Eclipsing X-ray binaries in M 51

# Discovery of two eclipsing X-ray binaries in M 51

Song Wang, Roberto Soria, Ryan Urquhart, and Jifeng Liu
Key Laboratory of Optical Astronomy, National Astronomical Observatories, Chinese Academy of Sciences, Beijing 100012, China
College of Astronomy and Space Sciences, University of Chinese Academy of Sciences, Beijing 100049, China
International Centre for Radio Astronomy Research, Curtin University, GPO Box U1987, Perth, WA 6845, Australia
Sydney Institute for Astronomy, School of Physics A28, The University of Sydney, Sydney, NSW 2006, Australia
E-mail: songw@bao.ac.cnE-mail: roberto.soria@curtin.edu.auE-mail: ryan.urquhart@icrar.orgE-mail: jfliu@bao.ac.cn
###### Abstract

We discovered eclipses and dips in two luminous (and highly variable) X-ray sources in M 51. One (CXOM51 J132943.3471135) is an ultraluminous supersoft source, with a thermal spectrum at a temperature of about 0.1 keV and characteristic blackbody radius of about km. The other (CXOM51 J132946.1471042) has a two-component spectrum with additional thermal-plasma emission; it approached an X-ray luminosity of erg s during outbursts in 2005 and 2012. From the timing of three eclipses in a series of Chandra observations, we determine the binary period ( hr) and eclipse fraction () of CXOM51 J132946.1471042. We also identify a blue optical counterpart in archival Hubble Space Telescope images, consistent with a massive donor star (mass of 20–). By combining the X-ray lightcurve parameters with the optical constraints on the donor star, we show that the mass ratio in the system must be , and therefore the compact object is most likely a neutron star (exceeding its Eddington limit in outburst). The general significance of our result is that we illustrate one method (applicable to high-inclination sources) of identifying luminous neutron star X-ray binaries, in the absence of X-ray pulsations or phase-resolved optical spectroscopy. Finally, we discuss the different X-ray spectral appearance expected from super-Eddington neutron stars and black holes at high viewing angles.

###### keywords:
galaxies: individual (M51) — X-rays: binaries — stars: black holes — stars: neutron

## 1 Introduction

Ultraluminous X-ray sources (ULXs) are extra-nuclear, accreting compact objects with an observed luminosity in excess of erg s, which is the Eddington limit for a typical stellar-mass black hole (BH) with a mass of 10 . Hundreds of ULXs have been discovered in nearby galaxies (Liu & Mirabel, 2005; Swartz et al., 2011; Walton et al., 2011) and all types of galaxies contain ULXs (Mushotzky, 2006). Although the first examples of ULXs were already discovered by the Einstein satellite more than 30 years ago (Long & van Speybroeck, 1983), the nature of these sources remains an unsolved fundamental question. The most popular explanation for the majority of ULXs is that they are the high-luminosity end of the X-ray binary (XRB) population (Gladstone et al., 2009; Feng & Soria, 2011). They may include: neutron stars (NSs) accreting at highly super-Eddington rates onto a magnetized surface (Bachetti et al., 2014; Fürst et al., 2016; Israel et al., 2017a); ordinary stellar-mass BHs () accreting at super-Eddington rates; more massive BHs () formed from the collapse of metal-poor stars, accreting around their Eddington limit; in a few rare cases (Farrell et al., 2009; Zolotukhin et al., 2016), intermediate-mass black holes (IMBHs), with , accreting below their Eddington limit.

