim$7.5\,pc,
4--10\,cm$^{-3}$ and $\gtrsim$150\,$M_{\odot}$, respectively, while the
diffuse outer nebula has a characteristic radius of $\sim$20\,pc.
Based on the spectra taken over a $25\arcsec\times25\arcsec$
field of view (FoV, i.e., $7.5\times7.5$\,pc$^2$ for the distance
of 55\,kpc), \cite{2012A&A...544A..86G}
presented the morphology of the ionized gas within the inner
nebula, for the first time indicated there a He\,{\scriptsize II}\,$\lambda$4686
emission region, and extracted the global spectrum of the ionization
nebula within their FoV (see Appendix~\ref{s:appB}, in detail).
Using the {\small CLOUDY} software and typical parameters of
a SSS, the authors modeled the CAL~83 nebula. However, none of
their models was able to fit the observed spectrum very well.
   It is of interest to note that searching for ionization nebulae
surrounding other strong SSSs in LMC and SMC has been negative,
which indicates that either the ISM densities in their environments
must be significantly lower than surrounding CAL~83, or the average
X-ray luminosities of these sources over the last $\lesssim$10000
years must be significantly lower than presently observed
\citep[][]{2016MNRAS.455.1770W,2020MNRAS.497.3234F}.
\subsection{The LMC SSS RX\,J0527.8-6954}
\label{ss:0527}
This source was discovered during the calibration phase of
\textsl{ROSAT} pointing the LMC field between 16 and 25 June
1990 \citep[][]{1991A&A...246L..17G}. Profile of its supersoft
spectrum was very similar to that of CAL~83, but it was fainter
by a factor of $\sim 10$. The model SED was done by
\cite{1991A&A...246L..17G} (Table~\ref{tab:lit}).

Repeated observations of this source exhibited a continuous
decline in the photon counts, from $\sim 0.2$ to
$\sim 0.01$\,cts\,s$^{-1}$,
during 1990 to 1995 \citep[][]{1996A&A...312...88G}.
The authors speculated that a likely mechanism causing the
X-ray variability could be a hydrogen flash on a massive WD
($\ge 1.1$\,$M_{\odot}$) accreting at a high rate of $10^{-7}$\,$M_{\odot}\,{\rm yr}^{-1}$.
This view is supported by the fact that the source was not
detected by the {\em Einstein} satellite 20 years ago,
which thus appears that the source is recurrent and was in
a declining phase during the \textsl{ROSAT} observations.
Also the 4-yr light curve revealed a steady fading by
$\lesssim$0.5\,mag and a 0.39-day modulation with
$\sim$0.05\,mag semi-amplitude.

Based on the optical photometry obtained via the MACHO project,
\cite{1997MNRAS.291L..13A} first suggested an optical counterpart
to RX\,J0527.8-6954, and \cite{1997PASP..109...21C} specified it
as a B8\,IV star with $V = 17.3$\,mag. Using a high-resolution
imaging, \cite{2010A&A...517L...5O} identified the X-ray source
with a B5e\,V star that is associated with a bipolar H$\alpha$\
subarcsecond extended emission. The authors pointed that for
a massive WD and the Be\,V companion with $M \sim 6$\,$M_{\odot}$, the
orbital period has to exceed 21 hours, and thus the 0.39-day
period cannot be associated with the orbit.
\begin{table*
\caption{Log of the used observations from the space}
\label{tab:log}
\begin{center}
\begin{tabular}{ccccc}
\hline
\hline
\noalign{\smallskip}
    Date   & Julian date  & Region  & Observing   & $T_{\rm exp}$ \\
yyyy/mm/dd & JD~2\,4...   &  [nm]   & satellite   &      [ks]     \\
\noalign{\smallskip}
\hline
\noalign{\smallskip}
\multicolumn{5}{c}{RX\,J0513.9-6951} \\
1990/10/30$^{1}$ & 48195.5 & 1.92--6.2 &
                       \textsl{ROSAT}$^{2}$ & 1.9 \\
2001/10/31 & 52214.5   & 94--118  &\textsl{FUSE}$^{3}$ & 6.6 \\
2003/07/05 & 52827.0   & 94--118  &\textsl{FUSE}$^{3}$ &33.0 \\
1996/11/13 & 50401.7   &115--144 &\textsl{HST}$^{3}$   & 2.8 \\
1992/04/24 & 48736.6   &115--198 &\textsl{IUE}$^{3}$   &24.0 \\
1992/04/25 & 48737.6   &186--335 &\textsl{IUE}$^{3}$   &23.0 \\
1995/06/29 & 49898.4   &115--198 &\textsl{IUE}$^{4}$   &22.8 \\
\multicolumn{5}{c}{RX\,J0058.6-7135 (LIN~333)}               \\
1991/10/08 & 48537.5   &2.5--6.2  &\textsl{ROSAT}      &17   \\
2007/06/04 & 54256.8   &2.5--6.3  &\textsl{XMM-Newton} & 7.7 \\
2009/05/14 & 54966.3   &2.5--6.3  &\textsl{XMM-Newton} &16.54\\
2009/09/25 & 55100.3   &2.5--6.3  &\textsl{XMM-Newton} &32.3 \\
2002/07/25 & 52480.5   & 92--119  &\textsl{FUSE}       &26.4 \\
1984/04/16 & 45806.5   &150 - 190 &\textsl{IUE}        &14   \\
1984/04/17 & 45807.5   &190 - 333 &\textsl{IUE}        &16   \\
1995/03/20 & 49796.5   &150 - 540 &\textsl{HST}        & 2.5 \\
\multicolumn{5}{c}{RX\,J0543.6-6822 (CAL~83)} \\
1990/06/20 & 48063.5 & 2.1--5.9   &\textsl{ROSAT}      & 3.6 \\
2000/04/23 & 51658.0 & 2.4--5.4   &\textsl{XMM-Newton} &45.1 \\
2001/08/15 & 52137.3 & 2.4--5.4   &\textsl{Chandra}    &35.4 \\
2001/09/22 & 52175.3 & 93.5--118  &\textsl{FUSE}       &45.6 \\
1996/11/10 & 50398.0 &  115--144  &\textsl{HST}        & 2.8 \\
1984/11/24 & 46029.1 &  115--198  &\textsl{IUE}        &15.1 \\
1987/12/12 & 47142.0 &  115--198  &\textsl{IUE}        &14.4 \\
1990/10/29 & 48194.1 &  115--198  &\textsl{IUE}        &24.4 \\
1990/11/07 & 48203.4 &  115--198  &\textsl{IUE}        &22.8 \\
1987/12/11 & 47141.0 &  186--332  &\textsl{IUE}        &16.1 \\
1988/08/12 & 47397.3 &  197--333  &\textsl{IUE}        &12.9 \\
\multicolumn{5}{c}{RX\,J0527.8-6954} \\
1990/06/20 & 48063.5 & 2.6--5.9   &\textsl{ROSAT}      &18.8 \\
1992/09/01 & 48867.2 & 115--198   &\textsl{IUE}        &16.7 \\
1992/09/01 & 48867.3 & 240--318   &\textsl{IUE}        & 6.0 \\
\noalign{\smallskip}
\hline
\end{tabular}
\end{center}
  $^{1}$~avearage of the second part,
  $^{2}$~the total spectrum
         \citep[see Fig.~2 of][]{1993A&A...270L...9S},
  $^{3}$~high state, $^{4}$~low state.
\end{table*}
\section{Observations}
\label{s:obs}
This section summarizes observations of our targets we used
to model their global SED in the continuum.
Spectroscopic observations with {\em Far Ultraviolet Spectroscopic
Explorer} (\textsl{FUSE}), {\em Hubble Space Telescope}
(\textsl{HST}) and {\em International Ultraviolet Explorer}
(\textsl{IUE}) were obtained from the satellite archives with
the aid of the MAST.
Other observations were taken from the literature and catalogs
as referred in the following subsections. Data obtained from
the space are collected in Table~\ref{tab:log}.
Stellar magnitudes in the optical--NIR were converted to fluxes
according to the calibration of \cite{1982asph.book.....H}
and \cite{1979PASP...91..589B}.
To correct the observed X-ray fluxes for absorptions we used the
{\em tbabs} absorption model for the interstellar matter
composition with abundances given by \cite{2000ApJ...542..914W}
(e.g., $\log(A_{\rm OI})+12 = 8.69$).
Observations for $\lambda > 912$\,\AA\ were dereddened with
$E_{\rm B-V}$ = 0.06 and 0.08 (unless otherwise specified),
and physical parameters were scaled with the distance
$d$ = 49 and 60\,kpc to objects in the LMC and SMC, respectively
\citep[][]{1998ARA&A..36..435M}.
\subsection{RX\,J0513.9-6951}
\label{ss:0513obs}
The observed SED of RX\,J0513.9-6951, used in this contribution,
covers the spectral range from 1.92\,nm to 2200\,nm. It consists
of the \textsl{ROSAT PSPC} observations (1.92 -- 6.20\,nm) as
published by \cite{1993A&A...270L...9S}. The data were adopted
from their figure 2.
The far-UV spectra with \textsl{FUSE} (B0160104, D0060102)
were taken during the high state of RX\,J0513.9-6951 as found
by \cite{2002AJ....124.2833H} for the 2001 observation, and
according to the light curve of \cite{2008A&A...481..193B} for
the 2003 spectrum.
The average continuum level of both spectra is comparable,
with $F(2001)/F(2003) \sim 1.2$.
According to the light curve of \cite{2002AJ....124.2233C},
the high resolution \textsl{HST/GHRS} spectrum (Z3HS0205T)
was also taken during a high state.
Further spectroscopic observation in the ultraviolet was
carried out with the \textsl{IUE} satellite. The 1992 spectrum
(SWP44467, LWP22883) corresponds to a high state, because
its short-wavelength part fits well the \textsl{HST} spectrum.
However, the 1995 spectrum (SWP55170) was taken at the optical
minimum, i.e., during a low state \citep[][]{2002AJ....124.2233C}.

