Illumination of the accretion disk in black hole binaries: An extended jet as the primary source of hard X-rays
aa r X i v : . [ a s t r o - ph . H E ] J a n Astronomy & Astrophysicsmanuscript no. ms © ESO 2021January 8, 2021
Illumination of the accretion disk in black hole binaries: Anextended jet as the primary source of hard X-rays
P. Reig , and N. D. Kylafis , Institute of Astrophysics, Foundation for Research and Technology-Hellas, 71110 Heraklion, Crete, Greecee-mail: [email protected] University of Crete, Physics Department, 70013 Heraklion, Crete, Greecee-mail: [email protected]
ABSTRACT
Context.
The models that seek to explain the reflection spectrum in black hole binaries usually invoke a point-like primary source ofhard X-rays. This source illuminates the accretion disk and gives rise to the discrete (lines) and continuum-reflected components.
Aims.
The main goal of this work is to investigate whether the extended, mildly relativistic jet that is present in black hole binaries inthe hard and hard-intermediate states is the hard X-ray source that illuminates the accretion disk.
Methods.
We use a Monte Carlo code that simulates the process of inverse Compton scattering in a mildly relativistic jet rather thanin a “corona” of some sort. Blackbody photons from the thin accretion disk are injected at the base of the jet and interact with theenergetic electrons that move outward with a bulk velocity that is a significant fraction of the speed of light.
Results.
Despite the fact that the jet moves away from the disk at a mildly relativistic speed, we find that approximately 15 − h < ∼ r g , where r g is the gravitational radius), but a non-negligible amountescape at a wide range of heights. At high heights, h ∼ − r g , the distribution falls o ff rapidly. The high-height cuto ff stronglydepends on the width of the jet at its base and is almost insensitive to the optical depth. The disk illumination spectrum is softer thanthe direct jet spectrum of the radiation that escapes in directions that do not encounter the disk. Conclusions.
We conclude that an extended jet is an excellent candidate source of hard photons in reflection models.
Key words. accretion, accretion disks – X-ray binaries: black holes – jets – X-ray spectra
1. Introduction
The observed X-ray spectral continuum (0.1–200 keV) of blackhole binaries (BHBs) exhibits a power law with a high-energyexponential cuto ff . This power law is a ff ected by interstellar pho-toelectric absorption at low energies (typically below 2 keV).The exponential cuto ff varies in a broad range of energies, froma few tens to a few hundred keV, and the photon-number power-law index Γ varies from 1.2 to 3. The values of these pa-rameters define spectral states that are broadly known as hard( Γ <
2) and soft ( Γ > . h above the black hole. This model isknown as the lamp post model, and it is often used to modelthe reflection features and determine the black hole spin (see,e.g., Reynolds 2014) in accreting black holes present both in ac-tive galactic nuclei (Martocchia & Matt 1996; Martocchia et al.2002; Miniutti et al. 2003; Emmanoulopoulos et al. 2014;Zoghbi et al. 2020) and X-ray binaries (Duro et al. 2016;Vincent et al. 2016; Basak & Zdziarski 2016; García et al.2019).The purpose of this work is to investigate whether the jet,moving away from the black hole at a mildly relativistic veloc-ity in the hard and hard-intermediate states, can be the sourceof the hard photons that illuminate the accretion disk. Here weare interested in the irradiation of the disk before it is reflected.Computing the reflected spectrum is beyond of the scope of thiswork.
2. The jet model
Hot-inner-flow Comptonization models have been invoked to ex-plain the hard X-ray emission of BHBs, and they have been verysuccessful at reproducing the observations (e.g., Esin et al. 1997;Done et al. 2007). Propagating-fluctuation models have beenused to explain the time lag of hard X-rays with respect to softerones (Lyubarskii 1997; Kotov et al. 2001; Arévalo & Uttley2006; Rapisarda et al. 2017), and they have also been quite suc-
Article number, page 1 of 5 & Aproofs: manuscript no. ms τ || B ac k - s ca tt e r e d pho t on s ( % ) (r g )1313.51414.515 1 2 3 γ R =100 r g γ =2.24 τ || =3 γ =2.24 τ || =3R =100 r g Fig. 1.
