ON THE ORIGIN OF THE NEAR-INFRARED EMISSION FROM THE NEUTRON-STAR LOW-MASS X-RAY BINARY GX 9+1^*

2.1.1. Chandra

GX 9+1 has been observed four times with Chandra. One of these observations (ObsID 6569) was done in continuous clocking mode and therefore does not provide useful imaging information. The properties of the remaining three observations are summarized in Table 1. The analysis of the observations was performed with CIAO 4.7. The observations were reprocessed using the chandra_repro script.

Table 1.  Chandra Observations of GX 9+1 Discussed in This Paper

ObsID	Detector	R.A.(J2000)	Decl.(J2000)	Uncertaintya	Remarks
717	ACIS-S/HETG	18h01m32.26s	−20°31' 479	06	Piled-up core
7030	HRC-I	18h01m32.15s	−20°31' 4595	$\leqslant 3^{\prime\prime}$	Large SIM offset
7031	ACIS-S	18h01m32.23s	−20°31' 4783	06	Piled-up core
⋯	⋯	18h01m32.15s	−20°31' 461	06	Curran et al. (2011)

Note.

^a90% confidence radius on the absolute astrometry.

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For the HRC-I observation (7030) we extracted an 800 × 800 pixel² image centered around GX 9+1, and ran the CIAO task wavdetect to obtain a source position. We note that during this observation the Science Instrument Module (SIM) was not in its usual position. Observations with a large SIM offset can have residual aspect offsets of up to 3'', which is substantially larger than the typical error in the Chandra absolute astrometry of $0\buildrel{\prime\prime}\over{.} 6$ (90% confidence) when the SIM is in its nominal position.⁵ For this reason, we do not consider the position obtained from this observation very accurate. The position is listed in Table 1, and is a close match (only 015 different) to the Chandra position reported by Curran et al. (2011). These authors used a position that they obtained through private communication, and they did not provide any details of the Chandra analysis. Nevertheless, it is plausible that their adopted X-ray position is derived from ObsID 7030, and therefore, that their adopted positional uncertainty (06) underestimates the actual uncertainty.

In the ACIS-S observation 7031 the image of GX 9+1 was heavily distorted due to a strongly piled-up core. While wavdetect cannot be used to obtain a source position in such a case, the deep and well-defined piled-up hole in the center of the source's image can still be used to obtain an accurate visual estimate of the source position. Since the observation was done with the nominal SIM offset, we assume a positional uncertainty of $0\buildrel{\prime\prime}\over{.} 6$. The source position is listed in Table 1 and differs from the one obtained from observation 7030 by more than 2''; the two positions are consistent, though, mainly due to the large error in the absolute astrometry of the latter.

Although the HETG was used during observation 717, the (zero-th order) image of GX 9+1 was still heavily distorted by pile-up. In this case we used the CIAO tool tg_findzo, which locates the position of the zero-th order centroid by finding the intersection of one of the grating arms with the detector readout streak. Like for observation 7031, we assume a positional uncertainty of $0\buildrel{\prime\prime}\over{.} 6$. The position we obtain with this tool (see Table 1) is consistent with that obtained from observation 7031.

2.1.2. RXTE/ASM and MAXI Light Curves

We constructed a long-term light curve of GX 9+1 from publicly available RXTE/ASM (Levine et al. 1996) and MAXI (Matsuoka et al. 2009) data. For the MAXI data we used the 4.0–10.0 keV band, since the data in 2.0–4.0 keV band appeared to be affected by calibration issues after MJD ∼56,200. To match the MAXI band as closely as possible, we used data in the 3.0–12.1 keV band for the ASM. Following van den Berg et al. (2014), we removed data points with large uncertainties ($\mathrm{ctr}/{\sigma }_{\mathrm{ctr}}\lt 20$, with ${\sigma }_{\mathrm{ctr}}$ the error on the count rate ctr). The count rates from both instruments were normalized to those of the Crab, in the selected energy bands. For MAXI we divided the count rates by an additional factor of 1.2, to match the count rates from the ASM around MJD 55,000–55,500. Finally, to reduce some of the scatter in the light curve, we rebinned the data in time by a factor of seven. The resulting light curve is shown in Figure 1. A strong long-term variation with a timescale of ∼9.5 years is clearly visible. The short vertical lines in Figure 1 indicate the times of the NIR observations analyzed and/or discussed in this paper.