Observations from the space were supplemented with the
ground-based optical spectroscopy obtained during both
the high state \citep[][]{1993A&A...278L..39P} and the low
state \citep[][]{1996A&A...309L..11R}.
The former was taken nearly simultaneously with the \textsl{IUE}
high-state spectra from 1992. In addition, optical $BVR$
broad-band photometry was estimated from Fig.~1
of \cite{1996A&A...309L..11R}. Further $RI$ and infrared
$JHK$ photometric measurements were found in the USNO-B1.0
Catalog (R = 16.54, I = 15.75) \citep[][]{2003AJ....125..984M},
the NOMAD Catalog (V = 16.640, R = 16.540)
\citep[][]{2005yCat.1297....0Z}, and the 2MASS All-Sky Catalog
of Point Sources ($J = 16.492\pm 0.157, H \sim 15.517,
K\sim 15.728$) \citep[][]{2006AJ....131.1163S}.
\subsection{RX\,J0058.6-7135 (LIN~333)}
\label{ss:0058obs}
Multiwavelength observations, we used to model the SED of this
SSS, cover the spectral range from the supersoft X-rays to
the optical ($\sim 2.4-360$\,nm). The supersoft X-ray fluxes
made by the \textsl{ROSAT} satellite were reconstructed with
the aid of Fig.~2 in \cite{1994A&A...288L..45H}, and those
carried out with the \textsl{XMM-Newton} satellite were estimated
according to the blackbody model of \cite{2010A&A...519A..42M}.
The ultraviolet spectra were obtained from the satellite
archives of \textsl{FUSE} (C0560301000), \textsl{IUE}
(SWP22766, LWP3168) and \textsl{HST FOS} (Y2N30104T, Y2N30105T,
Y2N30106T).
Spectroscopic observations were supplemented with the
$UBVR$ broad-band photometry, taken from the catalogs of
\cite{2002ApJS..141...81M} (U = 16.16, B = 16.86, V = 16.37,
R = 16.09), \cite{2002AJ....123..855Z} (U = 16.643, B = 17.240,
V = 16.924), \cite{2010yCat....102023S} (V = 16.90), and the 3rd
release of the \textsl{DENIS} catalog (I = 17.662, J = 16.156).
\subsection{RX\,J0543.6-6822 (CAL\,83)}
\label{ss:cal83obs}
The observed SED of CAL\,83, used in this paper, covers
the spectral range from 2.07\,nm to 790\,nm.
The calibrated supersoft X-ray fluxes were reconstructed
from Fig.~1 of \cite{1991A&A...246L..17G} (\textsl{ROSAT})
and Fig.~1 of \cite{2005ApJ...619..517L}
(\textsl{Chandra, XMM-Newton}).
In both cases the source was in the X-ray-on state
\citep[see][for the ROSAT observation]{1998A&A...331..328K}.

In the ultraviolet, eleven far-UV spectra of CAL\,83 were
carried out by \textsl{FUSE} (B0150101) on September 22, 2001
\citep[][]{2004AJ....127..469S}. The continuum fluxes were estimated
within the range of 93.5 -- 118\,nm.
The high resolution \textsl{HST/GHRS} spectrum (Z3HS0105T) covers
the region from $\sim 114.9$ to $\sim 143.5$\,nm.
Further spectroscopic observation in the ultraviolet was
carried out with the \textsl{IUE} satellite. Continuum of
the SWP spectra No. 24554, 32511, 39995, 40075 and the LWP
spectra No. 12257, 13902 were consistent best with those
of the \textsl{HST} and \textsl{FUSE} spectra. Therefore,
we used their average fluxes weighted with exposure times
to model the SED. Other \textsl{IUE} spectra had a higher
continuum, in particular the SWP30024 spectrum was a factor
of $>2$ above the used minimum values.
According to the measured variations in both the X-ray
and the UV--optical fluxes and their anticorrelation
\citep[see][]{2002A&A...387..944G}, it is probable that
the minimum level of the UV continuum, which we used to model
the SED, corresponds to the X-ray-on phase of CAL\,83.

Spectroscopic observations were supplemented with the optical
$UBVRI$ broad-band photometry, taken from catalogs of
\cite{2002ApJS..141...81M} ($U = 16.25$, $B = 17.18$, $V = 17.44$),
\cite{2004AJ....128.1606Z} ($U=16.022$, $B=16.864$, $V=16.976$)
and the 3rd release of the \textsl{DENIS} database
($R = 17.0$, $I = 16.538$). Compared are values reported
by \cite{1987ApJ...321..745C} ($B = 17.19-17.34$, $V=17.22-17.35$),
and fluxes from the optical, 400--680\,nm, spectrum
published by \cite{1985SSRv...40..229P}
scaled with their average photometric measurements
($U-B = -1.04\pm 0.06$, $B-V = 0.02\pm 0.06$, $B = 17.2\pm 0.3$).
In the near-IR \cite{2007PASJ...59..615K} measured $J = 16.98$,
$H = 16.81$ and $K = 16.77$, and 2MASS 6X Point Source Working
Database/Catalog reports $J = 17.433$, $H = 17.016$ and
$K = 16.079$.
\begin{table*}[t]
\scriptsize
\caption{Physical parameters of bright SSSs in LMC and SMC from
         multiwavelength SED models (see Sect.~\ref{ss:sed})}
\label{tab:par}
\begin{center}
\begin{tabular}{c|ccccc|cc|c}
\hline
\hline
\noalign{\smallskip}
 Object                         &
\multicolumn{5}{c|}{Supersoft X-ray source}   &
\multicolumn{2}{c|}{Nebula}     &
                                \\
                                &
$N_{\rm H}$                     &
$R_{\rm SSS}^{\rm eff}$         &
$T_{\rm BB}$                    &
$\log(L_{\rm SSS})$             &
$\log(L_{\rm X})^{7}$           &
$T_{\rm e}$                     &
$EM$                            &
$\chi^2_{\rm red}$/d.o.f.       \\
                                &
[$10^{20}\,{\rm cm^{-2}}$]      &
[$R_{\odot}$]                 &
[K]                           &
[${\rm erg\,s^{-1}}$]         &
[${\rm erg\,s^{-1}}$]         &
[K]                           &
[$10^{60}\,{\rm cm^{-3}}$]    &
                                \\
\noalign{\smallskip}
\hline
\noalign{\smallskip}
RX\,J0513$^{1}$~ &
        12$\pm 2$ & 0.19$\pm 0.02$~&~$350000\pm 10000$~ & 39.28$\pm 0.14$~&
        38.25$\pm 0.13$ & 30000$\pm 10000$ & 2.3$\pm 0.2$ & 2.8 / 40  \\
RX\,J0513$^{2}$~ &
        -- &0.26$\pm 0.03$ & $350000^{3}$ & 39.54$\pm 0.15$ &
        38.52$\pm 0.14$ & 30000$\pm 10000$ & 8.6$\pm 0.5$ & 3.6 / 38  \\
LIN~333$^{4}$~ &
        9.0$\pm 0.2$ & 0.17$\pm 0.02$ & $305000\pm 10000$ & 38.96$\pm 0.13$ &
        37.66$\pm 0.12$ & 37000$\pm 5000$ & 1.6$\pm 0.2$ & 2.6 / 39  \\
LIN~333$^{5}$~ &
        7.1$\pm 0.2$ & 0.18$\pm 0.02$ & $267000\pm 7000$ & 38.75$\pm 0.12$ &
        37.45$\pm 0.11$ & --          & --         & 4.4 / 22  \\
CAL~83$^{4}$~ &
        10.3$\pm 0.5$&0.15$\pm 0.02$ & $345000\pm 15000$ &39.04$\pm 0.16$ &
        37.99$\pm 0.15$ & 30000$\pm 15000$ & 2.9$\pm 0.3$ & 3.8 / 61  \\
CAL~83$^{6}$~ &
        12.6$\pm 0.5$&0.16$\pm 0.02$ & $357000\pm 15000$ &39.14$\pm 0.16$ &
        38.15$\pm 0.15$ & --           & --         & 2.9 / 35  \\
RX\,J0527~ &
        7.1$\pm 0.2$&0.16$\pm 0.02$ & $255000\pm 20000$ &38.57$\pm 0.06$ &
        36.83$\pm 0.05$ & 9000$\pm 2000$ & 4.3$\pm 0.3$ & 3.3 / 34  \\
\noalign{\smallskip}
\hline
\end{tabular}
\end{center}
$^{1}$ low state,
$^{2}$ high state: the $(1-9)\times 10^3$\,\AA\ model SED for
        $T_{\rm h}$ adapted from the low state
        (Fig.~\ref{fig:rx0513sed2}),
$^{3}$ fixed value,
$^{4}$ model SED with the \textsl{ROSAT} data,
$^{5}$ model SED with the \textsl{XMM-Newton} data,
$^{6}$ model SED with the \textsl{Chandra/XMM-Newton} data,
$^{7}$ the luminosity in the 0.2--1.0\,keV range.
\normalsize
\end{table*}
\subsection{RX\,J0527.8-6954}
\label{ss:0527obs}
In this case, the available observed SED in the continuum
covers the spectral range from 2.65\,nm to 550\,nm.
The calibrated supersoft X-ray fluxes were obtained by
the \textsl{ROSAT} satellite during the pointing observations
of the LMC field in 1990 \citep[][]{1991A&A...246L..17G}.
According to \cite{1996A&A...312...88G} the source was at
the brighter stage.

Ultraviolet spectra of RX\,J0527.8-6954 were carried out
with the \textsl{IUE} satellite on September 1, 1992
(SWP45499, LWP23826). The LWP23826 spectrum was underexposed,
therefore its part from the short-wavelength edge to
$\sim 240$\,nm was not used in the modeling
(dotted line in Fig.~\ref{fig:seds}d).

The optical brightness of RX\,J0527.8-6954 was measured by
\cite{1997PASP..109...21C} in $UBV$ passbands at the Cerro Tololo
Inter-American Observatory during December 1992, December 1993
and November 1994. They determined $V = 17.3$, $B = 17.4$
and $U = 17.2$.
On September 2004, \cite{2010A&A...517L...5O} observed RX\,J0527.8-6954
using the Gemini South Telescope with the Gemini Multi Object
Spectrograph and distinguished the original star into
two components. They determined the flux ratio in the V band
between the components to 1.43, and corrected the $V$ magnitude
of the RX\,J0527.8-695 optical counterpart to 17.9.
\begin{figure*}[t
 \begin{center}
\resizebox{\hsize}{!}
          {\includegraphics[angle=-90]{rx0513sed.eps}\hspace*{2mm}
           \includegraphics[angle=-90]{cal83sed.eps}}\vspace*{2mm}
\resizebox{\hsize}{!}
          {\includegraphics[angle=-90]{lin333sed.eps}\hspace*{2mm}
           \includegraphics[angle=-90]{rx0527sed.eps}}
 \end{center}
\caption{
A comparison of the measured (in magenta, Sect.~\ref{s:obs},
Table~\ref{tab:log}) and model SEDs (heavy black line) of our
targets with corresponding data-to-model ratios (d/m).
Filled/open squares are the unabsorbed/observed X-ray fluxes.
The blue and green lines denote components of radiation from
the SSS and the nebula, respectively (see Sect.~\ref{s:analysis},
Eq.~(\ref{eq:sed2})).
{\bf a} -- RX\,J0513.9-6951.
{\bf b} -- RX\,J0058.6-7135 (LIN~333): Two models fitting the
\textsl{ROSAT}---UV and \textsl{XMM-Newton}---UV fluxes were
performed. $U,B,V,R$ fluxes and the optical part of the \textsl{HST}
spectrum suggest the presence of an additional source of radiation
(marked by {\bf ?}, see Appendix~\ref{s:appC}).
{\bf c} -- RX\,J0543.6-6822 (CAL~83): Models performed for
the \textsl{ROSAT} and \textsl{Chandra/XMM-Newton} data
(each complemented with the same UV and optical fluxes), are
very similar (Table~\ref{tab:par}). The $J,H,K$ fluxes were
not used for the modeling.
{\bf d} -- RX\,J0527.8-6954: Dotted line is the underexposed
part of the LWP23826 spectrum.
}
\label{fig:seds}
\end{figure*}
\section{Analysis and results}
\label{s:analysis}
\subsection{Modeling the SED}
\label{ss:sed}
The primary aim of this paper is to reconstruct the SED of bright
SSSs in LMC and SMC from supersoft X-rays to the optical or NIR.
In this way to determine physical parameters of the main components
of radiation in the observed continuum. To achieve this aim we use
the method of multiwavelength modeling the composite continuum of
SSSs described by \cite{2015NewA...36..116S}. Here we introduce
its basic assumptions and relationships.