Fraction of input photons that are back-scattered (dashed lines) and also illuminate the accretion disk (solid lines) as a function of opticaldepth (left panel), jet width (middle panel), and the Lorentz factor (right panel). cessful. However, these models are independent of one anotherand have not been able to explain the observed correlation be-tween the spectrum and the time lags (Vignarca et al. 2003;Pottschmidt et al. 2003; Altamirano & Méndez 2015; Reig et al.2018). For this reason, we favor Comptonization in the jet, whichcan explain not only the spectra, but also the time lags and thecorrelation between the two (Reig & Kylafis 2015; Reig et al.2018; Kylafis & Reig 2018). It is natural to expect a correlationbetween the spectrum and the time lags when both are producedby the same mechanism, namely Comptonization. In addition,we remark that Comptonization in the jet quantitatively explainsthe type-B quasi-periodic oscillations (QPO) that have been ob-served in GX 339-4 (Kylafis et al. 2020).Our jet model was described in Reig & Kylafis (2019, seealso Kylafis et al. 2008), where we also gave a justification ofthe parameters used. Here, we only provide the essential points.We assume a parabolic jet of radius R ( z ) = R ( z / z ) / ,where R is the radius at the base of the jet, with an accel-eration zone at its bottom, from height z = r g to height z = r g , and a constant speed of v = . c above this. Here, r g = GM / c is the gravitational radius and the height of the jet is H = r g . The flow speed in the acceleration zone is modeledby v k ( z ) = ( z / z ) p v , where p = / τ k along the axis of the jet is τ k = Z Hz σ T n e ( z ) dz . (1)At any height z , the Thomson optical depth above this heightis τ out ( z ) = Z Hz σ T n e ( z ) dz , (2)while the Thomson optical depth perpendicular to the jet axis atheight z is τ ⊥ ( z ) = σ T n e ( z ) R ( z / z ) / . (3)The electrons are assumed to move on helical orbits aroundthe magnetic field, with velocity components v k ( z ) and v ⊥ = . c . Their Lorentz factor is γ ( z ) = / q − ( v k + v ⊥ ) / c ,and in the coasting region of the flow, z > z , it is γ = / q − ( v + v ⊥ ) / c . We assume a 10 M ⊙ non-spinning black hole. The inputsource of photons has a blackbody distribution with kT = .
3. Results
Our Monte Carlo code records the number of photons that escapefrom the jet as a function of time (travel time in the Comptoniz-ing medium), energy, and direction (angle θ with respect to thejet axis). It also records the height h in the jet from which thephotons escape. Thus, we are able to compute not only the frac-tional number of photons escaping directly toward the observerand those that are back-scattered and hit the accretion disk, butalso their spectrum and the height distribution of the points ofescape.The input parameters in our model calculations are τ k , R ,and γ . The parameter space that we consider here for the opticaldepth and jet width is determined from the range of values of theparameters that produce good fits to the time lag–photon indexcorrelation in GX 339–4 (Kylafis et al. 2008), namely 2 ≤ τ k ≤ r g ≤ R ≤ r g . For γ , we consider the results fromSaikia et al. (2019), who used the near infrared excess observedin BHBs to constrain the Lorentz factor in the jet in the range1.3–3.5. Figure 1 shows the fraction of back-scattered photons as a func-tion of optical depth (left panel), jet width (middle panel), andLorentz factor (right panel). In each case, one parameter is var-ied and the other two are kept at reasonable values. The solidlines give the fraction of back-scattered photons that hit the diskbetween R = R ISCO and R = r g , while the dashed lines givethe fraction of back-scattered photons (i.e., with cos θ < τ k , the large majority of pho-tons escape in such directions that they will not encounter thedisk, which is expected. What is interesting is that a significantfraction of the escaping photons go back to the disk, despite thebulk motion of the electrons in the jet that tends to push them Article number, page 2 of 5eig & Kylafis 2020: Disk irradiation in BHBs P ho t on s ( % ) τ || =2 τ || =3 τ || =4 τ || =5 P ho t on s ( % ) R =100 r g R =200 r g R =300 r g R =400 r g R =500 r g h (r g ) P ho t on s ( % ) γ =1.44 γ =2.24 γ =2.92 γ =3.67 R =100 r g γ =2.24 γ =2.24 τ || =3 τ || =3R =100 r g Fig. 2.