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For this work we obtained NIR imaging and spectroscopy during four runs with the 6.5 m Magellan Baade Telescope in Las Campanas, Chile. Table 2 gives a summary of the runs, while more details of the observations and the data reduction are given below.

Table 2.  NIR Observations of the GX 9+1 Field Reported in This Paper

Epoch	Date	MJDa	Instrument	${T}_{\exp }$	Seeing
	(UTC)	(UTC)		(s)	('')
1b	2010 Mar 29	55284.40076	SOFI	540	1.4
2-a	2010 Jul 25	55402.05384	PANIC	540	0.9
2-b	2010 Jul 26	55403.00737	PANIC	540	0.55
3	2012 May 1	56048.36185	FIRE	3614	0.45
4	2012 Aug 8	56146.97466	Fourstar	707	0.9
5-a	2015 Apr 5	57117.35880	FIRE	4217	0.4
5-b	2015 Apr 6	57118.36038	FIRE	4819	0.4

Notes.

^aModified Julian Date at the midpoint of the observation. ^bData retrieved from the ESO archive. More details can be found in Curran et al. (2011).

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2.2.1. PANIC Imaging

2.2.2. FourStar Imaging

2.2.3. FIRE Spectroscopy

The estimate of d = 5 kpc that was adopted by Iaria et al. (2005) was chosen to lie in between the values that follow from two extremes in N_H. In their best-fitting model to the GX 9+1 BeppoSAX spectra, N_H is as low as $(8\pm 1)\times {10}^{21}$ cm⁻². Using the Taylor & Cordes (1993) model for the spatial distribution of the ionized hydrogen in the Galaxy, combined with an assumed ionized-hydrogen fraction of 10%, Iaria et al. estimated that the corresponding distance is 4.4 ± 1.3 kpc. Alternative modeling of the BeppoSAX spectra at especially the lower energies, resulted in an N_H that is almost two times higher. A higher column density was also reported by others; White et al. (1988) derived ${N}_{{\rm{H}}}\approx 1.5\times {10}^{22}$ cm⁻² or even higher, and more recently, Valencic & Smith (2015) found ${N}_{{\rm{H}}}=1.24(5)\times {10}^{22}$ cm⁻². The distance estimate increases accordingly, to about 6.4 ± 1.9 kpc for ${N}_{{\rm{H}}}=1.5\times {10}^{22}$ cm⁻² in the Taylor & Cordes model (Iaria et al. 2005).

Using more recent maps of the Galactic extinction to turn N_H into a distance, we find relatively small distances for the lower limit of ${N}_{{\rm{H}}}=(8\pm 1)\times {10}^{21}$ cm⁻², viz. 3.7 ± 0.3 kpc (based on the Drimmel et al. 2003 map for the optical extinction A_V), and 2.1 ± 0.3 kpc (for the Schultheis et al. 2014 $E(J-{K}_{s})$ maps⁷ ). We used Nishiyama et al. (2008, 2009) to convert the NIR extinction to the V-band extinction (${A}_{V}:\,{A}_{J}:\,{A}_{{K}_{s}}\,=1:\,0.188:\,0.062$), and ${N}_{{\rm{H}}}=1.79(3)\times {10}^{21}\,{A}_{V}$ cm⁻² (Predehl & Schmitt 1995). Valencic & Smith (2015) and Güver & Özel (2009) derived higher ${N}_{{\rm{H}}}/{A}_{V}$ ratios, viz. ${N}_{{\rm{H}}}\,=2.08(9)\times {10}^{21}\,{A}_{V}$ cm⁻² and ${N}_{{\rm{H}}}=2.21(9)\times {10}^{21}\,{A}_{V}$ cm⁻², respectively. The distance to GX 9+1 based on these relations, is even smaller: using Güver & Özel (2009), we find values down to 3.3 ± 0.3 kpc (Drimmel) and 1.7 ± 0.2 kpc (Schultheis). These estimates place GX 9+1 in front, or at most on the near edge, of the Galactic bulge. However, the concentration of many bright X-ray binaries—including GX 9+1—in the direction of the bulge, makes it plausible that many are actually located in the bulge. This implies a conservative lower limit of $d\approx 4\,\mathrm{kpc}$ according to the Galaxy model by Picaud & Robin (2004). This consideration does not put a firm constraint on the distance to any individual X-ray binary, but it does make these small distances for GX 9+1, and therefore low column densities, less likely.

