Coronal Properties of Black Hole X-Ray Binaries in the Hard State as Seen by NuSTAR and Swift

Zhen Yan; Fu-Guo Xie; Wenda Zhang

doi:10.3847/2041-8213/ab665e

1. Introduction

In the current understanding, the hard X-rays from active galactic nuclei (AGNs) and black hole X-ray binaries (BHXRBs) are produced by a central hot corona (or hot accretion flow; below we use them interchangeably). The soft seed photons, originating either externally from the underlying cold accretion disk or internally from the corona itself, are inversely Compton scattered by the hot electrons in the corona (see reviews by Done et al. 2007; Yuan & Narayan 2014). The corresponding hard X-ray continuum spectrum can be well described by a power-law shape, with a high-energy cutoff at tens to hundreds of keVs. The X-ray luminosity ${L}_{{\rm{x}}}$ , the photon index Γ, and the cutoff energy ${E}_{{\rm{c}}}$ determined from X-ray spectral fitting reveal important properties of the corona. For example, the cutoff energy empirically relates to the electron temperature ${{kT}}_{{\rm{e}}}$ as ${E}_{{\rm{c}}}$ = 2 ∼ 3 ${{kT}}_{{\rm{e}}}$ (Petrucci et al. 2001), while the Γ is mostly determined by ${{kT}}_{{\rm{e}}}$ and optical depth (Titarchuk & Lyubarskij 1995; Zdziarski et al. 1996). With given ${{kT}}_{{\rm{e}}}$ and ${L}_{{\rm{x}}}$ , the optical depth then provides a constraint on the size of the corona.

Observationally the power-law index Γ can be measured much more easily than the electron temperature ${{kT}}_{{\rm{e}}}$ . The power-law index can be derived based on the X-ray spectrum below 10 keV, a band covered by most X-ray missions, among which some have high sensitivity. Consequently, the power-law indices have been extensively studied in BHXRBs and AGNs using different samples spanning a large range in X-ray luminosity (e.g., Younes et al. 2011; Yang et al. 2015). A "V" shape in the Γ– ${L}_{{\rm{x}}}$ diagram is found: below a certain luminosity (∼1% ${L}_{\mathrm{Edd}}$ ) the power-law index increases with a decreasing X-ray luminosity (so called "harder when brighter") and above that the power-law index increases with an increasing X-ray luminosity ("softer when brighter").

The hard and hard-intermediate states of BHXRBs, where the X-ray spectrum is usually dominated by the thermal Comptonization of the corona (Done et al. 2007; Yuan & Narayan 2014), provide an excellent opportunity to study the corona properties. In order to constrain the electron temperature ${{kT}}_{{\rm{e}}}$ (or cutoff energy ${E}_{{\rm{c}}}$ ) of the corona, a high-quality X-ray spectrum extending to at least tens of keV are necessary. The most well-studied case is the prototype BHXRB GX 339-4 in its hard and hard-intermediate states, in which an anticorrelation between E_c and ${L}_{{\rm{x}}}$ has been found (e.g., Miyakawa et al. 2008; Motta et al. 2009). Similar anticorrelation in hard and/or hard-intermediate states has also been observed in other BHXRBs, such as XTE J1550−564 (Rodriguez et al. 2003) and GRO J1655−40 (Joinet et al. 2008).

Because of strong background, previous hard X-ray (above 10 keV) instruments are only capable of investigating bright sources, e.g., in most BHXRBs only the ${L}_{{\rm{x}}}$ ≳ 10³⁷ $\mathrm{erg}\,{{\rm{s}}}^{-1}$ regime. Only close sources have good enough hard X-ray spectra to constrain the electron temperature (or cutoff energy). Nuclear Spectroscopic Telescope Array (NuSTAR; Harrison et al. 2013), the first focusing telescope in hard X-rays, has unprecedented sensitivity, low background, and no pile-up effect. It can provide high signal-to-noise ratio spectra at the 3–79 keV energy band for the corona at not only high but also low luminosities.

In this Letter, we combine the NuSTAR and Swift spectra to study the coronal properties (including Γ and ${{kT}}_{{\rm{e}}}$ ) of the hard state of BHXRBs, with a focus on the low-luminosity regime, the electron temperature of which that was poorly explored before. Section 2 presents the sample selection and data analysis. Section 3 presents our results. Brief discussions and a summary are devoted to Section 4.

2. Sample Selection and Data Analysis

2.1. Sample/Data Selection

We list in Table 1 the sources selected in our sample and in Table 2 (in the Appendix) the details of each observation and spectral result (see Section 2.2 for details of the spectral modeling). We assume MAXI J1813−095 has a distance of 8 kpc, as it lacks a distance measurement (see Table 1).

Table 1. Sample

Source	R.A.	Decl.	Distance (kpc)	References
Swift J1357.2−0933	13:57:16.84	−09:32:38.79	6.3	[1]
GS 1354−64	13:58:09.70	−64:44:05.80	25.0	[2]
MAXI J1535−571	15:35:19.73	−57:13:48.10	4.1	[3]
GX 339-4	17:02:49.31	−48:47:23.16	9.0	[4]
IGR J17091−3624	17:09:07.61	−36:24:25.70	12.0	[5]
GRS 1716−249	17:19:36.93	−25:01:03.43	2.4	[6]
GRS 1739−278	17:42:40.03	−27:44:52.70	7.5	[7]
H1743−322	17:46:15.60	−32:14:00.86	8.5	[8]
Swift J1753.5−0127	17:53:28.29	−01:27:06.26	7.15	[9]
MAXI J1813−095	18:13:34.07	−09:32:07.30
MAXI J1820+070	18:20:21.90	+07:11:07.30	3.46	[9]
GRS 1915+105	19:15:11.55	+10:56:44.76	8.6	[10]
Cyg X-1	19:58:21.68	+35:12:05.78	1.86	[11]
V404 Cyg	20:24:03.82	+33:52:01.90	2.4	[12]

References. [1] Armas Padilla et al. (2014); [2] Corral-Santana et al. (2016); [3] Chauhan et al. (2019); [4] Heida et al. (2017); [5] Iyer et al. (2015); [6] della Valle et al. (1994); [7] Yan & Yu (2017); [8] Steiner et al. (2012); [9] Gandhi et al. (2019); [10] Reid et al. (2014); [11] Reid et al. (2011); [12] Miller-Jones et al. (2009).

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Our motivation is to investigate the coronal properties; we thus first restrict to BHXRBs that have publicly available NuSTAR observations. NuSTAR lacks soft X-ray coverage below 3 keV, which is crucial for the thermal emission component. We then supplement during the spectral analysis with Swift/XRT observations that cover the 0.3–10 keV band. We cross-match the NuSTAR archive with the Swift archive for searching quasi-simultaneous observations within one day. The exact observational times of NuSTAR and Swift observations are given in Table 2 (in the Appendix).

We further select those whose X-ray spectra are dominated by the Comptonization emission. We thus take the following two criteria: one is that the X-ray spectrum can be well fitted with our model (χ² < 2), and the other is that the X-ray flux from the Comptonization component contributes more than 70% of the total X-ray flux (see details in Section 2.2 and Figure 1). Observations that meet these two criteria are all in the hard or hard-intermediate states (Dunn et al. 2010). During this step, 4U 1630−472 and V4641 Sgr are excluded, since none of their observations meet these two criteria.