Fraction of input photons that illuminate the disk as a functionof the height h from where they escape the jet. in the forward direction. The fraction of back-scattered photonsincreases with optical depth, and the relatively low bulk veloc-ity in the acceleration zone helps. The fraction of back-scatteredphotons (dashed line) is slightly larger than that of those that hitthe disk (solid line), and this is expected too.In the middle panel of Fig. 1, we show the dependence of theback-scattered photons on the size of the jet, as measured by theradius R at its base. An increase in R results in a decrease in theback-scattered fraction, albeit a small one. For an increase by afactor of six in R , the back-scattered fraction decreases by ∼ ∼
10% (solid line).In the right panel of Fig. 1, one can see the dependence of theback-scattered photons on the Lorentz factor γ of the electronsin the coasting region of the flow ( z > z ). The variation of γ isdue to the variation of the flow speed v , and v ⊥ is kept constant.As expected, the fraction of back-scattered photons decreasesrapidly with increasing γ . The leveling o ff at large γ may seemunphysical, but it is due to the scatterings that occur in the ac-celeration zone. Irrespective of the final v , the parallel velocityis significantly smaller than v in the lower parts of the accelera-tion zone, and hence there are no large variations of the Lorentzfactor for the cases considered in Fig. 1 in this region. We now examine the percentage of photons that have back-scattered and hit the accretion disk as a function of the height h of the point of last scattering. The height distribution (Fig. 2)is characterized by a sharp peak at a low height (within a few Energy (keV) -8 -7 -6 -5 -4 -3 -2 -1 d N / d E "disk" spectrum"direct" spectrum Fig. 3.
Comparison of the "direct" and "disk" spectra. The direct spec-trum is the spectrum seen by observers at infinity at an inclination θ ,and the "disk" spectrum is the spectrum of the photons that are back-scattered and illuminate the disk. The direct spectrum was computedfor 0 . < cos θ ≤ . τ k = R = r g , and γ = . gravitational radii), an extended plateau, and a high-height cut-o ff . In our jet model, Comptonization can occur anywhere in thejet (not only at its base). Thus, it is not surprising to see photonsescaping from a large range of heights.Figure 2 shows the results of running di ff erent models withdi ff erent optical depth τ k , jet width R , and Lorentz factor γ . Ineach model, we vary one parameter and keep the other two atreasonable values. The results can be summarized as follows: i) the height distribution does not depend strongly on optical depth(top panel), ii) the cuto ff at high h moves to smaller values as R increases (middle panel), and iii) as γ increases, the fraction ofthe photons back-scattered toward the disk at every h decreases(bottom panel). Having demonstrated that a significant fraction of Comptonizedphotons move back toward the disk, we computed their spec-trum. Figure 3 compares the spectrum of the photons that illu-minate the disk, the "disk" spectrum (solid line), with the "direct"spectrum of the photons seen by observers at angles θ , with re-spect to the jet axis, in the range 0 . < cos θ ≤ . ∼ ◦ . Both spectracan be fitted with power laws with a high-energy cuto ff . The diskspectrum is clearly softer than the direct spectrum. We empha-size that the disk spectrum is not the spectrum of the reflectedradiation. It simply represents the energy distribution of the pho-tons that illuminate the disk.From the disk and the direct spectra, we can compute the ra-tio of the illuminating and the directly observed radiation. Thisratio is generally known as the reflection fraction R F , althoughdi ff erent authors give di ff erent definitions depending on whetherthe reflected flux, as opposed to the illuminating flux, is consid-ered or whether relativistic (i.e., light-bending) e ff ects are takeninto account (see the appendix of Basak & Zdziarski 2016, fora detailed account of the reflection fraction). In the lamp postmodel, R F has been used to constrain the spin of the black hole(Dauser et al. 2014) and the geometry of the source of hard X-rays (Dauser et al. 2016).Here we define R F simply as the ratio of the intensity that il-luminates the disk to the intensity that directly reaches observers Article number, page 3 of 5 & Aproofs: manuscript no. ms inner /R isco R e f l ec ti on fr ac ti on θ ≤ 0.7 θ ≤ 0.8 θ ≤ 0.9 Fig. 4.
