Evolution of Thermally Driven Disk Wind in the Black Hole Binary 4U 1630–47 Observed with Suzaku and NuSTAR

Since 4U 1630−47 suffers from heavy absorption by the interstellar matter (${N}_{{\rm{H}}}\sim 8\times {10}^{22}\,{\mathrm{cm}}^{-2}$), effects by the dust scattering are not negligible (Smith et al. 2002; Ueda et al. 2010). A part of the direct emission is "scattered-out" by interstellar dust in the line of sight, while photons emitted with slightly different angles from the line of sight are "scattered-in" toward the observer, producing a dust-scattering halo around the source. When the source flux and spectrum is constant, integrating all scattered-in photons will cancel the scattered-out ones, and therefore no correction is necessary. This is not the case in our data, however, because the spectrum extraction regions of Suzaku/XIS and NuSTAR/FMP do not fully cover the dust-scattering halo. Hence, we have to estimate the fraction of the dust-scattering-halo photons contained in the spectrum extraction region (hereafter "scattering fraction") and to correct for this effect in the spectral analysis.⁶ The situation becomes even more complex for a variable source because of the time delay between the direct and scattered-in components (see, e.g., Tiengo et al. 2010; Heinz et al. 2015, 2016).

In this paper, we follow the same procedures as those described in Hori et al. (2014). We estimate the scattering fraction to be 87% and 67% for the Suzaku/XIS spectra during the 2006 and 2015 outbursts, respectively, with the FTOOL xissimarfgen by assuming the image profile of the dust-scattering halo obtained by Smith et al. (2002).⁷ For the NuSTAR/FMP data, we approximately estimate it to be 66% by ignoring the point-spread function. Then, in the spectral fit, we utilize the Dscat model, which is a local model developed by Ueda et al. (2010), to take into account the effects of dust-scattering. We check effects by time variability of 4U 1630−47 during the 2015 observations. The maximum time delay at the outer integration radius 12 is estimated to be ∼1 day by assuming that the scatterers are located at the half distance of 10 kpc (see, e.g., Heinz et al. 2015 for the calculation). The source shows a flux decay of ∼20% around the Suzaku observations on this timescale (Figure 2(c)), which would lead to an enhancement of the scattering fraction by <4% in OBS 8. We confirm that it does not affect our final results (Section 4). Hence, for simplicity, we ignore time variability in estimating the scattering fraction in the following analysis.

Spectral analysis is performed separately to the data of OBS 1 through 8. We use the spectra of Suzaku/XIS, Suzaku/PIN, and NuSTAR/FMP in the energy range of 1.9–9.0 keV, 12–40 keV, and 6–80 keV, respectively. Conservatively, the XIS data above 9.0 keV are not utilized to minimize pileup effects, and those in the 2.1–2.3 keV and 3.0–3.4 keV are also excluded to avoid calibration uncertainties. The spectra of the two FI-XISs (XIS0 and 3) are summed together. Spectral fitting is performed by using XSPEC version 12.8.2.

We apply a conventional model consisting of a multi-color disk (MCD) component and a power law with a low energy cutoff (diskbb and simpl in XSPEC terminology, respectively). The simpl model has two free parameters, the photon index Γ and the fraction of the seed photons f_PL. To take into account adsorption by interstellar medium, we use the tbabs model with the Wilms et al. (2000) abundances and the Verner et al. (1996) cross section. To estimate the column density of iron ions in a simple manner, we utilize the "kabs" model (Ueda et al. 2004), an XSPEC local model calculating the Voigt profile from multiple fine-structure lines. The kabs model has three free parameters, the column density of each ion ${N}_{\mathrm{ion}}^{\mathrm{wind}}$, the velocity dispersion, which is fixed at 500 km s⁻¹ in this analysis (Kubota et al. 2007), and the wind velocity v/c. The model is thus expressed as tbabs∗Dscat∗kabs∗kabs∗simpl∗diskbb in the XSPEC terminology, where the first and second kabs terms represent the absorption lines of H-like and He-like iron ions, respectively. We apply this model to all the XIS spectra in the 2006 and 2015 outbursts.