**Figure 1.** Corona radiation fraction L_corona/ ${L}_{{\rm{x}}}$ for BHXRBs in their hard/hard-intermediate state. The uncertainties are not shown here for clarity.
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**Figure 1.** Corona radiation fraction L_corona/ ${L}_{{\rm{x}}}$ for BHXRBs in their hard/hard-intermediate state. The uncertainties are not shown here for clarity.
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We notice that there are four NuSTAR observations that have no quasi-simultaneous (within one day) Swift/XRT observations. We still include them to enlarge our sample size at low luminosities. Among them, two have Swift observations within two days: the observation of V404 Cyg on modified Julian date (MJD) 56578 and the observation of GRS 1739−278 on MJD 57692. In this work, we still consider them as quasi-simultaneous observations. Meanwhile, the other two, MAXI J1820+070 on MJD 58604 and H1743−322 on MJD 57230, have no quasi-simultaneous Swift observations. They are also included in our sample, but during the spectral modeling, they are fit without the thermal diskbb component; see Section 2.2.

We additionally exclude from our sample the following NuSTAR observations based on various reasons. The observation of H1743−322 in its quiescent state on MJD 57250 is not included since it is not robustly detected. The observations of V404 Cyg on MJD 56198 and 57197 associate with many large amplitude flares, during which both the X-ray spectrum and the local absorption are highly variable (Walton et al. 2017). Time-resolved spectra or flux-resolved spectra are necessary (e.g., Walton et al. 2017). We thus exclude these two observations to avoid the complexities mentioned above.

2.2. Data Reduction and Spectral Analysis

The NuSTAR data are processed through the nupipeline task of the nustardas package contained in HEASoft 6.25, with calibration files of version 20181030. The source spectra were extracted using a circular region with a radius of 90'' at the source position, and the background spectra were extracted from an annulus with inner and outer radii of 180'' and 200''.

The Swift/XRT data were first processed with xrtpipeline (v 0.13.4) in order to generate the cleaned event file. We then extract the source and background spectra by using xselect, while the events at the central pixels were excluded if the data suffered from pile-up effects (Evans et al. 2009).

The joint spectral fitting of quasi-simultaneous Swift/XRT and NuSTAR observations was performed using PyXspec with XSPEC 12.10.1. For the modeling, we consider Swift/XRT and NuSTAR spectra in 0.5–10 keV and 4–78 keV, respectively.

We fit the spectra with a model that is an absorption of a combination of multi-colored disk blackbody (diskbb), thermal Comptonization (nthcomp; Zdziarski et al. 1996), and Gaussian iron line reflection (Gauss) components, i.e., constant*tbabs*(diskbb+nthcomp+Gauss) in XSPEC notation. Note that for the two cases without Swift/XRT observations, diskbb is omitted. Three observations (on MJD 56578, 56579, and 56628) of V404 Cyg are in the quiescent state; we only consider using the nthcomp component (see also Rana et al. 2016). For the absorption by the Galactic interstellar medium, the abundances and cross sections are set to Wilms et al. (2000) and Verner et al. (1996). Note that the column density N_H of Swift J1357.2−0933, MAXI J1820+070, and GRS 1915+105 is fixed to 0.012 × 10²² cm⁻² (Beri et al. 2019), 0.15 × 10²² cm⁻² (Uttley et al. 2018), and 6.5 × 10²² cm⁻² (Miller et al. 2013), respectively, since they cannot be tightly and consistently constrained under our data set.

The thermal Comptonization model nthcomp includes three main parameters (Zdziarski et al. 1996): the power-law photon index Γ, the electron temperature ${{kT}}_{{\rm{e}}}$ , and the temperature of seed thermal photons kT_s. The kT_s is tied to the disk temperature when the diskbb component is applied. During the modeling, the value of constant is fixed for NuSTAR/FPMA, but is set free for Swift/XRT and NuSTAR/FPMB. Once the best-fitting result is derived, we then use the convolution model cflux to estimate the 0.1–100 keV X-ray fluxes for the three different components. In most cases parameters Γ and ${{kT}}_{{\rm{e}}}$ are well-constrained. Only for the observation of MAXI J1820+070 on MJD 58404, we have a lower limit constraint on ${{kT}}_{{\rm{e}}}$ .

3. Results

We first show in Figure 1 the fraction of corona luminosity, which is defined as the nthcomp-to-all luminosity ratio L_corona/ ${L}_{{\rm{x}}}$ . Obviously because of the sample selection, all observations have L_corona/ ${L}_{{\rm{x}}}$ > 70%, i.e., all are dominated by corona emission.

The left panel of Figure 2 shows the correlation between the photon index Γ and the X-ray luminosity L_X. Obviously Γ and $\mathrm{log}({L}_{{\rm{X}}})$ exhibit a "V"-shaped correlation, consistent with previous results (e.g., Yamaoka et al. 2005; Yuan et al. 2007; Wu & Gu 2008; Yang et al. 2015). We take the following piecewise linear function to fit the data:

$\begin{eqnarray}Y(X)=\left\{\begin{array}{cc}{f}_{1}(X-{X}_{c})+{Y}_{c} & \quad (X\leqslant {X}_{c}),\\ {f}_{2}(X-{X}_{c})+{Y}_{c} & \quad (X\geqslant {X}_{c}).\end{array}\right.\end{eqnarray} \tag{ 1 }$

By replacing the X and Y with $\mathrm{log}{L}_{{\rm{x}}}$ and Γ in Equation (1), we fit the Γ– ${L}_{{\rm{x}}}$ correlation by using the Levenberg–Marquardt method with the Python package LMFIT (Newville et al. 2014). The best-fit result is shown by the dashed curve in the left panel of Figure 2. We find the correlation slope turns between positive (f₂ = 0.17 ± 0.05) and negative (f₁ = −0.11 ± 0.03) at $\mathrm{log}{L}_{{\rm{x}}}=36.95\pm 0.27$ ( ${L}_{{\rm{x}}}$ ∼ 9 × 10³⁶ $\mathrm{erg}\,{{\rm{s}}}^{-1}$ ). For a 10 M_⊙ black hole, the turnover happens at nearly 0.01 ${L}_{\mathrm{Edd}}$ , which roughly agrees with previous results (e.g., Yuan et al. 2007; Wu & Gu 2008; Yang et al. 2015). The Spearman coefficients of the correlation for the data below and above this turning luminosity are −0.81 and 0.11 at the significances of 5.47σ and 0.81σ, respectively. Note that it seems that different sources/outbursts follow different tracks of the positive Γ– ${L}_{{\rm{x}}}$ correlation branch (see also in Yamaoka et al. 2005; Yang et al. 2015), which results in large scatters and low significance of the positive correlation.

**Figure 2.** Relationship between photon index Γ and the X-ray luminosity ${L}_{{\rm{x}}}$ (left panel) and that between the electron temperature kT_e and the X-ray luminosity (right panel) for BHXRBs in their hard/hard-intermediate state. The figure legend is the same as in Figure 1.
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We then investigate the relationship between the electron temperature ${{kT}}_{{\rm{e}}}$ and the X-ray luminosity ${L}_{{\rm{x}}}$ . As shown in the right panel of Figure 2, they follow a "Λ"-shaped ${{kT}}_{{\rm{e}}}$ – ${L}_{{\rm{x}}}$ correlation. Discarding the lower limit value of ${{kT}}_{{\rm{e}}}$ during the fitting, we find the turnover happens at $\mathrm{log}{L}_{{\rm{x}}}=36.47\pm 0.15$ ( ${L}_{{\rm{x}}}$ ∼ 3 × 10³⁶ $\mathrm{erg}\,{{\rm{s}}}^{-1}$ ), which is ∼1/3 that of the Γ– ${L}_{{\rm{x}}}$ correlation. Considering the uncertainties of the fitting results and large scatter of data, we caution that the exact difference in turnover luminosity awaits future investigations, either statistically or individually. The best-fit slopes of positive and negative branches are f₁ = 0.26 ± 0.03 and f₂ = −0.27 ± 0.04, respectively. The Spearman coefficients are 0.77 and −0.77 at the significances of 4.21σ and 8.06σ for the low- and high-luminosity branches, respectively. Admittedly, the chi-square of some observations at the high-luminosity branch are relatively larger with the thermal Comptonization model (see Table 2 in the Appendix). The estimation of ${{kT}}_{{\rm{e}}}$ is probably affected by the relativistic reflection components (see the discussion in Section 4.2). To avoid their contamination, we additionally exclude those data with reduced χ² greater than 1.3 and do the fitting again. The slope of the bright branch is now revised to f₂ = −0.31 ± 0.05, which agrees with the previous value (f₂ = −0.27 ± 0.04) within uncertainties. The Spearman coefficient of the remaining data is −0.81 at a significance of 7.97σ.