In our SED modeling the observed continuum, $F(\lambda)$, is
assumed to consist of a stellar component of radiation,
$F_{\rm SSS}(\lambda)$, from the WD pseudo-photosphere, and
nebular continuum, $F_{\rm N}(\lambda)$, from the ionized
out-flowing gas (see Appendix~\ref{s:appA} and
Sect.~\ref{ss:dotM}), i.e.,
\begin{equation}
  F(\lambda) =  F_{\rm SSS}(\lambda) + F_{\rm N}(\lambda).
\label{eq:sed1}
\end{equation}
In the model we compare the stellar continuum with the blackbody
radiation at a temperature $T_{\rm BB}$, while the nebular
continuum is approximated by contributions from f--b and
f--f transitions in hydrogen plasma radiating at the electron
temperature $T_{\rm e}$.
In cases, where observations suggest a discontinuity in the
continuum around $\lambda 2050$\,\AA, contributions from
doubly ionized helium are also included, and the He$^{++}$
abundance is set to 0.1.
According to Eqs.~(6) and (8) of \cite{2015NewA...36..116S},
Eq.~(\ref{eq:sed1}) can be expressed in the form,
\begin{equation}
  F(\lambda) =
    \theta_{\rm SSS}^2 \pi B_{\lambda}(T_{\rm BB})
    e^{-\sigma_{\rm X}(\lambda)\,N_{\rm H}} +
    k_{\rm N}\times\varepsilon_{\lambda}({\rm H,He^{+}},T_{\rm e}),
\label{eq:sed2}
\end{equation}
where
$\theta_{\rm SSS} = R_{\rm SSS}^{\rm eff}/d$ is the angular radius
of the SSS, given by its effective radius (i.e. the radius of
a sphere with the same luminosity) and the distance $d$.
Attenuation of the light in the X-ray domain is given by the
total cross-section for photoelectric absorption per hydrogen
atom, $\sigma_{\rm X}(\lambda)$ \citep[][]{1974ApJ...187..497C}, and
the total column density of neutral atoms of hydrogen, $N_{\rm H}$
(i.e., given by both the interstellar and circumstellar matter
component).
The second term at the right is the nebular continuum
expressed by its volume emission coefficient
$\varepsilon_{\lambda}({\rm H,He^{+}},T_{\rm e})$ scaled with
the factor $k_{\rm N}= EM/4\pi d^2$, where
$EM=\int_{V}n_{\rm e}n^{+}{\rm d}V$ is the emission measure
of the nebula given by the electron and a ion concentration,
$n_{\rm e}$ and $n^{+}$, in the volume $V$ of the ionized
element under consideration.
The assumption that the nebular radiation in the continuum can
be characterized by a single $T_{\rm e}$ is supported by the
velocity distribution of free electrons in nebulae that tends
to be Maxwellian, because the electrostatic encounters of free
electrons are much more likely than any other inelastic
scatterings \citep[see][]{1947ApJ...105..131B}.
Therefore, using a single-temperature nebula in the SED modeling
expresses the measured UV--NIR fluxes quite well
\citep[see the SED models in][and Fig.~\ref{fig:seds} here]{
2005A&A...440..995S,2015NewA...36..116S,2019ApJ...878...28S}.
In the modeling procedure we simultaneously fit absorbed
X-ray continuum fluxes and dereddened UV to NIR fluxes
searching for parameters $\theta_{\rm SSS}$, $T_{\rm BB}$,
$N_{\rm H}$, $T_{\rm e}$ and $k_{\rm N}$
\citep[see][in detail]{2015NewA...36..116S}\footnote{The
corresponding software and application example are available
at \url{https://doi.org/10.5281/zenodo.6985175}}.
The luminosity of the SSS is calculated as
\begin{equation}
  L_{\rm SSS} = 4\pi d^2 \theta_{\rm SSS}^2 \sigma T_{\rm BB}^4 .
\label{eq:lsss}
\end{equation}
Physical parameters corresponding to our SED models are
collected in Table~\ref{tab:par}.

\subsection{$N_{\rm H}$ from Rayleigh scattering}
\label{ss:ray}
The high-resolution \textsl{HST/GHRS} spectra ($\lambda$115--144\,nm)
show a pronounced attenuation of the continuum around the Ly-$\alpha$
line that is caused by Rayleigh scattering on atomic hydrogen.
This effect can be used to independently determine $N_{\rm H}$ in
the direction of the SSS
\citep[see Sect.~2.3.1 of][]{2015NewA...36..116S}.
For this purpose we compare the function,
\begin{equation}
 F(\lambda) =
   \theta_{\rm SSS}^2 \pi B_{\lambda}(T_{\rm BB})\,
    e^{-\sigma_{\rm Ray}(\lambda)\,N_{\rm H}} +
    k_{\rm N}\times\varepsilon_{\lambda}({\rm H},T_{\rm e}),
\label{eq:nhray}
\end{equation}
to the observed spectrum. The Rayleigh cross-section for scattering
by hydrogen in its ground state, $\sigma_{\rm Ray}(\lambda)$, is
approximated by Eq.~(5) of \cite{1989A&A...211L..27N}. Other
parameters have the same meaning as in Eq.~(\ref{eq:sed2}), and
are fixed according to the solution of the global SED.

\subsection{Multiwavelength model SED of RX\,J0513.9-6951}
\label{ss:0513sed}
Owing to the strict soft X-ray/optical flux anticorrelation,
it was possible to perform the X-ray---NIR model SED only
for the low state of RX\,J0513.9-6951 (Fig.~\ref{fig:seds}a),
while during the high state, only the far-UV--NIR observations
were available to model the corresponding SED
(Fig.~\ref{fig:rx0513sed2}).
The best fitting X-ray---NIR model SED parameters,
$N_{\rm H} = (1.2\pm 0.2)\times 10^{21}$\,cm$^{-2}$,
$\theta_{\rm SSS} = 8.8\times 10^{-14}$
and
$T_{\rm BB} = (350000\pm 10000)$\,K,
correspond to a very high luminosity of the SSS source,
$L_{\rm SSS} = (1.9\pm 0.7)\times 10^{39}$$\rm\,erg\,s^{-1}$,
with the effective radius,
$R_{\rm SSS}^{\rm eff} = (0.19\pm 0.02)$\,$R_{\odot}$.
The model SED shows also a significant contribution from
the thermal nebula with the emission measure,
$EM = (2.3\pm 0.2)\times 10^{60}$\,cm$^{-3}$\ that dominates
the spectrum for $\lambda \gtrsim 2000$\,\AA.

During the optical-high state, the nebular emission increased
by a factor of $\sim$3.5 (Table~\ref{tab:par}), and the WD's
effective radius inflated to $(0.26\pm 0.03)$\,$R_{\odot}$\ for the same
$T_{\rm BB}$ as during the optical-low state.
The former suggests that the variable nebular emission is
responsible for the optical variability with
$\Delta V \approx 1$\,mag, while the latter reflects the
increase of the far-UV fluxes of the stellar component of
radiation (the blue lines in Fig.~\ref{fig:rx0513sed2},
see Sect.~\ref{ss:anti} in detail).

Finally, fitting the far-UV \textsl{HST/GHRS} spectrum by
Eq.~(\ref{eq:nhray}) we found that the hollow around Ly-$\alpha$
corresponds to $N_{\rm H} = (8\pm 2)\times 10^{20}$\,cm$^{-2}$.
A comparison of the model SED and the \textsl{HST} spectrum
constrains the reddening $E_{\rm B-V} = 0.11 \pm 0.02$.
The spectrum and model (\ref{eq:nhray}) are shown in
Fig.~\ref{fig:rx0513ray}.

\subsection{Multiwavelength model SED of RX\,J0058.6-7135}
\label{ss:0058sed}
Observations of LIN~333 span the wavelength range from supersoft
X-rays to the optical. Fluxes in the near-UV and $UBV$ bands
($\sim 1\times 10^{-15}$$\,\rm erg\,cm^{-2}\,s^{-1}\,\AA^{-1}$, see Fig.~\ref{fig:seds}b),
suggest a contribution from the nebula and, possibly, from
a companion to the SSS in a binary
(see Appendix~\ref{s:appC}).
In modeling the supersoft X-ray---optical SED we fitted
13 flux-points between 24 and 62\,\AA\ and 31 flux-points
between 1500 and 3600\,\AA\ by Eq.~(\ref{eq:sed2}).
Observations with \textsl{FUSE} were not used directly in
the SED-fitting procedure, because their continuum level is
a factor of 1.1--1.5 above that given by the \textsl{IUE}
and \textsl{HST} spectra.
Nevertheless, the steep slope of their dereddened fluxes
follows the short-wavelength ends of the \textsl{IUE} and
\textsl{HST} spectra, which documents dominant contribution
from the SSS to the far-UV (compared are selected fluxes from
the LiF2A channel spectrum (1087 -- 1181\,\AA)).