Table 2 summarizes the best-fit parameters and chi-squared value for each observation. Reasonably good fits are obtained with this model yielding the best-fit disk temperature of T_disk ≈ 1.2–1.4 keV and photon index of Γ ≈ 2–3. For OBS 0, Γ and f_PL are fixed to be 2.5 and 1.0%, respectively, because the spectrum only covered the energy range below 9 keV. During the 2006 outburst, the disk temperature and luminosity change together as expected in standard disk model to maintain a constant inner radius (Shakura & Sunyaev 1973). The inner disk radius (and column density) are slightly different in the 2015 outburst, most probably due to residual calibration uncertainties. The fraction f_PL is also almost constant from OBS 1–7 at around 1%, but then increases significantly in OBS 8.

Table 2.  Best-fit Parameters for Spectral Modeling

Component	TBabs	diskbb		simpl		kabs
Parameter	NHa	${T}_{\mathrm{in}}(\mathrm{keV})$	${R}_{\mathrm{in}}(\mathrm{km})$	Γ	fPL (%)	${N}_{{\mathrm{Fe}}_{{\rm{XXVI}}}}^{\mathrm{wind}}$ b	${N}_{{\mathrm{Fe}}_{{\rm{XXV}}}}^{\mathrm{wind}}$ b	${v}_{\mathrm{wind}}(\mathrm{km}\,{{\rm{s}}}^{-1}$)	${\chi }^{2}/$ dof
OBS 1	${7.85}_{-0.05}^{+0.03}$	${1.16}_{-0.01}^{+0.01}$	${27.2}_{-0.4}^{+0.5}$	${3.20}_{-0.36}^{+0.42}$	${1.1}_{-0.4}^{+0.7}$	${1.59}_{-0.32}^{+0.39}$	${0.58}_{-0.13}^{+0.18}$	${400}_{-400}^{+400}$	522/684
OBS 2	${7.85}_{-0.02}^{+0.05}$	${1.19}_{-0.01}^{+0.01}$	${27.2}_{-0.4}^{+0.4}$	${2.03}_{-0.36}^{+0.37}$	${0.3}_{-0.1}^{+0.2}$	${1.21}_{-0.22}^{+0.28}$	${0.37}_{-0.10}^{+0.10}$	${700}_{-600}^{+600}$	539/699
OBS 3	${7.99}_{-0.06}^{+0.06}$	${1.20}_{-0.01}^{+0.01}$	${28.3}_{-0.6}^{+0.5}$	${2.38}_{-0.28}^{+0.30}$	${0.5}_{-0.2}^{+0.3}$	${1.18}_{-0.31}^{+0.41}$	${0.32}_{-0.12}^{+0.14}$	${700}_{-800}^{+700}$	603/699
OBS 4	${8.04}_{-0.07}^{+0.05}$	${1.22}_{-0.01}^{+0.01}$	${28.5}_{-0.5}^{+0.4}$	${2.42}_{-0.24}^{+0.22}$	${0.8}_{-0.3}^{+0.3}$	${1.11}_{-0.27}^{+0.39}$	${0.25}_{-0.09}^{+0.11}$	${1400}_{-600}^{+600}$	557/696
OBS 5	${8.00}_{-0.05}^{+0.06}$	${1.30}_{-0.01}^{+0.01}$	${25.5}_{-0.4}^{+0.5}$	${2.79}_{-0.19}^{+0.20}$	${1.8}_{-0.4}^{+0.6}$	${1.33}_{-0.31}^{+0.41}$	${0.26}_{-0.09}^{+0.11}$	${1300}_{-500}^{+500}$	558/699
OBS 6	${8.06}_{-0.05}^{+0.05}$	${1.34}_{-0.01}^{+0.01}$	${27.0}_{-0.4}^{+0.3}$	${2.27}_{-0.14}^{+0.14}$	${0.9}_{-0.2}^{+0.3}$	${1.04}_{-0.21}^{+0.26}$	${0.08}_{-0.06}^{+0.06}$	${1300}_{-700}^{+600}$	576/713
OBS 7	${8.33}_{-0.02}^{+0.04}$	${1.32}_{-0.01}^{+0.01}$	${30.9}_{-0.3}^{+0.2}$	${2.90}_{-0.08}^{+0.08}$	${1.4}_{-0.2}^{+0.1}$	${1.25}_{-0.19}^{+0.23}$	${0.18}_{-0.05}^{+0.07}$	${1400}_{-100}^{+100}$	1422/1497
OBS 8	${8.40}_{-0.03}^{+0.04}$	${1.35}_{-0.01}^{+0.01}$	${32.2}_{-0.3}^{+0.2}$	${2.24}_{-0.02}^{+0.02}$	${3.3}_{-0.2}^{+0.1}$	${0.30}_{-0.06}^{+0.06}$	$\lt 0.02$	${1300}_{-400}^{+500}$	1454/1497
OBS 0	${8.46}_{-0.05}^{+0.04}$	${1.32}_{-0.01}^{+0.01}$	${31.7}_{-0.4}^{+0.3}$	2.5(fixed)	1.0(fixed)	${0.90}_{-0.18}^{+0.21}$	$\lt 0.04$	${2600}_{-700}^{+700}$	846/843

Notes.