In parallel with the uncertainty on the nature of the compact objects in ULXs, the physical interpretation of their phenomenological X-ray spectral states remains unclear (Soria, 2007; Gladstone et al., 2009; Sutton et al., 2013; Urquhart & Soria, 2016a; Pintore et al., 2017; Kaaret et al., 2017). ULX spectra are often classified into three empirical regimes (Sutton et al., 2013), characterized by either a single-component curved spectrum (broadened disk regime), or a two-component spectrum peaking in the soft band, below 1 keV (soft ultraluminous regime), or in the hard band, around 5 keV (hard ultraluminous regime). It is not clear how those empirical regimes quantitatively depend on the nature of the compact object, the accretion rate, and/or the viewing angle. The most plausible scenario is that in super-critical accretion, a massive radiatively driven disk outflow forms a lower-density polar funnel around the central regions. In this scenario, those three different regimes correspond to different amounts of scattering and absorption of the X-ray photons along our line of sight, function of (mass-scaled) accretion rate and viewing angle; softer X-ray emission is mostly emerging through the down-scattering wind, while harder X-ray emission from the innermost regions can only be directly seen for relatively low (face-on) viewing angles, as we look into the funnel.

A fourth spectral class has recently been added to the three ULX regimes mentioned above: that of ultraluminous supersoft sources (ULSs), characterized by thermal spectra with –100 eV and little or no emission above 1 keV (Kong & Di Stefano, 2003, 2005). Although their observed X-ray luminosity barely reaches the ULX threshold at erg s, their accretion rate may be highly super-Eddington, and their ultrasoft thermal spectra may result from reprocessing of the emitted photons in an optically thick wind (Urquhart & Soria, 2016a; Soria & Kong, 2016; Shen et al., 2015; Poutanen et al., 2007). ULSs had previously been interpreted as IMBHs in the sub-Eddington high/soft state, or as white dwarfs with nuclear burning of accreted materials on their surfaces (analogous to Galactic super-soft sources). However, serious difficulties with both the IMBH scenario and the white dwarf scenario were highlighted by Urquhart & Soria (2016a) and Liu & Di Stefano (2008), respectively.

The main reason for the continuing uncertainty in the ULX nature, accretion flow geometry, and spectral state classification is the scarcity of reliable measurements of mass and viewing angle. Dynamical measurements of BH masses in ULXs with phase-resolved optical spectroscopy are particularly challenging, given the faintness of their optical counterparts in external galaxies. Moreover, some of the line emission may come from a wind, in which case the observed velocity shifts would not be reliable for dynamical measurements. Independent measurements of the viewing angle (i.e., not based on spectral appearance) are also not available in most cases.

To make progress on those two issues, we searched for eclipsing ULXs and/or ULSs in nearby galaxies. Eclipsing XRBs give us two advantages. Firstly, we know by default that their orbital plane is seen nearly edge-on from our line of sight. Secondly, mass measurements are made relatively simpler by the presence of eclipses. It is obvious that the projected orbital velocities of the two components in an edge-on binary system, and therefore the Doppler shifts of their emission and absorption lines, are higher than in systems seen face-on, and therefore it is easier to determine a mass function from phase-resolved spectroscopy; this led to spectroscopic mass measurements for example in M 33 X-7 (Pietsch et al., 2006; Orosz et al., 2007) and M 101 X-1 (Liu et al., 2013). More importantly, even in the absence of phase-resolved optical spectroscopic data (which is the case for almost all ULXs/ULSs), the mass ratio and inclination are constrained by the observed eclipse fraction (i.e., the relative fraction of time spent in eclipse); thus, if the mass of the donor star is also known or constrained, we can constrain the mass of the compact object from photometry alone, as we discuss in this paper.

Here, we report on our search for eclipsing X-ray sources in the grand-design spiral galaxy M 51, located at a distance of 8.0 0.6 Mpc (Bose & Kumar, 2014). We have already found (Urquhart & Soria, 2016b) two eclipsing ULXs in M 51 and have noted the small probability to find two luminous, eclipsing sources so close to each other in the same Chandra/ACIS field of view. In this paper, we illustrate the discovery of two new eclipsing binaries in the same Chandra field. The two sources were catalogued as CXOM51 J132943.3471135 (hereafter S1) and CXOM51 J132946.1471042 (hereafter S2) in Terashima & Wilson (2004); based on the full stacked dataset of Chandra observations, the most accurate positions for the two sources are R.A. 132943.32 and Dec. for S1, and R.A. 132946.13 and Dec. for S2 (Wang et al., 2016). We used archival data from Chandra and XMM-Newton to analyze their X-ray timing and spectral properties. For one of the two sources (S2), we determine the orbital period, identify a candidate optical counterpart, and show that the compact object is most likely a neutron star, exceeding its Eddington limit in outburst.

