Complex accretion geometry of GX 339-4

The complex accretion geometry of GX 3394 as seen by NuSTAR and Swift

F. Fürst1 M. A. Nowak2 J. A. Tomsick3 J. M. Miller4 S. Corbel5 6 M. Bachetti7 8 9 S. E. Boggs3 F. E. Christensen10 W. W. Craig3 11 A. C. Fabian12 P. Gandhi13 14 V. Grinberg2 C. J. Hailey15 F. A. Harrison1 E. Kara12 J. A. Kennea16 K. K. Madsen1 K. Pottschmidt17 18 D. Stern19 D. J. Walton19 1 J. Wilms20 W. W. Zhang17
1affiliation: Cahill Center for Astronomy and Astrophysics, California Institute of Technology, Pasadena, CA 91125, USA
2affiliation: Massachusetts Institute of Technology, Kavli Institute for Astrophysics, Cambridge, MA 02139, USA
3affiliation: Space Sciences Laboratory, University of California, Berkeley, CA 94720, USA
4affiliation: Department of Astronomy, The University of Michigan, Ann Arbor, MI 48109, USA
5affiliation: Laboratoire AIM (CEA/IRFU - CNRS/INSU - Université Paris Diderot), CEA DSM/IRFU/SAp, 91191 Gif-sur-Yvette, France
6affiliation: Station de Radioastronomie de Nançay, Observatoire de Paris, CNRS/INSU, USR 704 - Univ. Orléans, OSUC, 18330 Nançay, France
7affiliation: Université de Toulouse; UPS-OMP; IRAP; Toulouse, France
8affiliation: CNRS; Institut de Recherche en Astrophysique et Planétologie, 31028 Toulouse cedex 4, France
9affiliation: INAF/Osservatorio Astronomico di Cagliari, 09047 Selargius (CA), Italy
10affiliation: DTU Space, National Space Institute, Technical University of Denmark, 2800 Lyngby, Denmark
11affiliation: Lawrence Livermore National Laboratory, Livermore, CA 94550, USA
12affiliation: Institute of Astronomy, Cambridge CB3 0HA, UK
13affiliation: Department of Physics, Durham University, Durham DH1 3LE, UK
14affiliation: School of Physics & Astronomy, University of Southampton, Highfield, Southampton SO17 1BJ, UK
15affiliation: Columbia Astrophysics Laboratory, Columbia University, New York, NY 10027, USA
16affiliation: Department of Astronomy & Astrophysics, The Pennsylvania State University, University Park, PA 16802, USA
17affiliation: CRESST, UMBC, and NASA GSFC, Code 661, Greenbelt, MD 20771,USA
18affiliation: NASA Goddard Space Flight Center, Greenbelt, MD 20771, USA
19affiliation: Jet Propulsion Laboratory, California Institute of Technology, Pasadena, CA 91109, USA
20affiliation: Dr. Karl-Remeis-Sternwarte and ECAP, University of Erlangen-Nuremberg, 96049 Bamberg, Germany
Abstract

We present spectral analysis of five NuSTAR and Swift observations of GX 3394 taken during a failed outburst in summer 2013. These observations cover Eddington luminosity fractions in the range 0.9–6%. Throughout this outburst, GX 3394 stayed in the hard state, and all five observations show similar X-ray spectra with a hard power-law with a photon index near 1.6 and significant contribution from reflection. Using simple reflection models we find unrealistically high iron abundances. Allowing for different photon indices for the continuum incident on the reflector relative to the underlying observed continuum results in a statistically better fit and reduced iron abundances. With a photon index around 1.3, the input power-law on the reflector is significantly harder than that which is directly observed. We study the influence of different emissivity profiles and geometries and consistently find an improvement when using separate photon indices. The inferred inner accretion disk radius is strongly model dependent, but we do not find evidence for a truncation radius larger than in any model. The data do not allow independent spin constraints but the results are consistent with the literature (i.e., ). Our best-fit models indicate an inclination angle in the range 40–60, consistent with limits on the orbital inclination but higher than reported in the literature using standard reflection models. The iron line around 6.4 keV is clearly broadened, and we detect a superimposed narrow core as well. This core originates from a fluorescence region outside the influence of the strong gravity of the black hole and we discuss possible geometries.

Subject headings:
X-rays: individual (GX 3394) — accretion, accretion disks — X-rays: binaries — stars: black holes

1. Introduction

Black holes accreting via Roche-lobe overflow from a low-mass companion star typically demonstrate a strongly transient behavior: while they spend most of their time in quiescence, during outbursts they can reach luminosities up to  erg s, the Eddington limit for a 10  black hole (Remillard & McClintock, 2006, and references therein). The X-ray spectra can primarily be described by two components: a multi-temperature accretion disk and a hot electron gas corona. The corona shows up as a power-law component, originating from Compton up-scattering of soft disk seed photons by coronal hot electrons. Outbursts typically start in a so-called low/hard state in which a power-law with a photon index dominates the X-ray spectrum. The accretion disk contributes only weakly to the X-ray spectrum, with typical disk temperatures  keV. The disk is more evident as a reflector of the hard X-ray continuum, resulting in a characteristic iron K line at 6.4 keV and a Compton hump between 20–40 keV (Ross & Fabian, 2005). In the later stages of the outburst, the source typically enters the high/soft state, in which the accretion disk gets hotter and becomes the dominant contributor to the X-ray spectrum, while at the same time the power-law becomes softer.

