Evidence of disc reflection in the X-ray spectrum of the neutron star low mass X-ray binary 4U 1636-536
aa r X i v : . [ a s t r o - ph . H E ] S e p Mon. Not. R. Astron. Soc. , 000–000 (0000) Printed 30 September 2020 (MN L A TEX style file v2.2)
Evidence of disc reflection in the X-ray spectrum of NSLMXB 4U 1636-536
Aditya S. Mondal ⋆ , B. Raychaudhuri , G. C. Dewangan Department of physics, Visva-Bharati, Santiniketan, West Bengal-731235, India Inter-University Centre for Astronomy & Astrophysics (IUCAA), Pune, 411007 India30 September 2020
ABSTRACT
We present a broadband spectral analysis of the atoll source 4U 1636-536 observed for ∼
92 ks with
NuSTAR . The source was found to be in a low-luminosity state during thisobservation with 3 −
79 keV X-ray luminosity of L − keV = (1 . ± . × ergs/s,assuming a distance of 6 kpc. We have identified and removed twelve type-I X-raybursts during this observation to study the persistent emission. The continuum is welldescribed by a thermal Comptonization model nthcomp with Γ ∼ . kT e ∼
28 keV,and kT s ∼ . NuSTAR data reveal a clear signature of disc reflection,a significantly broad Fe-K emission line (around 5 − −
30 keV). By modelling the spectrum with a self-consistentrelativistically blurred reflection model, we find that the inner disc is truncated withan inner radius of R in = (3 . − . R ISCO ( ≃ − R g or 36 −
54 km). This innerdisc radius suggests that the neutron star magnetic field strength is B . × G. Key words: accretion, accretion discs - stars: neutron - X-rays: binaries - stars:individual 4U 1636-536
A neutron star low mass X-ray binary system (NS LMXB)consists of a neutron star (NS) and a low mass ( M ⊙ )companion star. When the NS in an NS LMXB accretesmatter from the companion star via Roche-lobe overflow,a geometrically thin, optically thick disc-like structure isformed (Shakura & Sunyaev 1973). The radiation spectrumfrom the accretion disc, which is usually accompanied by ahot corona is quasi-thermal in nature and is well known tobe multicolor blackbody. The inverse Compton scatteringof the thermal disc photon generates a power-law spectrum.Moreover, a hot single-temperature blackbody emission mayarise from the boundary layer between the inner accretiondisc and the NS surface. Hard X-rays (either a power-lawcontinuum or a blackbody component) can illuminate theaccretion disc and produce a reflection spectrum whichconsists of several emission lines and a broad hump-likeshape.The fluorescent Fe K α line is the most prominentemission line due to its large cosmic abundance andhigh fluorescent yield (Bhattacharyya & Strohmayer 2007;Cackett et al. 2008; Pandel et al. 2008; Reis et al. 2009;Degenaar et al. 2015). In the reflection spectrum, a broad ⋆ E-mail: [email protected] hump-like shape is seen which is created by the highenergy photons which tend to Compton scatter back outof the disc (Ballantyne et al. 2001; Ross & Fabian 2007).Although the Fe K α line is intrinsically narrow as expected,it becomes broad and asymmetric in the X-ray spectrumof the LMXBs due to the Doppler and the Gravitationalshift (Fabian et al. 2000). A profound study of this lineprofile is important due to its ability to provide informationon the inner accretion flow in the NS LMXBs which inturn provides constraints to the structure of the inner discand inclination. In an NS binary system, the accretiondisc may be truncated by a strong stellar magnetic fieldor by the boundary layer between the disc and the NSouter surface. The upper limit to the radius of the NSis related to the inner disc radius and may constrainthe NS EOS (Piraino et al. 2000; Cackett et al. 2008;Bhattacharyya 2011). Moreover, the Fe K α line is also usedto find out an upper limit to the strength of the magneticfield related to the NS (Ludlam et al. 2019; Degenaar et al.2016; King et al. 2016).4U 1636-536 is an atoll type, bursting LMXB consistingof an NS and an 18th magnitude, 0.4 M ⊙ companion star(van Paradijs et al. 1990). The source has been studiedextensively in the literature. The