## 2 X-ray data analysis

M 51 has been observed many times by the Chandra/ACIS and XMM-Newton/EPIC detectors. We listed (Table 1) the observations that cover the location of S1 and S2, including Obsid, instrument, exposure time, observation date, off-axis angle, vignetting factor. There are twelve Chandra observations between 2000 June and 2012 October, and six XMM-Newton observations between 2003 January and 2011 June. The two sources are displayed and labelled in Figure 1, together with the two eclipsing ULXs studied by Urquhart & Soria (2016b).

The Chandra data were downloaded from the public archive and reprocessed with the Chandra Interactive Analysis of Observations software (CIAO), version 4.6 (Fruscione et al., 2006). We used the wavdetect tool (Freeman et al., 2002) to determine whether S1 and S2 are significantly detected in each of the Chandra/ACIS images, measure the position of their centroids, and define their elliptical source regions for subsequent extraction of lightcurves and spectra. For both sources, local background regions were taken as elliptical annuli around the source regions, with the length of the inner and outer major axes fixed at 2 and 4 times the length of the major axes of the source ellipses. Using mkexpmap task, we created an exposure map and calculated the vignetting factor for each observation, that is the ratio between the local effective and the nominal exposure time. For our timing analysis, we first applied axbary to all observations for the barycenter correction, and then used dmextract to produce light-curves. Background-subtracted source spectra and their corresponding response matrices were created with specextract.

We processed the XMM-Newton/EPIC data with the Science Analysis System (SAS), version 15.0.0. A circular region of 13 radius was used as the source region, and a neighboring circular region of 26 radius was used to estimate the local background. The event patterns were selected in the 0 to 12 range for the MOS detectors and in the 0 to 4 range for the pn detector. The flagging criteria #XMMEA_EM and #XMMEA_EP were also applied for the MOS and pn detectors respectively, together with a “FLAG=0” filter for the pn. To account for vignetting, we created an exposure map with evselect and eexpmap. For our timing study, we applied the barycenter correction with barycen, and extracted the light-curves with evselect and epiclccorr. We created background-subtracted MOS and pn spectra and their corresponding response files, using evselect, backscale, rmfgen, and arfgen. To create a weighted-average EPIC spectrum, we combined the MOS1, MOS2, and pn spectra of each observation with epicspeccombine. Finally, we grouped the spectra with specgroup so that the number of channels does not oversample the spectral resolution.

For both sources, we used xspec (Arnaud, 1996) version 12.09.0 to perform spectral fitting to the data from each observation with more than 200 counts.

## 3 Long-term X-ray monitoring

For both sources in each observation (excluding observations when either source unfortunately fell onto a chip gap), we computed the net counts from aperture photometry: , where are the raw counts, the background counts, the source region area, and the background region area. We also computed the corresponding net count errors , defined as (Gehrels, 1986). In observations where a source is not detected ( 0), we report the upper limit () to their net counts. We defined X-ray colours for both Chandra and XMM-Newton data using the standard soft band from 0.3 keV to 1.0 keV, medium band from 1.0 keV to 2.0 keV, and hard band from 2.0 keV to 8.0 keV (Prestwich et al., 2003). We applied the hierarchical classification of Di Stefano & Kong (2003a, b) to classify the observed X-ray colours in the various epochs as supersoft, quasi-soft, or hard. Table 1 lists the background-subtracted photon counts with error, expected background counts in the source region, X-ray colors, and source classification.

