NuSTAR AND SWIFT OBSERVATIONS OF THE BLACK HOLE CANDIDATE XTE J1908+094 DURING ITS 2013 OUTBURST

The NuSTAR data (ObsID 80001014002) were processed using version 1.3.1 of the NuSTARDAS pipeline with NuSTAR CALDB version 20131223. The spectra and light curves were extracted from a region centered at the position of XTE J1908+094 with a radius of 120''. The source region was contaminated by stray light from the nearby bright source GRS 1915+105. Thus, the background region was chosen carefully. We used a circular background region with a radius of 80'' from the part of the field of view that was illuminated by the GRS 1915+105 stray light and was as far away from XTE J1908+094 as possible. The background count rate is less than 6% of the source count rate, which means that even considering the stray light, the source still strongly dominates the spectra and light curves. The spectra of the two NuSTAR focal plane modules A and B (FPMA and FPMB), were rebinned to have at least 50 counts per bin. The light curves were binned to a time resolution of 100 s.

We reduced the Swift/XRT data from 2013 October 29 to 2013 December 3 (see Table 1). All data were taken in windowed timing mode. Using XSELECT with XRT CALDB version 20140709, the spectra were extracted from a circular region with a radius of 20 pixels ($\sim 47^{\prime\prime}$). The background extraction region is a box that is 20 pixels long, centered 100 pixels from the middle of the source extraction region. Ancillary response files were created using the ftool xrtmkarf. At lower energies, the windowed timing mode shows a bump between 0.4–1 keV and a turn up at the lowest energies.¹⁵ In order to reduce the low-energy spectral residuals, the grade 0 data and the position-dependent response matrices¹⁶ from the latest XRT calibration files were used. Finally, the extracted spectra were rebinned to contain a minimum of 25 counts per bin.

The Swift monitoring observations reveal a clear evolution starting from 2013 October 25 (MJD 56590) (see Figure 1). The Swift/BAT count rate in the 15–50 keV band¹⁷ increased rapidly from 0.0022 ± 0.0008 $\mathrm{cts}\;{\mathrm{cm}}^{-2}\;{{\rm{s}}}^{-1}$ on MJD 56590 to 0.026 ± 0.002 $\mathrm{cts}\;{\mathrm{cm}}^{-2}\;{{\rm{s}}}^{-1}$ on MJD 56595 and then decreased sharply to ∼0.0015 $\mathrm{cts}\;{\mathrm{cm}}^{-2}\;{{\rm{s}}}^{-1}$ and stayed close to that level after MJD 56604. In Swift/XRT's 0.3–10 keV band, the source brightened from 9.2 ± 0.1 $\mathrm{cts}\;{{\rm{s}}}^{-1}$ on MJD 56595, reaching its peak count rate of 36.2 ± 0.2 $\mathrm{cts}\;{{\rm{s}}}^{-1}$ on MJD 56607 and then dimmed. The hardness, defined as the ratio of the count rates in the 2.5–10 keV to 0.3–2.5 keV bands, started to decrease from 2.15 ± 0.05 on MJD 56595 to 1.030 ± 0.011 on MJD 56605, and then stayed at a value of ∼1. All of these measurements suggest that the source entered a state transition around MJD 56595 and was in the soft state 10 days later. The long exposure obtained with NuSTAR between MJD 56605 and MJD 56606 occurred after the source reached the soft state.

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First, we fitted the 0.5–10 keV Swift/XRT spectra using a single absorbed power-law model. The Swift data below 0.5 keV were ignored during the spectral fits in order to exclude the low-energy spectral residuals in windowed timing mode. The values of the photon index, ${\rm{\Gamma }}$, and the reduced ${\chi }^{2}$ are plotted in Figure 2(a). The value of Γ increased steeply from 1.6 on MJD 56595 to 4.4 on MJD 56605, and remained at ∼4.5 until MJD 56629, consistent with the source going through the hard to soft state transition. After the source begins the state transition, the accretion disk is significant for most of the observation. For these observations, a single power law does not provide a good fit to the spectra, and the addition of a disk-blackbody component provides a significant improvement to the fit. The inner disk temperature ${T}_{\mathrm{in}}$, the normalization of the diskbb model, the photon index Γ, and the reduced ${\chi }^{2}$ are shown in Figure 2(b). The absorbed disk blackbody plus power-law model could successfully fit all spectra, with ${T}_{\mathrm{in}}$ increasing from 0.3 before the state transition and stabilizing at about 0.7–0.8 keV in soft state.