source has exhibited type-IX-ray bursts, double-peaked X-ray bursts, superbursts,Quasi-Periodic Oscillations (QPOs), and millisecond oscil- c (cid:13) Mondal et al. lation during thermonuclear bursts (Wijnands et al. 1997;Galloway et al. 2006; Strohmayer & Markwardt 2002).It has an orbital period of ∼ . ± . ∼ − ◦ from optical observations (Casares et al. 2006).The source is well known to show burst oscillations at 581Hz which is remarkably coherent (Strohmayer & Markwardt2002). This is possibly related to the rotation of the NS.The soft X-ray emission, modulated at the QPO frequencyof kHz range is known to have a phase lag behind thehard X-ray emission (Kaaret et al. 1999). This lag couldbe produced by the reprocessing of hard X-rays in a coolerComptonizing corona with a size of at most a few kilometers.Pandel et al. (2008) analysed the XMM-Newton and
RXTE data of the source 4U 1636-536. They found clearevidence of a broad, asymmetric iron emission line extend-ing over the energy range 4 − α emission line from the accretion disc. They found ahigh disc inclination of 36 ◦ − ◦ . They reported an upperlimit of the inner disc radius ( R in ) which is larger than theISCO. Agrawal & Hasan (2016) analysed four simultaneous NuSTAR and
SWIFT observations of the source 4U 1636-536 in the 1 −
79 keV energy band. They also observed abroad iron emission line. During these observations, thesource flux varied from 1 . × − to 4 . × − ergs s − cm − and the inner disc radius varied from 6 . GM/c .In this work, we present a broadband NuSTAR ob-servation of the source 4U 1636-536. We search for thepresence of reflection features and place constraints onthe position of the inner disc. In the presence of highquality, pile-up free
NuSTAR data and with the correctastrophysical model, X-ray reflection spectroscopy can bequite a powerful tool to probe the accretion geometry. Thepaper is structured in the following format: Sec.2 presentsthe observations and the details of data reduction. Sec.3discusses spectral analysis and results and Sec. 4 providesthe discussion of the results.
NuSTAR (Harrison et al. 2013) observed the source4U 1636-536 on 2019 April 27 for a total exposure time of ∼
92 ks (Obs. ID: 30401014002). The data were collectedwith the two co-aligned grazing incidence hard X-rayimaging Focal Plane Modules (FPM) A and B telescopes inthe 3 −
79 keV energy band.The data were reduced with the standard
NuSTAR data analysis software (
NuSTARDAS v1.7.1 ) and
CALDB ( v nupipeline (version v 0.4.6) to filter the event lists. Using the nuproducts tool we created lightcurve, spectra, and re-sponse files for both the telescopes FPMA and FPMB. To produce a source spectrum for both the telescopes, we ex-tracted a circular region with a radius of 100 arcsec cen-tered around the source position. We extracted the back-ground spectrum from a same-sized radial region away fromthe source. We grouped the FPMA and the FPMB spectraldata with a minimum of 100 counts per bin and fitted thetwo spectra simultaneously. The source 4U 1636-536 is known to exhibit type-I X-raybursts. The
NuSTAR
FPMA and FPMB light curves con-tain 12 type-I X-ray bursts which are shown in Figure 1.We have also shown the light curve after removing the timeinterval when the type-I X-ray bursts occur. The source wasdetected at an average intensity of ∼
38 counts/s duringthe non-burst period. After excluding all the type-I X-raybursts, we have fitted both the
NuSTAR
FPMA and FPMBspectra simultaneously as the initial fits have showed a goodagreement between these two spectra. An initial inspectionof the FPMA and the FPMB spectra also suggests that thesource is detected significantly in the entire energy bandpassof the
NuSTAR . We have therefore performed the spectralanalysis over the entire 3 −
79 keV energy band using
XSPECv 12.9 (Arnaud 1996). Due to flux variations between thedetectors, we have added a multiplicative constant in eachfit. We have fixed the constant for the FPMA spectrum tounity and allowed it to vary for the FPMB spectrum. A valueof 1 .