S1 shows strong long-term variability in its observed count rate over the almost 13 years of sporadic monitoring (Figure 2, and Table 2), including a couple of epochs when it is below the detection limit. We will argue (Section 5) that the apparent luminosity variability is due to changes in the optical depth of the thick outflow surrounding the compact object, rather than changes in the accretion rate or in the geometry of the system. Changes in the radius and temperature of the outflow photosphere have been invoked to explain the spectral properties and evolution of ULSs (Soria & Kong, 2016; Urquhart & Soria, 2016a), and other sources where the primary X-ray photons are reprocessed in an optically thick, variable wind (Shidatsu et al., 2016).

S2 behaves like a standard XRB, with a broadband X-ray spectrum; therefore, we can use its net count rates as a rough proxy for X-ray luminosity, before doing any detailed spectral modelling. Assuming a power-law spectrum with photon index and line-of-sight Galactic absorption, we find that in most of the observations, its luminosity (Figure 2 and Table 2) hovers at 0.5–1 erg s; it reached –7 erg s during the 2005 and 2012 outbursts. The long-term average as well as the peak luminosity suggest disk accretion via Roche-lobe overflow, rather than wind accretion. Instead, a non-detection in the Chandra ObsID 1622 (2001 June 23) means that it must have been fainter than erg s at that time. There are several physical mechanisms for XRB outbursts, depending on the nature of the primary and secondary stars and on the system parameters. Therefore, we need to determine such parameters before we can favour any scenario.

## 4 X-ray Timing Results

### 4.1 Eclipse and dips for S1

Source S1 was discussed by Urquhart & Soria (2016a) in the context of its supersoft spectrum, and high-inclination viewing angle. They noted the presence of a deep dip in the light-curve from Chandra ObsID 13814, and of a very low flux state at the beginning of Chandra ObsID 13815. The light-curves of other X-ray sources in the same observation and same ACIS chip do not display similar variability: this rules out instrumental problems.

We re-examined the data and confirm the findings of Urquhart & Soria (2016a). We interpret the step-like flux behaviour at the beginning of Chandra ObsID 13815 (Figure 3, top right) as a strong candidate for an eclipse of the X-ray source by the donor star. The quick transition from low to high count rates all but rules out other explanations such as state transitions. The eclipse was already in progress at the beginning of the observation, so we can only place a lower limit on its duration, 12 ks. We also recover the detection of the sharp dip (Figure 3, top left); the count rate falls from an average baseline to zero over a time-scale of 4000 s, and rises back in a similar short time. In addition, we found another dip in the EPIC light-curve from XMM-Newton Obsid 0303420201 (Figure 3, bottom left) . The duration from ingress to egress is slightly longer than 10 ks. Unlike the other two episodes, in this case the count rate does not decrease to zero; there is also a bump during the dip. We do not see a repeat of such dipping profile in any other observation of this source.

### 4.2 Eclipses and orbital period for S2

If the interpretation of the flux dips in S1 is somewhat uncertain, the behaviour of S2 is much clearer. The long-term monitoring of this source shows that it is most often in quiescence or in a low state, but went into outburst for a few weeks during the 2012 Chandra observations (Figure 4, bottom right panel). It is during this outburst that we discovered three unambiguous stellar eclipses, in ObsIDs 13813, 13812, and 13814111Notice that the order of the three observations is not a typo, that is ObsID 13813 did precede ObsID 13812. (Figure 4). In two of those three cases, we could measure the eclipse duration as ks hr. Luckily, the scheduling of the Chandra observations enabled us to catch the moment of ingress of all three eclipses, only a few days from each other. The interval between the ingress times in ObsIDs 13813 and 13812 is 104.02 hr, while the interval between the ingress times in ObsIDs 13812 and 13814 is 156.75 hr. Therefore, the binary period should be

 P≈104.02/n1≈156.75/n2, (1)

where and are integer numbers and . Thus, we can define where is an integer. For , hr; this is an acceptable solution. For , hr; however this is not an acceptable solution, because it would produce two eclipses during each of the long observations (ObsIDs 13813, 13812 and 13814, with a duration of 2 days each; see Table 1) as well as one eclipse (or part of) during ObsIDs 13815 and 13816, which is not observed. Even shorter periods () are ruled out for the same reason. In summary, the only possible binary period is hr, with a rather long eclipse fraction .