Reflection fraction as a function of the inner radius for modelparameters τ k = R = r g , and γ = . at infinity in a range of observing angles θ . The reflection frac-tion is then R F = I disk / I direct , where the intensities I disk and I direct are computed as I i = Z E max E min E × ( dN / dE ) i × dE , (4)where dN / dE is the number of photons per unit energy in thespectrum and the subscript i refers to either "disk" or "direct."We calculated the reflection fraction in the energy range 1–100keV, which is the range where the power law dominates. We di-vided the disk into 13 radial zones and computed the intensityof the photons that hit the disk between R i and R max , where R i isthe inner radius of each zone. In other words, we mimicked thesituation of a truncated disk whose inner radius decreases (i.e.,the disk is approaching the black hole). We note that becausethe direct spectrum I direct depends on the angle θ between the jetaxis and the observer (Reig & Kylafis 2019; Kylafis et al. 2020),so does the reflection fraction.In the computation of the reflection fraction, we ignored rel-ativistic light-bending e ff ects. In our model, we assume that pho-tons are injected at the sides of the jet at its base. Because R ison the order of tens of gravitational radii, the number of photonsthat pass near the black hole is very small. Typically, the frac-tion of the input photons that enter the sphere r < r g centeredaround the black hole is < ∼ .
01% for R > ∼ r g .In Fig. 4, we show R F as a function of a disk inner radiusfor three di ff erent inclinations, 0 . < cos θ ≤ . θ ∼ ◦ ),0 . < cos θ ≤ . θ ∼ ◦ ), and 0 . < cos θ ≤ . θ ∼ ◦ ). The R F increases as the inner disk radius R i decreases,and it increases as the inclination of the system increases. Theflat part of the curve reflects the fact that the inner parts of thedisk are scarcely illuminated by back-scattered photons.
4. Discussion
The reflection spectrum results from the reprocessing of hardX-ray photons by the optically thick accretion disk. Therefore,we expect the properties of the illuminating radiation to have aprofound impact on the spectral features of the reflection spec-trum (Dauser et al. 2013; García et al. 2015; Steiner et al. 2017).Because of the complexity of the physics involved, many au-thors assume a static point source that emits isotropically, as inthe lamp post model or coronal models (see, e.g., Vincent et al.2016). In reality, the source is expected to be variable, extended, anisotropic, and partly o ff -axis (Dauser et al. 2013). Constrain-ing the nature and geometry of the source of the hard X-rays thatilluminates the disk will allow us to consider more realistic mod-els. The aim of this work has been to investigate whether the jetitself can be the disk-illuminating source.In this section, we discuss the process of disk illuminationas well as the results obtained in the previous section. We haveshown that a significant fraction of the photons return toward theaccretion disk after being scattered in the jet. We have also de-termined the height at which the photons that are back-scatteredtoward the disk escape from the jet. Finally, we have computedthe spectrum that illuminates the disk. Below, we elaborate onall three of these findings.We have shown that, regardless of the optical depth, jetwidth, and jet velocity, a significant fraction of the Comptonizedphotons are back-scattered and hit the disk (Fig. 1). The decreasein the number of back-scattered photons as the optical depth de-creases is expected because, for low optical depths, the photonsfind it easier to move along the jet and travel longer distances.The higher up in the jet they travel, the less likely it is for theback-scattered photons to hit the disk. Likewise, a larger outflowvelocity of the electrons imposes a stronger forward motion onthe photons and makes back-scattering more di ffi cult. The de-crease in the number of back-scattered photons as the jet widthincreases reflects the fact that photons can travel a longer dis-tance along a wider jet before they escape via the sides of thejet; again, they are less likely to hit the disk.An interesting result of our work is the height distributionof the photons that illuminate the disk. We have found that themajority of photons that hit the disk escape within a few gravita-tional radii, as expected in the lamp post model. The exact rangeof heights depends on our choice of the variable z , which is thedistance from the center of the base of the jet to the black hole.However, there is a significant contribution of photons that es-cape at larger radii (Fig. 2). The large fraction of back-scatteredphotons at small heights h is easily explained: In our model, weassume that photons are injected at the sides of the jet at its base.At the bottom of the jet, the optical depth is large (typically largerthan 1). In