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The NuSTAR light curves of FPMA and FPMB (see the top panels of Figure 3) with background subtraction show a flare of ∼40 ks duration with the peak rate being ∼40% above the non-flare rate. The background light curves are also shown in Figure 3 in order to evaluate if the variability might be from the nearby source GRS 1915+105 rather than XTE J1908+094. The background light curves are stable at an average value of 1.3 $\mathrm{cts}\;{{\rm{s}}}^{-1}$, less than 6% of the net source count rate. Thus, although the high background caused by GRS 1915+105 affects the statistical quality of the XTE J1908+094 spectrum, Figure 3 demonstrates that the flare in the light curves comes from XTE J1908+094. To study whether the flare has a different spectrum from the non-flare emission, we first checked the ratios of the 10–79 keV count rates to the 3–10 keV count rates. During the flare, this hardness ratio increased (bottom panels of Figure 3), indicating that there is spectral variation.

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To investigate further, we extracted the 3–79 keV spectra prior to the flare, during the flare, and after the flare and fitted them together using a simple model combining an energy-independent multiplicative factor (constant), an absorption model (tbabs), adopting abundances from Wilms et al. (2000), a power-law model (pegpwrlw) and a multi-temperature disk-blackbody model (diskbb), i.e., constant ∗ tbabs ∗ (pegpwrlw + diskbb). Untying the model parameters individually or in combination, we found that only changing the power-law model could explain the variability, with a reduced ${\chi }^{2}=1.25$ for 2697 degrees of freedom (dof). As shown in the top panel of Figure 4, the power-law component changes significantly between the flare and non-flare spectra: before the flare, Γ = 1.96, during the flare, Γ = 2.23, and after the flare, Γ = 2.03. Here, we quote the best fit parameters without error bars because this simple model does not provide an acceptable fit to the data. Moreover, as shown in Figures 4(b)–(d), all spectra exhibit similar residuals when the power-law parameters are allowed to vary prior to the flare, during the flare, and after the flare. Very poor fits are obtained if the power-law component is required to be the same for all three spectra. All of this suggests that the corona, rather than the mass accretion rate and the accretion disk, went through great changes during the NuSTAR observation.

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Given the strong spectral variability during the flare and the similar spectral properties before the flare and after the flare, the NuSTAR data in the 3–79 keV band was divided into two parts: the flare spectra and non-flare spectra. The two Swift/XRT observations, ObsID 00033014004 and 00033014005, from prior to the flare and after the flare, respectively (see Figure 3), were combined with the non-flare spectra. Then, we used the model constant ∗ tbabs ∗ (pegpwrlw + diskbb) (model 1) to fit the flare spectra plus combined non-flare spectra, and freed the power-law component in these two data sets. We find that Swift/XRT and NuSTAR have residuals that are not consistent with each other in the soft X-ray region where they overlap. The residuals are also not the same for the two Swift observations. Note that the exposure times of the Swift observations are about 1 ks (see Table 1), much shorter than that of NuSTAR, allowing for the possibility that Swift might catch short-term spectral variations in its short snapshots. For NuSTAR, the largest residuals are in the iron Kα emission line region (Figures 4(b)–(d)), rather than in the soft X-ray band observed by Swift. Therefore, in the following, we fit the NuSTAR spectra alone.