We then analyzed our X-ray light-curves with two independent techniques, to derive an even more precise and accurate value of the orbital period. The first technique is the Lomb-Scargle method (astropy.stats.LombScargle; Press & Rybicki, 1989) which is devised for unevenly spaced data. We used the five observations with the highest number of counts (Obsid 13813, 13812, 15496, 13814, 13815) to compute the Lomb periodogram. We found three significant peaks (true period and/or aliases) at 161.55 hr, 53.84 hr, and 69.31 hr, with a probability that any of those peaks are due to random fluctuations of photon counts. The searching is on the assumption of the null hypothesis of no signal. The second technique is the phase dispersion minimization (PDM) analysis (Stellingwerf, 1978). A first search of periods in the range of 50–80 hr with steps of 0.01 hr returns a group of phase dispersion minima at approximately 52.29 hr, 52.75 hr, 52.79 hr, 52.84 hr, 52.89 hr, 53.02 hr, 53.09 hr, 53.21 hr, 53.23 hr, 53.25 hr, 53.34 hr, and 53.36 hr. We then performed a second search with finer steps of 1 s around each of those minima, with an interval width of 30 s.

Having collected a sample of period candidates from our Lomb-Scargle and PDM searches, we folded the light-curves on each candidate period to compute averaged light-curves; we compared them to the individual light-curves to check the phase preservation. The most likely candidate periods are 52.2908 hr and 52.7530 hr. For hr, the three egress profiles are consistent with the averaged Chandra light-curve; however, the light-curve of the XMM-Newton observation is clearly inconsistent with the folded profile, because it does not show an eclipse at a phase when it should have (Fig. 6, left panel). For hr (Fig. 6, right panel), the three egress profiles from Chandra are still approximately consistent, and the light-curve from the XMM-Newton observation is also consistent with the folded light-curve (it does not cover the expected phase of the eclipse). We conclude that the true period is hr. The small phase offsets of the three egress profiles can be used to estimate the uncertainty on the period. The time span between ObsID 13813 and ObsID 13814 covers only 5 orbital cycles, so we can only obtain a rough estimate of the period uncertainty; in other Chandra observations separated by a longer time interval (e.g., ObsIDs 354 and 3932), the count rate is too low to provide meaningful constraints. We estimate a preserved phase better than over the 5 orbital cycles between ObsIDs 13813 and 13814; hence, the fractional error in the period is ()/5 0.012. In conclusion, the binary period of the bright XRB S2 is hr.

We determined a precise eclipse duration from Chandra ObsIDs 13813 and 13814; we defined the eclipse as the time when the count rate was less than 0.002 ct s. The two observations show an eclipse duration of s and s, respectively. Henceforth, we adopt the average of those two values, s. The eclipse fraction is then derived as the mean eclipse duration divided by the orbital period: we obtain .

## 5 X-ray spectral results

### 5.1 Spectral models for S1

We tried two single-component models to fit the background-subtracted spectra of S1: phabs*phabs*bbody and phabs*phabs*diskbb. The first photoelectric absorption component was fixed at the line-of-sight value for M 51 (cm: Dickey & Lockman 1990), and the second component was left free. We find (Table 3) that a single thermal component at keV is a good fit, with no additional power-law at high energies; blackbody and disk-blackbody models are statistically equivalent, as expected given the low temperature. However, in most epochs (for example in Chandra ObsID 13812: Figure 7), as previously noted by Urquhart & Soria (2016a), we confirm the presence of significant soft x-ray residuals. In those cases, the fit is improved by the addition of one or two thermal-plasma components (mekal model in xspec) and/or an absorption edge (edge in xspec). This is also in good agreement with the findings of Urquhart & Soria (2016a). We also recover the inverse trend between characteristic radius and temperature of the thermal component (Figure 8), noted and discussed in previous work (Soria & Kong, 2016; Urquhart & Soria, 2016a); the Spearman’s rank correlation coefficient is 0.92.