In the high/soft state strong evidence exists that the accretion disk extends all the way to the innermost stable circular orbit (ISCO, Shakura & Sunyaev, 1973). The radius of the ISCO depends strongly on the black hole spin and with it the distortions of the fluorescent iron line due to orbital motions and general relativistic effects. By modeling these distortions, it is possible to estimate the spin of the black hole. An alternative method to measure the spin is to use the continuum flux from the disk black body component, which is also a function of the ISCO (Zhang, Cui & Chen, 1997; Davis et al., 2005; McClintock, Narayan & Steiner, 2014).

In the low/hard state it has been postulated that the accretion disk is truncated and that the inner regions of the accretion flow are described by an optically thin, advection dominated accretion flow (ADAF, see, e.g., Narayan & Yi, 1995; Esin, McClintock & Narayan, 1997; Taam et al., 2008). The truncation radius is predicted to be at several , and therefore the fluorescent line from disk reflection should be narrow, and the blackbody radiation from the disk should be relatively cold.

Measurements of the inner accretion disk radius at luminosities in the low/hard state typically are consistent with, or even require, an accretion disk extending all the way to the ISCO (see, e.g. Nowak, Wilms & Dove, 2002; Miller et al., 2006; Petrucci et al., 2014; Miller et al., 2014). Reis, Fabian & Miller (2010) extend these measurements down to 0.05% using a sample of 8 sources and find that there is still evidence for an accretion disk close to the ISCO. However, Tomsick et al. (2009) measure a truncated disk with an inner radius for GX 3394 at , assuming an inclination of . This is the lowest luminosity of GX 3394 for which such a measurement is available and is the first time a clearly truncated disk is seen. The authors speculate that the accretion disk moves quickly outwards at luminosities , but it is not clear what mechanism triggers this change in the accretion disk geometry. This idea of a recession below 1%  in GX 3394 is supported by Allured et al. (2013) who measure inner radii around for luminosities between 0.5–5% .

GX 3394 is the archetypical transient black hole binary. It has been studied intensively since its discovery in 1973 (Markert et al., 1973) and shows a high level of activity, with an average of one outburst of varying strength every 2 years. During the hard-states it reaches fluxes in excess of 150 mCrab in the Swift/BAT 15–50 keV energy band. This high flux and semi-regular outburst activity makes GX 3394 an ideal target to study the low/hard state in detail.

The optical companion is not directly observable, and the only measurement of the orbital period has been obtained by measuring Doppler shifts of fluorescent lines caused by the irradiation of the companion (Hynes et al., 2003). These measurements give an orbital period  d and together with the upper limit on the companion’s magnitude and assumed spectral type, Zdziarski et al. (2004) estimate the black hole mass to be and the distance  kpc. These values are consistent with the mass limit of calculated by Muñoz-Darias, Casares & Martínez-Pais (2008) using a similar method and we adopt them throughout this paper.

The inclination of the binary orbit is only weakly constrained. As GX 3394 is a non-eclipsing system, the inclination has to be lower than (Cowley et al., 2002), and Zdziarski et al. (2004) estimate from the secondary mass function a lower limit of . Shidatsu et al. (2011) summarize all constraints and derive a best estimate of .

The spin of the black hole in GX 3394 is currently under debate in the literature. Estimates from reflection modeling and disk continuum models do not yet give consistent results regarding spin and inclination. This discrepancy is likely due to different underlying assumptions in the models (for recent reviews on both methods, see Reynolds, 2014, and McClintock, Narayan & Steiner 2014). However, both methods rule out a Schwarzschild (i.e. non-spinning) black hole with high significance (Kolehmainen & Done, 2010; Miller et al., 2008).

Miller et al. (2004, 2008) use Suzaku and XMM-Newton data to measure the relativistic broadening of the line outside of the low/hard state and obtain . Reis et al. (2008), using XMM-Newton and RXTE data of both a soft and a hard state, confirm that value but require an inclination as low as of the inner accretion disk. At these very low inclinations fitting the disk continuum to measure the spin gives consistent results, however, Kolehmainen & Done (2010) argue that this requires a strong misalignment between the orbit’s rotation axis and the spin axis, as the orbital inclination is limited to be . Kolehmainen & Done (2010) therefore prefer a disk inclination which results in significantly lower spin ().

Plant, O’Brien & Fender (2014) present XMM-Newton data taken during the same failed outburst in 2013 presented here (see below), and fit an inclination while fixing the spin at =0.9. They find consistent results between the disk continuum method and the reflection modeling assuming this inclination, and measure a small but significant truncation of the disk, with an inner radius of 20–30 . They do not, however, address the misalignment between orbital and disk inclination.

Therefore both the inner disk inclination and the spin value remain under discussion and need further investigation with sensitive X-ray instruments, especially covering the hard X-rays to get a good measure of the continuum parameters.

As shown by Corbel et al. (2003, and references therein), the radio flux of GX 3394 is strongly correlated with the X-ray flux in the low/hard state, following the non-linear relationship . This correlation has been connected to synchrotron radiation from the the jet also influencing the hard X-ray spectrum (Markoff et al., 2003). Corbel et al. (2013) have shown that the onset of an outburst is also observed in the radio spectrum, which switches from a negative spectral index , where the radio spectrum is described by , to during the low/hard state. This correlation therefore provides information about the connection between accretion and ejection and between the jet and the corona.