The modeling solution with the \textsl{ROSAT} data has the
reduced $\chi^{2} = 2.6$, and corresponds to the fitting
parameters of the SSS,
$\theta_{\rm SSS} = (6.6\pm 0.7)\times 10^{-14}$,
$T_{\rm BB} = 305\,000 \pm 10\,000$\,K and
$N_{\rm H} = (9.0 \pm 0.2) \times 10^{20}$\,cm$^{-2}$.
These parameters imply the effective radius,
$R_{\rm SSS}^{\rm eff} = 0.17\pm 0.02 (d/60\,\,{\rm kpc})$\,$R_{\odot}$,
and the luminosity,
$L_{\rm SSS} = 9.1\pm 3.0\times 10^{38}(d/60\,\,{\rm kpc})^2$$\rm\,erg\,s^{-1}$,
which translates into the unabsorbed X-ray luminosity
$L_{\rm X}(0.2-1.0\,{\rm keV}) =
      (4.6 \pm 1.6)\times 10^{37} (d/60\,\,{\rm kpc})^2$$\rm\,erg\,s^{-1}$.
Using the average fluxes of the three \textsl{XMM-Newton}
spectra \citep[see Table~\ref{tab:log},
Sect.~\ref{ss:0058obs},][]{2010A&A...519A..42M}
and the same UV--optical
fluxes as above, yield the following parameters of
the SSS:
 $N_{\rm H} = (7.1 \pm 0.2) \times 10^{20}$\,cm$^{-2}$,
 $T_{\rm BB} = 267\,000 \pm 7\,000$\,K,
 $R_{\rm SSS}^{\rm eff} = 0.18\pm 0.02 (d/60\,\,{\rm kpc})$\,$R_{\odot}$\
and
 $L_{\rm SSS} = 5.7\pm 1.8\times 10^{38}(d/60\,\,{\rm kpc})^2$$\rm\,erg\,s^{-1}$.

The nebular component of radiation dominates the spectrum
from around 2500\,\AA\ to longer wavelengths
(Fig.~\ref{fig:seds}b). Its amount is scaled with
$k_{\rm N} = 3.8\pm 0.4\times 10^{12}\,{\rm cm^{-5}}$,
which corresponds to
$EM = (1.6\pm 0.2)\times 10^{60}(d/60\,\,{\rm kpc})^2$\,cm$^{-3}$.
The nebula radiates at a high $T_{\rm e} = 37\,000\pm 5000$\,K.
Both, $EM$ and $T_{\rm e}$ are in a good agreement with those
derived by \cite{1987ApJ...320..159A} from emission lines:
$EM \sim 1.8\times 10^{60}(d/63.1\,\,{\rm kpc})^2$\,cm$^{-3}$,
$T_{\rm e} \sim 25\,300 - 31\,600$\,K (see their Tables~5
and 7, Appendix~\ref{s:appA} here).

Finally, it is of interest to note that the long time-scale
of observations of LIN~333 (1984 -- 2009, Table~\ref{tab:log})
with comparable X-ray and UV fluxes demonstrates a stability
of this bright SSS \citep[][]{2010A&A...519A..42M}.
\begin{figure*}[t]
 \begin{center}
\resizebox{16cm}{!}{\includegraphics[angle=-90]{rx0513uvopt.eps}}
 \end{center}
\caption{
The UV--optical SED during the optical-high ({\bf a}) and low
({\bf b}) state of RX\,J0513.9-6951. This demonstrates that
the pronounced optical variability with $\Delta V \approx 1$\,mag
{\bf can be} caused by the variable nebular emission
(Sect.~\ref{ss:0513sed}).
}
\label{fig:rx0513sed2}
\end{figure*}
\begin{figure}
\begin{center}
\resizebox{\hsize}{!}{\includegraphics[angle=-90]{rx0513ray.eps}}
\end{center}
\caption{
The \textsl{HST/GHRS} spectrum of RX\,J0513.9-6951 dereddened
with $E_{\rm B-V} = 0.11$ (in magenta).
A strong depression of the continuum around the Ly-$\alpha$
line (grey area) is caused by Rayleigh scattering of the SSS
radiation on hydrogen atoms with a column density of
$(8\pm 2)\times 10^{20}$\,cm$^{-2}$\ (black and dotted lines).
Meaning of blue and green lines as in Fig.~\ref{fig:seds}.
Geocoronal Ly-$\alpha$ line is denoted by $\oplus$.
}
\label{fig:rx0513ray}
\end{figure}
\begin{figure}
 \begin{center}
\resizebox{\hsize}{!}{\includegraphics[angle=-90]{cal83ray.eps}}
 \end{center}
\caption{
As in Fig.~\ref{fig:rx0513ray}, but for CAL~83. The spectrum
is dereddened with $E_{\rm B-V} = 0.11$.
}
\label{fig:cal83ray}
\end{figure}

\subsection{Multiwavelength model SED of CAL~83}
\label{ss:cal83sed}
As in the case of RX\,J0513.9-6951, the high values of the
near-UV--optical fluxes (a few $\times 10^{-15}$$\,\rm erg\,cm^{-2}\,s^{-1}\,\AA^{-1}$), their
steepness (e.g., $U-B \sim -1$\,mag) and the presence of
emission lines of the hydrogen Balmer series, He\,{\scriptsize II}\,$\lambda$4686,
N\rm {\scriptsize I}\I\rm {\scriptsize I}\,4640\,\AA\ and [O\rm {\scriptsize I}\I\rm {\scriptsize I}]\,5007\,\AA\
in the optical spectrum \citep[e.g.,][]{1985SSRv...40..229P}
indicate a strong nebular continuum that dominates
the spectrum for $\lambda > 1\,800$\,\AA\
(see Fig.~\ref{fig:seds}c).

We modeled the SED of CAL~83 between 20.7 and 9\,000\,\AA\
by Eq.~(\ref{eq:sed2}). The best model with \textsl{ROSAT}
data has the reduced $\chi^{2} = 3.8$ (for 61 d.o.f.) and
determines the variables of the SSS,
 $\theta_{\rm SSS} = (6.9\pm 0.6)\times 10^{-14}$,
 $T_{\rm BB} = 345\,000 \pm 15\,000$\,K and
 $N_{\rm H} = (1.03\pm 0.05)\times 10^{21}$\,cm$^{-2}$,
which yields
 $R_{\rm SSS}^{\rm eff} = 0.15\pm 0.02 (d/49\,{\rm kpc})$\,$R_{\odot}$\
and
 $L_{\rm SSS} = (1.1\pm 0.5)\times 10^{39}
                (d/49\,{\rm kpc})^2$$\rm\,erg\,s^{-1}$.
Model variables of the nebular component of radiation,
 $k_{\rm N} = (1.0\pm 0.1)\times 10^{13}$\,cm$^{-5}$ and
 $T_{\rm e} = 30\,000 + 20\,000/-10\,000$\,K
correspond to
 $EM = (2.9\pm 0.3)\times 10^{60}(d/49\,{\rm kpc})^2$\,cm$^{-3}$\
(Table~\ref{tab:par}).

The model SED with \textsl{Chandra/XMM-Newton} fluxes is very
similar to that with the \textsl{ROSAT} data
(see Fig.~\ref{fig:seds}c, Table~\ref{tab:par}).
The corresponding parameters of the SSS are,
 $N_{\rm H} = (1.3 \pm 0.05) \times 10^{21}$\,cm$^{-2}$,
 $T_{\rm BB} = 357\,000 \pm 15\,000$\,K,
 $R_{\rm SSS}^{\rm eff} = 0.16\pm 0.02 (d/49\,\,{\rm kpc})$\,$R_{\odot}$\
and
 $L_{\rm SSS} = (1.4\pm 1.1)\times 10^{39}(d/49\,\,{\rm kpc})^2$$\rm\,erg\,s^{-1}$.
As in the case of LIN~333, the long time-scale of observations
demonstrate that CAL~83 is a stable SSS during its X-ray-on
states.

Finally, the attenuation of the continuum around Ly-$\alpha$,
observed on the \textsl{HST/GHRS} spectrum, corresponds to
$N_{\rm H} = (8 \pm 2)\times 10^{20}$\,cm$^{-2}$\
(see Fig.~\ref{fig:cal83ray}).
\subsection{Multiwavelength model SED of RX\,J0527.8-6954}
\label{ss:0527sed}
The steepness of the SWP45499 spectrum suggests that the SSS
radiation dominates also a wide range of the far-UV continuum
(115--190\,nm), while the LWP23826 spectrum has an opposite
slope, whose profile suggests a dominant contribution from
a low temperature nebula (see Fig.~\ref{fig:seds}d).
Available observations allow us to model the continuum
fluxes between 26.5 and 5\,500\,\AA.
The best fit to the X-ray and UV data (39 fluxes) has
the reduced $\chi^{2} = 3.3$ (for 34 d.o.f.) and determines
the model variables,
 $\theta_{\rm SSS} = (7.3\pm 0.7)\times 10^{-14}$,
 $T_{\rm BB} = 255\,000 \pm 20\,000$\,K and
 $N_{\rm H} = (7.1\pm 0.2)\times 10^{20}$\,cm$^{-2}$,
which yield
 $R_{\rm SSS}^{\rm eff} = 0.16\pm 0.02
                        (d/49\,{\rm kpc})$\,$R_{\odot}$\
and
 $L_{\rm SSS} = (3.7\pm 0.5)\times 10^{38}
              (d/49\,{\rm kpc})^2$$\rm\,erg\,s^{-1}$.
The nebular component of radiation is determined by
 $k_{\rm N} = (1.5\pm 0.1)\times 10^{13}$\,cm$^{-5}$ and
 $T_{\rm e} = 9\,000\pm 2\,000$\,K that gives
 $EM = (4.3\pm 0.3)\times 10^{60}(d/49\,{\rm kpc})^2$\,cm$^{-3}$\
(Table~\ref{tab:par}).