^aHydrogen column densities in the unit of ${10}^{22}\,{\mathrm{cm}}^{-2}$. ^bIon column densities in the unit of ${10}^{18}\,{\mathrm{cm}}^{-2}$.

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In this subsection, we focus on the iron-K absorption line features in OBS 1–8. No other line feature is significantly detected in the XIS spectra. Figure 4 shows the XIS unfolded spectra of OBS 1, 6, 7, and 8 in the 6–7.5 keV range together with the best-fit continuum model including the interstellar absorption and dust scattering. For comparison, we also plot the spectrum in the VHS (OBS α), which does not show any iron-K absorption line feature. Here we adopt the model D in Hori et al. (2014) for the continuum, which gives the best description of the Suzaku spectra. This model properly takes into account Comptonization of the inner disk emission with energetic coupling between the disk and corona, and the reflection of the Comptonized component from the accretion disk with general relativistic smearing effects. For further details, see Hori et al. (2014).

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Figure 5 plots the column density of He-like and H-like irons against the 2–6 keV flux in the HSS during the 2006 (black) and 2015 outbursts (red). OBS 1 and OBS 6 are the faintest and brightest observations in the 2006 outburst, while OBS 7 and OBS 8 are the faintest and brightest observations in the 2015 outburst, respectively. The degree of ionization of the disk wind can be traced by the ratio of the column density in H-like to He-like iron. This gradually increases with 2–6 keV luminosity in the 2006 outburst, and then increases much more rapidly in the 2015 outburst, especially in the brightest observation, OBS 8. This result might be explained by photoionization of the disk wind because the observed X-ray spectrum shows significant hardening in the brightest observation owning to the increase of the hard tail component; we will quantitatively examine this possibility in the next section. We also note that the absorption lines in OBS 6 are weaker than those in OBS 7 as expected from the harder spectrum in OBS 6.

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We find that the ratio between the column densities of H-like and He-like iron ions increased at fluxes above ${F}_{2\mbox{--}6\mathrm{keV}}\sim 3.5\times {10}^{-9}\,\mathrm{erg}\,{\mathrm{cm}}^{-2}\,{{\rm{s}}}^{-1}$ where their spectra became harder with increasing contribution from the hard tail (Figure 3). In order to examine whether an increase of photoionizing photons solely explains the observed increase of the ionization degree or not, we perform simulations of a photoionized gas, using XSTAR version 2.3. In XSTAR simulations, the ionization parameter of the absorber at the nearest point (i.e., the launching radius for a disk wind), ξ₀, is defined as

$$\begin{eqnarray}&&{\xi }_{0}=\displaystyle \frac{{L}_{\mathrm{bol}}}{{n}_{0}{R}_{0}^{2}},\end{eqnarray} \tag{ 2 }$$

where L_bol is the luminosity in the 0.0136–13.6 keV band, R₀ is the distance of the absorber from the central source, and n₀ is the density. We use the observed continuum corrected for absorption and dust scattering in the 0.01–1000 keV range as the input of the source spectrum. To consider a self-similarly expanding wind with a constant velocity (Begelman et al. 1983), we assume a density (n) profile with respect to radius $R(\gt {R}_{0})$ as $n={n}_{0}{(R/{R}_{0})}^{-1.9}$, which gives an almost constant ionization parameter profile ($\xi ={\xi }_{0}{(R/{R}_{0})}^{-0.1}$).⁸ The turbulent velocity is set to be ${V}_{\mathrm{turb}}=500\,\mathrm{km}\,{{\rm{s}}}^{-1}$ in this simulation as a representative value, which has not been measured in this source (but not less than $100\,\mathrm{km}\,{{\rm{s}}}^{-1};$ Kubota et al. 2007). To directly apply the simulation results to the Suzaku/XIS spectra, we make a grid XSPEC model of absorption by utilizing the XSTAR2XSPEC tool. Through the fitting, we are able to obtain the column density ${N}_{{\rm{H}}}^{\mathrm{wind}}$ and the ionization parameter ξ₀.