As shown in Figures 4 and 5, a strong reflection component is apparent in the residuals of this fit (model 1), leading to a large reduced ${\chi }^{2}=2709.8$ for 2099 dof (see Table 2). Similar to some other Galactic X-ray binaries, the reflection component is composed of an iron Kα emission line and a broad reflection excess (Lightman & White 1988; Miller 2007; Tomsick et al. 2014). The emission line feature was also detected in the 2002 outburst (in't Zand et al. 2002; Göǧüş et al. 2004). Following in't Zand et al. (2002) and Göǧüş et al. (2004), we used the Gaussian emission line model Gaussian to fit this feature and performed fits with the neutral hydrogen column density, ${N}_{{\rm{H}}}$, fixed to $2.5\times {10}^{22}\;{\mathrm{cm}}^{-2}$ (model 2a). We also tested fits where ${N}_{{\rm{H}}}$ was a free parameter (model 2b). Adding a Gaussian significantly improves the spectral fits with ${\rm{\Delta }}{\chi }^{2}\gtrsim 400$ (see Table 2 and Figure 5). The unabsorbed disk flux fractions, i.e., the relative disk flux contribution to the total, unabsorbed flux in the 2–20 keV range, are larger than 80% for both the flare and non-flare spectra, which meet the soft state criterion of Remillard & McClintock (2006) and also confirm that the NuSTAR observation was taken in the soft state. The measurement of Gaussian line centroid, ${E}_{\mathrm{cent}}$, is dependent on ${N}_{{\rm{H}}}$. Freezing ${N}_{{\rm{H}}}$ at $2.5\times {10}^{22}\;{\mathrm{cm}}^{-2}$, ${E}_{\mathrm{cent}}$ is in the iron line region (6.4–7.1 keV); leaving ${N}_{{\rm{H}}}$ as a free parameter, ${E}_{\mathrm{cent}}$ is well below this energy region. Given this, we then tested fits with ${N}_{{\rm{H}}}$ fixed at $4.3\times {10}^{22}\;{\mathrm{cm}}^{-2}$, the average ${N}_{{\rm{H}}}$ when fitting the Swift spectra in soft state with a two component model consisting of power-law and disk components (Section 3.1). We obtained ${E}_{\mathrm{cent}1}={6.2}_{-0.3}^{+0.2}\mathrm{keV}$ and ${E}_{\mathrm{cent}2}=5.9\pm 0.3\mathrm{keV},$ and the line widths ${\sigma }_{1}={1.29}_{-0.14}^{+0.16}\mathrm{keV}$ and ${\sigma }_{2}={1.51}_{-0.18}^{+0.19}\mathrm{keV},$ respectively, for the non-flare and flare spectra, with ${\chi }^{2}/\mathrm{dof}=2224.1/2094$.

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Table 2.  Spectral Fitting of XTE J1908+094: Part I

Model	C	${N}_{{\rm{H}}}$	${{\rm{\Gamma }}}_{1}$	${N}_{\mathrm{PL}1}$	${E}_{\mathrm{cent}1}$	${\sigma }_{1}$	${N}_{\mathrm{gauss}1}$	kT	${N}_{\mathrm{disk}}$	${\chi }^{2}/\mathrm{dof}$
			${{\rm{\Gamma }}}_{2}$	${N}_{\mathrm{PL}2}$	${E}_{\mathrm{cent}2}$	${\sigma }_{2}$	${N}_{\mathrm{gauss}2}$
1	0.993	1.6	2.00	385	⋯	⋯	⋯	0.783	650	2709.8/2099
			2.23	554	⋯	⋯	⋯
2a	0.993 ± 0.003	2.5a	1.95 ± 0.03	387 ± 4	${6.82}_{-0.16}^{+0.14}$	${0.98}_{-0.14}^{+0.15}$	${0.74}_{-0.14}^{+0.17}$	0.755 ± 0.003	${873}_{-19}^{+20}$	2321.7/2094
			2.15 ± 0.03	${545}_{-6}^{+5}$	${6.1}_{-0.4}^{+0.3}$	${1.3}_{-0.2}^{+0.3}$	${2.2}_{-0.6}^{+1.0}$
2b	0.993 ± 0.003	${5.8}_{-0.6}^{+0.8}$	1.99 ± 0.03	391 ± 4	${5.3}_{-1.0}^{+0.6}$	${1.6}_{-0.2}^{+0.3}$	${5}_{-2}^{+7}$	${0.671}_{-0.026}^{+0.018}$	${2300}_{-400}^{+800}$	2207.8/2093
			2.16 ± 0.03	551 ± 6	${4.9}_{-0.9}^{+0.5}$	${1.8}_{-0.2}^{+0.3}$	${10}_{-4}^{+8}$