In August 2013, optical and X-ray monitoring detected the onset of a new outburst of GX 3394 (Buxton et al., 2013; Pawar et al., 2013). We triggered observations with the Nuclear Spectroscopic Telescope Array (NuSTAR, Harrison et al., 2013), Swift (Gehrels et al., 2004), and with the Australia Telescope Compact Array (ATCA). Overall we obtained five observations with NuSTAR, four during the rise of the outburst and one at the end of the outburst and Swift observations every other day, as well as three ATCA observations. Figure 1 shows the lightcurve of the outburst, as seen with the X-ray monitors Swift/BAT (Krimm et al., 2013) and MAXI (Matsuoka et al., 2009). In a full outburst, the soft X-rays (as observed by MAXI) are expected to brighten as soon as the hard X-rays (as observed by BAT) decline, indicating the switch to the high/soft state. This outburst, however, did not follow that pattern and GX 3394 never left the low/hard state resulting in a so-called failed outburst. Table 1 gives a detailed observation log of the NuSTAR and simultaneous Swift observations.

Figure 1.— Light curves of Swift/BAT (15–50 keV, orange crosses), MAXI (2–20 keV, green circles), NuSTAR (3–79 keV, red diamonds), and Swift/XRT (2–10 keV, blue squares) of the 2013 outburst. All count-rates have been rescaled to mCrab fluxes in the respective energy band of the instrument. The right-hand -axis gives the average measured NuSTAR count-rates of each observation. The downwards-pointing arrows at the top indicate the times of the ATCA observations.

2. Observations and data reduction

No. ObsID NuSTAR ObsID Swift MJD range exp. NuSTAR exp. XRT
(800010130XX ) FPMA / B [ks] [ks]
I 02 00032490015 56515.907–56516.994 42.25/ 42.26 1.1
II 04 00080180001 56520.709–56521.914 47.38 / 47.50 1.9
III 06 00080180002 and 56528.525–56529.792 43.78 / 43.94 1.6
00032898009
IV 08 00032898013 and 56538.414–56539.897 61.94 / 62.29 2.0
00032898015
V 10 00032988001 56581.994–56584.299 98.21 / 98.22 9.6
Swift IIIb N/A 00032898008 56527.788 N/A 0.97
Swift IVb N/A 00032898024 56559.747 N/A 1.26
Table 1NuSTAR and Swift observations and exposure times.

2.1. Swift

Swift monitored the complete outburst with 1 ks snapshots every other day. The evolution of the 2–10 keV count rate (scaled to mCrab units) as measured by the Swift X-ray Telescope (XRT, Burrows et al., 2005) is shown in Figure 1. For data reduction, we used HEASOFT v6.15.1 and the XRT calibration released on 2013 March 13. For each ObsID that we used for the spectral analysis, we reprocessed the raw XRT data to produce new event files using xrtpipeline. Then, we used xselect to create source and background spectra. We included source counts from within 20 pixels () of the GX 3394 position and background counts from an annulus centered on GX 3394 with an inner radius of 90 pixels and an outer radius of 110 pixels. XRT was in Windowed Timing mode for the observations, and we scaled the background to account for the active detector area. For the response matrix, we used the file swxwt0to2s6_20010101v015.rmf and xrtmkarf to account for the effective area, including a correction using the exposure map for each observation. The XRT spectra were rebinned to a S/N of 6 between 0.8–10 keV using the Interactive Spectral Interpretation System (ISIS, Houck & Denicola, 2000). All analysis was done with ISIS v1.6.2-17 in this paper unless otherwise noted and uncertainties are given at the 90% level. Observations Swift IIIb and IVb listed in Table 1 were not used in the X-ray spectral analysis as no simultaneous NuSTAR data are available. We use those observations only for comparison with the radio flux, as they occurred closest in time to the radio observations described in Section 2.3.

2.2. NuSTAR

NuSTAR consists of two independent grazing incidence telescopes which focus X-rays between 3–78 keV onto corresponding focal planes consisting of cadmium zinc telluride (CZT) pixel detectors. NuSTAR, sensitive to X-ray energies from 3–79 keV, provides unprecedented sensitivity and high spectral resolution at energies above 10 keV, ideally suited to study the Compton reflection hump. The two focal planes are referred to as focal plane module (FPM) A and B. NuSTAR data were extracted using the standard NUSTARDAS v1.3.1 software. Source spectra were taken from a radius region centered on the J2000 coordinates. The background was extracted as far away from the source as possible, from a radius region. This approach induces small systematic uncertainties in the background, as the background is known to change over the field of view and from chip to chip (Wik et al., 2014). However, GX 3394 is over five times brighter than the background even at the highest energies, so that these uncertainties are negligible. NuSTAR data were binned to a S/N of 36 in the relevant energy range of 4–78 keV within ISIS. To reduce the spectral overlap which might be influenced by cross-calibration differences between Swift/XRT and NuSTAR, we exclude NuSTAR data below 4 keV.

Timing analysis of NuSTAR observations I–IV is presented by Bachetti et al. (2015). The power spectral density (PSD) between 0.001–200 Hz is consistent with typical hard-state PSDs and well described by three Lorentzian components (see, e.g. Belloni et al., 2005). We also calculated the PSD for observation V and find consistent results.

2.3. Atca

We obtained quasi-simultaneous radio observations with ATCA, as a radio jet is expected to be launched during the low/hard state of GX 3394 (Corbel et al., 2000). ATCA’s synthesis telescope is located in Narrabri, New South Wales, Australia, and consists of six 22 m antennas in an east-west array, using linearly orthogonal polarized feeds which allow the recording of full Stokes parameters. The observations were conducted simultaneously at 5.5 and 9 GHz on MJD 56516.4, 56527.46, and 56559.29, i.e. simultaneous to observation I, Swift IIIb, and Swift IVb (see Fig. 1), using the upgraded Compact Array Broadband Backend (CABB) system (Wilson et al., 2011). The first observation was conducted and reported by Miller-Jones et al. (2013). The array was in a compact configuration (H214 or H168) during this period of ATCA observations.