We find that the higher ionization degree in OBS 8 than in the other HSS observations cannot be explained solely by the change of the source spectrum luminosity if we assume that the wind launching radius and density were the same as in the other epochs. This fact is found for the first time from 4U 1630–47, whereas similar results (i.e., that photoionization alone cannot explain changes of the ionization degree of a disk wind) were reported from other sources (Yamaoka et al. 2001 and Neilsen & Homan 2012 for GRO J1655–40, Neilsen et al. 2012 for GRS 1915+105). In OBS 8, we are able to obtain only lower limits for ξ₀ and ${N}_{{\rm{H}}}^{\mathrm{wind}}$ because of the nondetection of He-like iron absorption line and of strong coupling between ξ₀ and ${N}_{{\rm{H}}}^{\mathrm{wind}}$. If we fix the column density at ${N}_{{\rm{H}}}^{\mathrm{wind}}=2.3\,\times {10}^{23}\,{\mathrm{cm}}^{-2}$, which is obtained in OBS 7 showing the closest luminosity to that in OBS 8 (see Table 3), the ionization parameter in OBS 8 becomes ${\xi }_{0}={5.27}_{-0.14}^{+0.19}$. This is significantly higher at a >90% confidence level than the value expected from the photoionization effect alone (i.e., the ${\xi }_{0}={4.74}_{-0.12}^{+0.14}$, which is converted from the result of OBS 7 by replacing the luminosity with that of OBS 8). This result indicates that other physical parameters of the wind, such as wind launching radius R₀ and/or density at the launching radius n₀, must have changed from OBS 7 to OBS 8.

In the following, we show that these results can be explained by a theory of thermally driven winds. The Compton temperature T_IC and the wind escape velocity V_wind depend on the wind launching radius (or Compton radius, R_IC) as

$$\begin{eqnarray}&&{{kT}}_{\mathrm{IC}}\propto \displaystyle \frac{{{GM}}_{\mathrm{BH}}}{{R}_{\mathrm{IC}}}\end{eqnarray} \tag{ 3 }$$

and

$$\begin{eqnarray}&&\displaystyle \frac{1}{2}{V}_{\mathrm{wind}}^{2}\propto \displaystyle \frac{{{GM}}_{\mathrm{BH}}}{{R}_{\mathrm{IC}}}\propto {T}_{\mathrm{IC}}.\end{eqnarray} \tag{ 4 }$$

Here, k, G, and M_BH are the Boltzmann constant, the gravitational constant, and the mass of the BH, respectively. From numerical simulations, Woods et al. (1996) showed that the mass flux per unit area of an isothermal disk wind, $\dot{m}$, is given by

$$\begin{eqnarray}&&\dot{m}\sim 0.5{\left(\displaystyle \frac{{{kT}}_{\mathrm{IC}}}{\mu }\right)}^{-0.5}\displaystyle \frac{L}{4\pi {R}^{2}c{{\rm{\Xi }}}_{c,\mathrm{crit}}},\end{eqnarray} \tag{ 5 }$$

where μ, c, and Ξ_c,crit are the mean mass per particle, the light speed, and the critical pressure ionization parameter determined by the spectrum, respectively. The mass-loss rate of the disk wind $\dot{M}$ and the density at the base of the wind n₀ given as the following equations (Done et al. 2018)

$$\begin{eqnarray}\begin{array}{rcl}\dot{M} & = & 2{\displaystyle \int }_{{R}_{\mathrm{in}}}^{{R}_{\mathrm{out}}}\dot{m}2\pi {RdR}\\ & = & {\left(\displaystyle \frac{{{kT}}_{\mathrm{IC}}}{\mu }\right)}^{-0.5}\displaystyle \frac{L}{4\pi c{{\rm{\Xi }}}_{c,\mathrm{crit}}}\mathrm{log}\left(\displaystyle \frac{{R}_{\mathrm{out}}}{{R}_{\mathrm{in}}}\right)\\ & \mathop{\propto }\limits_{\sim } & L\times {T}_{\mathrm{IC}}^{-0.5},\end{array}\end{eqnarray} \tag{ 6 }$$

$$\begin{eqnarray}\begin{array}{rcl}{n}_{0} & = & \displaystyle \frac{\dot{M}}{{\rm{\Omega }}{R}_{\mathrm{IC}}^{2}{V}_{\mathrm{wind}}{m}_{{\rm{p}}}}\\ & \propto & L\times {T}_{\mathrm{IC}}.\end{array}\end{eqnarray} \tag{ 7 }$$