We emphasis that the "cooler when brighter" behavior above $3\times {10}^{36}\,\mathrm{erg}\,{{\rm{s}}}^{-1}$ is consistent with previous results (e.g., Miyakawa et al. 2008; Motta et al. 2009). However, the "cooler when fainter" behavior with ${L}_{{\rm{x}}}$ spanning over ∼4 orders of magnitude below 3 × 10³⁶ $\mathrm{erg}\,{{\rm{s}}}^{-1}$ has never been reported before.

Due to limitation in the sensitivity of the hard X-ray telescopes, previous studies of electron temperature ${{kT}}_{{\rm{e}}}$ mostly covered the ${L}_{{\rm{x}}}$ > 10³⁷ $\mathrm{erg}\,{{\rm{s}}}^{-1}$ high-luminosity regime (e.g., Yamaoka et al. 2005; Joinet et al. 2008; Miyakawa et al. 2008; Motta et al. 2009), among which only a negative ${{kT}}_{{\rm{e}}}$ – ${L}_{{\rm{x}}}$ (in some cases, ${E}_{{\rm{c}}}$ – ${L}_{{\rm{x}}}$ ) correlation is reported. For example, Yamaoka et al. (2005) have analyzed the X-ray spectra of nine BHXRBs with both RXTE and Beppo-SAX observations, and found a negative ${E}_{{\rm{c}}}$ – ${L}_{{\rm{x}}}$ correlation is observed for ${L}_{{\rm{x}}}$ > 2 × 10³⁷ $\mathrm{erg}\,{{\rm{s}}}^{-1}$ . However, as shown in their Figure 3, data of two nearby BHXRBs (XTE J118+480 and XTE J1650−500) below 2 × 10³⁶ $\mathrm{erg}\,{{\rm{s}}}^{-1}$ also hint at a positive relationship. Such turnover is ignored by Yamaoka et al. (2005), mostly because of the poor ${E}_{{\rm{c}}}$ measurement quality for ${L}_{{\rm{x}}}$ in the range 10³⁶–10³⁷ $\mathrm{erg}\,{{\rm{s}}}^{-1}$ .

For completeness, we also estimate the optical depth τ of the corona according to the following equation (Zdziarski et al. 1996):

$\begin{eqnarray}&&\tau \approx \sqrt{\displaystyle \frac{9}{4}+\displaystyle \frac{{m}_{e}{c}^{2}}{{{kT}}_{e}}\displaystyle \frac{3}{({\rm{\Gamma }}-1)({\rm{\Gamma }}+2)}}-\displaystyle \frac{3}{2},\end{eqnarray} \tag{ 2 }$

i.e., τ can be crudely determined by ${{kT}}_{{\rm{e}}}$ and Γ. The results are listed in Table 2 (in the Appendix).

4. Summary and Discussions

Corona or hot accretion flow, which is responsible for the continuum emission in hard X-rays, is one of the key ingredients in black hole accretion systems. In this work, through a detailed modeling of quasi-simultaneous NuSTAR + Swift observations, we analyze the coronal properties of BHXRBs in their hard and hard-intermediate states that spans six orders of magnitudes of the luminosity range, from ∼5 × 10³² to ∼5 × 10³⁸ $\mathrm{erg}\,{{\rm{s}}}^{-1}$ .

We confirm previous work that Γ and ${L}_{{\rm{x}}}$ follow a "V"-shaped correlation, and the turnover happens at ${L}_{{\rm{x}}}$ ≈ 9 × 10³⁶ $\mathrm{erg}\,{{\rm{s}}}^{-1}$ . Meanwhile, we unexpectedly find a "Λ"-shaped relationship between electron temperature ${{kT}}_{{\rm{e}}}$ and ${L}_{{\rm{x}}}$ , i.e., it shows a "cooler when brighter" behavior when ${L}_{{\rm{x}}}$ ≳ 3 × 10³⁶ $\mathrm{erg}\,{{\rm{s}}}^{-1}$ , and an opposite "cooler when fainter" behavior when ${L}_{{\rm{x}}}$ ≲ 3 × 10³⁶ $\mathrm{erg}\,{{\rm{s}}}^{-1}$ . As discussed below, this result challenges the existing models of BHXRBs in the hard state.

4.1. Theoretical Implication

The leading model for the hard and hard-intermediate states of BHXRBs is the truncated accretion–jet model (Done et al. 2007; Yuan & Narayan 2014). In this model, the hard X-rays are produced by the inverse Compton scattering of electrons within the inner hot accretion flow, the residual thermal emission below ∼1–2 keV is mostly produced by the outer truncated cold Shakura–Sunyaev disk (SSD), and the radio up to infrared is from a relativistic jet.

This model has been applied to understand the "V"-shaped Γ– ${L}_{{\rm{x}}}$ correlation, where the primary reason for the opposite spectral behavior relates to the change in the origin/source of seed photons for the Compton scattering process (Yang et al. 2015). At the relative high accretion rate, the seed photons are mainly external, from quasi-thermal emission of cold clumps within the hot accretion flow (Yang et al. 2015) and/or SSD (Qiao & Liu 2013), while at a low accretion rate they are mainly internal, from synchrotron emission within the hot accretion flow/corona itself.

Despite the change in the seed photons, we should always expect that more radiative cooling (i.e., higher ${L}_{{\rm{x}}}$ ) will result in cooler electrons, i.e., it should always follow a "cooler when brighter" track in the ${{kT}}_{{\rm{e}}}$ – ${L}_{{\rm{x}}}$ correlation, the case as observed for ${L}_{{\rm{x}}}$ > 3 × 10³⁶ $\mathrm{erg}\,{{\rm{s}}}^{-1}$ . ${L}_{{\rm{x}}}$ < 3 × 10³⁶ $\mathrm{erg}\,{{\rm{s}}}^{-1}$ represents the typical regime of the hot accretion flow, where theory predicts that the hot accretion flow will be closer to the ideal nonradiative or at least radiatively inefficient case (Yuan & Narayan 2014). In this regime, the electron temperature will reach its maximal value, nearly independent of accretion rate (or ${L}_{{\rm{x}}}$ ). Obviously, such theoretical expectation contradicts the observation of the positive ${{kT}}_{{\rm{e}}}$ – ${L}_{{\rm{x}}}$ correlation branch, where the electrons become cooler at lower luminosity. Interestingly, we notice that Yu et al. (2015) investigated an optically thin but radiatively efficient accretion flow, where strong magnetic fields are considered to avoid thermal instabilities. In this model, a "cooler when fainter" behavior is indeed achieved (Yu et al. 2015). On the other hand, it has been noticed for a long time that quantitatively the observed electron temperature ${{kT}}_{{\rm{e}}}$ is systematically lower than that predicted by hot accretion flow (see, e.g., Yuan & Zdziarski 2004; Xie et al. 2010). Our measurements of ${{kT}}_{{\rm{e}}}$ are also much below the prediction of hot accretion flow, especially at the low-luminosity regime.