002 has been measured for the FPMB spectrum. Wehave used the tbabs model to account for absorption alongthe line of sight to the source with the abundance set to wilm (Wilms et al. 2000) and vern cross sections (Verner et al.1996). We have fixed the absorption column density to theDickey & Lockman (1990) value of 4 . × cm − as the NuSTAR low-energy bandpass cuts off at 3 keV and havefound it difficult to constrain from the spectral fits. Allquoted uncertainties in this paper are at 90% of the con-fidence level if not stated otherwise in particular.
This
NuSTAR observation has detected the source 4U 1636-536 with a luminosity of ∼ . × erg/s whichcorresponds to ∼
5% of the Eddington luminosity ( L Edd ).So, the source is detected in a low-luminosity state with
L/L
Edd in the range of 0 . − .
1. The spectra of thelow-luminosity state sources are typically characterizedby a thermal Comptonization model with an electrontemperature ( kT e ) around 25 −
30 keV (Barret et al. 2000).In the low-luminosity state, a soft component may beobserved probably to represent the unscattered emissionfrom an optically thick accretion disk (Barret et al. 2000).Additionally, Lin et al. (2007) also suggested that low/hardstate spectra could be modelled with a cutoff power-lawcomponent and a single-temperature blackbody componentwhen needed.We have modeled the continuum above 3 keV using onlya thermal Comptonization model nthcomp (Zdziarski et al.1996; ˙Zycki et al. 1999) which may arise from either a hot c (cid:13) , 000–000 uSTAR view of 4U 1636-536 R a t e ( C o u n t s / s e c ) R a t e ( C o u n t s / s e c ) Figure 1.
Left: 3 −
79 keV
NuSTAR /FPMA light curve of 4U 1636-536 with a binning of 100 sec. It shows the presence of 12 brief type-IX-ray bursts. Right: Light curve after removing all the type-I X-ray bursts. In this observation, the source detected with an averageintensity of ∼
38 counts/s. −3 no r m a li z ed c oun t s s − k e V −
105 20 5005 χ Energy (keV)
Figure 2.
NuSTAR (FPMA in black, FPMB in red) unfolded spectra. The data were fit with an absorbed, thermal Comptonizationmodel nthcomp . There are prominent residuals at ∼ − ∼ −
20 keV. Those can be indentified as a broad Fe-K emissionline and the corresponding Compton back-scattering hump. The spectral data were rebinned for visual clarity corona associated with accretion disc or a boundary layer be-tween the disc and the NS surface (see e.g. King et al. 2016;Ludlam et al. 2019). This thermal Comptonization modelhas a power-law component with an index Γ, a low energycutoff determined by the temperature of the seed-photons( kT s ) and a high energy roll-over determined by the elec-tron temperature ( kT e ). Here we have assumed that theseed spectrum is a multi-temperature blackbody spectrumemitted from the disc. In our fits, we have allowed boththese temperatures and the power-law index to vary. Thismodel describes the continuum very well with χ /dof =4412 / nthcomp component, we have obtainedΓ ∼ . kT e ∼
28 keV, and kT s ∼ . ∼ − ∼ −
30 keV, which can be identified as a broad Fe-K emission line and the corresponding Compton hump (seeFigure 2). However, it may be noted that we have not de-tected any soft blackbody component in the spectrum. Itmay possibly be due to the inadequate low-energy coverageas in the case of
NuSTAR . As our continuum fit indicates the presence of reflectionfeatures (see Figure 2), we, therefore, have proceededby modelling our data with a physical reflection model. c (cid:13) , 000–000 Mondal et al. −3 k e V ( P ho t on s c m − s − k e V − )
105 20 50−202 χ Energy (keV)
Figure 3.