addition, the flow velocity v k is small (the accelerationzone extends up to ∼ r g ). Hence, the photons do not experi-ence a strong forward push. As a result, many photons escapeafter one (or very few) scattering(s) and do not travel long dis-tances. The cuto ff at high heights is also easily explained: Asthe height of the last scattering increases, the number of photonsthat hit the disk decreases because the solid angle that the disksubtends at this position decreases. Therefore, we expect a steepdrop at high h , which is shown in Fig. 2. Finally, the plateausseen in Fig. 2 are due to the fact that the optical depth in theseregions is of order unity and the photons are scattered with equalprobability there.The height distribution is fairly insensitive to changes in op-tical depth τ k . Large values of the optical depth parallel to the jetaxis also imply large values of the optical depth perpendicular tothe jet axis. The two e ff ects compensate for each other, and pho-tons travel more or less the same distance before they escape.Indeed, the ratio τ k /τ ⊥ as a function of h is about the same irre-spective of the values of the optical depths. In contrast, the heightcuto ff decreases significantly as the jet width increases. This re-sult can be explained by the fact that photons escape from thesides more easily in a narrow jet. As the width increases, morephotons are able to travel along the jet before they escape fromthe sides. But, as mentioned above, the angle subtended by thedisk becomes smaller as the escaping height increases. Hence, Article number, page 4 of 5eig & Kylafis 2020: Disk irradiation in BHBs photons that escape at high heights have a high chance of miss-ing the disk.The explanation of why the back-scattered spectrum is softerthan the forward, direct one is also quite simple. Consider softphotons entering a scattering region of an optical depth τ thatis significantly larger than one. On average, the photons pene-trate the scattering region one mean free path (i.e., optical depthequal to one) . The photons that escape in the forward direc-tion encounter an optical depth τ −
1, while the photons thatare back-scattered encounter an optical depth of one. The pho-tons that escape in the forward direction are scattered more timesthan the back-scattered ones and therefore gain more energy thanthe back-scattered ones. This is because, on average, the photonsgain energy with every scattering. If there is bulk flow in the scat-tering region in the direction of the incoming photons, as is thecase of a jet, then this e ff ect is stronger because the photons arepushed in the forward direction by the bulk flow.There is strong evidence that indicates that R F increaseswith luminosity (Plant et al. 2015; Basak & Zdziarski 2016;Steiner et al. 2016; Walton et al. 2017; Wang-Ji et al. 2018;Wang et al. 2020). This result is expected in the truncated diskmodel because, as the luminosity increases – that is to say, as thesystem moves from the hard state to the intermediate and softstates – the inner disk radius decreases (the disk moves inward),and hence the area irradiated in the disk increases. In Fig. 4, wenaturally reproduce this trend.Finally, there is the crucial question of whether there isany observational evidence for an extended and inhomogeneouslamp post. In this respect, García et al. (2019) showed that inorder to achieve a good description of the reflected spectrumof GX 339–4, two sources of hard X-rays were needed: one lo-cated a few gravitational radii from the black hole and the sec-ond lying at h ∼ r g . The second lamp post provided abetter fit to the narrow component of the Fe K emission. Sim-ilarly, Chakraborty et al. (2020) obtained an improvement in themodel that fitted the observed spectrum by considering a two-component corona at two di ff erent temperatures. This di ff erencein coronal temperatures could be interpreted as originating fromthe fact that the two components are located at di ff erent dis-tances from the black hole. The high-energy corona is muchcloser to the black hole and contributes to the broad iron linethrough blurred reflection, while the low-energy corona is far-ther away and contributes to the narrow core of the iron linecomplex. Basak & Zdziarski (2016) also found that, in the lamppost model, if the inner radius of the accretion disk is fixed tothe ISCO, then the height of the source of hard X-rays is large (afew hundred r g ).The report of a number of discrete lamp posts most likelyreflects the fact that the assumption of the lamp post model (anisotropic, stationary, point-like source) is an idealized case ofthe real physical source, which is likely extended, variable, andhighly anisotropic (Dauser et al. 2013). Our model predicts acontinuum of values of h at which the photons escape, and itappears to be a more natural and physical representation.