Here, R_in (R_out) is the inner (outer) disk radius, m_p is the proton mass, and Ω is the solid angle of the disk wind, which is assumed to be constant against the distance from the BH. The n₀ value in the OBS 1 is set to be $1.0\times {10}^{13}\,{\mathrm{cm}}^{-3}$, which yields the mean number density of $\bar{n}\sim 5\times {10}^{12}\,{\mathrm{cm}}^{-3}$ estimated by Kubota et al. (2007). In the following XSTAR simulations, n₀ for each observation is calculated from Equation (7) (see Table 3). From these equations, we finally obtain the dependence of the column density ${N}_{{\rm{H}}}^{\mathrm{wind}}$ and the ionization parameter at the base of wind ξ₀ on luminosity and Compton temperature as

$$\begin{eqnarray}\begin{array}{rcl}{N}_{{\rm{H}}}^{\mathrm{wind}} & = & {\displaystyle \int }_{{R}_{\mathrm{IC}}}^{\infty }{ndR}\\ & \propto & L\end{array}\end{eqnarray} \tag{ 8 }$$

and

$$\begin{eqnarray}\begin{array}{rcl}{\xi }_{0} & = & \displaystyle \frac{L}{{n}_{0}{R}_{\mathrm{IC}}^{2}}\\ & \propto & {T}_{\mathrm{IC}},\end{array}\end{eqnarray} \tag{ 9 }$$

respectively.

Table 3.  Fitting Results

Parameter	OBS 1	OBS 2	OBS 3	OBS 4	OBS 5	OBS 6	OBS 7	OBS 8
${L}_{\mathrm{bol}}\,({10}^{38}\,\mathrm{erg}\,{{\rm{s}}}^{-1})$ a	1.20	1.34	1.48	1.61	1.63	2.13	2.61	3.14
${T}_{\mathrm{IC}}\,(\mathrm{keV})$ b	0.70	1.37	0.92	0.99	0.95	1.38	0.83	3.25
${n}_{0}\,({10}^{13}\,{\mathrm{cm}}^{-3})$ c	1.0	2.1	1.6	1.9	1.8	3.5	2.6	12.0
log(${\xi }_{0}$)	${4.62}_{-0.11}^{+0.13}$	${4.61}_{-0.11}^{+0.11}$	${4.64}_{-0.14}^{+0.15}$	${4.62}_{-0.14}^{+0.14}$	${4.55}_{-0.10}^{+0.18}$	${4.74}_{-0.17}^{+0.29}$	${4.62}_{-0.15}^{+0.19}$	$\gt 4.38$
${N}_{{\rm{H}}}^{\mathrm{wind}}\,({10}^{23}\,{\mathrm{cm}}^{-2})$	${1.23}_{-0.24}^{+0.31}$	${1.03}_{-0.23}^{+0.27}$	${1.06}_{-0.30}^{+0.37}$	${0.99}_{-0.29}^{+0.37}$	${1.48}_{-0.37}^{+0.65}$	${1.58}_{-0.47}^{+0.49}$	${2.27}_{-0.60}^{+0.74}$	$\gt 0.43$
${V}_{\mathrm{wind}}\,(\mathrm{km}\,{{\rm{s}}}^{-1})$	${500}_{-400}^{+400}$	${800}_{-600}^{+500}$	${800}_{-700}^{+700}$	${1400}_{-600}^{+600}$	${1400}_{-500}^{+500}$	${1500}_{-600}^{+600}$	${2200}_{-500}^{+500}$	${2100}_{-1100}^{+1200}$

Notes.

^aUnabsorbed luminosities in the range of 0.0136–13.6 keV assuming isotropic emission. ^bCalculated by Equation (1) with the integration range of 0.01–1000 keV. ^cCalculated by Equation (7). n₀ in OBS 1 is set to be $1.0\times {10}^{13}\,{\mathrm{cm}}^{-12}$.

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The spectral fitting results (the best-fit values and 1σ errors of ${\xi }_{0}$, ${N}_{{\rm{H}}}^{\mathrm{wind}}$, and V_wind) are summarized in Table 3 along with the luminosity L, Compton temperature kT_IC, and the density n₀ assumed in the XSTAR simulations. Figures 6(a) and (b) plots N_H^wind against L, and ξ₀ against kT_IC, respectively. Only lower limits of ${N}_{{\rm{H}}}^{\mathrm{wind}}$ and ξ₀ are obtained in OBS 8 (orange arrows).