The other scenario in literature considers the possibility of electron–positron pair production (Svensson 1984; Coppi 1999). In this model, electron–positron pairs are created when energetic photons collide with one another. This process acts as an ${L}_{{\rm{x}}}$ /R-dependent thermostat (R is the size of emission site; see Svensson 1984; Coppi 1999), thus playing a major role in determining the outgoing spectrum and overall composition of the corona. This model predicts a negative ${{kT}}_{{\rm{e}}}$ − ${L}_{{\rm{x}}}$ /R correlation (see e.g., Fabian et al. 2015). Obviously our results at low luminosities also contradict this model.

Another competing scenario suggested in the literature for the hard state of BHXRBs is the maximal jet model (e.g., Markoff et al. 2001, 2005).³ In this model, the X-rays are the synchrotron emission of the accelerated particles in the jet base. However, synchrotron emission cannot produce a sharp cutoff feature in hard X-rays (Zdziarski et al. 2003). Moreover, it is still unclear to us how to understand in this model not only the newly discovered "Λ"-shaped ${{kT}}_{{\rm{e}}}$ – ${L}_{{\rm{x}}}$ relationship, but also the well-established "V"-shaped Γ– ${L}_{{\rm{x}}}$ correlation.

4.2. Reflection Emission

The reflection emission is known to have affects on the determination of ${{kT}}_{{\rm{e}}}$ (Fabian et al. 2015; García et al. 2015). However, the reflection emission in the low-luminosity regime ( ${L}_{{\rm{x}}}$ ≲ 10³⁷ $\mathrm{erg}\,{{\rm{s}}}^{-1}$ ) is systematically weak (e.g., Fürst et al. 2016; Beri et al. 2019). For example, the reflection fraction is found to be less than 5% for a joint NuSTAR and XMM-Newton observation of GRS 1739−278 at ${L}_{{\rm{x}}}$ ∼ (2–3) × 10³⁵ $\mathrm{erg}\,{{\rm{s}}}^{-1}$ (Fürst et al. 2016). Consequently, the cutoff energy and the ${{kT}}_{{\rm{e}}}$ constrained from the Comptonization model are consistent with those derived by reflection models (Fürst et al. 2016). Since we expect the reflection fraction to decrease with decreasing ${L}_{{\rm{x}}}$ , we thus argue that for ${L}_{{\rm{x}}}$ ≲ 3 × 10³⁶ $\mathrm{erg}\,{{\rm{s}}}^{-1}$ the estimation of ${{kT}}_{{\rm{e}}}$ is insensitive to whichever reflection model is adopted. We also emphasize that GRS 1739−278 individually also follows a positive ${{kT}}_{{\rm{e}}}$ – ${L}_{{\rm{x}}}$ correlation at the low-luminosity regime, as is clearly demonstrated in Figure 2.

We also examine our results by using the nonrelativistic reflection model xillverCp, which includes nthcomp as an incident spectrum. We find that (not shown here), although in numerous cases the exact value of ${{kT}}_{{\rm{e}}}$ is different from that derived by nthcomp, we still obtain a "Λ"-shaped ${{kT}}_{{\rm{e}}}$ – ${L}_{{\rm{x}}}$ correlation. The best-fit values of slopes of positive and negative branches are f₁ = 0.11 ± 0.02 and f₂ = −0.19 ± 0.06, respectively. The Spearman coefficients for the low- and high-luminosity branches are respectively 0.88 and −0.36 at the significances of 6.08σ and 2.10σ. The separation of the two branches locates at the luminosity $\mathrm{log}{L}_{X}=36.94\pm 0.24$ . So our main conclusions are still solid with the reflection model. We do not report our results based on the xillverCp model, mainly because some bright observations are poorly fitted by this model (with reduced chi-square larger than two). The relativistic reflection model may be required for accurate estimation of ${{kT}}_{{\rm{e}}}$ in those bright observations. For example, Basak et al. (2017) also analyzed the NuSTAR data of the bright persistent BHXRB Cyg X-1. The ${{kT}}_{{\rm{e}}}$ derived by elaborated models (including multiple reflection components) is about 90 keV, which is roughly three times larger than our results (see also Ibragimov et al. 2005). On the other hand, this negative correlation at the high-luminosity branch has been demonstrated in previous studies with different models (e.g., Yamaoka et al. 2005; Fabian et al. 2015).

In this work we are not aimed at deriving the exact value of ${{kT}}_{{\rm{e}}}$ , but instead at the trend of the ${{kT}}_{{\rm{e}}}$ – ${L}_{{\rm{x}}}$ correlation, especially at the low-luminosity regime, which has been poorly investigated before. For this motivation, we adopt the same model for all the observations (see Section 2.2) instead of elaborately examining/modeling each observation in detail. The discrepancy of ${{kT}}_{{\rm{e}}}$ in different models is beyond the scope of this Letter.

4.3. Quiescent State of BHXRBs

All the data points with ${L}_{{\rm{x}}}$ < 10³³ $\mathrm{erg}\,{{\rm{s}}}^{-1}$ are from V404 Cyg in its quiescent state (Plotkin et al. 2017). A component with a cutoff at ∼20 keV is clearly detected (Rana et al. 2016). However, the origin of the hard X-ray emission in the quiescent state remains unclear, and various models have been proposed (e.g., Narayan et al. 1996; Xie et al. 2014; Rana et al. 2016; Plotkin et al. 2017).

Although we cannot directly eliminate the debate, the data points in quiescent state roughly agree with the extrapolation (to the fainter end) of the two correlations observed in the low-luminosity regime of hard state, i.e., the negative Γ– ${L}_{{\rm{x}}}$ relationship (see the left panel of Figure 2 and also Plotkin et al. 2017) and the positive ${{kT}}_{{\rm{e}}}$ – ${L}_{{\rm{x}}}$ one (see the right panel of Figure 2). This implies that the hard X-rays in the quiescent state have the same origin as that in the faint-hard state, although the accretion physics in the latter is also unclear as of yet.

4.4. Corona in AGNs

A similar "V"-shaped Γ– ${L}_{{\rm{x}}}$ correlation has also been observed in AGNs (e.g., Younes et al. 2011; Yang et al. 2015), implying that the accretion physics in both stellar and supermassive black hole systems is at least similar (Yang et al. 2015).

The electron temperatures of the corona in AGNs have been probed extensively by various hard X-ray missions (e.g., Dadina 2007; Molina et al. 2013; Tortosa et al. 2018). A negative correlation between electron temperature (or cutoff energy) and the luminosity in the Eddington unit is reported by a sample of AGNs as observed by Swift/BAT (e.g., Ricci et al. 2018). However, this result is not confirmed by a smaller sample that is better in data quality (Molina et al. 2019; Rani et al. 2019). A large sample of AGNs (especially including the low-luminosity ones) is necessary to reach a consensus of coronal properties. If the accretion physics is similar, we will expect to observe a similar Λ-shaped correlation between ${{kT}}_{{\rm{e}}}$ and ${L}_{{\rm{x}}}$ in AGNs; or in other words, a different result will reveal distinctive differences between AGNs and BHXRBs.

We would like to thank Wenfei Yu and Anabella Araudo for discussion and Andrzej Zdziarski for his helpful comments. This research has made use of data and software provided by the High Energy Astrophysics Science Archive Research Center (HEASARC), which is a service of the Astrophysics Science Division at NASA/GSFC and the High Energy Astrophysics Division of the Smithsonian Astrophysical Observatory. Z.Y. and F.G.X. are supported in part by the National Program on Key Research and Development Project of China (grant 2016YFA0400704) and the Natural Science Foundation of China (grants 11773055, 11873074, U1938114, and U1838203). W.Z. acknowledges financial support provided by Czech Science Foundation grant 17-02430S. W.Z. is also supported by the project RVO:67985815.