\section{Discussion}
\label{s:dis}
\subsection{Amount of absorption to the SSSs}
\label{ss:nh}
Independently of the SED modeling, we estimated the value of
$N_{\rm H}$ also from Rayleigh scattering of the SSS radiation on
H atoms that creates a strong depression of the continuum around
the Ly$\alpha$ line (see Figs.~\ref{fig:rx0513ray} and
\ref{fig:cal83ray}).
The larger inaccuracy of this method is given by a weaker
sensitivity of the Rayleigh scattering process to the amount
of scatterers in the Ly$\alpha$ wings, and by the complexity
of the depression profile due to superposition of rich
absorption-line spectrum to the continuum.
On the other hand, determination of $N_{\rm H}$ from the SED
modeling suffer by rather uncertain X-ray fluxes taken from
already published figures and their extreme sensitivity to
the amount of absorption within the supersoft X-ray wavelengths.
Another source of uncertainties in determining values of
$N_{\rm H}$ is given by using non-simultaneous X-ray and UV
observations, the temporal variability of the SSS radiation,
and/or the circumstellar component of $N_{\rm H}$ originating
in the surrounding nebula (Sect.~\ref{ss:anti},
Appendix~\ref{s:appA}).
Nevertheless, $N_{\rm H}$ values obtained by these two different
methods are comparable (see Table~\ref{tab:par}, and
Figs.~\ref{fig:rx0513ray} and \ref{fig:cal83ray} for
RX\,J0513.9-6951 and CAL~83).
In the case of LIN~333 and CAL~83 we modeled different X-ray
data together with the same UV--optical observations
(Table~\ref{tab:par}, Figs.~\ref{fig:seds}b and \ref{fig:seds}c).
Despite this shortcoming, the $N_{\rm H}$ values we found for
LIN~333 are in good agreement with the total column density
$N_{\rm H}\approx (7\pm 4)\times 10^{20}$\,cm$^{-2}$\ determined by
\cite{1991MNRAS.252P..47W}, which includes contributions in
the Galaxy, in the SMC, and inside the nebula.
For RXJ0527.8-6954 we used X-ray fluxes from June 1990 and
probably fainter far-UV fluxes from September 1992 as
suggested by the X-ray and optical light curves
\citep[see][]{1996A&A...312...88G,1997MNRAS.291L..13A}.
If this is so, the true value of $N_{\rm H}$ should be little
higher than that given in Table~\ref{tab:par}.
\begin{figure*}
 \begin{center}
\resizebox{16cm}{!}{\includegraphics[angle=-90]{seds_comp.eps}}
 \end{center}
\caption{
Comparison of the multiwavelength SED models of this paper (dark
thick lines, Table~\ref{tab:par}) and the corresponding X-ray-data
blackbody models from the literature (see legends,
Table~\ref{tab:lit}, Sect.~\ref{ss:comp}).
}
\label{fig:comparison}
\end{figure*}

\subsection{Comparison with previous models}
\label{ss:comp}
Figure~\ref{fig:comparison} compares our multiwavelength models
and the X-ray-data models from the literature described in
Sects.~\ref{ss:0513} to \ref{ss:0527}, and summarized in
Table~\ref{tab:lit}.
In both cases, the SED models match satisfactorily the absorbed
X-ray fluxes. However, the unabsorbed models differ, often
significantly, from our multiwavelength models. Mostly, they are
a factor of $\sim 10-100$ below the far-UV data.
Such the discrepancy between the multiwavelength modeling and
the modeling only the X-ray data can be ascribed to the mutual
dependence between $N_{\rm H}$, $L_{\rm SSS}$, and $T_{\rm BB}$
parameters, as described in Sect.~4.1 of
\cite{2015NewA...36..116S}.

RX\,J0513.9-6951: The X-ray blackbody solution of
\cite{1993A&A...270L...9S} corresponds
to $L_{\rm SSS} = 2.3\times 10^{38}$$\rm\,erg\,s^{-1}$, which is a factor of
$\sim 15$ below the far-UV fluxes. The model atmosphere fit
by \cite{1998A&A...333..163G} yields even lower luminosity of
$(2.5 - 9)\times 10^{37}$$\rm\,erg\,s^{-1}$\ (see Sect.~\ref{ss:0513}).

RX\,J0058.6-7135 (LIN~333): Blackbody and atmospheric X-ray SED
models performed by \cite{1994A&A...288L..45H} are a factor
of $\sim$9 and $\sim$300 below the \textsl{FUSE} data,
respectively.
They were already discussed by \cite{2015NewA...36..116S} as
an illustrative example of the mutual dependence of the model
parameters, $N_{\rm H}$, $L_{\rm SSS}$ and $T_{\rm BB}$
(see Sect.~4.1 and Fig.~7 there).
Similar results were obtained also by \cite{2010A&A...519A..42M}
using the \textsl{XMM-Newton} observations
(see Table~\ref{tab:lit}).
The authors questioned their atmospheric model when they found
that the flux predicted in the visible band is lower by $\sim$30\%
than the upper limit ($V\sim 21$) obtained from the \textsl{HST}
imaging of the central star by \cite{2004ApJ...614..716V}.

RX\,J0543.6-6822 (CAL~83): Blackbody solution at the Eddington
limit \citep[$N_{\rm H} = 8\times 10^{20}$\,cm$^{-2}$,
     $kT_{\rm BB} = 43$\,eV,
     $R_{\rm BB} = 1.5\times 10^9$\,cm,][]{1991A&A...246L..17G}
is a factor of $\sim 20$ below the far-UV continuum, while
their softer model
($N_{\rm H} = 1.7\times 10^{21}$\,cm$^{-2}$, $kT_{\rm BB} = 26$\,eV)
fits the absorbed X-ray data for
$\theta_{\rm SSS}\sim 4\times 10^{-13}$
(i.e., $R_{\rm BB} = 6.0\times 10^{10}$\,cm,
$L_{\rm SSS} \sim 2\times 10^{40}$$\rm\,erg\,s^{-1}$)
that is a factor of $\sim 30$ above the far-UV fluxes.
Independent modeling of the \textsl{BeppoSAX} spectrum of
CAL~83 by \cite{1998A&A...332..199P} also matches
well the observed X-ray data, but the unabsorbed model is
by a factor of $\sim 80$ below the far-UV continuum.

RX\,J0527.8-6954: Similar results were obtained also for
this SSS by \cite{1991A&A...246L..17G}.

Figure~\ref{fig:compAD} compares our SED model for RX\,J0513.9-6951
and that of \cite{1996LNP...472...65P},
who calculated models of irradiated flared accretion disks around
luminous steady-burning WDs in bright LMC SSSs (CAL~83, CAL~87, and
RX\,J0513.9-6951) and compared the resulting disk fluxes to optical
and UV observations.
To increase the radiation from the disk at these wavelengths,
the disk has to be flared to reprocess sufficiently large amount
(more than 1/4) of the WD radiation into the optical and UV
(see their Fig.~2).
Figure~\ref{fig:compAD} shows their resulting model (gray line)
that consists of three components of radiation:
  (i) From a 1.2\,$M_{\odot}$\ steady-burning WD
($\dot M_{\rm acc} = 5\times 10^{-7}$\,$M_{\odot}\,{\rm yr}^{-1}$,
$L_{\rm WD} = 1.5\times 10^{38}$$\rm\,erg\,s^{-1}$,
$T_{\rm BB} = 5\times 10^{5}$\,K and
$R_{\rm WD} = 1.84\times 10^{9}$\,cm),
  (ii) from the irradiated disk, whose heated surface increases
the optical and UV fluxes by a factor of 3--5, while the heated
star-disk boundary makes much brighter the high-energy spectrum,
and
  (iii) from the irradiated fraction of the donor star that
contributes mainly in the optical spectrum.
For a comparison, the disk spectrum with no external heating
corresponding to the above-mentioned parameters (i.e., the
accretion luminosity of $2.7\times 10^{36}$$\rm\,erg\,s^{-1}$) and the outer
disk edge of $1.35\times 10^{11}$\,cm
\citep[][]{1996LNP...472...65P} is shown by
the dashed line\footnote{For the sake of simplicity, we adopted
optically thick disk that radiates locally like a blackbody
\citep[][]{1995cvs..book.....W}.}.
Note that a more sophisticated calculation performed by
\cite{1996LNP...472...65P} provides similar profile of the disk
spectrum, but it is just somewhat shifted to shorter wavelengths
(see their Figs.~1 and 2).
The Popham \& Di Stefano's model is calculated for the disk
inclination of 60$^{\circ}$. If viewing the disk face-on, its
flux increases twice, and will match better the measured
UV and optical fluxes. However, it is rather below the NIR
fluxes and does not reproduce their slope.
The model does not match the X-ray fluxes, at all.

Our multiwavelength SED models of the bright SSSs correspond to
super-Eddington luminosity even for a high-mass WD accretor.
The SED from the near-UV to longer wavelengths indicates
a dominant contribution from thermal nebula. Both results
are fairly startling with respect to the present picture of
SSSs, whose luminosities can reach in maximum the Eddington
limit for a WD accretor, and the UV--optical spectrum is
thought to be dominated by the light from accretion disk
irradiated by the central steady-burning WD
\citep[][]{1996LNP...472...65P}.
Below, we discuss these properties in detail.
\begin{figure
 \begin{center}
\resizebox{\hsize}{!}{\includegraphics[angle=-90]{rx0513comp96.eps}}
 \end{center}
\caption{
Comparison of our SED model for RX\,J0513.9-6951 and that
including the steady-burning WD at the Eddington limit
irradiating the flared accretion disk and the donor star
\citep[gray line, adopted from Fig.~4 of][]{1996LNP...472...65P}.
The model is aimed to explain the strong UV and optical
fluxes. Compared is a spectrum of accretion disk with no
external heating (dashed line, Sect.~\ref{ss:comp}).
}
\label{fig:compAD}
\end{figure}

\subsection{Problem of the high luminosity}
\label{ss:lum}
\subsubsection{Accreting white dwarf ?}
\label{sss:wd}
According to \cite{1992A&A...262...97V},
the radiation of SSSs is generated by a stable nuclear burning
of hydrogen accreted onto massive WDs. This idea is based on
a theoretical conclusion that there is a small range of accretion
rates, $\dot M_{\rm acc}$, at which the hydrogen-rich material is
quasi-steady burning on the WD's surface as it is accreting
\citep[][]{1978ApJ...222..604P,1982ApJ...257..767F}.
The material is transported onto the accretor trough an accretion
disk. Then, the maximum luminosity of a SSS is given by that
generated by the nuclear burning on the WD surface and the
gravitational potential energy of the accretor, converted into
the radiation by the disk and its boundary layer, i.e.,
\begin{equation}
 L_{\rm SSS} = \eta X \dot M_{\rm acc} +
               \frac{G M_{\rm WD}\dot M_{\rm acc}}{R_{\rm WD}},
\label{eq:ltot}
\end{equation}
where
$\eta\sim 0.007\times c^2 \sim 6.3 \times 10^{18}$\,erg\,g$^{-1}$
is the energy production of 1 gram of hydrogen due to the nuclear
fusion of 4 protons, and $X\equiv0.7$ is the hydrogen mass fraction
in the accreted matter. $M_{\rm WD}$ and $R_{\rm WD}$ are the WD
mass and radius.
However, even the extreme parameters of the WD accretor,
$M_{\rm WD} \sim 1.4$\,$M_{\odot}$, $R_{\rm WD} \sim 0.003$\,$R_{\odot}$\
\citep[][]{2000A&A...353..970P} and
the mass transferred through the disk at a high rate of
a few times $10^{-7}$\,$M_{\odot}\,{\rm yr}^{-1}$\ that sustains the stable H-burning
\citep[see e.g., Fig.~2 of][]{2007ApJ...660.1444S} generates
the total luminosity of $\gtrsim 10^{38}$$\rm\,erg\,s^{-1}$, which
is one order of magnitude below that suggested by our
multiwavelength models SED (Table~\ref{tab:par}).
The observed luminosity would require a high accretion rate
of $\dot M_{\rm acc} \sim 10\,\dot M_{\rm Edd}$, where
$\dot M_{\rm Edd}$ is the Eddington accretion rate.
This result is not consistent with the model of steady burning
WD for the brightest SSSs in LMC and SMC, unless the radiation
of the source is not isotropic. Here, the emission from steady
nuclear burning onto a WD should be beamed with a factor,
$L/L_{\rm sph}\lesssim 0.1$, where $L_{\rm sph}$ is the inferred
isotropic luminosity and $L$ is the true source luminosity.