Notes. Model 1: constant ∗ tbabs ∗ (pegpwrlw + diskbb). Model 2: constant ∗ tbabs ∗ (pegpwrlw + Gaussian + diskbb); 2a: fixed ${N}_{{\rm{H}}}$ at $2.5\times {10}^{22}\;{\mathrm{cm}}^{-2}$; 2b: ${N}_{{\rm{H}}}$ was set as a free parameter. Model 1 is not an acceptable fit to the spectrum so we just quote the best fit parameters without error bars.

^afixed value; C is the NuSTAR FPMB normalization factor relative to FPMA; ${N}_{{\rm{H}}}$ is the X-ray absorption column density in units of ${10}^{22}\;{\mathrm{cm}}^{-2}$; ${{\rm{\Gamma }}}_{1}$ and ${{\rm{\Gamma }}}_{2}$ are the power-law photon indices of the non-flare and flare spectra; ${N}_{\mathrm{PL}1}$ and ${N}_{\mathrm{PL}2}$ are the power-law component flux normalizations over the 3–79 keV energy band in units of ${10}^{-12}$ erg cm⁻² s⁻¹; ${E}_{\mathrm{cent}1}$ and ${E}_{\mathrm{cent}2}$ are the Gaussian emission line energies in keV; ${\sigma }_{1}$ and ${\sigma }_{2}$ are the line widths in keV; ${N}_{\mathrm{gauss}1}$ and ${N}_{\mathrm{gauss}2}$ are the Gaussian component normalizations in units of ${10}^{-3}\;\mathrm{photons}\;{\mathrm{cm}}^{-2}\;{{\rm{s}}}^{-1}$; kT is the accretion disk temperature of the diskbb model in units of keV; ${N}_{\mathrm{diskbb}}$ is the normalization of the diskbb model; All errors and limits are at the 90% confidence level.

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Instead of the Gaussian emission line model, we then used the more physical model reflionx_hc to fit the reflection component, and replaced the simple power-law model with a power-law with an exponential cutoff cutoffpl (model 3). The reflionx_hc model is an update of the model reflionx (Ross et al. 1999; Ross & Fabian 2005), which calculates the reflected spectrum from an optically thick atmosphere ionized by illuminating X-rays with a cutoff power-law spectrum. The power-law photon index of reflionx_hc is linked to that of cutoffpl. Compared with reflionx, the folding energy HighECut in reflionx_hc is a free parameter also linked to that of cutoffpl. In addition, the ionization parameter, $\xi$, and the abundance of iron, Fe/solar, extend over larger ranges in reflionx_hc.

When left as a free parameter, the best fit value for the exponential folding energy, HighECut, is 500 keV, which is the upper limit of the parameter range. As this parameter is not well-constrained, we performed fits with HighECut fixed at 100 keV and 500 keV, respectively. Moreover, we also performed fits with Fe/solar fixed at the initial value of 1.5 and as a free parameter. Good fits with reduced ${\chi }^{2}$ less than 1.08 were obtained if a reflection component was added. Changing HighECut from 100 to 500 keV, or unfreezing Fe/solar, other model parameters change only slightly, as seen for model 3a (HighECut = 100 keV, Fe/solar = 1.5) and model 3b (HighECut = 500 keV, free Fe/solar) in Table 3. Similar to the power-law photon index, the ionization parameter in the flare stage is also larger than that in the non-flare stage.