Facilities: NuSTAR - The NuSTAR (Nuclear Spectroscopic Telescope Array) mission, Swift(XRT) - .

Appendix: Table of Observations and Spectral Fitting Result

In Table 2 we list all of the NuSTAR and/or Swift observations of each source and the best-fitting parameters of the coronae.

Table 2. List of Quasi-simultaneous Observations of Swift and NuSTAR and Best-fitting Parameters

Source	NuSTAR		Swift		Γ	kT_e	τ	Flux (0.1–100 keV)	χ²/dof
	ObsID	Date(MJD)	ObsID	Date (MJD)		(keV)		(erg s⁻¹ cm⁻²)
Swift J1357.2-0933	90201057002	57871.54	00088094002	57871.62	${1.69}_{-0.01}^{+0.01}$	${42.21}_{-7.33}^{+12.84}$	${2.56}_{-0.42}^{+0.42}$	${3.70}_{-0.07}^{+0.19}\times {10}^{-10}$	$1160.47/1210$
Swift J1357.2-0933	90301005002	57914.57	00031918066	57914.61	${1.76}_{-0.02}^{+0.03}$	${46.70}_{-13.39}^{+49.76}$	${2.20}_{-1.05}^{+1.05}$	${9.65}_{-0.62}^{+1.70}\times {10}^{-11}$	$385.48/422$
Swift J1357.2-0933	90501325002	58632.51	00031918085	58632.29	${1.84}_{-0.06}^{+0.12}$	${23.68}_{-7.29}^{+22.26}$	${3.21}_{-1.35}^{+1.35}$	${1.24}_{-0.29}^{+0.34}\times {10}^{-11}$	$218.04/209$

GS 1354-64	90101006002	57186.29	00033811005	57186.61	${1.49}_{-0.00}^{+0.01}$	${23.00}_{-1.56}^{+1.56}$	${4.94}_{-0.21}^{+0.21}$	${1.14}_{-0.03}^{+0.03}\times {10}^{-9}$	$1954.83/1839$
GS 1354-64	90101006004	57214.57	00033811017	57214.35	${1.57}_{-0.00}^{+0.00}$	${14.57}_{-0.26}^{+0.20}$	${5.84}_{-0.06}^{+0.06}$	${6.26}_{-0.17}^{+0.12}\times {10}^{-9}$	$3301.82/2805$
GS 1354-64	90101006006	57240.30	00033811040	57240.55	${1.65}_{-0.05}^{+0.05}$	${15.39}_{-0.68}^{+0.54}$	${5.18}_{-0.33}^{+0.33}$	${6.04}_{-1.60}^{+0.75}\times {10}^{-9}$	$3789.37/2852$

MAXI J1535-571	90301013002	58003.78	00010264003	58004.28	${1.75}_{-0.06}^{+0.03}$	${13.95}_{-0.49}^{+0.35}$	${4.93}_{-0.26}^{+0.26}$	${6.02}_{-0.75}^{+0.76}\times {10}^{-8}$	$6878.04/3923$
MAXI J1535-571	80302309002	58008.54	00010264005	58008.26	${2.24}_{-0.01}^{+0.01}$	${16.21}_{-0.68}^{+0.75}$	${3.00}_{-0.09}^{+0.09}$	${9.16}_{-0.16}^{+0.20}\times {10}^{-8}$	$3117.38/2613$
MAXI J1535-571	80402302002	58010.22	00010264006	58010.93	${2.14}_{-0.05}^{+0.05}$	${14.21}_{-0.32}^{+0.49}$	${3.51}_{-0.14}^{+0.14}$	${9.55}_{-1.06}^{+1.63}\times {10}^{-8}$	$3133.83/2795$
MAXI J1535-571	80402302004	58010.55	00010264006	58010.93	${2.21}_{-0.10}^{+0.01}$	${15.23}_{-0.24}^{+0.55}$	${3.20}_{-0.13}^{+0.13}$	${9.96}_{-0.52}^{+1.59}\times {10}^{-8}$	$3235.94/2821$
MAXI J1535-571	80302309004	58013.17	00088245001	58013.18	${2.39}_{-0.13}^{+0.04}$	${22.11}_{-0.78}^{+0.72}$	${2.19}_{-0.14}^{+0.14}$	${1.07}_{-0.13}^{+0.23}\times {10}^{-7}$	$3795.49/2522$
MAXI J1535-571	80302309006	58013.44	00088245001	58013.18	${2.37}_{-0.09}^{+0.08}$	${18.69}_{-0.57}^{+0.77}$	${2.49}_{-0.15}^{+0.15}$	${1.11}_{-0.25}^{+0.51}\times {10}^{-7}$	$4733.99/2830$
MAXI J1535-571	80302309014	58048.88	00088245004	58048.99	${2.23}_{-0.01}^{+0.01}$	${20.33}_{-0.81}^{+1.00}$	${2.59}_{-0.08}^{+0.08}$	${6.05}_{-0.12}^{+0.13}\times {10}^{-8}$	$3414.27/2786$
MAXI J1535-571	80402302009	58050.96	00088246001	58050.98	${2.14}_{-0.01}^{+0.01}$	${18.19}_{-0.73}^{+1.20}$	${2.98}_{-0.11}^{+0.11}$	${5.86}_{-0.14}^{+0.16}\times {10}^{-8}$	$2582.16/2478$
MAXI J1535-571	80402302010	58051.36	00088246001	58050.98	${2.13}_{-0.01}^{+0.01}$	${17.47}_{-0.61}^{+0.84}$	${3.08}_{-0.09}^{+0.09}$	${5.81}_{-0.13}^{+0.16}\times {10}^{-8}$	$2978.61/2781$
MAXI J1535-571	90501314002	58587.55	00088862002	58587.54	${1.72}_{-0.05}^{+0.06}$	${16.84}_{-3.02}^{+4.88}$	${4.51}_{-0.70}^{+0.70}$	${3.26}_{-0.25}^{+0.35}\times {10}^{-11}$	$656.60/789$