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We have confirmed that correlation between ${N}_{{\rm{H}}}^{\mathrm{wind}}$ and L is significant at a 95% confidence level, by performing an F-test between the cases when we fit those data with a constant and with a linear function. The linear fit yields a slope of 0.67 ± 0.25 and a y-intercept of 0.23 ± 0.39, which is consistent with zero. Accordingly, we fit the data again by assuming Equation (8) (i.e., proportional relation). The best-fit line with the 90% confidence interval is plotted in Figure 6(a), showing that all the data in OBS 1 through 8 are consistent with the theoretical relation. On the basis of our disk wind model, we are able to estimate the ionization parameter in OBS 8 to be $\mathrm{log}({\xi }_{0})={5.31}_{-0.14}^{+0.18}$ through the spectral fit, by adopting ${N}_{{\rm{H}}}^{\mathrm{wind}}={2.56}_{-0.37}^{+0.37}\times {10}^{23}\,{\mathrm{cm}}^{-2}$ predicted from Equation (8). This result is plotted in the orange dotted line in Figure 6(b). By including this data point, correlation between ξ₀ and T_IC is also confirmed at a 91% confidence level via an F-test. The best-fit relation of Equation (9) is plotted in Figure 6(b), with which all the data are consistent. We note that the possible increase of the scattering fraction in OBS 8 (discussed in Section 3.1) does not affect our final results. The maximum increase of the scattering fraction (4%) leads to an only ∼1% luminosity decrease and a ∼2% Compton temperature increase.

The nondetection of the iron-K absorption lines in the VHS during the 2012 outburst does not contradict this theory. The column density and ionization parameter are predicted to be ${N}_{{\rm{H}}}^{\mathrm{wind}}={4.39}_{-0.63}^{+0.64}\times {10}^{23}\,{\mathrm{cm}}^{-2}$ and $\mathrm{log}({\xi }_{0})=5.37\,\pm \,0.07$ by using ${L}_{\mathrm{bol}}=5.36\times {10}^{38}\,\mathrm{erg}\,{{\rm{s}}}^{-1}$ and ${T}_{\mathrm{IC}}=5.57\,\mathrm{keV}$ with Equations (8) and (9). Analyzing the VHS spectra in the same way as for the HSS data, we obtain a lower limit of the ionization parameter of ξ₀ > 5.38 at a 99% confidence level. This is still consistent with the theoretical prediction (see Figure 6(b)). We do not rule out, however, the possibility that the geometrical configuration between the central source and outer disk might have changed in the VHS, leading to a more efficient ionization of the disk wind in the VHS than in the HSS. We note that runaway ionization of the wind via thermodynamical instability is unlikely to occur in the VHS (Chakravorty et al. 2013).

Figure 7 plots the relation between the wind velocity V_wind and the Compton temperature T_IC in the 2006 outburst. We find that the correlation is not statistically significant in our data, which are subject to large uncertainties. Nevertheless, the green line, representing the best-fit relation of ${V}_{\mathrm{wind}}\propto {T}_{\mathrm{IC}}^{0.5}$ (see Equation (4)), is consistent with the observed data except for OBS 7. We note that V_wind has a systematic error of ∼200 km s⁻¹ due to a possible energy-gain uncertainty of Suzaku/XIS, which became larger in the 2015 observations (OBS 7 and 8).⁹

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From these results, we conclude that the evolution of the observed iron-K absorption line features in the spectra of 4U 1630–47 are consistent with a simple theory of thermally driven disk winds. We have shown that it is important to consider the dependence of the launching radius of a disk wind on the Compton temperature T_IC, which is determined by the shape of the continuum. Further observational studies with high-resolution spectroscopy that enable us to more accurately determine the outflow velocity would be useful to confirm our scenario.

Although the data and model agree fairly well, there are potential uncertainties in our calculation; here we assumed very simple velocity/density structures to predict the observable of thermally driven wind. Also we ignored the reduction of R_IC by radiation pressure, which becomes significant above ∼0.3L_Edd (Done et al. 2018). Hydrodynamic simulations and radiation transfer calculation based on their results would be required for more accurate discussion, which we left for future work.