Table 3.  Spectral Fitting of XTE J1908+094: Part II

Para.	Model 3a	Model 3b	Model 4	Model 5
C	0.993 ± 0.003	0.993 ± 0.003	0.993 ± 0.003	0.993 ± 0.003
${N}_{{\rm{H}}}$	4.1 ± 0.3	4.4 ± 0.3	${5.1}_{-0.3}^{+0.4}$	5.3 ± 0.4
${{\rm{\Gamma }}}_{1}$	${1.84}_{-0.06}^{+0.04}$	${2.01}_{-0.05}^{+0.04}$	2.02 ± 0.04	${2.02}_{-0.07}^{+0.05}$
${{\rm{\Gamma }}}_{2}$	${2.02}_{-0.05}^{+0.04}$	${2.15}_{-0.05}^{+0.04}$	${2.16}_{-0.04}^{+0.05}$	2.20 ± 0.04
${E}_{\mathrm{fold}1}$	${100}^{\star }$	${500}^{\star }$	${500}^{\star }$	${500}^{\star }$
${E}_{\mathrm{fold}2}$	${100}^{\star }$	${500}^{\star }$	${500}^{\star }$	${500}^{\star }$
${N}_{\mathrm{PL}1}$	${0.027}_{-0.018}^{+0.012}$	${0.033}_{-0.024}^{+0.017}$	${0.036}_{-0.027}^{+0.019}$	⋯
${N}_{\mathrm{PL}2}$	${0.05}_{-0.03}^{+0.02}$	${0.03}_{-0.03}^{+0.05}$	0.06 ± 0.06	⋯
${f}_{\mathrm{scat}1}$	⋯	⋯	⋯	0.010 ± 0.010
${f}_{\mathrm{scat}2}$	⋯	⋯	⋯	${0.016}_{-0.012}^{+0.010}$
kT	0.719 ± 0.007	0.711 ± 0.007	${0.689}_{-0.012}^{+0.008}$	⋯
${N}_{\mathrm{diskbb}}$	${1310}_{-100}^{+110}$	${1420}_{-110}^{+120}$	${1810}_{-160}^{+240}$	⋯
${M}_{\mathrm{BH}}$	⋯	⋯	⋯	${2.8}_{-0.2}^{+15.7}$
$\dot{M}$	⋯	⋯	⋯	${1.3}_{-0.7}^{+6.6}$
${D}_{\mathrm{BH}}$	⋯	⋯	⋯	${10}^{\star }$
${N}_{\mathrm{kerrbb}}$	⋯	⋯	⋯	${1.7}_{-0.8}^{+4.9}$
${\xi }_{1}$	${5300}_{-1600}^{+1300}$	${4200}_{-1000}^{+1300}$	${9000}_{-3000}^{+7000}$	${5700}_{-1900}^{+1200}$
${\xi }_{2}$	10400 ± 1700	10000 ± 2000	${19500}_{-6800}^{+500}$	${11900}_{-1500}^{+2300}$
${N}_{\mathrm{ref}1}$	${1.33}_{-0.15}^{+0.16}$	${2.4}_{-0.7}^{+0.8}$	${1.2}_{-0.6}^{+0.5}$	${2.4}_{-0.3}^{+0.4}$
${N}_{\mathrm{ref}2}$	1.46 ± 0.14	${2.4}_{-0.7}^{+0.9}$	1.2 ± 0.5	2.2 ± 0.3
Fe/solar	${1.5}^{\star }$	${0.9}_{-0.3}^{+0.5}$	${4.0}_{-1.5}^{+8.4}$	${1.5}^{\star }$
a	⋯	⋯	$-{0.998}_{-0}^{+1.9}$	$-{0.96}_{-0.04}^{+1.63}$
i	⋯	⋯	${27}_{-4}^{+7}$	${33}_{-4}^{+3}$
${\chi }^{2}/\mathrm{dof}$	2256.9/2095	2227.7/2094	2209.5/2092	2208.5/2092