The amplitude and band-pass calibrator was PKS 1934638, and the antennas’ gain and phase calibration, as well as the polarization leakage, were usually derived from regular observations of the nearby calibrator PMN 164650. The editing, calibration, Fourier transformation with multifrequency algorithms, deconvolution, and image analysis were performed using the MIRIAD software package (Sault & Killeen, 1998).

We show the observed 9 GHz fluxes as a function of the 3–9 keV X-ray flux as measured with Swift/XRT in Figure 2 and compare them with archival data presented by Corbel et al. (2013). The data points fall below the measured correlation from all outbursts given by these authors and agree better when taking only the data of other failed outbursts in 2008 and 2009 into account. This behavior seems to indicate that the jet power is somewhat reduced in failed outbursts and hints at a different accretion geometry.

Figure 2.— ATCA 9 GHz flux as function of Swift/XRT 3–9 keV flux. Our 2013 data are shown with red diamonds, data from failed outbursts in 2008 and 2009 presented by Corbel et al. (2013) as black circles and black squares, respectively. The superimposed black line is the best-fit correlation from all archival data (containing full and failed outbursts, Corbel et al., 2013), the orange line is the best-fit to the observations during failed outbursts. Note that the error-bars on the 2013 data are smaller than the symbol size.

3. Spectral Modeling

3.1. Basic Fits

As shown in Fig. 3 all five observations show very similar spectral shapes in NuSTAR, with clear evidence of reflection features. To highlight these features, we fit each NuSTAR observation with a simple absorbed power-law, using only data between 4–6 keV, 8–10 keV, and 50–78 keV, i.e., ignoring the energy ranges where the strongest contribution from reflection features is expected. The residuals shown in Fig. 3 clearly indicate a strong line and Compton hump. The shape of the iron lines appears to be constant over all observations, while we see indications that the Compton hump is more significant in the high flux data.

Figure 3.— (a) Unfolded spectra of all five observations. Only NuSTAR/FPMA data are shown for clarity. Observation I is shown in red, observation II in blue, observation III in magenta, observation IV in orange and observation V in green. (b) Ratio residuals to a simple power-law fit. See text for details.

For the remainder of the paper we fit all Swift/XRT data between 0.8–10 keV and all NuSTAR data between 4–78 keV simultaneously, unless otherwise noted. To model the reflection component we add the reflionx model (Ross & Fabian, 2005), with its high-energy cutoff energy set to 500 keV. While this model was originally calculated for AGN spectra, it has been applied successfully in the literature to describe black-hole binaries (see, e.g., the discussion in Fabian et al., 2012). This model self-consistently describes the effects of reflection of an input power-law spectrum off an optically thick accretion disk, including the Compton hump and the fluorescent iron lines. For consistency we initially tie the photon index of the reflionx model to that of the primary power law (model M1). To allow for relativistic effects close to the black hole we fold the model components through the relconv convolution kernel (Dauser et al., 2010). We fix the outer radius of the accretion disk to , as at these distances relativistic influences are negligible and the reflected flux is expected to be low.

In XSPEC notation the model is represented as constant * tbabs * [powerlaw + relconv (reflionx)]. Here, constant takes into account small flux differences in the calibration of the different instruments. We quote all fluxes relative to NuSTAR/FPMA.

While the continuum and reflection parameters are expected to change over the outburst, some parameters can be assumed to stay constant. In our model, these include the Galactic absorption towards the source (), the black hole spin (), the inclination of the accretion disk () and the iron abundance in the disk (Fe/solar), expressed in units of solar iron abundance. To obtain the best statistics for these parameters, we fit all five observations simultaneously, requiring that these parameters are the same for all observations.

The absorption is described using an updated version of the tbabs model (Wilms, Allen & McCray, 2000), with the corresponding abundances and cross-sections from Verner et al. (1996). The fitted absorption column is only marginally higher than the expected Galactic absorption column of  cm (Kalberla et al., 2005) and is in good agreement with values used in literature for this source (e.g., Tomsick et al., 2009; Plant, O’Brien & Fender, 2014). We therefore do not add an additional absorption column intrinsic to the source.

As a first approach (model M1-q3, Table 7), we assume a standard Shakura-Sunyaev accretion disk (Shakura & Sunyaev, 1973), and we use an emissivity index () of 3 (Reynolds & Begelman, 1997). The data quality does not allow us to constrain the spin of the black hole at the same time as the inner radius of the accretion disk. We therefore fix the spin to , as measured by Miller et al. (2008). As described in Sect. 4.2, the choice of does not influence our results significantly.

Allowing the emissivity index to vary individually for each observation (model M1-qv, Table 8) improves the fit to for 1698 dof and results in a steeper emissivity for all observations but observation V, where it is fitted to . All other parameters do not change significantly.

The relconv model also allows us to use the “lamppost” geometry (M1-LP, Table 9), where the corona is assumed to be a point source on the spin axis above the black hole (Miniutti & Fabian, 2004). The main free parameter in this geometry is the height of the corona above the accretion disk plane and the illumination and emissivity index of the accretion disk is self-consistently calculated taking effects of general relativity into account (Dauser et al., 2010). This model also provides a small improvement above the M1-q3 model ( for 1698 dof) and the coronal height is fitted to be for all observations. All other parameters do not change significantly.