Another argument against a small distance comes from comparing the X-ray properties of GX 9+1 with those of the transient NS-LMXB XTE J1701–462. This system has a distance estimate (8.8 ± 1.3 kpc, Lin et al. 2009a) obtained from two type I radius expansion bursts. During the decay of its 2006/2007 outburst it displayed X-ray behavior quite similar to GX 9+1, i.e., it traced out tracks in its color–color (CDs) and hardness-intensity diagrams (HIDs) that have shapes similar to those of GX 9+1. The closest resemblance between the CD/HID tracks of GX 9+1 (Fridriksson 2011) and XTE J1701–462 (Lin et al. 2009b; Homan et al. 2010) occurs for a bolometric luminosity range of the latter of about $(6\mbox{--}18)\times {10}^{37}$ erg s⁻¹ (see Figures 3 and 5 in Lin et al. 2009b). Given the 0.12–18 keV flux reported by Iaria et al. (2005) (∼2.0 × 10⁻⁸ erg cm⁻² s⁻¹), a distance of $\lesssim 4\,\mathrm{kpc}$ would imply a luminosity of $\lesssim 3.8\times {10}^{37}$ erg s⁻¹ for GX 9+1. Such low values are at odds with the luminosity suggested by the analogy with XTE J1701–462.⁸

An N_H of $1.5\times {10}^{22}$ cm⁻² gives a distance of ∼7 kpc (Drimmel) or 5.5 kpc (Schultheis) when using Predehl & Schmitt (1995), or 4.9 kpc (Drimmel) or 3.3 kpc (Schultheis) when using Güver & Özel (2009). Except for the latter estimate, this is more in line with a bulge origin of GX 9+1.

High mass accretion rates (∼10⁻⁹–${10}^{-8}\,{M}_{\odot }$ yr⁻¹) are required to power the most luminous NS-LMXBs, which are thought to be accreting up to ∼0.5 ${L}_{\mathrm{edd}}$ (for the bright atolls) or even close to or above the Eddington limit (Z sources). It has been suggested that the mass donors in these systems are evolved stars, whose evolutionary expansion upon ascent of the giant branch drives the high mass transfer rate (Taam 1983; Webbink et al. 1983). For the persistent Z sources with known orbital periods (P_b) this is indeed a plausible scenario: Sco X-1, Sco X-2, Cyg X-2, and GX 13+1 have orbital periods between ∼19 hr and ∼25 day (Gottlieb et al. 1975; Cowley et al. 1979; Wachter & Margon 1996; Iaria et al. 2014), which is too long for a Roche–lobe-filling main-sequence star. On the other hand, the (tentative) orbital periods of the bright atolls Ser X-1 (∼2 hr; Cornelisse et al. 2013), GX 9+9 (4.2 hr; Hertz & Wood 1988), and 4U 1735–44 (4.7 hr; Corbet et al. 1986) are in the expected range for a main-sequence donor. Similarly, the estimated absolute K_s magnitudes (${M}_{{K}_{s}}$) of the NIR counterparts to GX 3+1 and 4U 1705–44 (a source that is often as bright as the other bright atolls) exclude that the neutron star is fed by a late-type giant (van den Berg et al. 2014; Homan et al. 2009). This implies that other scenarios must be invoked to explain the high accretion rate in these systems (see e.g., Verbunt & Zwaan 1981), although the distinction in orbital period between Z sources and bright atolls cannot be that straightforward. With ${P}_{b}\approx 21\,\mathrm{hr}$ (Jones & Watson 1989), the luminous dipping atoll source 4U 1624–49 likely hosts an evolved star. Conversely, with an estimated ${M}_{K}\approx +2.9$ (Jonker et al. 2000) in the non-flaring state, the Z-source GX 17+2 is far too faint to allow a giant donor if the assumed distance of ∼7.5 kpc is correct (see also Callanan et al. 2002).