The
NuSTAR (FPMA in black, FPMB in red) unfolded spectra of 4U 1636–536 with the best-fitting fitted model consistingof a thermal Comptonization model and a relativistically blurred reflection model i.e.,
TBabs × (nthcomp+highecut*relconv*reflionx) .Lower panel shows residuals in units of σ . We have applied the standard reflionx (Ross & Fabian2005) model that assumes a high energy exponentialcutoff power-law irradiating the accretion disc. The modelcomponents of reflionx model are as follows: Γ is thephoton index of the illuminating spectrum, ξ is the discionization parameter, A F e is the iron abundance relative tothe solar value, N norm is the normalization of the reflectedspectrum and z is the redshift of the source.We have modified this reflection model reflionx insuch a way that it assumes nthcomp illuminating spectruminstead of a cutoff power-law, as our broad-band fits prefera Comptonized model to describe the continuum spectrum.The cutoff power-law does not have a low-energy cutoffwhile Comptonization spectra require a low-energy cutoffat the seed photon temperature ( kT s ). Moreover, the highenergy cutoff of the illuminating power law in the reflionx model is set to 300 keV. Therefore, we have modified reflionx in such a manner that it mimics the nthcomp continuum. In order to introduce low and high energycutoff, we have multiplied reflionx by a high energy cutoff, highecut , with the folding energy E fold set to ∼ kT e and the cutoff energy E cutoff tied to 0 . nthcomp component. Thus, we have modified the reflectionmodel reflionx in order to reproduce the nthcomp contin-uum by introducing the model component highecut (fordetails see Matranga et al. 2017; Mondal et al. 2020). Totake relativistic blurring into account, we have convolved reflionx with relconv component (Dauser et al. 2010). Itsparameters include the inner and the outer disc emissivityindices ( q in , q out ), break radius ( R break ), the inner andouter disk radii R in and R out , the disk inclination ( i ) andthe dimensionless spin parameter ( a ).We have imposed a few reasonable conditions when making fits with reflection models. We have assumed anunbroken emissivity profile with a fixed slope of q = 3, asthe slope is not constrained by the data. We have also fixedthe outer disc radius R out to 1000 R g . We set a redshift of z = 0 since 4U 1636-536 is a Galactic source. From previousmeasurements of the NS spin frequency 581 Hz, we haveapproximated the spin parameter a = 0 .
27 as a ≃ . /P ms (Braje et al. 2000) where P ms is the spin period in ms.Furthermore, we have fixed the disc inclination, i , to 60 ◦ as it was poorly constraint when left free to vary (seealso Pandel et al. 2008; Agrawal & Hasan 2016). Moreover,prior knowledge of disc inclination can significantly reducethe uncertainty of the measurement of the inner disc radius(Pandel et al. 2008).Adding the relativistic reflection significantly improvesour spectral fits with a χ /dof = 2178 / .
16. Thebest fit parameters for the continuum and the reflectionspectrum are listed in Table 1. The reflection componentimplies a large disc truncation prior to the ISCO at(3 . − . R ISCO ( ≃ − R g or 36 −
54 km). Thismodel yields an intermediate disc ionization of ξ ∼ − cm which is consistent with log ξ ∼ (2 −
3) seenin other NS LMXBs (see e.g. Cackett et al. 2010). The Feabundance obtained is consistent with solar composition( A F e = 1 . ± . χ for the parameter inner disc radius ( R in ) using steppar command in xspec to determine how the goodness-of-fitchanged as a function of this parameter. Figure 4 indicatesthat R in is well constrained by the data. Moreover, itshows that R in is inconsistent with the position of theISCO, indicating that it is truncated far from the NS surface.It may be noted that the reflection features are betterexplained by the utilization of the self-consistent reflectionmodel RELXILL . Some new flavors of the
RELXILL model are c (cid:13) , 000–000 uSTAR view of 4U 1636-536 σ σ Δ χ Inner disc radius R in (R ISCO ) Figure 4.