GX 339-4	80001013002	56515.99	00032490015	56516.02	${1.53}_{-0.00}^{+0.00}$	${33.55}_{-3.01}^{+3.98}$	${3.68}_{-0.25}^{+0.25}$	${1.62}_{-0.02}^{+0.02}\times {10}^{-9}$	$2086.36/2213$
GX 339-4	80001013004	56520.71	00080180001	56520.77	${1.52}_{-0.00}^{+0.00}$	${32.14}_{-3.06}^{+4.20}$	${3.82}_{-0.28}^{+0.28}$	${2.70}_{-0.05}^{+0.05}\times {10}^{-9}$	$2484.27/2453$
GX 339-4	80001013006	56528.53	00080180002	56528.17	${1.52}_{-0.00}^{+0.00}$	${30.73}_{-2.06}^{+2.36}$	${3.92}_{-0.18}^{+0.18}$	${4.22}_{-0.05}^{+0.05}\times {10}^{-9}$	$2793.80/2706$
GX 339-4	80001013007	56538.38	00032898013	56537.79	${1.59}_{-0.04}^{+0.04}$	${30.95}_{-7.75}^{+40.85}$	${3.54}_{-1.81}^{+1.81}$	${4.46}_{-0.87}^{+1.38}\times {10}^{-9}$	$577.60/563$
GX 339-4	80001013008	56538.41	00032898013	56537.79	${1.53}_{-0.00}^{+0.00}$	${27.22}_{-0.97}^{+0.87}$	${4.21}_{-0.09}^{+0.09}$	${5.58}_{-0.07}^{+0.08}\times {10}^{-9}$	$3632.28/3414$
GX 339-4	80001013010	56581.99	00032898035	56581.56	${1.56}_{-0.00}^{+0.00}$	${35.67}_{-2.69}^{+4.22}$	${3.39}_{-0.21}^{+0.21}$	${9.16}_{-0.10}^{+0.14}\times {10}^{-10}$	$2458.88/2473$
GX 339-4	80102011002	57262.55	00032898124	57263.37	${1.66}_{-0.01}^{+0.01}$	${31.38}_{-3.43}^{+4.79}$	${3.25}_{-0.28}^{+0.28}$	${2.78}_{-0.08}^{+0.08}\times {10}^{-9}$	$2289.81/2219$
GX 339-4	80102011003	57267.49	00032898126	57268.03	${1.88}_{-0.00}^{+0.00}$	${63.06}_{-0.01}^{+0.00}$	${1.55}_{-0.00}^{+0.00}$	${1.90}_{-0.00}^{+0.00}\times {10}^{-9}$	$509.07/536$
GX 339-4	80102011004	57267.53	00032898126	57268.03	${1.61}_{-0.01}^{+0.00}$	${37.94}_{-4.73}^{+6.16}$	${3.04}_{-0.29}^{+0.29}$	${2.48}_{-0.08}^{+0.09}\times {10}^{-9}$	$2268.84/2220$
GX 339-4	80102011006	57272.62	00032898130	57272.02	${1.59}_{-0.01}^{+0.01}$	${38.70}_{-5.64}^{+8.90}$	${3.09}_{-0.39}^{+0.39}$	${2.15}_{-0.06}^{+0.08}\times {10}^{-9}$	$2137.45/2144$
GX 339-4	80102011008	57277.66	00081534001	57277.68	${1.59}_{-0.01}^{+0.01}$	${48.93}_{-10.10}^{+15.36}$	${2.63}_{-0.47}^{+0.47}$	${1.54}_{-0.03}^{+0.03}\times {10}^{-9}$	$1821.91/1760$
GX 339-4	80102011010	57282.42	00032898138	57282.00	${1.57}_{-0.01}^{+0.01}$	${85.72}_{-29.90}^{+95.55}$	${1.83}_{-0.97}^{+0.97}$	${1.15}_{-0.03}^{+0.03}\times {10}^{-9}$	$1992.58/2004$
GX 339-4	80102011012	57295.05	00081534005	57295.23	${1.60}_{-0.01}^{+0.01}$	${56.66}_{-13.38}^{+33.73}$	${2.35}_{-0.68}^{+0.68}$	${5.97}_{-0.12}^{+0.16}\times {10}^{-10}$	$1539.28/1547$
GX 339-4	80302304002	58028.15	00032898148	58027.28	${1.60}_{-0.02}^{+0.02}$	${70.01}_{-24.91}^{+81.88}$	${2.02}_{-1.10}^{+1.10}$	${3.43}_{-0.10}^{+0.12}\times {10}^{-10}$	$1029.14/982$
GX 339-4	80302304004	58051.57	00032898158	58051.38	${1.52}_{-0.01}^{+0.00}$	${29.39}_{-1.96}^{+2.14}$	${4.06}_{-0.18}^{+0.18}$	${3.51}_{-0.06}^{+0.09}\times {10}^{-9}$	$2379.42/2302$
GX 339-4	80302304007	58148.36	00032898163	58148.16	${1.58}_{-0.01}^{+0.01}$	${41.17}_{-7.61}^{+12.90}$	${2.98}_{-0.50}^{+0.50}$	${5.28}_{-0.15}^{+0.13}\times {10}^{-10}$	$1311.36/1337$

IGR J17091-3624	80001041002	57454.08	00031921099	57454.08	${1.57}_{-0.00}^{+0.00}$	${19.52}_{-0.54}^{+0.95}$	${4.87}_{-0.12}^{+0.12}$	${2.14}_{-0.03}^{+0.07}\times {10}^{-9}$	$2760.57/2665$
IGR J17091-3624	80202014002	57459.59	00031921104	57459.58	${1.62}_{-0.00}^{+0.01}$	${18.83}_{-0.71}^{+0.82}$	${4.72}_{-0.12}^{+0.12}$	${2.56}_{-0.04}^{+0.04}\times {10}^{-9}$	$2386.88/2381$
IGR J17091-3624	80202014004	57461.81	00031921106	57461.90	${1.65}_{-0.00}^{+0.00}$	${18.67}_{-0.64}^{+0.66}$	${4.55}_{-0.10}^{+0.10}$	${2.68}_{-0.04}^{+0.04}\times {10}^{-9}$	$2332.66/2283$
IGR J17091-3624	80202014006	57476.11	00031921118	57475.59	${2.08}_{-0.01}^{+0.02}$	${26.72}_{-1.35}^{+3.86}$	${2.41}_{-0.16}^{+0.16}$	${2.41}_{-0.09}^{+0.09}\times {10}^{-9}$	$2354.90/2183$
IGR J17091-3624	80202015004	57534.66	00081917002	57534.67	${2.00}_{-0.01}^{+0.02}$	${31.41}_{-4.07}^{+4.91}$	${2.31}_{-0.23}^{+0.23}$	${1.47}_{-0.06}^{+0.07}\times {10}^{-9}$	$1951.30/1943$

GRS 1716-249	80201034007	57781.31	00034924001	57781.00	${1.59}_{-0.00}^{+0.00}$	${24.77}_{-0.44}^{+0.51}$	${4.11}_{-0.05}^{+0.05}$	${1.86}_{-0.01}^{+0.03}\times {10}^{-8}$	$4428.11/4079$
GRS 1716-249	90202055002	57850.60	00034924029	57850.37	${1.70}_{-0.00}^{+0.00}$	${25.95}_{-0.84}^{+1.21}$	${3.50}_{-0.09}^{+0.09}$	${1.60}_{-0.02}^{+0.02}\times {10}^{-8}$	$4352.30/3511$
GRS 1716-249	90202055004	57853.69	00034924031	57853.88	${1.75}_{-0.00}^{+0.00}$	${26.78}_{-1.36}^{+1.27}$	${3.27}_{-0.11}^{+0.11}$	${1.65}_{-0.02}^{+0.02}\times {10}^{-8}$	$3588.63/3340$

GRS 1739-278	80002018002	56742.67	00033203003	56742.15	${1.86}_{-0.00}^{+0.01}$	${10.75}_{-0.10}^{+0.12}$	${5.24}_{-0.04}^{+0.04}$	${9.89}_{-0.11}^{+0.12}\times {10}^{-9}$	$4436.78/3162$
GRS 1739-278	80101050002	57280.88	00081764002	57280.93	${1.57}_{-0.07}^{+0.06}$	${14.95}_{-2.51}^{+2.56}$	${5.75}_{-0.73}^{+0.73}$	${3.89}_{-0.36}^{+0.44}\times {10}^{-11}$	$767.09/793$
GRS 1739-278	80102101002	57660.89	00033812058	57661.07	${1.62}_{-0.01}^{+0.02}$	${35.95}_{-4.77}^{+12.50}$	${3.11}_{-0.50}^{+0.50}$	${4.23}_{-0.11}^{+0.16}\times {10}^{-10}$	$1268.15/1339$
GRS 1739-278	80102101004	57680.63	00081979001	57680.76	${1.60}_{-0.03}^{+0.02}$	${20.57}_{-4.00}^{+3.90}$	${4.54}_{-0.56}^{+0.56}$	${1.12}_{-0.07}^{+0.07}\times {10}^{-10}$	$847.17/1002$
GRS 1739-278	80102101005	57692.84	00033812067	57691.10	${1.60}_{-0.02}^{+0.02}$	${27.13}_{-4.17}^{+5.83}$	${3.83}_{-0.46}^{+0.46}$	${2.65}_{-0.10}^{+0.11}\times {10}^{-10}$	$1033.37/1026$