Notes. Model 3: constant ∗ tbabs ∗ (reflionx_hc + cutoffpl + diskbb); 3a: fix ${E}_{\mathrm{fold}}=100\mathrm{keV}$ and Fe/solar = 1.5; 3b: fix ${E}_{\mathrm{fold}}=500\mathrm{keV}$ and thaw Fe/solar. Model 4: constant ∗ tbabs ∗ (relconv ∗reflionx_hc + cutoffpl + diskbb). Model 5: constant ∗ tbabs ∗ (relconv ∗reflionx_hc + simpl ∗kerrbb). ${E}_{\mathrm{fold}1}$ and ${E}_{\mathrm{fold}2}$ are the folding energy of exponential rolloff for the non-flare and flare spectra in units of keV; ${N}_{\mathrm{PL}1}$ and ${N}_{\mathrm{PL}2}$ are the cutoff power-law normalizations at 1 keV in photons keV⁻¹cm⁻²s⁻¹; ${f}_{\mathrm{scat}1}$ and ${f}_{\mathrm{scat}2}$ are the scattered fractions of the simpl model; ${M}_{\mathrm{BH}}$ is the black hole mass in units of the solar mass; $\dot{M}$ is the disk mass accretion rate in units of 10¹⁸ g s⁻¹; ${D}_{\mathrm{BH}}$ is the distance of the black hole in units of kpc; ${N}_{\mathrm{kerr}}$ is the normalization of the kerrbb model; ${\xi }_{1}$ and ${\xi }_{2}$ are the ionization parameters of the reflionx_hc model in units of erg cm ${{\rm{s}}}^{-1}$; ${N}_{\mathrm{ref}1}$ and ${N}_{\mathrm{ref}2}$ are the normalizations of reflected spectrum (reflionx_hc) in units of 10⁻⁷; Fe/solar is the abundance of iron relative to solar value; a is the dimensionless black hole spin; i is the inclination angle of the accretion disk in units of degree; other parameters are the same as in Table 2. All errors and limits are at the 90% confidence level.

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The iron Kα emission line may be distorted by relativistic effects; therefore, a convolution model, relconv (Dauser et al. 2010), was adopted to calculate the relativistic smearing (model 4). The relconv model also allows for a broken power-law emissivity function for the incident emission. Compared with other relativistic smearing models, relconv extends the BH spin parameter range to negative values, corresponding to a disk rotating counter to the BH's spin.

The fits also favored a high folding energy and were performed with HighECut fixed to 100 and 500 keV. We included fits with the iron abundance free and also fixed to a value of 1.5 solar. Similarly to before, freezing Fe/solar or changing HighECut causes little difference in the residuals and other model parameters. The inner disk radius was set to be at the innermost stable circular orbit (ISCO), and the outer disk radius was set to 400 ${r}_{g}$, where ${r}_{g}={GM}/{c}^{2}$ is the gravitational radius. The emissivity indices were fixed at the default values, and we noted that thawing these parameters or fixing the inner emissivity index at $3\lt {q}_{\mathrm{in}}\lt 10$ and the outer emissivity index at $0\lt {q}_{\mathrm{out}}\lt 3$ (e.g., ${q}_{\mathrm{in}}=5$ and ${q}_{\mathrm{out}}=2$, or ${q}_{\mathrm{in}}=8$ and ${q}_{\mathrm{out}}=1$) did not improve the fits significantly (the decrease in ${\rm{\Delta }}{\chi }^{2}$ was less than 2.7). The best fit model is shown in Table 3 and Figure 5. Adding a relativistic blurring model led to only a marginally significant improvement in ${\chi }^{2}$. For the spin of the BH, a wide range is allowed, with the full parameter range (from $-0.998$ to 0.998) being covered when all the models we used are considered. This will be discussed in Section 4.