\subsubsection{Accreting neutron star ?}
\label{sss:ns}
A neutron star (NS) as the accretor in the brightest SSSs provides
a somewhat better possibility to explain their high luminosities,
because of a larger efficiency in converting gravitational
energy into the heat and radiation. The efficiency of radiative
emission in units of the total mass energy accreted on
a compact object is
\begin{equation}
 \xi = \frac{L_{\rm SSS}}{\dot M_{\rm acc}\,c^2}
     = \frac{G M_{\rm acc}}{R_{\rm acc}\, c^2}.
\end{equation}
For a 1.4\,$M_{\odot}$\ NS with a radius of 10--15\,km,
$\xi \sim 0.2-0.14$, while for a WD (1\,$M_{\odot}$, 7000\,km),
$\xi \sim 2\times 10^{-4}$.
Considering that the efficiency of turning mass energy into
radiation via the nuclear fusion is of $\sim 7\times 10^{-3}$
(Eq.~(\ref{eq:ltot})), the nuclear fusion reactions can be
a vital source of energy for accreting WDs, but are negligible
in converting the mass energy accreted by a NS.

To generate the luminosity of $\sim 10^{39}$$\rm\,erg\,s^{-1}$, the above
mentioned parameters of a NS require the accretion rate
$\dot M_{\rm acc} = 0.85-1.3\times 10^{-7}$\,$M_{\odot}\,{\rm yr}^{-1}$.
These values are more realistic than those required by the WD
accretor. Such the material can be supplied by mass transfer
from a close Roche-lobe filling companion. However, these
accretion rates are still above the critical values even
for a high mass NS.

The presence of a NS as the accretor in the luminous SSSs
could be evidenced by e.g., detection of strictly periodic
short-term light variation on the time-scale of milliseconds
to seconds, or by direct measuring of the size of the X-ray
emission region from eclipse analysis
\citep[][]{2017PASP..129f2001M}.
However, no such observations indicating these properties of
SSSs have been reported yet.
In the cases, where a NS probably accretes from the wind of its
companion, we measure a significantly harder X-ray spectrum
dominating 1--10\,keV
\citep[][]{2007A&A...470..331M,2007A&A...464..277M}
than it is generated by our brightest SSSs.
Therefore, the presence of accreting NSs in the brightest LMC
and SMC SSSs seems unlikely.

\subsubsection{Accreting black hole ?}
\label{sss:bh}
The high X-ray luminosities $L_{\rm X} \gtrsim 10^{39}$$\rm\,erg\,s^{-1}$\
can be interpreted by a sub-Eddington accretion onto
intermediate-mass black hole \citep[BH,][]{2006MNRAS.372..630F}.
For example, \cite{2003ApJ...590L..13K} applied this
possibility to the luminous SSS XMMU\,J005510.7--373855 in the
spiral galaxy NGC\,300 ($L_{\rm bol} = 0.2-2\times 10^{39}$$\rm\,erg\,s^{-1}$),
and found that accretion disk around a $\approx$2800\,$M_{\odot}$\ BH
radiating at $kT = 60$\,eV is required to generate the luminosity
of $10^{39}$$\rm\,erg\,s^{-1}$.
However, such the massive BHs, that are usually connected with
the star-forming regions \citep[][]{2004ApJ...601L.143I}, are
unlikely to be present in LMC and SMC.

On the other hand, \cite{2008MNRAS.385L.113K} considered that the
high luminosity of ultraluminous X-ray sources (ULXs) is generated
by a stellar-mass BH accreting material from a close companion star
at super-Eddington rates ($\dot M_{\rm acc} > \dot M_{\rm Edd}$)
with some degree of geometric beaming.
According to \cite{2009MNRAS.397.1836G},
a relatively cool SSS photosphere for the super-Eddington
accretion flows could be created by a massive wind that
completely envelopes the inner-disc regions. They also
concluded that all spectral features in their sample of ULXs
can be explained by stellar mass BHs at high accretion rates.

However, there are two main observational arguments contradicting
the presence of BHs in the brightest SSSs in LMC and SMC.
\begin{itemize}
\item
First, it is the profile of the X-ray spectrum that is considerably
harder than that produced by our brightest SSSs
\citep[][]{2010ApJ...716..181J,2016MNRAS.456.1837S}.
In addition, the spectral shape of ULXs can show either a single
peak at 2-3\,keV or two peaks \citep[one below 1\,keV and one
above 3\,keV, see][]{2009MNRAS.397.1836G}, or otherwise
structured shape of the spectrum
\citep[][]{2014Natur.514..198M,2016MNRAS.456.1859U} -- all totally
different from those, here studied, brightest SSSs.
\item
Second, if the jets are observed, their velocities are expected
to be comparable to the escape velocity of the central compact
object \citep[][]{1997ASPC..121..845L}.
Accordingly, jets observed from objects containing a BH accretor
are accelerated to relativistic speed
\citep[][]{1999ARA&A..37..409M,
           2006MNRAS.369..603F,
           2010PASJ...62L..43T,
           2015Natur.528..108L},
while those launched by a WD accretor reach speeds of the order
of thousands of \kms\ only
\citep[][]{1996ApJ...470.1065S,
           1998ApJ...506..880B,
           2009ApJ...690.1222S}.
\end{itemize}
Therefore, considering the observed X-ray SEDs of our targets,
and taking into account that jets from RX\,J0513.9-6951 are
ejected at $\pm$3800\kms\ \citep[][]{1996ApJ...470.1065S},
there is no other option than that a WD is present also in
the most luminous SSSs in LMC and SMC.

\subsubsection{Luminous post-nova supersoft X-ray sources ?}
\label{sss:postnova}
Due to the above reasons, we assume that the accretor in
the brightest SSSs, we investigate in this paper, is a WD.
A possibility how to keep a SSS at the super-Eddington state for
a long time is to fuel the burning WD after the classical nova
eruption, when it is in the post-nova SSS state, and is burning
at/above the nuclear Eddington limit, i.e., producing the
super-Eddington luminosity.
Below we support this idea by observations of similar cases, and
theoretical considerations.

{\sf Examples from observations.}
A transient post-nova SSS phase occurs after the optical outburst
and is of varying duration. The shortest one is measured for
the 1\,yr recurrent nova M31N 2008-12a in the Andromeda galaxy
that lasts for about two weeks \citep[][]{2018ApJ...857...68H},
while in the cases of GQ~Mus and LMC~1995, the SSS phase was
detected for $\sim$10\,yr
\citep[][]{1993Natur.361..331O,1995ApJ...438L..95S}
and 6--8\,yr \citep[][]{2003ApJ...594..435O}, respectively.
Long-lasting super-Eddington luminosity was also documented for
some extraordinary novae, e.g., FH~Ser
\citep[][]{1987A&A...179..164F},
LMC~1988 $\#$1 \citep[][]{1998MNRAS.300..931S},
LMC~1991 \citep[][]{2001MNRAS.320..103S},
SMCN~2016-10a \citep[][]{2018MNRAS.474.2679A},
and nova V339~Del \citep[][]{2019ApJ...878...28S}.
The unusually long phase of hydrogen burning was indicated for
the nova V723~Cas (1995) by detecting it as a bright SSS more
than 12 years after the outburst, with possible super-Eddington
luminosity
\citep[depending on the spectral model, see][]{2008AJ....135.1328N}.
The transient SSS in the nearby galaxy NGC 300, denoted as SSS$_1$,
has the bolometric luminosity of $\approx10^{39}$$\rm\,erg\,s^{-1}$\
\citep[][]{2003ApJ...590L..13K}.
The source was found in outburst in 1992, 2000, 2008 and 2016
suggesting a possible recurrence period of about 8 years, and
thus could be associated with a recurrent nova
\citep[][]{2019MNRAS.490.4804C}.
Recently, \cite{2020MNRAS.499.2007V}
discovered a 30-yr long-lived post-nova SSS in LMC undergoing
residual surface nuclear burning.
A large number of post-nova SSSs (250--600) was identified
in M31 \citep[][]{2016MNRAS.455..668S}. The authors found that
depending on the WD mass distribution in novae, their unabsorbed
X-ray luminosity distribution shows significant steepening around
$L_{\rm X}{\rm (0.2-1.0\,keV)}\approx 10^{38}$$\rm\,erg\,s^{-1}$\ with a maximum
at $\approx2\times10^{38}$$\rm\,erg\,s^{-1}$. According to our multiwavelength
SED modeling,
$L_{\rm SSS}/L_{\rm X}{\rm (0.2-1.0\,keV)}\gtrapprox 10$
(see Table~\ref{tab:par}), which would correspond to the
bolometric luminosities of the brightest SSSs in M31 of
$\approx10^{39}$$\rm\,erg\,s^{-1}$. Note, however, that this ratio is a strong
function of the temperature:
$L_{\rm SSS}/L_{\rm X}{\rm (0.2-1.0\,keV)}\sim 21$
or $\sim$2.4 only for 300\,000 or 600\,000\,K, respectively.
Finally, long-term accretion at/above the nuclear Eddington limit
is also indicated for symbiotic X-ray binaries RXJ0059.1-7505
(LIN~358) in SMC
\citep[][]{2015NewA...36..116S,
           2021MNRAS.500.3763K,
           2021ApJ...918...19W}
and Draco~C1 in the Draco dwarf spheroidal galaxy
\citep[][]{2018MNRAS.473..440S,2020ApJ...900L..43L}, where
the donor star is an evolved red giant.