H1743-322	80001044002	56918.65	00031121055	56918.35	${1.54}_{-0.00}^{+0.00}$	${22.70}_{-0.61}^{+0.84}$	${4.62}_{-0.09}^{+0.09}$	${3.96}_{-0.03}^{+0.05}\times {10}^{-9}$	$3246.68/3143$
H1743-322	80001044004	56923.76	00031121061	56924.08	${1.59}_{-0.01}^{+0.00}$	${22.08}_{-0.64}^{+0.60}$	${4.41}_{-0.08}^{+0.08}$	${5.43}_{-0.12}^{+0.15}\times {10}^{-9}$	$3341.25/3185$
H1743-322	80001044006	56939.76	00080797002	56940.20	${1.57}_{-0.00}^{+0.00}$	${21.45}_{-0.86}^{+0.66}$	${4.64}_{-0.10}^{+0.10}$	${4.40}_{-0.06}^{+0.05}\times {10}^{-9}$	$2901.29/2924$
H1743-322	80002040002	57206.12	00080797003	57206.31	${1.55}_{-0.04}^{+0.07}$	${30.50}_{-1.71}^{+1.18}$	${3.81}_{-0.31}^{+0.31}$	${2.81}_{-0.65}^{+0.86}\times {10}^{-9}$	$2338.93/2357$
H1743-322	80002040004	57230.16	⋯	⋯	${1.65}_{-0.02}^{+0.02}$	${25.92}_{-7.34}^{+18.68}$	${3.71}_{-1.20}^{+1.20}$	${1.87}_{-0.10}^{+0.20}\times {10}^{-10}$	$931.74/959$
H1743-322	80202012002	57460.07	00031441056	57460.24	${1.69}_{-0.00}^{+0.00}$	${22.02}_{-0.59}^{+0.79}$	${3.92}_{-0.08}^{+0.08}$	${5.83}_{-0.61}^{+0.71}\times {10}^{-9}$	$3504.28/3303$
H1743-322	80202012004	57462.28	00031441058	57462.90	${1.70}_{-0.00}^{+0.00}$	${22.33}_{-0.47}^{+0.74}$	${3.86}_{-0.07}^{+0.07}$	${5.07}_{-0.34}^{+0.40}\times {10}^{-9}$	$3495.04/3386$

Swift J1753.5-0127	80002021002	56751.15	00080730001	56752.02	${1.72}_{-0.00}^{+0.00}$	${105.54}_{-32.43}^{+61.31}$	${1.26}_{-0.43}^{+0.43}$	${9.33}_{-0.05}^{+0.17}\times {10}^{-10}$	$1903.75/1917$
Swift J1753.5-0127	80002021003	56751.89	00080730001	56752.02	${1.72}_{-0.01}^{+0.00}$	${125.46}_{-53.18}^{+110.42}$	${1.12}_{-0.57}^{+0.57}$	${9.98}_{-0.18}^{+0.20}\times {10}^{-10}$	$1908.30/1911$
Swift J1753.5-0127	30001148002	56913.41	00080770001	56913.49	${1.72}_{-0.00}^{+0.00}$	${50.34}_{-6.74}^{+14.40}$	${2.18}_{-0.32}^{+0.32}$	${1.64}_{-0.04}^{+0.04}\times {10}^{-9}$	$2400.69/2316$

MAXI J1813-095	80402303004	58183.60	00088654002	58183.56	${1.60}_{-0.01}^{+0.01}$	${29.94}_{-2.49}^{+3.26}$	${3.60}_{-0.22}^{+0.22}$	${1.87}_{-0.03}^{+0.03}\times {10}^{-9}$	$2084.45/2127$
MAXI J1813-095	80402303006	58202.73	00088654004	58202.84	${1.64}_{-0.01}^{+0.01}$	${30.15}_{-2.45}^{+3.41}$	${3.41}_{-0.22}^{+0.22}$	${1.94}_{-0.05}^{+0.07}\times {10}^{-9}$	$2199.20/2162$
MAXI J1820+070	90401309002	58191.85	00010627001	58191.87	${1.48}_{-0.00}^{+0.00}$	${27.32}_{-0.61}^{+0.59}$	${4.50}_{-0.06}^{+0.06}$	${3.38}_{-0.05}^{+0.05}\times {10}^{-8}$	$4746.61/3842$
MAXI J1820+070	90401309004	58198.02	00010627009	58197.77	${1.53}_{-0.00}^{+0.00}$	${19.65}_{-0.22}^{+0.53}$	${5.11}_{-0.06}^{+0.06}$	${1.30}_{-0.01}^{+0.02}\times {10}^{-7}$	$4493.20/3602$
MAXI J1820+070	90401309006	58198.30	00010627010	58198.78	${1.52}_{-0.00}^{+0.00}$	${18.54}_{-0.25}^{+0.25}$	${5.35}_{-0.05}^{+0.05}$	${1.33}_{-0.01}^{+0.01}\times {10}^{-7}$	$5195.07/3865$
MAXI J1820+070	90401309008	58201.52	00010627013	58201.11	${1.53}_{-0.00}^{+0.00}$	${18.22}_{-0.22}^{+0.31}$	${5.35}_{-0.05}^{+0.05}$	${1.30}_{-0.01}^{+0.01}\times {10}^{-7}$	$4338.68/3608$
MAXI J1820+070	90401309010	58201.85	00010627014	58202.17	${1.53}_{-0.00}^{+0.00}$	${18.43}_{-0.28}^{+0.41}$	${5.30}_{-0.06}^{+0.06}$	${1.34}_{-0.02}^{+0.02}\times {10}^{-7}$	$4476.90/3561$
MAXI J1820+070	90401309012	58212.19	00088657001	58212.20	${1.54}_{-0.00}^{+0.00}$	${19.78}_{-0.18}^{+0.18}$	${5.05}_{-0.03}^{+0.03}$	${1.20}_{-0.01}^{+0.01}\times {10}^{-7}$	$6307.59/4206$
MAXI J1820+070	90401309013	58224.93	00010627043	58224.95	${1.58}_{-0.00}^{+0.00}$	${22.75}_{-0.80}^{+0.66}$	${4.40}_{-0.09}^{+0.09}$	${1.15}_{-0.01}^{+0.02}\times {10}^{-7}$	$3871.94/3242$
MAXI J1820+070	90401309014	58225.27	00010627045	58225.47	${1.56}_{-0.00}^{+0.00}$	${20.75}_{-0.23}^{+0.23}$	${4.76}_{-0.03}^{+0.03}$	${1.16}_{-0.01}^{+0.01}\times {10}^{-7}$	$6038.07/4112$
MAXI J1820+070	90401309016	58241.79	00088657003	58241.67	${1.59}_{-0.00}^{+0.00}$	${23.18}_{-0.29}^{+0.38}$	${4.27}_{-0.04}^{+0.04}$	${1.01}_{-0.01}^{+0.01}\times {10}^{-7}$	$6766.12/4165$
MAXI J1820+070	90401309018	58255.15	00088657004	58255.90	${1.64}_{-0.00}^{+0.00}$	${31.61}_{-1.67}^{+1.58}$	${3.28}_{-0.11}^{+0.11}$	${8.94}_{-0.10}^{+0.09}\times {10}^{-8}$	$4277.60/3270$
MAXI J1820+070	90401309019	58255.60	00088657004	58255.90	${1.63}_{-0.00}^{+0.00}$	${30.32}_{-1.01}^{+1.02}$	${3.42}_{-0.07}^{+0.07}$	${8.98}_{-0.09}^{+0.04}\times {10}^{-8}$	$6821.45/3946$
MAXI J1820+070	90401309037	58404.95	00010627112	58404.26	${1.70}_{-0.00}^{+0.01}$	${1000.00}_{-567.61}^{+0.00}$	${0.19}_{-0.05}^{+0.05}$	${2.24}_{-0.08}^{+0.09}\times {10}^{-9}$	$1975.57/1939$
MAXI J1820+070	90401309039	58420.05	00010627120	58419.60	${1.81}_{-0.01}^{+0.00}$	${173.74}_{-65.69}^{+191.84}$	${0.76}_{-0.47}^{+0.47}$	${4.44}_{-0.14}^{+0.17}\times {10}^{-10}$	$2116.84/2065$
MAXI J1820+070	90501311002	58567.83	00010627149	58567.16	${1.69}_{-0.00}^{+0.00}$	${148.69}_{-60.93}^{+116.01}$	${1.01}_{-0.48}^{+0.48}$	${2.02}_{-0.06}^{+0.08}\times {10}^{-9}$	$2283.13/2296$
MAXI J1820+070	90501320002	58604.40	⋯	⋯	${2.19}_{-0.11}^{+0.18}$	${6.75}_{-2.17}^{+2.66}$	${5.41}_{-1.29}^{+1.29}$	${5.85}_{-0.41}^{+0.64}\times {10}^{-12}$	$871.47/998$