In order to constrain the spin of BH, the diskbb model was replaced by a more physical disk blackbody model, kerrbb (Li et al. 2005). The model calculates the disk continuum around a Kerr BH and fully takes the relativistic effects into account. Moreover, following previous papers (e.g., Tomsick et al. 2014), an empirical Comptonization convolution model, simpl (Steiner et al. 2009), which assumes that a fraction of seed photons are scattered into a power-law component, was used instead of the power-law model (model 5).

Similar to the fits above, a high folding energy was preferred by model 5. Although we also tested the fits with ${E}_{\mathrm{fold}}$ fixed at 100 keV and the iron abundance left as a free parameter, we only show the spectral fitting with ${E}_{\mathrm{fold}}=500\mathrm{keV}$ and Fe/solar = 1.5 in Table 3 and Figure 5 because there is only a slight change in the goodness of fit for other values of those parameters. The distance of XTE J1908+094 is thought to be $\sim 2-10\;\mathrm{kpc}$; thus, ${D}_{\mathrm{BH}}$ was set to be 2 kpc or 10 kpc. The spin and the inclination of kerrbb are linked to those of relconv. Other model parameters were fixed at the default values. We obtained a very small improvement in the fits with the reduced ${\chi }^{2}$ of 1.06 for 2092 dof. Except for the normalization of the kerrbb model, all model parameters show little changes if ${D}_{\mathrm{BH}}$ was changed from 10 kpc to 2 kpc. Thus, we only show the spectral fitting with ${D}_{\mathrm{BH}}=10\;\mathrm{kpc}$ (see Figure 6). The BH spin can take values in a wide range, from $-0.998$ to ∼0.7. The unabsorbed flux in the 2–12 keV band are $2.7\times {10}^{-9}$ erg cm⁻² s⁻¹ and $2.9\times {10}^{-9}$ erg cm⁻² s⁻¹ for the non-flare and flare spectra, respectively. Using the average flux over the non-flare and flare stages, and assuming a typical ${M}_{\mathrm{BH}}$ of $10\;{M}_{\odot }$ and ${D}_{\mathrm{BH}}$ = (2–10) kpc, the source luminosity is $(1-34)\times {10}^{36}$ erg s⁻¹ and the Eddington fraction ($L/{L}_{\mathrm{Edd}}$) is 0.1%–2.7%. While the upper part of the $L/{L}_{\mathrm{Edd}}$ range would not be unusual for a soft state, the lower part of the range is low for a soft state (e.g., Yu & Yan 2009), and this may favor a source distance closer to 10 kpc than 2 kpc.

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Previously, using the BeppoSAX MECS spectra from the 2002 outburst, Miller et al. (2009) measured the spin of the BH in XTE J1908+094. The thermal emission was not detected in these spectra; thus, they used the reflection component to constrain the spin and reported a value of 0.75 ± 0.09. If we fix the spin at 0.75 and set the other parameters to be the same as for model 5, the quality of the spectral fit is still good. Other than the BH mass being larger, the parameters are similar to those of model 5. However, given the large uncertainties in the spin, distance, and inclination, it is impossible to constrain ${M}_{\mathrm{BH}}$ with our current data. The inclination measurement is independent of the BH spin that we assume with a value of ∼30°−40°, similar to i = 45° ± 8° reported by Miller et al. (2009).

Although these models containing the disk, the power-law (Comptonization), and the reflection components fit the NuSTAR spectra well, upon closer inspection, we find a small bump in the residuals near 8–9 keV (see Figure 5). A similar feature is also observed in some other NuSTAR spectra, such as Cyg X-1 (Tomsick et al. 2014). Adding a Gaussian emission line with ${E}_{\mathrm{cent}}\sim 8.2\mathrm{keV}$ and $\sigma \sim 0.3\mathrm{keV},$ the spectral fits are improved, with ${\rm{\Delta }}{\chi }^{2}\sim 16$, and the key parameters change only slightly. The line feature is likely related to a combination of iron Kβ and nickel emission, neither of which are included in the reflionx_hc model (D. J. Walton 2015, in preparation).