Including a soft black-body component in any of the models does not improve the fit quality significantly nor does allowing the cutoff energy to vary. The 90% lower limits on the cutoff energy are, in all observations,  keV. Using models not accounting for a Compton hump, Miyakawa et al. (2008) and Motta, Belloni & Homan (2009) find somewhat lower cutoff energies at similar luminosities (0.9–5.6 erg s between 2–200 keV). However, when including a reflection component, Miyakawa et al. (2008) do not find evidence for a cutoff at  keV at these luminosities. This is in agreement with results presented by Plant et al. (2014). The continuum in our data is therefore well described by a power-law, consistent with previous studies.

In all models (M1-q3, M1-qv, and M1-LP) we find an unphysically high iron abundance (, , and solar, respectively). In the literature, abundances of 1 or 2 times solar are typically assumed (Miller et al., 2008; Reis et al., 2008; Tamura et al., 2012; Allured et al., 2013; Plant et al., 2014). Forcing a lower iron abundance results in clearly worse fits, with strong residuals around the line energy. Using the xillver reflection model (García & Kallman, 2010) instead of reflionx does not improve the fit and requires an equally high or higher iron abundance.

3.2. More sophisticated modeling

3.2.1 Reflector sees a different continuum

The large iron abundance can be lowered and the statistically unacceptable values improved by using more complex models, going beyond the traditional power-law plus reflection model. The standard geometries assume that the corona is a point-source and uniform, but we have to expect that the geometry in reality is more complex. The simplest approach to describe a corona which is physically extended with a non-uniform temperature profile is to allow different photon indices for the observed power law continuum and the input spectrum to the reflionx reflection (model M2).

When fixing the emissivity index to (M2-q3), this model improves the value significantly by for five additional parameters over M1-q3. We show the best-fit parameters for this model in Table 2. We also apply the lamppost geometry (M2-LP) for which we give the best-fit values in Table 3. Both models give mostly similar results and a comparable quality of the fit. The evolution of the spectral parameters with time for both models is shown in Figure 4.

Parameter I II III IV V
Fe/solar
0.64 0.71 0.78 0.83 0.52
1.65 2.74 4.35 5.63 0.93
2124/1698
1.25
Table 2Best-fit parameters for emissivity index , spin and allowing for two different photon indices (M2-q3).
Parameter I II III IV V
Fe/solar
ccThe lower limit of is the ISCO at for an assumed spin of .
0.63 0.70 0.77 0.81 0.51
1.63 2.73 4.32 5.60 0.93
2103/1693
1.24
Table 3Same as Table 2 but for the lamppost geometry (M2-LP).
Figure 4.— Results of the spectral fit for models M2-q3 and M2-LP. Results of model M2-q3, i.e. with a fixed emissivity , are shown as black diamonds, while results for model M2-LP, i.e. using the lamppost geometry, are shown as red circles. The latter are shifted in -direction for clarity. (a) photon index of the primary continuum, (b) ionization parameter, (c) input photon index for the reflection component, (d) inner disk radius in .

We show the residuals for the M2-q3 model for all five observations in Figure 5. As can be seen, there is good agreement between all three instruments, though the NuSTAR data clearly dominate the statistics. Small systematic residuals at the lowest NuSTAR energy end can be attributed to calibration uncertainties. All five observations show very similar residuals and have a comparable quality of the fit.

Figure 5.— (a) Data and best-fit model for M2-q3 for observation IV, showing the reflection component in magenta and the power-law components in orange. Swift/XRT data are shown in green, NuSTAR/FPMA in red, and FPMB in blue. (b)-(f) Residuals in terms of model to data ratio of the best-fit model for observation I–V, respectively. Data were rebinned for clarity. See Table 2 for the model parameters.

The inner radius is highly unconstrained, with best fit values around for M2-q3 but close to the ISCO for M2-LP. Both models are marginally consistent with values around . Due to the large uncertainties and geometry dependence of the values, it is not clear if a truncation of the accretion disk is present or not. In the lamppost geometry the large uncertainties can be understood as being due to the large coronal height, which results in an emissivity index clearly below 3 between 3–100  (Vaughan et al., 2004; Dauser et al., 2010). Therefore, the inner parts of the disk contribute less to the reflection model and the inner radius cannot be well constrained.

We find very similar coronal heights around for each observation with large uncertainties. The height is completely unconstrained in observation V in the allowed range between 3–300 . We therefore conclude that we see no indication for an evolution of the corona over the outburst and that the corona seems to be located relatively far away from the black hole.

In the M2-q3 model the inclination is fitted to be ( in M2-LP). These values are in very good agreement with the limits on the orbital inclination so that no misalignment between the accretion disk and the orbital plane is necessary.

We also obtain similar results when allowing the emissivity index to vary (M2-qv). The best-fit emissivity indices are relatively flat, around 1.6–1.8 and the models indicate a non-truncated accretion disk. The other parameters do not change significantly. The fit statistics improve by for five additional degrees of freedom over the M2-q3 model, which corresponds to an -test false alarm probability of , see Table 10.