Although the observed and de-absorbed fluxes in the X-ray band are in broad agreement between the bbody and diskbb models, the two models predict different bolometric luminosities , because they have a different behaviour in the UV band, and because they have a different dependence on the viewing angle; in general, the blackbody model represents the idealized case of isotropic emission while the disk-blackbody model represents the equally idealized case of disk-like emission. For the bbody model, erg s, where is the xspec model normalization and the distance in units of 10 kpc. For the diskbb model, , where is the apparent inner-disk radius, defined as km, and the viewing angle to the disk plane (with corresponding to a face-on view). All the bolometric luminosities are estimated in the 0.01–20 keV band, and do not include the mekal components. For the conversion of band-limited fluxes to X-ray luminosities, first we calculated the de-absorbed fluxes and their errors with the task cflux within XSPEC; then, we calculated the emitted luminosities, defined as for the bbody model, and for the diskbb model. The presence of dips and a likely eclipse suggest a high viewing angle with respect to the orbital plane. On the other hand, the spin axis of the compact object may be misaligned with respect to the spin axis of the binary system (Fragos et al., 2010). In that case, the inner disk is expected to be aligned with the equatorial plane of the compact object rather than with the binary plane (Bardeen & Petterson, 1975). However, the degree of warping and the location of the transition radius between inner and outer disk (suggested to be at a radius 300 gravitational radii by Fragile et al. 2001) are still a matter of debate (e.g., Fragile et al., 2007, 2009; McKinney et al., 2013; Sorathia et al., 2013; Nixon & Salvesen, 2014; Zhuravlev et al., 2014; King & Nixon, 2016; Motta et al., 2018; Middleton et al., 2018). In the case of M 51 S1, for the disk scenario, the characteristic radius of the emitting region would be 5,000–10,000 km (Figure 8), that is several 100s gravitational radii for a stellar-mass BH. It is unclear whether this region of the disk would still be aligned with the binary plane, especially in the case of highly super-Eddington accretion, with a spherization radius (Shakura & Sunyaev, 1973; Poutanen et al., 2007) also located at a similar distance from the compact object. In Table 3, for the luminosity estimates in the disk scenario, we have arbitrarily assumed as an extreme upper limit to the plausible luminosity range. By comparison, we note that all other ULSs (Urquhart & Soria, 2016a) have isotropic luminosities of the soft thermal component 10 erg s.

### 5.2 Spectral models for S2

Unlike for S1, the spectra of S2 have significant emission 2 keV. First, we tried single-component models: power-law and disk-blackbody; for the disk model, we tried both a standard disk and a -free disk, the latter choice justified by the near-Eddington regime (Sutton et al., 2017). The power law is a good model (Table 4) for the Chandra spectra (with very low sensitivity below 0.5 keV and above 7 keV) but does not account for the broad-band curvature detected only in the XMM-Newton spectrum, because of its larger band coverage. Instead, both disk models fit poorly, for the opposite reason—too much curvature. Predictably, the model is a better fit than the standard disk () because it has a broader shape. Both the power-law and the disk model show significant residuals around 1 keV; such residuals are well accounted for by an additional thermal-plasma component (mekal model). Once the thermal plasma emission is included, the best-fitting power-law photon index is 2.0–2.3 for all four epochs.