{\sf Theoretical considerations.}
According to \cite{1988ApJ...325..828K}
the irradiation of the donor star after the nova outburst can
cause the red dwarf to expand and induce a mass transfer rate
enhanced by two orders of magnitude.
If the donor is a red giant (symbiotic binaries), the high
wind-mass-transfer efficiency is achieved by the wind focusing
to the orbital plane
\citep[][]{2015A&A...573A...8S,
           2016A&A...588A..83S,
           2021A&A...646A.116S}.
In this case, the enhanced accretion can be sustained also
through the disk warping that leads to ejection of transient
jets \citep[][]{2018ApJ...858..120S}.
If the accretion resumes immediately at the beginning of
the post-nova SSS phase,
the SSS lifetime can be substantially lengthened
\citep[][]{2017ApJ...838..153K}. Illustration of this effect is in
Fig.~15 of \cite{2018ApJ...857...68H}.
At a high accretion rates ($\gtrsim 5\times 10^{-7}$\,$M_{\odot}\,{\rm yr}^{-1}$), so
that a new outburst can occur on the human lifetime, the SSS
phase can be interrupted for a relatively short time by the
optical outburst being followed by the SSS phase at very high
bolometric luminosity.
Such the type of variability has been observed for the SSS SSS$_1$
in NGC 300 (see above), and here for RX\,J0527.8-6954, where
the repeatability of its visibility is indicated on the timescale
of $\approx 20$ years (Sect.~\ref{ss:0527}).

According to the above-mentioned reasons we suggest that the
brightest SSSs could be unidentified optical novae that are in
a post-nova SSS state, when the residual surface nuclear burning
is supported by rapid re-accretion from the donor, which can
help in sustaining the high luminosity of the burning WD for
a long time.
The lifetime of the high luminosity, possibly super-Eddington,
will then depend on the energy output from both the residual
burning and the resumed accretion.

\subsection{Mass-loss rate from the nebular emission}
\label{ss:dotM}
The high luminosities of SSSs, whose WDs probably accrete at
a high rate, lead to a mass-outflow in the form of a wind
\citep[e.g.,][and Appendix~\ref{s:appA} here]{1994ApJ...437..802K,
2001ApJ...558..323H}.
According to \cite{1994ApJ...437..802K} the optically thick/thin
interface of the wind represents the SSS pseudo-photosphere.
In our cases, its average value is
$R_{\rm SSS}^{\rm eff}\sim 0.17$\,$R_{\odot}$\ (Table~\ref{tab:par}).
The optically thin wind above the hot and luminous pseudo-photosphere
is ionized, giving rise to the nebular radiation
(see Appendix~\ref{s:appA}).
Assuming that the wind flows out spherically symmetrically
at a constant velocity $v_{\infty}$, begins at the
$R_{\rm SSS}^{\rm eff}$, and its radial density distribution
satisfies the mass continuity equation, then the relationship
between the mass-loss rate of the ionized wind,
$\dot M_{\rm SSS}$, and its emission measure, $EM$, can be
expressed as,
\begin{equation}
 \dot M_{\rm SSS} =
     \left[4\pi\,(\mu m_{\rm H} v_{\infty})^2
     R_{\rm SSS}^{\rm eff} EM\right]^{1/2}  {\rm g s^{-1}},
\label{eq:mdot1}
\end{equation}
\citep[see Eq.~(7) of][]{2014A&A...569A.112S}, where $\mu$ is
the mean molecular weight and $m_{\rm H}$ is the mass of
the hydrogen atom. This relation assumes that the outer radius
of the ionized wind $\gg R_{\rm SSS}^{\rm eff}$.
The average value of $R_{\rm SSS}^{\rm eff} = 0.17$\,$R_{\odot}$\ and
$EM\gtrsim 10^{60}$\,cm$^{-3}$\ (Table~\ref{tab:par}) yield
$\dot{M}_{\rm SSS}\gtrsim 2\times 10^{-6}$\,$M_{\odot}\,{\rm yr}^{-1}$\
for $v_{\infty}\equiv 1000$\kms.

Using the same assumptions as for the nebular continuum,
similar values of $\dot M_{\rm SSS}$ can be obtained also from
hydrogen emission lines, because they are formed in the same
volume of the ionized hydrogen as the continuum. For example,
for the measured flux in the \hb\ line, $F_{{\rm H}\beta}$,
we can express its luminosity as,
\begin{equation}
L_{{\rm H}\beta} = 4\pi d^2 F_{{\rm H}\beta} =
                   h\nu_{\beta}\alpha({\rm H}\beta,T_{\rm e})
                   \int_{R_{\rm SSS}^{\rm eff}}^{\infty}\!\! n_{\rm e}(r)
                   n_{\rm p}(r)\,{\rm d}V,
\label{eq:lhb}
\end{equation}
where $\alpha({\rm H}\beta,T_{\rm e})$ is the effective
recombination coefficient for the \hb\ transition, and $n_{\rm e}$
and $n_{\rm p}$ is the concentration of electrons and protons in
the spherical H$^{+}$ zone with the inner radius
$R_{\rm SSS}^{\rm eff}$, from which the wind can become optically
thin in the \hb\ line. The integral in Eq.~(\ref{eq:lhb}) represents
the emission measure of the H$^{+}$ region (see Sect.~\ref{ss:sed}).
Using its expression from Eq.~(\ref{eq:mdot1}), we obtain,
\begin{equation}
 \dot M_{\rm SSS} = \left[4\pi\,(\mu m_{\rm H} v_{\infty})^2
                    R_{\rm SSS}^{\rm eff}\frac{L_{{\rm H}\beta}}
                    {h\nu_{\beta}\alpha({\rm H}\beta,T_{\rm e})}
                    \right]^{1/2}  {\rm g s^{-1}} ,
\label{eq:mdot2}
\end{equation}
which corresponds to a lower limit of $\dot M_{\rm SSS}$, because
in a line transition the wind becomes optically thin above
the photosphere, at distances $>R_{\rm SSS}^{\rm eff}$. This
problem was treated by \cite{1988ApJ...326..356L}, who found
that stellar winds of luminous hot stars become optically thin
in the H$\alpha$\ line from a distance of $\sim$1.5 times the star's
radius.
Accordingly, $F_{{\rm H}\beta} = 1.45\times 10^{-13}$$\rm\,erg\,cm^{-2}\,s^{-1}$\
measured in the spectrum of LIN~333 by \cite{1987ApJ...320..159A}
corresponds to $\dot{M}_{\rm SSS}\sim 1.7\times 10^{-6}$\,$M_{\odot}\,{\rm yr}^{-1}$\
for
$\alpha({\rm H}\beta,30000) = 1.088\times 10^{-14}$\,cm$^3$\,s$^{-1}$
\citep[][]{1987MNRAS.224..801H}, $R_{\rm SSS}^{\rm eff} = 0.17$\,$R_{\odot}$\
and $v_{\infty}\equiv 1000$\kms.
These observational values of $\dot{M}_{\rm SSS}$ are also
consistent with those suggested by the optically thick wind
theory, for winds from the nuclear-burning WDs of a high mass
\citep[see Eq.~(23) of][]{1994ApJ...437..802K}.
It is of interest to note
that wind mass-loss rate of the order of $10^{-6}$\,$M_{\odot}\,{\rm yr}^{-1}$\ was
measured during the long-lasting SSS-phase of the classical
nova V339~Del, whose bolometric luminosity was kept at a high
level of $1-2\times 10^{39}$$\rm\,erg\,s^{-1}$\ for $\sim$150 days
\citep[see Fig.~12 of][]{2019ApJ...878...28S}.

\subsection{Dense unresolved circumstellar nebulae in SSSs}
\label{ss:ducn}

According to the mass continuity equation the particle density
of the wind $n(r)\propto r^{-2}$, where $r$ is the radial distance
from the source of the wind.
For example, $n(1\,R_{\odot})\sim 9\times 10^{12}$\,cm$^{-3}$, while
$n(1\,AU)\sim 2\times 10^{8}$\,cm$^{-3}$\ for wind parameters
given in Sect.~\ref{ss:dotM}. Further, the emitted flux by
the wind at the distance $r$ is proportional to $n^2$ (e.g.,
Eq.~(\ref{eq:lhb})), so the densities in our example correspond
to the flux ratio of the wind layers, $F(1\,AU)/F(1\,R_{\odot}) =
4\pi(1\,AU)^2n(1\,AU)^2/4\pi(1\,R_{\odot})^2n(1\,R_{\odot})^2
\sim 2\times10^{-5}$. This implies that the vast majority of
the nebular emission is produced within a relatively small
central part of the ionized wind -- from its optically thick/thin
interface up to a few AU.
Such dimensions of nebular medium are similar to those generated
by accreting nuclear-burning WDs in symbiotic stars
\citep[][]{2005A&A...440..995S}, and were also considered by
\cite{2015MNRAS.453.2927N} in calculations the circumstellar
mass-loss rates required for obscuration of supersoft X-ray
sources.
For the purpose of our work, it is important to note that such
a small size of the circumstellar nebulae in SSSs at the distance
of LMC and SMC is not spatially resolvable by the current
observational technique.
Further, the circumstellar nebulae generated by the ionized wind
in a binary are also very dense. In our cases, the emission
measure ($\sim n^2 V$) of a few times $10^{60}$\,cm$^{-3}$\
(Table~\ref{tab:par}) corresponds to the mean particle density
of a few times 10$^{9}$\,cm$^{-3}$.
Such the dense nebulae are characterized with a specific type of
the emission line spectrum, whose fluxes and their theoretical
ratios significantly differ from those produced by the low-density
planetary nebulae and/or ISM nebulae predicted to be photoionized
by the central SSS (see suggestions for future work in
Sect.~\ref{s:sum}).
Here, for a comparison with a dense circumstellar nebula in the
symbiotic star AX~Per, \cite{2001A&A...367..199S} found the electron
concentration in the H\,{\scriptsize II} and [O\,{\scriptsize III}] zone
surrounding its burning WD to be of a few times $10^9$ and
$\approx 3\times10^7$\,cm$^{-3}$, respectively. Further, they suggested
that the extremely steep Balmer decrement (e.g., H$\alpha$/\hb\ $\sim 7-10$)
could be due to electron collisions in a very dense
H\,{\scriptsize II} region.

Finally, we note that the dense unresolvable circumstellar nebulae
can be indicated for a given object only by the method of
disentangling its composite spectrum (Sect.~\ref{ss:sed}).