The reflection fraction given in Tables 2 and 3 is the ratio of the flux of the reflection component between 0.001–1000 keV to the flux of the primary unabsorbed power-law component between 0.1–1000 keV. While this implies extrapolation of the model far outside the fitting range, it captures the whole energy range used in the calculation of reflionx. The reflection fraction is correlated with the X-ray luminosity, as already indicated by the variable Compton hump strength shown in Figure 3. As the inner accretion disk radius seems to be constant, this indicates a change in coronal geometry where at higher flux more of the coronal emission is intercepted and reprocessed by the accretion disk.

The reflection fractions given in the tables are not directly comparable to the one given by Plant et al. (2014), as these authors use only the 4–10 keV energy band to calculate it for the outbursts between 2002–2008. In this energy band we measure a reflection fraction around 0.05, about a factor of 2–3 lower than Plant et al. (2014).

The photon index incident to the reflection component is very hard (), indicating a strongly photon starved Comptonization region (Haardt & Maraschi, 1991). Its difference to the photon index of the primary power law, , is relatively constant over the outburst in all models; . If this difference is due to the geometry of the corona, the corona seems to stay stable, even though the reflection fraction changes as a function of flux. We note, however, that the lamppost intrinsically assumes a point-like corona so that the different photon-indices we find here cannot directly be geometrically interpreted.

If we want to model an extended corona along the spin axis, perhaps corresponding to the extended base of a jet (Markoff, Nowak & Wilms, 2005), this can be done more self-consistently in XSPEC or ISIS by adding a second relativistically smeared reflection component, with a coronal height larger than the first component and with its photon index tied to the observed primary continuum (M2b-LP). That is, we require that the observed continuum is also reflected and add as additional free parameters the flux of its reflection component and the second lamppost height. The incident spectrum to the first reflector is understood to originate much closer to the black hole such that it is invisible to the observer. This model results in a good fit, with =1.214 which corresponds to an improvement for six additional degrees of freedom over the M2-LP model. While this is only a marginal improvement, the added self-consistency is important for the physical interpretation of the model.

Parameter I II III IV V
Fe/solar
0.63 0.69 0.77 0.84 0.47
1.65 2.73 4.34 5.62 0.94
2053/1691
1.21
Table 4Same as Table 2 but for the lamppost geometry and two reflection components whose input spectra originate from different heights (M2b-LP)

Table 4 shows the best fit values of this model. As in the other M2 models, the inner accretion disk radius is consistent with being at the ISCO. The inner reflection height, is fit to the minimal allowed value, , while the outer reflection height, , pegs at the upper limit, . Thus the model describes a very strongly elongated corona, and one would expect that intermediate heights also contribute to both the reflection and the observed primary continuum. Such a model, however, is not uniquely definable in ISIS or XSPEC as all reflectors and continua would be degenerate. We therefore take the two reflectors presented here as the best approximation to an elongated corona with varying power-law emission.

3.2.2 Secondary continuum component

In continuation of the idea that two different hard power-laws are present in the system, perhaps from gradients in the coronal temperature, we apply a model which consists of two power-law components, with only one being the input to the reflection component (M3). We tie the photon index of one power-law to the photon index of the reflection component. With respect to the models presented in the previous section (M2), we have another free parameter, the normalization of the second power-law component.

Parameter I II III IV V
Fe/solar
0.46 0.52 0.62 0.74 29.87
0.31 0.33 0.36 0.39 0.49
2.16 3.66 5.88 7.71 0.94
2072/1693
1.22
Table 5Same as Table 2 but for 2 power-law continua (M3-q3).

We again fit three different models: the first with the emissivity fixed at (M3-q3), the second allowing the emissivity index to vary (M3-qv), and finally using the lamppost geometry (M3-LP). Figure 6 shows the residuals for M3-q3, separately for each observation for clarity. Table 5 gives the best-fit values for M3-q3. We give two values for the reflection fraction: is calculated using only the first continuum, which has the photon index used for the reflection component. is calculated using the total observed flux from both continuum models.

All three models result in very comparable qualities of fit with /dof=1.22/1693 (M3-q3), 1.21/1688 (M3-qv), and 1.22/1686 (M3-LP). However, the relative strengths of the two continuum components depend on the assumed geometry. The lamppost model, in particular, gives very different results (all model parameters can be found in Tables 11 and 12). Additionally, in observation V, the first power-law normalization in all three models is consistent with , reducing this model to the M2 described in Sect. 3.2.1. In the M3-q3 model the second, non-reflected power-law contributes between 30–50% of the broad-band flux in observations I–IV.

Figure 6.— Same as Figure 5 but for model M3-q3. The power-law incident to the reflection model is shown in orange, the second power-law in blue. Residuals are shown in units of . The best-fit parameters are given in Table 5.

The best fit iron abundance is found to be between 2–2.5 the solar value, depending on the geometry. The inner radius of the accretion disk is again consistent with being close to the ISCO, especially in the model with a free emissivity index where the best fit values are below 20 . The differences between the two photon-indices are typically larger than in the previous model, with values around . Overall, this model confirms the previous results that we can obtain a reasonable iron abundance by using a more complicated continuum model and that the accretion disk is not significantly truncated. However, through the introduction of another free parameter, the parameters are less well constrained and the fit quality is not significantly improved.

3.3. Iron line complex

Parameter I II III IV V
Fe/solar
0.65 0.73 0.80 0.85 0.53
Eqw (FeK) [eV]
1.64 2.74 4.36 5.62 0.94
2009/1693
1.19
Table 6Same as Table 2 but adding an additional narrow Gaussian line at 6.4 keV (M2-q3-Fe).