GRS 1915+105	90201053002	57840.67	00080228002	57840.82	${2.06}_{-0.01}^{+0.01}$	${21.68}_{-1.20}^{+1.40}$	${2.83}_{-0.12}^{+0.12}$	${1.42}_{-0.03}^{+0.03}\times {10}^{-8}$	$3326.08/2846$
GRS 1915+105	90301001002	57875.18	00088091001	57875.48	${1.99}_{-0.01}^{+0.01}$	${22.62}_{-1.23}^{+1.63}$	${2.90}_{-0.13}^{+0.13}$	${1.18}_{-0.04}^{+0.03}\times {10}^{-8}$	$3166.05/2830$

Cyg X-1	30001011005	56776.92	00080732001	56776.89	${1.70}_{-0.00}^{+0.00}$	${27.75}_{-1.07}^{+1.07}$	${3.37}_{-0.09}^{+0.09}$	${3.06}_{-0.04}^{+0.04}\times {10}^{-8}$	$4258.02/3626$
Cyg X-1	30001011007	56797.24	00080732002	56798.01	${1.65}_{-0.00}^{+0.00}$	${28.59}_{-0.60}^{+0.78}$	${3.50}_{-0.06}^{+0.06}$	${2.43}_{-0.02}^{+0.02}\times {10}^{-8}$	$5048.51/4163$
Cyg X-1	90101020002	57429.45	00081820001	57429.55	${1.60}_{-0.00}^{+0.00}$	${30.04}_{-0.91}^{+1.35}$	${3.59}_{-0.09}^{+0.09}$	${2.67}_{-0.02}^{+0.02}\times {10}^{-8}$	$4346.34/3871$
Cyg X-1	30002150004	57537.89	00034310002	57537.54	${1.59}_{-0.00}^{+0.00}$	${30.06}_{-0.66}^{+0.53}$	${3.63}_{-0.05}^{+0.05}$	${2.76}_{-0.01}^{+0.01}\times {10}^{-8}$	$6582.65/4512$
Cyg X-1	30002150006	57539.91	00034310003	57539.55	${1.59}_{-0.00}^{+0.00}$	${30.16}_{-0.64}^{+0.51}$	${3.62}_{-0.04}^{+0.04}$	${2.63}_{-0.01}^{+0.01}\times {10}^{-8}$	$6364.94/4494$
Cyg X-1	30002150008	57541.92	00034310004	57541.48	${1.59}_{-0.00}^{+0.00}$	${29.51}_{-0.68}^{+0.75}$	${3.68}_{-0.06}^{+0.06}$	${2.45}_{-0.01}^{+0.01}\times {10}^{-8}$	$5207.24/4264$
Cyg X-1	30202032002	57587.65	00081903001	57587.72	${1.59}_{-0.00}^{+0.00}$	${27.39}_{-0.84}^{+0.97}$	${3.84}_{-0.08}^{+0.08}$	${2.51}_{-0.02}^{+0.02}\times {10}^{-8}$	$4016.08/3798$

V404 Cyg	30001010002	56578.50	00080264001	56579.78	${2.33}_{-0.46}^{+1.01}$	${5.69}_{-3.30}^{+8.85}$	${5.50}_{-4.31}^{+4.31}$	${6.64}_{-1.64}^{+2.53}\times {10}^{-13}$	$127.48/154$
V404 Cyg	30001010003	56579.91	00080264001	56579.78	${2.08}_{-0.13}^{+0.42}$	${6.48}_{-3.04}^{+6.57}$	${5.98}_{-2.90}^{+2.90}$	${7.38}_{-1.47}^{+2.80}\times {10}^{-13}$	$203.23/209$
V404 Cyg	30001010005	56628.73	00080264002	56628.75	${1.78}_{-0.45}^{+0.60}$	${4.38}_{-3.05}^{+4.24}$	${9.50}_{-6.27}^{+6.27}$	${7.95}_{-2.41}^{+7.63}\times {10}^{-13}$	$79.74/79$
V404 Cyg	90102007005	57204.05	00031403068	57203.93	${1.72}_{-0.03}^{+0.04}$	${17.02}_{-2.00}^{+2.98}$	${4.47}_{-0.44}^{+0.44}$	${2.19}_{-0.14}^{+0.17}\times {10}^{-10}$	$1148.85/1217$
V404 Cyg	90102007007	57209.28	00031403080	57209.51	${1.90}_{-0.08}^{+0.08}$	${10.83}_{-1.57}^{+2.76}$	${5.05}_{-0.71}^{+0.71}$	${2.56}_{-0.38}^{+1.74}\times {10}^{-11}$	$363.57/449$
V404 Cyg	90102007009	57211.97	00031403085	57211.72	${1.88}_{-0.03}^{+0.05}$	${16.10}_{-2.92}^{+4.13}$	${4.00}_{-0.58}^{+0.58}$	${3.10}_{-0.43}^{+1.30}\times {10}^{-11}$	$830.18/857$
V404 Cyg	90102007011	57226.35	00031403109	57226.40	${1.84}_{-0.11}^{+0.19}$	${8.03}_{-1.72}^{+4.69}$	${6.36}_{-1.72}^{+1.72}$	${4.15}_{-0.91}^{+1.49}\times {10}^{-12}$	$220.02/249$
V404 Cyg	90102007013	57380.43	00031403122	57380.62	${1.81}_{-0.02}^{+0.08}$	${39.44}_{-3.73}^{+2.31}$	${2.35}_{-0.18}^{+0.18}$	${8.45}_{-2.34}^{+0.67}\times {10}^{-11}$	$935.86/900$
V404 Cyg	90102007015	57393.64	00031403145	57393.57	${1.95}_{-0.03}^{+0.09}$	${37.93}_{-6.30}^{+4.74}$	${2.11}_{-0.25}^{+0.25}$	${2.72}_{-0.73}^{+0.71}\times {10}^{-11}$	$690.02/751$