5. Conclusion
Comptonization in the jet is inescapable. The jet is fed from thehot inner flow. Thus, scattering in the hot inner flow, below thejet, will result in photons entering the jet and being scatteredthere as well. After all, the hot inner flow and the base of the jethave no boundary. Since in Comptonization it is the last scatter-ings that determine the outcome and not the first ones, scattering in the jet plays a fundamental role in shaping the radiation emit-ted by BHBs. We have shown that a significant fraction of pho-tons that are Comptonized in a jet are back-scattered toward theaccretion disk, despite the outward relativistic bulk velocity inthe jet, and contribute to the illumination of the disk. The jet ap-pears to be an excellent candidate for the source of hard X-raysin disk reflection models.
References
Altamirano, D. & Méndez, M. 2015, MNRAS, 449, 4027Arévalo, P. & Uttley, P. 2006, MNRAS, 367, 801Bambi, C., Brenneman, L. W., Dauser, T., et al. 2020, arXiv e-prints,arXiv:2011.04792Basak, R. & Zdziarski, A. A. 2016, MNRAS, 458, 2199Belloni, T. M. 2010, in Lecture Notes in Physics, Berlin Springer Verlag, Vol.794, Lecture Notes in Physics, Berlin Springer Verlag, ed. T. Belloni, 53Chakraborty, S., Navale, N., Ratheesh, A., & Bhattacharyya, S. 2020, MN-RAS[ arXiv:2009.02465 ]Dauser, T., Garcia, J., Parker, M. L., Fabian, A. C., & Wilms, J. 2014, MNRAS,444, L100Dauser, T., García, J., Walton, D. J., et al. 2016, A&A, 590, A76Dauser, T., Garcia, J., Wilms, J., et al. 2013, MNRAS, 430, 1694Done, C., Gierli´nski, M., & Kubota, A. 2007, A&A Rev., 15, 1Duro, R., Dauser, T., Grinberg, V., et al. 2016, A&A, 589, A14Emmanoulopoulos, D., Papadakis, I. E., Dovˇciak, M., & McHardy, I. M. 2014,MNRAS, 439, 3931Esin, A. A., McClintock, J. E., & Narayan, R. 1997, ApJ, 489, 865Fabian, A. C. & Ross, R. R. 2010, Space Sci. Rev., 157, 167García, J. A., Dauser, T., Steiner, J. F., et al. 2015, ApJ, 808, L37García, J. A., Tomsick, J. A., Sridhar, N., et al. 2019, ApJ, 885, 48Kotov, O., Churazov, E., & Gilfanov, M. 2001, MNRAS, 327, 799Kylafis, N. D., Papadakis, I. E., Reig, P., Giannios, D., & Pooley, G. G. 2008,A&A, 489, 481Kylafis, N. D. & Reig, P. 2018, A&A, 614, L5Kylafis, N. D., Reig, P., & Papadakis, I. 2020, A&A, 640, L16Lyubarskii, Y. E. 1997, MNRAS, 292, 679Martocchia, A. & Matt, G. 1996, MNRAS, 282, L53Martocchia, A., Matt, G., & Karas, V. 2002, A&A, 383, L23McClintock, J. E. & Remillard, R. A. 2006, Black hole binaries, ed. W. H. G.Lewin & M. van der Klis, 157–213Miniutti, G., Fabian, A. C., Goyder, R., & Lasenby, A. N. 2003, MNRAS, 344,L22Plant, D. S., Fender, R. P., Ponti, G., Muñoz-Darias, T., & Coriat, M. 2015, A&A,573, A120Pottschmidt, K., Wilms, J., Nowak, M. A., et al. 2003, A&A, 407, 1039Rapisarda, S., Ingram, A., & van der Klis, M. 2017, MNRAS, 472, 3821Reig, P. & Kylafis, N. D. 2015, A&A, 584, A109Reig, P. & Kylafis, N. D. 2019, A&A, 625, A90Reig, P., Kylafis, N. D., Papadakis, I. E., & Costado, M. T. 2018, MNRAS, 473,4644Reynolds, C. S. 2014, Space Sci. Rev., 183, 