Next, we tried a set of two-component models (Table 4): diskbb powerlaw (standard phenomenological models of XRBs); a Comptonization model, simpl diskbb (Steiner et al., 2009); a double-thermal model, diskbb bbodyrad; and a thermal model with a bremsstrahlung model, bbodyrad bremss. In all four cases, we also added a mekal component to account for the line emission around 1 keV. Physically, the power-law plus thermal component model, and the Comptonization model, are applicable to a variety of physical scenarios for BH or NS accretors (especially at the low resolution of CCD spectra): either lower-temperature thermal emission from the disk, up-scattered in a hotter corona; or direct emission of hard X-ray photons, partly down-scattered in a cooler outflow. The double-thermal model may represent the two-component emission from the inner disk and the surface or boundary layer of a NS (in which case we expect the disk component to be cooler than the surface blackbody component); it may also represent the thermal emission from a disk plus that from the photosphere of a dense outflow (in which case we expect the disk emission to be hotter than the down-scattered blackbody emission). We find that all those two-component models provide a better fit (an improvement –12 for the loss of two degrees of freedom) to the XMM-Newton spectrum than the power-law model; however, they are equivalent to each other, so we cannot rule out any physical scenario, or distinguish between a BH or NS accretor, from spectral fitting. For the Chandra spectra, as noted above, there is no advantage of multi-component models over a simple power-law. In the rest of this Section, we briefly examine the best-fitting values of the main parameters for the alternative models, to determine whether they are physically plausible and whether they resemble typical spectral parameters of other ULXs and XRBs.

First, we consider the best-fitting double-thermal model with (Figure 9), which is more suited to a NS accretor. The characteristic size of the blackbody emitter is km (90% confidence level), and its temperature is keV, in the XMM-Newton spectrum (Table 4); both values are consistent with thermal emission from the surface of a NS or from a boundary layer between disk and surface. The best-fitting peak colour temperature of the diskbb component is 0.3 keV. The apparent inner-disk radius is km; the physical inner disk radius is generally estimated as (Kubota et al., 1998) for a standard thin disk. In this scenario, the inner disk is truncated very far from the innermost stable circular orbit (or from the NS surface), which inevitably reduces the radiative efficiency of the disk to , two orders of magnitude lower than the efficiency of the boundary layer/surface emission. If so, it becomes difficult to explain why the disk and the surface emission contribute a similar luminosity ( a few erg s) to the X-ray spectrum, when we would expect the X-ray emission from the disk to be negligible compared with the total emission. For this reason, we conclude that the simplistic interpretation of the double thermal model as “standard disk plus surface emission from the NS” is physically not self-consistent.

Then, we consider the other double-thermal model (), which is equally applicable to BHs or weakly magnetized NSs. The best-fitting colour temperature of the diskbb component is 3 keV, and the apparent inner-disk radius is km; for example, for , km. In this case, it makes no sense to use the standard-disk conversion of , because a disk with a peak temperature of 3 keV is not consistent with a standard, sub-Eddington thin disk. In other words, the diskbb model is not self-consistent, and the only information we should take away from this fit is that the hottest thermal component is consistent with an emitting region close to the innermost stable circular orbit or to the surface of a weakly magnetized NS ( G), at near-Eddington mass accretion rates (Takahashi & Ohsuga, 2017). The characteristic radius of the second (cooler) thermal component (bbodyrad) is km. Thus, if this second component comes from reprocessing of hotter photons, its size suggests the photosphere of a thick disk outflow, analogous to the explanation invoked for ULSs (Soria & Kong, 2016), or the walls of a polar funnel. However, a geometrically and optically thick outflow should prevent our direct view of the innermost disk, if we are looking at a high-inclination system (as suggested by the presence of long eclipses. Thus, the co-existence of two optically thick thermal components with similar intensities but different temperature and radii requires a degree of misalignment, so that we see at the same time part of the direct inner-disk emission, and reprocessed emission for example from the outflow funnel walls. Alternatively, a double thermal model may be taken as a purely phenomenological way to approximate more complex spectra of super-critical flows (including both thermal and bulk-motion Comptonization), such as those predicted by the MHD simulations of Kitaki et al. (2017) for super-critical BH accretion, or the accretion disk and magnetospheric envelope structure proposed by Mushtukov et al. (2017) for super-critical NS accretion.

We then used the model (Figure 10) to represent Comptonized emission of an input disk spectrum (Steiner et al., 2009). For the XMM-Newton spectrum, the best-fitting parameters (Table 4) include: a power-law photon index ; a fraction of scattered photons of ; for the seed photon component, an inner-disk colour temperature