In all previous fits we modeled the line self-consistently as arising from reflection off an accretion disk with constant ionization, as described by the reflionx model. However, close inspection of the residuals reveals that none of these models captures the shape of the line perfectly. We therefore add an ad-hoc narrow Gaussian component to the M2 models, with its energy fixed at 6.4 keV, the energy of neutral . This line could, for example, be produced further out in the disk, where we encounter near neutral iron and the influence of the relativistic effects of the black hole are negligible. With this addition, we find significantly better fits for all versions of the M2 model, i.e., when the photon indices between the continuum and reflector are independent.

We note that Plant, O’Brien & Fender (2014) do not see evidence for such an additional narrow component. However, their data lack the crucial coverage above 10 keV and therefore the reflection model is entirely driven by the iron line shape. When applying a model similar to their best-fit model using the lamppost geometry to our observation IV, and limiting the fitting range to below 10 keV, we obtain very similar results, most notably an ionization around and no residuals in the iron line band. However, this model clearly underpredicts the flux in the hard X-ray band, especially around the Compton hump.

As an example of a model with an additional Gaussian component, we give the best values for a fixed emissivity index of in Table 6 (M2-q3-Fe). The narrow core is fitted to an equivalent width around 20 eV in all observations and does not show a dependence on flux. Fits for a variable emissivity index (M2-qv-Fe) and the lamppost geometry (M2-LP-Fe), can be found in Tables 13 and 14, respectively. Note that a variable emissivity results in best-fit values consistent with .

As can be seen in Table 6, the inclination is higher than in our other models, particularly compared to M2b-LP and M3-q3. However, it is still consistent with being below as required by the lack of eclipses and consistent with all M2 models. See Section 4.2 for a more detailed discussion about the inclination. Furthermore, this is the only model where we find a significant truncation of the inner accretion disk around 30 . None of the other model parameters changes significantly.

4. Discussion

We have presented simultaneous spectral fits to five Swift/XRT and NuSTAR observations during the failed 2013 outburst of GX 3394 covering luminosities between 0.9–6% . All observations show a very hard power-law, with a photon index and clear evidence for reflection. We have shown that standard models, consisting of a power-law continuum and an additive reflection model fail to reproduce the data within sensible physical parameters. The data, thanks to the very high S/N, clearly indicate that the input to the reflection model needs to be different from the continuum emission observed directly. Our best fit solutions typically require that the inner radius of the accretion disk extends close to the ISCO ().

For comparison, we analyzed XMM-Newton data presented by Plant, O’Brien & Fender (2014) taken during the same outburst (between our observations IV and V; XMM-Newton ObsIDs 0692341201, 0692341301, and 0692341401). We used a similar annular extraction region as these authors with an inner radius of and an outer radius of to excise the heavily piled-up core. Applying the best-fit relxill model presented by Plant, O’Brien & Fender (2014) and fitting all three observations simultaneously results in an acceptable fit with /dof=1.25/5079. When applying model M2-q3, and fixing the secondary power-law and the ionization to the best-fit NuSTAR values, we find a very similar quality of fit with /dof=1.26/5081 and similar structures in the residuals. This similarity shows that the soft X-ray band-pass of XMM-Newton is not sufficient to constrain the complex accretion geometry, as the Compton hump is not covered and that at the same time our model is fully compatible with the XMM-Newton data.

Besides the input power-law to the reflector, the biggest difference between our models and the ones presented by Plant, O’Brien & Fender (2014) is that they find evidence for the presence of a cold disk thermal component. Such a component is often observed in GX 3394 in the hard state (see, e.g. Miller et al., 2006; Reis et al., 2008; Wilkinson & Uttley, 2009), but we do not find an improvement by adding it. Its absence is likely connected to the less sensitive XRT data compared to XMM-Newton as well as a degeneracy between the absorption column and the disk. This degeneracy is seen when describing the XMM-Newton data of Plant, O’Brien & Fender (2014) with the M2-q3 model, where we find slightly lower values of the absorption column ( cm compared to  cm).

We note that the calculated reflection fractions are all below unity. In a static geometry, the reflection fraction corresponds approximately to the solid angle covered by the reflector in units of , i.e., a reflection fraction of 1 would correspond to an infinite slab illuminated from above. We measure values below 0.5, which could indicate a truncation of the accretion disk at the inner radius. On the other hand, a outflowing corona would also result in a reduced reflection fraction, as the coronal radiation is beamed away from the accretion disk (Beloborodov, 1999).

The photon index of the observed primary continuum seems to show a hysteresis effect, with observation V showing a significantly softer spectrum than observations I and II, despite being much fainter. This hysteresis could be connected to the hysteresis observed in the radio/X-ray and NIR/X-ray correlation (Corbel et al., 2013; Russell et al., 2007) which might be related to different jet behavior between rising and decaying hard state observations. However, this hysteresis is typically observed in a full outburst, in which the hard states are separated by a soft or intermediate state, where we expect stronger changes in the accretion geometry.

With our complex corona models (M2, M2b, and M3), we find an iron abundance of typically 1.8 times solar, in line with previous work and as expected in LMXBs (e.g. Allured et al., 2013). The fit statistically constrains the iron abundance extremely well, but the value strongly depends on the model assumptions. For example, with a variable emissivity index (models M2-qv and M3-qv) we find an iron abundance around 2.5 times solar, while it drops to around 1.5 solar in all models when a narrow Gaussian line is included (e.g., M2-q3-Fe). The absolute value and the error bars are therefore model dependent and subject to systematic uncertainties not accounted for in the tables.