277Saikia, P., Russell, D. M., Bramich, D. M., et al. 2019, ApJ, 887, 21Steiner, J. F., García, J. A., Eikmann, W., et al. 2017, ApJ, 836, 119Steiner, J. F., Remillard, R. A., García, J. A., & McClintock, J. E. 2016, ApJ,829, L22Vignarca, F., Migliari, S., Belloni, T., Psaltis, D., & van der Klis, M. 2003, A&A,397, 729Vincent, F. H., Ró˙za´nska, A., Zdziarski, A. A., & Madej, J. 2016, A&A, 590,A132Walton, D. J., Mooley, K., King, A. L., et al. 2017, ApJ, 839, 110Wang, J., Kara, E., Steiner, J. F., et al. 2020, ApJ, 899, 44Wang-Ji, J., García, J. A., Steiner, J. F., et al. 2018, ApJ, 855, 61Zoghbi, A., Kalli, S., Miller, J. M., & Mizumoto, M. 2020, ApJ, 893, 97]Dauser, T., Garcia, J., Parker, M. L., Fabian, A. C., & Wilms, J. 2014, MNRAS,444, L100Dauser, T., García, J., Walton, D. J., et al. 2016, A&A, 590, A76Dauser, T., Garcia, J., Wilms, J., et al. 2013, MNRAS, 430, 1694Done, C., Gierli´nski, M., & Kubota, A. 2007, A&A Rev., 15, 1Duro, R., Dauser, T., Grinberg, V., et al. 2016, A&A, 589, A14Emmanoulopoulos, D., Papadakis, I. E., Dovˇciak, M., & McHardy, I. M. 2014,MNRAS, 439, 3931Esin, A. A., McClintock, J. E., & Narayan, R. 1997, ApJ, 489, 865Fabian, A. C. & Ross, R. R. 2010, Space Sci. Rev., 157, 167García, J. A., Dauser, T., Steiner, J. F., et al. 2015, ApJ, 808, L37García, J. A., Tomsick, J. A., Sridhar, N., et al. 2019, ApJ, 885, 48Kotov, O., Churazov, E., & Gilfanov, M. 2001, MNRAS, 327, 799Kylafis, N. D., Papadakis, I. E., Reig, P., Giannios, D., & Pooley, G. G. 2008,A&A, 489, 481Kylafis, N. D. & Reig, P. 2018, A&A, 614, L5Kylafis, N. D., Reig, P., & Papadakis, I. 2020, A&A, 640, L16Lyubarskii, Y. E. 1997, MNRAS, 292, 679Martocchia, A. & Matt, G. 1996, MNRAS, 282, L53Martocchia, A., Matt, G., & Karas, V. 2002, A&A, 383, L23McClintock, J. E. & Remillard, R. A. 2006, Black hole binaries, ed. W. H. G.Lewin & M. van der Klis, 157–213Miniutti, G., Fabian, A. C., Goyder, R., & Lasenby, A. N. 2003, MNRAS, 344,L22Plant, D. S., Fender, R. P., Ponti, G., Muñoz-Darias, T., & Coriat, M. 2015, A&A,573, A120Pottschmidt, K., Wilms, J., Nowak, M. A., et al. 2003, A&A, 407, 1039Rapisarda, S., Ingram, A., & van der Klis, M. 2017, MNRAS, 472, 3821Reig, P. & Kylafis, N. D. 2015, A&A, 584, A109Reig, P. & Kylafis, N. D. 2019, A&A, 625, A90Reig, P., Kylafis, N. D., Papadakis, I. E., & Costado, M. T. 2018, MNRAS, 473,4644Reynolds, C. S. 2014, Space Sci. Rev., 183, 277Saikia, P., Russell, D. M., Bramich, D. M., et al. 2019, ApJ, 887, 21Steiner, J. F., García, J. A., Eikmann, W., et al. 2017, ApJ, 836, 119Steiner, J. F., Remillard, R. A., García, J. A., & McClintock, J. E. 2016, ApJ,829, L22Vignarca, F., Migliari, S., Belloni, T., Psaltis, D., & van der Klis, M. 2003, A&A,397, 729Vincent, F. H., Ró˙za´nska, A., Zdziarski, A. A., & Madej, J. 2016, A&A, 590,A132Walton, D. J., Mooley, K., King, A. L., et al. 2017, ApJ, 839, 110Wang, J., Kara, E., Steiner, J. F., et al. 2020, ApJ, 899, 44Wang-Ji, J., García, J. A., Steiner, J. F., et al. 2018, ApJ, 855, 61Zoghbi, A., Kalli, S., Miller, J. M., & Mizumoto, M. 2020, ApJ, 893, 97