Shows the variation of ∆ χ (= χ − χ min ) as a functionof inner disc radius (in the unit of R ISCO ) obtained from therelativistic reflection model. We varied the inner disc radius as afree parameter in between 2 R ISCO to 6 R ISCO . The parameteris clearly well constrained by the data. The value of the inner discradius is inconsistent with the position of the ISCO. Horizontallines are indicating 2 σ and 3 σ significance level. available today. A flavor of the RELXILL model,
RELXILLCP ,uses nthcomp as a illuminating continuum. This model hasa hard-coded seed photon temperature of 0 .
05 keV. Thismodel may not be appropriate to describe this spectral stateas we detect a higher seed photon temperature of ∼ . nthcomp . Therefore, we did notattempt to use RELXILLCP . We have presented here a broadband spectral analysisof the
NuSTAR observation of the source 4U 1636-536,aimed to study the reflection spectrum and to constraintthe accretion geometry. The continuum spectrum is hardand well described by a thermal Comptonization model nthcomp with Γ ∼ . kT e ∼
28 keV, and kT s ∼ . − −
30 keVare clearly visible in the spectrum. A correct choice ofself-consistent relativistically blurred disc reflection modelhelps us to determine the position of the inner disc alongwith some other important NS parameters. The 3 −
79 keVpersistent spectrum is well described by a combinationof the Comptonization model nthcomp and a relativisticreflection of this Comptonized emission relconv*reflionx .It may be physically interpreted as the region of mainenergy release, where hard X-rays are produced wouldbe either an optically thin boundary layer between thedisc and the NS surface or a hot corona associated withthe disc. A part of this hard X-ray emission may illumi-nate the accretion disc and produces the reflection spectrum.The source was detected at an average intensity of ∼
38 counts/s during the non-burst state. Our best-fitmodel yield an unabsorbed flux in the 3 −
79 keV band
Table 1.
Best-fitting spectral parameters of the
NuS-TAR observation of the source 4U 1636-536 using model:
TBabs × (nthcomp+highecut*relconv*reflionx) .Component Parameter (unit) Value tbabs N H ( × cm − ) 4 . f ) nthcomp Γ 1 . ± . kT e ( keV) 28 . +3 . − . kT s ( keV) 0 . ± . . ± . highecut E cut ( keV) 0 . f ) E fold ( keV) ≃ kT e relconv i (degrees) 60( f ) R in ( × R ISCO ) 3 . +0 . − . reflionx ξ (erg cm s − ) 223 +8 − Γ 1 . ± . A F e ( × solar) 1 . ± . × − ) 1 . ± . F ∗ total ( × − ergs/s/cm ) 2 . ± . F nthcomp ( × − ergs/s/cm ) 1 . ± . F reflionx ( × − ergs/s/cm ) 0 . ± . L − keV ( × ergs/s) 1 . ± . χ /dof / Note:
Here we have used the standard reflionx model thatassumes a high energy exponential cutoff power-law irradiatingthe accretion disc, modified in such a manner that it mimics the nthcomp continuum (see text). The outer radius of the relconv spectral component was fixed to 1000 R g . We fixed emissivityindex q = 3. The E fold parameter is fitted to be 3 times the kT e . ∗ All the unabsorbed fluxes are calculated in the energy band3 −
79 keV of F − ∼ . × − ergs s − cm − , which is consistentwith Agrawal & Hasan (2016). The source was observedin a low luminosity and hard spectral state (low/hard)during this observation and we measured a 3 −
79 keVluminosity of L X ∼ . × ergs s − which corre-sponds to ∼
5% of the Eddington luminosity assuminga distance of 6 kpc. It suggests that the rate of anyoutflow in 4U 1636-536 is significantly below the Eddingtonmass accretion rate. It also allows us to study the discreflection of NS LMXBs in a relatively low accretion regime.From the reflection spectrum, we have measured ainner disc radius of R in = (3 . − . R ISCO , given that c (cid:13) , 000–000 Mondal et al. R ISCO = 5 . GM/c for an NS spinning at a ≃ .
3. Thiswould correspond to R in = (16 − R g or (36 −
54) km for a1 . M ⊙ NS. It indicates that the disc is truncated at a largedistance away from the NS surface. The disc has a relativelylow ionization ( ξ ∼
223 erg s − cm) and iron abundanceis comparable to the solar abundance ( A F e ∼ . α emission line( σ ∼ .