4.1. Accretion geometry

As discussed in Fabian et al. (2014), due to light-bending, the regions of the corona closer to the black hole contribute more irradiating flux on the accretion disk than regions further away, while the opposite is true for the primary observed continuum. A change in the coronal parameters with height will therefore result in an observed continuum with a different spectral index than the one incident to the reflector. This effect is most relevant if the corona extends close to the black hole where relativistic effects are strongest (Dauser et al., 2013).

We can best approximate this geometry by using model M2b-LP consisting of two coronae at different heights above the black hole with different photon indices, as presented in Table 4. We find that the inner corona originates very close to the black hole, and thus is subject to strong light bending effects. These effects prevent most of the flux from that part of the corona from reaching the observer directly, and we only see the reflected part.

We also find evidence for a complex shape of the line, which is clearly relativistically broadened with an additional narrow core, close to 6.4 keV. A detailed discussion of its shape is beyond the scope of this paper and will be presented in a forthcoming publication making use of Suzaku/XIS data with better spectral resolution (Tomsick et al., in prep.). The broadened component is constrained in our fits through the relconv smearing kernel. In the models without an extra component for the narrow core, the presence of a reflector within 100  is clearly required (see Table 3). Adding the narrow core moves the lower limit of the inner accretion disk radius out to about 20 .

For the faintest observation (V) all models indicate the possibility that the accretion disk is truncated. These values are only weakly constrained and strongly dependent on the assumed X-ray source geometry (see Tables 2 and 3). It is clear, however, that during observation V the source spectrum was different from the first four observations (see also Figure 4) with either a change in the inner accretion disk radius or the corona’s location and spectrum or a combination thereof.

4.2. Inclination and spin

All our models indicate an inclination in the range around . This value is significantly higher than found when modeling other observations with similar reflection models (Miller et al., 2004; Reis et al., 2008; Plant, O’Brien & Fender, 2014). Kolehmainen & Done (2010) find that inclinations give better fits in the high-soft state when fitting the disk continuum to measure the spin. Our result seems to reconcile the continuum fits with the reflection fits with respect to the disk inclination. All of these previous data, however, were taken during a full outburst, i.e., an outburst that followed the standard evolution through the high-soft state. The data presented here were taken during a failed outburst, which might have a different geometry.

Our models do not constrain the spin. We use throughout, as measured by Miller et al. (2004). However, as the inner radius is only weakly constrained and typically of the order of , lower spin values are completely consistent with our results. To test this, we set the spin to for the M2-q3 model and obtained basically identical fits (see Table 15).

5. Summary

While the combined NuSTAR and Swift data provide one of the best data-sets on GX 3394 in the low/hard state to date, we have shown that it is difficult to measure the inner truncation radius of the accretion disk precisely. The measured value depends strongly on the assumed geometry and emissivity profile of the accretion disk. However, we find no evidence for a strongly truncated disk, i.e., with an inner radius . Furthermore, our spectral fits clearly show that the continuum spectrum incident to the reflector is significantly different from the observed primary continuum. The spectrum reflected by the accretion disk is significantly harder, which is necessary to explain the relative strength of the Compton hump to the line. A lamppost geometry with changing spectral hardness as a function of coronal height seems to describe the observed spectra well, but can only be regarded as a crude approximation to the true physical geometry.

We would like to stress again that the data were taken during a failed outburst, during which the source did not switch into the soft state. It is currently unknown what the difference between failed and standard outbursts is, and how a transition to the soft state is triggered. Continued monitoring of GX 3394 and similar black hole transients is necessary to answer these questions and study if we can measure significantly different accretion geometries in these two types of outbursts.

We thank the anonymous referee for the very constructive and helpful comments. This work was supported under NASA Contract No. NNG08FD60C, and made use of data from the NuSTAR mission, a project led by the California Institute of Technology, managed by the Jet Propulsion Laboratory, and funded by the National Aeronautics and Space Administration. We thank the NuSTAR Operations, Software and Calibration teams for support with the execution and analysis of these observations. This research has made use of the NuSTAR Data Analysis Software (NuSTARDAS) jointly developed by the ASI Science Data Center (ASDC, Italy) and the California Institute of Technology (USA). JAT acknowledges partial support from NASA Swift Guest Investigator grant NNX13AJ81G and NNX14AC56G. SC acknowledges funding support from the ANR “CHAOS” (ANR-12-BS05-0009). We would like to thank John E. Davis for the slxfig module, which was used to produce all figures in this work.

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Appendix A Additional model parameters

Parameter I II III IV V
Fe/solar
0.48 0.54 0.59 0.64 0.42
1.63 2.72 4.26 5.49 0.92
2391.96/1703
1.405
Table 7Best-fit parameters for an emissivity index and spin (M1-q3).
Parameter I II III IV V
Fe/solar
0.52 0.58 0.63 0.68 0.43
1.62 2.71 4.25 5.48 0.93
2214.67/1698
1.304
Table 8Best-fit parameters for a free emissivity index (M1-qv).
Parameter I II III IV V
Fe/solar
0.49 0.55 0.60 0.65 0.43
1.63 2.71 4.25 5.51 0.92
2330.59/1698
1.373
Table 9Best-fit parameters for the lamppost geometry (M1-LP).
Parameter I II III IV V
Fe/solar
0.60 0.68 0.73 0.79 0.48
1.63 2.72 4.30 5.55 0.93
2077.77/1693
1.227
Table 10Best-fit parameters for a free emissivity parameter and untied photon indices (M2-qv).
Parameter I II III IV V
Fe/solar