\subsection{Origin of the X-ray/optical flux anticorrelation}
\label{ss:anti}
The presence of a strong nebular radiation in the UV to NIR
spectrum of our targets ($EM \gtrsim 2\times 10^{60}$\,cm$^{-3}$,
Table~\ref{tab:par}) and its variation
(Fig.~\ref{fig:rx0513sed2}, Sect.~\ref{ss:0513sed}) allow
us to explain the anticorrelation between their supersoft X-ray
and optical fluxes by a variable mass-outflow from the accreting
burning WD as in the case of the symbiotic binary AG~Dra
\citep[see][]{2008A&A...481..725G,
              2009A&A...507.1531S}.
It is assumed that the variable mass-outflow results from a variable
mass-transfer. \cite{2010NewAR..54...75C} suggested a similar view
for the SSS RX\,J0513.9-6951, and also estimated the mass outflow
rate of $\approx 10^{-7}$\,$M_{\odot}\,{\rm yr}^{-1}$\ for the luminosity at the Eddington
limit.

An increase of the mass-loss increases the particle density above
the hot WD's pseudo-photosphere, and thus the number of {\rm b--f}
absorptions. This leads to a {\em decrease} of the supersoft
X-ray photons, and consequently to an increase of {\rm f--b} and
{\rm f--f} transitions that causes an {\em increase} of the nebular
emission, which dominates the spectrum from the near-UV to longer
wavelengths.

In this way the enhanced (wind) mass-outflow increases the optical
depth for the supersoft X-ray photons, and thus increases its
optically thick/thin interface, which is the WD's pseudo-photosphere.
That is why we indicate a larger effective radius of the SSS
during the X-ray-off/optical-high states.
For RX\,J0513.9-6951 the $R_{\rm SSS}^{\rm eff}$ radius inflated
from $\sim$0.19\,$R_{\odot}$\ during the optical-low state to $\sim$0.26\,$R_{\odot}$\
during the optical-high state (Sect.~\ref{ss:0513sed},
Table~\ref{tab:par}).
Independently, the connection between the flux anticorrelation
and the WD's radius was demonstrated for RX\,J0513.9-6951 by
\cite{2010NewAR..54...75C} on the basis of the \textsl{XMM-Newton}
simultaneous soft X-ray, UV and optical observations (see their
Figs.~2 and 3).
Finally, the inflated WD can also increase its radiation for
$\lambda > 912$\,\AA\ (compare the blue lines in the panel
{\bf a} and {\bf b} of Fig.~\ref{fig:rx0513sed2}).

In this way, the ionization/recombination process in the
{\em variable} wind from the SSS causes the simultaneous
presence of the X-ray-on/off and optical-low/high states.
Corresponding changes in the nebular emission can explain
$\sim$1\,mag changes in the optical brightness
(Sect.~\ref{ss:0513sed}).

\section{Conclusions and future work}
\label{s:sum}
In this paper we performed the multiwavelength modeling of
the supersoft X-ray---NIR SED for the brightest Magellanic
Cloud SSSs, RX\,J0513.9-6951, RX\,J0543.6-6822,
RX\,J0058.6-7135 and RX\,J0527.8-6954.
The global SED models satisfactorily fit the measured multi-band
fluxes.
The main results of the modeling can be summarized as follows.
\begin{enumerate}
\item
The SED models revealed that their fundamental parameters,
$L_{\rm SSS}$, $T_{\rm BB}$ and $R_{\rm SSS}^{\rm eff}$ are
$\gtrsim 10^{38}-10^{39}$$\rm\,erg\,s^{-1}$, $\approx3\times 10^{5}$\,K and
$\sim0.17$\,$R_{\odot}$, respectively.
Their supersoft radiation is attenuated with the total
$N_{\rm H}\sim (7 - 12)\times 10^{20}$\,cm$^{-2}$.
The modeling identified the nebular component of radiation
with $EM\gtrsim 2\times 10^{60}$\,cm$^{-3}$\ (Table~\ref{tab:par}).
Luminosities of our targets differ significantly from those
inferred previously from modeling the X-ray data only
(Sect.~\ref{ss:comp}, Fig.~\ref{fig:comparison}).
\item
In spite of super-Eddington luminosities for a 1.4\,$M_{\odot}$\ compact
object, the accretor has to be a WD, because the X-ray spectrum
profile and a low speed of jets are not consistent with those of
accreting NS or BH (Sects.~\ref{sss:ns} and \ref{sss:bh}).
\item
The high luminosities lead to the mass-loss at high rates.
Assuming that the nebular component of radiation is produced by
the ionized wind from SSSs, its emission measure corresponds to
the mass-loss rate $\gtrsim 2\times 10^{-6}$\,$M_{\odot}\,{\rm yr}^{-1}$\
(Sect.~\ref{ss:dotM}). The ionized wind represents a dense
unresolved circumstellar nabula in SSSs (Sect.~\ref{ss:ducn},
Appendix~\ref{s:appA}).
\item
Accordingly, we suggest that the brightest SSSs in LMC and SMC
could be unidentified optical novae in a post-nova SSS state,
whose lifetime and luminosity are enhanced by the resumed
accretion, possibly at super-Eddington rates
(Sect.~\ref{sss:postnova}).
\item
The observed anticorrelation between the supersoft X-ray and
optical fluxes can be caused by a variable mass-outflow from
the SSS due to variations in the mass-transfer. A higher
mass-loss absorbs more X-ray photons that are re-emitted
in the form of the nebular emission, and vice versa.
As a result, we observe simultaneously the X-ray-off/on and
optical-high/low states (Sect.~\ref{ss:anti}).
\end{enumerate}

For future investigation, we suggest to use the multiwavelength
modeling including simultaneously obtained fluxes from both
ascending and descending part of the SSS spectrum.
In this way to determine more reliable parameters than can be
obtained by modeling only one part of the spectrum.
To test the proposed model, and develop its more perfect
version we suggest to acquire new observations, and using
better theoretical modeling. In particular the following.
\begin{itemize}
\item
Flux calibrated low-resolution optical/NIR spectrum
($\lambda\gtrsim 350$\,nm) should verify the presence of
the nebular continuum in the spectrum by its specific profile
and the presence of the Balmer jump in emission. Moreover, for
LIN~333, such the spectrum should confirm or refute its binary
nature proposed in Appendix~\ref{s:appC}.
\item
High-resolution spectra should directly indicate a high-velocity
mass-outflow by (presumably) broad wings of the strongest lines
as H$\alpha$, \hb\ and He\,{\scriptsize II}\,$\lambda$4686.
In addition, for RX\,J0513.9-6951, the presence of satellite
components to these lines would indicate a collimated bipolar
outflow resulting from a very high accretion rate onto the WD
\citep[see][]{1996ApJ...470.1065S}.
\item
In accordance with the study of \cite{2015MNRAS.453.2927N}, using
the photoionization code {\small CLOUDY}, determine the critical
value of the mass-loss rate, $\dot M_{\rm crit}$, from the burning
WD that causes the obscuration of the central X-ray source for
parameters determined by our modeling.
The corresponding $EM$ should be comparable with that obtained
from the SED modeling during the X-ray-off states.
In this way to test the origin of the X-ray/optical flux
anticorrelation by a variable wind from the SSS proposed
in Sect.~\ref{ss:anti}.

Furthermore, the calculated emission line spectrum produced
by the ionized wind from the X-ray source should provide
additional constraints on the SSS environment.
By analogy with symbiotic stars, a dense (unresolved) nebula,
here suggested also for SSSs by our SED modeling
(Sect.~\ref{ss:ducn}; Appendix~\ref{s:appA}), should be
characterized by an anomalous Balmer decrement
(e.g., H$\alpha$/\hb$\gg 3$), and a very low rate of the nebular
[O\,{\scriptsize III}] lines to [O\,{\scriptsize III}]\,$\lambda$4363 -- in strong contrast
to values produced by the low-density planetary nebulae
\citep[e.g.,][]{1997pdpn.book.....G}, and/or nebulae predicted
to exist around SSSs imbedded in the low-density ISM
\citep[][Sect.~\ref{ss:ducn} here]{2015MNRAS.453.2927N}.
\item
In modeling the global SED, consider also the component of
radiation from the irradiated accretion disk proposed by
\cite{1996LNP...472...65P}. Its possible contribution in
the far-UV will reduce the radiation from the burning WD
here, and thus its bolometric luminosity, and amount of
the required absorption.
\end{itemize}

These tasks present new challenges for further observations
and theoretical modeling, which should help us in understanding
the nature and evolutionary status of the most luminous SSSs.

\begin{acknowledgments}
The author thanks the anonymous referee for constructive comments.
This research is based on observations made with the Far Ultraviolet
Spectroscopic Explorer, International Ultraviolet Explorer obtained
from the MAST data archive at the Space Telescope Science Institute,
which is operated by the Association of Universities for Research
in Astronomy, Inc., under NASA contract NAS 5–26555, and
on observations made with the NASA/ESA Hubble Space Telescope,
and obtained from the Hubble Legacy Archive, which is a collaboration
between the Space Telescope Science Institute (STScI/NASA),
the Space Telescope European Coordinating Facility (ST-ECF/ESAC/ESA)
and the Canadian Astronomy Data Centre (CADC/NRC/CSA).
\textsl{DENIS} is the result of a joint effort involving human
and financial contributions of several Institutes mostly
located in Europe. It has been supported financially mainly
by the French Institut National des Sciences de l'Univers,
CNRS, and French Education Ministry, the European Southern
Observatory, the State of Baden-Wuerttemberg, and the European
Commission under networks of the SCIENCE and Human Capital
and Mobility programs, the Landessternwarte, Heidelberg and
Institut d'Astrophysique de Paris.
This publication makes use of data products from the Two Micron
All Sky Survey, which is a joint project of the University of
Massachusetts and the Infrared Processing and Analysis Center/California
Institute of Technology, funded by the National Aeronautics and Space
Administration and the National Science Foundation.

This research was supported by the Slovak Research and
Development Agency under the contracts No. APVV-15-0458 and
APVV-20-0148, and by the Slovak Academy of Sciences grant
VEGA No. 2/0030/21.
\end{acknowledgments}
\facilities{ROSAT(PSPC), XMM-Newton, Chandra, FUSE, HST(GHRS, FOS),
            IUE(SWP, LWP), USNO-B Catalog, NOMAD Catalog,
            2MASS All-Sky Catalog,
            IRSF Magellanic Clouds Point Source Catalog,
            2MASS 6X Point Source Working Database/Catalog,
            The SMC Stellar Catalog and Extinction Map,
            The LMC Stellar Catalog and Extinction Map,
            Catalogue of Stellar Spectral Classifications,
            the 3rd release of the DENIS database}

redpajama_set_name: RedPajamaArXiv


text:
Let the Fire Burn
Let the Fire Burn is composed entirely with archival footage yet unfurls with the tension of a thriller. Jason Osder's documentary recounts the steps that led to a horrific massacre on May 13, 1985, when a longtime feud between the "authorities" in Philadelphia and the revolutionary group MOVE came to a deadly climax.
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