98 keV) from this source. The broadness of the linerequires it to be located deep within the potential wellwhere the orbital velocities are mildly relativistic (see alsoKing et al. 2016). Moreover, the observed symmetric nature(a broad blue wing in addition to the broad red wing) of theFe K α line profile requires it to be located far enough awayas to not suffer severe relativistic Doppler beaming (seealso King et al. 2016). Pandel et al. (2008) suggests thatsuch a broader Fe K α line needs a higher disc inclination ofaround 60 ◦ − ◦ .Disc truncation is likely the result of the presence ofa boundary layer that lies between the disc and the NSsurface or the associated magnetic field of the NS. Herewe estimate the mass accretion rate ( ˙ m ) per unit areaat the NS surface using Equation (2) of Galloway et al.(2008). The estimated value of ˙ m during this observationto be ∼ . × − M ⊙ y − using the persistent flux F p = 2 . × − erg s − cm − and assuming the bolo-metric correction c bol is ∼ .
38 for the nonpulsing sources(Galloway et al. 2008) and considering 1 + z = 1 .
31 for aNS with mass 1.5 M ⊙ and radius 10 km where z is thesurface redshift. At this mass accretion rate, we estimatethe maximum radial extent ( R max ) of the boundarylayer region using Equation (2) of Popham & Sunyaev(2001). It estimates a maximum radial extent of ∼ . R g for the boundary layer (assuming M NS = 1 . M ⊙ and R NS = 10 km). The extent of the boundary layer region issmall to account for the disc position. It may be becauseit does not account for a spin and viscous effects in this layer.The inferred radial extension of the boundary layeris small compared to the disc truncation radius and themagnetic field of the NS would be responsible for the disctruncation. We can use our measured inner disc radius toestimate an upper limit for the magnetic field strength ofthe NS. We use Equation (1) of Cackett et al. (2009) tocalculate the magnetic dipole moment ( µ ). We estimatea bolometric flux of F bol ≃ . × − erg cm − s − by extrapolating the best fit over the 0 . −
100 keVrange. We assume an NS of mass 1 . M ⊙ , radius 10km, and distance of 6 kpc. We keep similar assumptionsregarding the geometrical and efficiency parameters as inCackett et al. (2009): k A = 1 which is a factor dependingon the geometry, spherical or disk-like, of the accretionflow, f ang = 1 which is known as the anisotropy correctionfactor and accretion efficiency in the Schwarzschild metric η = 0 .
1. The constraint that R in R g from the bestfit model, then yields B . × G at the magnetic poles.In this observation, we have observed 12 brief (10 − This data set with Obs. ID: 30401014002 dated 27.04.2019is in public domain put by NASA at their websitehttps://heasarc.gsfc.nasa.gov. The public date is 08.05.2020.
This research has made use of data and/or software providedby the High Energy Astrophysics Science Archive ResearchCentre (HEASARC). This research also has made use of the
NuSTAR data analysis software (
NuSTARDAS ) jointly devel-oped by the ASI science center (ASDC, Italy) and the Cali-fornia Institute of Technology (Caltech, USA). ASM and BRwould like to thank Inter-University Centre for Astronomyand Astrophysics (IUCAA) for their hospitality and facil-ities extended to them under their Visiting AssociateshipProgramme.
REFERENCES
Agrawal V. K., Hasan M., 2016, arXiv e-prints,arXiv:1611.09004Arnaud K. A., 1996, in Astronomical Society of the PacificConference Series, Vol. 101, Astronomical Data AnalysisSoftware and Systems V, Jacoby G. H., Barnes J., eds.,p. 17Ballantyne D. R., Ross R. R., Fabian A. C., 2001, MNRAS,327, 10Barret D., Olive J. F., Boirin L., Done C., Skinner G. K.,Grindlay J. E., 2000, ApJ, 533, 329Barret D., Olive J.-F., Miller M. C., 2007, MNRAS, 376,1139Bhattacharyya S., 2011, MNRAS, 415, 3247Bhattacharyya S., Strohmayer T. E., 2007, ApJl, 664, L103Braje T. M., Romani R. W., Rauch K. P., 2000, ApJ, 531,447Cackett E. M., Altamirano D., Patruno A., Miller J. M.,Reynolds M., Linares M., Wijnands R., 2009, ApJl, 694,L21Cackett E. M. et al., 2010, ApJ, 720, 205Cackett E. M. et al., 2008, ApJ, 674, 415 c (cid:13) , 000–000 uSTAR view of 4U 1636-536 Casares J., Cornelisse R., Steeghs D., Charles P. A., HynesR. I., O’Brien K., Strohmayer T. E., 2006, MNRAS, 373,1235Dauser T., Wilms J., Reynolds C. S., Brenneman L. W.,2010, MNRAS, 409, 1534Degenaar N. et al., 2016, MNRAS, 461, 4049Degenaar N., Miller J. M., Chakrabarty D., Harrison F. A.,Kara E., Fabian A. C., 2015, MNRAS, 451, L85Dickey J. M., Lockman F. J., 1990, ARAA, 28, 215Fabian A. C., Iwasawa K., Reynolds C. S., Young A. J.,2000, PASP, 112, 1145Galloway D. K., Muno M. P., Hartman J. M., Psaltis D.,Chakrabarty D., 2008, ApJS, 179, 360Galloway D. K., Psaltis D., Muno M. P., Chakrabarty D.,2006, ApJ, 639, 1033Harrison F. A. et al., 2013, ApJ, 770, 103Kaaret P., Piraino S., Ford E. C., Santangelo A., 1999,ApJl, 514, L31King A. L. et al., 2016, ApJl, 819, L29Kluzniak W., Wilson J. R., 1991, ApJl, 372, L87Lamb F. K., Boutloukos S., Van Wassenhove S. o., Cham-berlain R. T., Lo K. H., Clare A., Yu W., Miller M. C.,2009, ApJ, 706, 417Lamb F. K., Fabian A. C., Pringle J. E., Lamb D. Q., 1977,ApJ, 217, 197Lin D., Remillard R. A., Homan J., 2007, ApJ, 667, 1073Ludlam R. M. et al., 2019, ApJ, 873, 99Matranga M., Di Salvo T., Iaria R., Gambino A. F., Bur-deri L., Riggio A., Sanna A., 2017, A&A, 600, A24Mondal A. S., Dewangan G. C., Raychaudhuri B., 2020,MNRAS, 494, 3177Pandel D., Kaaret P., Corbel S., 2008, ApJ, 688, 1288Piraino S., Santangelo A., Kaaret P., 2000, A&A, 360, L35Popham R., Sunyaev R., 2001, ApJ, 547, 355Reis R. C., Fabian A. C., Young A. J., 2009, MNRAS, 399,L1Ross R. R., Fabian A. C., 2005, MNRAS, 358, 211Ross R. R., Fabian A. C., 2007, MNRAS, 381, 1697Shakura N. I., Sunyaev R. A., 1973, A&A, 500, 33Strohmayer T. E., Markwardt C. B., 2002, ApJ, 577, 337van Paradijs J. et al., 1990, A&A, 234, 181Verner D. A., Ferland G. J., Korista K. T., Yakovlev D. G.,1996, ApJ, 465, 487Wijnands R. A. D., van der Klis M., van Paradijs J., LewinW. H. G., Lamb F. K., Vaughan B., Kuulkers E., 1997,ApJl, 479, L141Wilms J., Allen A., McCray R., 2000, ApJ, 542, 914Zdziarski A. A., Johnson W. N., Magdziarz P., 1996, MN-RAS, 283, 193Zhang W., Lapidus I., White N. E., Titarchuk L., 1996,ApJl, 469, L17˙Zycki P. T., Done C., Smith D. A., 1999, MNRAS, 309, 561 c (cid:13)000