Evidently, the distance to GX 9+1 is poorly determined as a result of uncertainties in N_H, the Galactic distribution of the absorbing material, and the relation between N_H and A_V. However, none of the combinations for N_H, A_V, and d described above predict an absolute K_s magnitude of GX 9+1 that is less than ${M}_{{K}_{s}}=1.4$. For example, for d = 4 kpc (the minimum plausible distance) and ${N}_{{\rm{H}}}=8\times {10}^{21}$ cm⁻², ${M}_{{K}_{s}}\approx 3.3$, while for $d=8.3\,\mathrm{kpc}$ (the maximum distance according to the Taylor & Cordes model) and ${N}_{{\rm{H}}}=1.5\times {10}^{22}$ cm⁻², ${M}_{{K}_{s}}\approx 1.4$ (the choice of ${N}_{{\rm{H}}}/{A}_{V}$ ratio has an effect of $\lesssim 0.1$ mag). Like in most bright atolls, a giant secondary for GX 9+1 is therefore excluded, as giants with spectral types of G0 or later have ${M}_{{K}_{s}}\lesssim -0.45$ (Bessell & Brett 1988; Ostlie & Carroll 2007) and are therefore brighter than GX 9+1 in the K_s band. Main-sequence secondaries of spectral type G0 to M5 have ${M}_{{K}_{s}}=3.0\mbox{--}8.4$.⁹ In the K_s band, an M5 dwarf would therefore contribute only ∼1% of the light at most, if GX 9+1 would have ${M}_{{K}_{s}}\approx 3.3$. As a result, there is no hope of detecting its Na I absorption lines at 2.206 μm and 2.209 μm or its ¹²CO bandhead at 2.294 μm (the strongest features in this wavelength range; Rayner et al. 2009) in our spectra, which have a signal-to-noise ratio $S/N\approx 25$ around 2.1–2.2 μm, and $S/N\approx 5$ around 2.29 μm. Even a G0 or K0 dwarf would be difficult to detect: their strongest absorption features in the K_s band (apart from Br γ) have a depth of at most ∼10% below the continuum, so even if such a star would dominate the K_s-band emission, the depth of these lines would at most be similar to the 3σ noise level. Our non-detection of any spectral features other than the Br γ emission line is therefore consistent with the secondary being a late-type dwarf.

Synchrotron emission and thermal emission can both contribute to the NIR spectra of luminous NS-LMXB binaries. The dominant emission process can be inferred from the spectral slope, i.e., the index α if the spectra are written as ${F}_{\nu }\propto {\nu }^{\alpha }$ with F the flux and ν the frequency.

In systems where accreted matter is carried away from the system via a jet, synchrotron emission from the jet is detected in the radio and, in some cases, all the way to the NIR/optical. The signature characteristic of the optically thick part of a steady jet is the flat-spectrum ($\alpha \approx 0$) radio emission. Emission from the optically thin inner regions of the jet can be significant at higher frequencies, and produces a distinctive negative spectral index ($\alpha \lt 0$). For example, millisecond X-ray pulsars and atolls that are less luminous than GX 9+1 but have ${L}_{{\rm{X}}}\gtrsim {10}^{36}$ erg s⁻¹ (Russell et al. 2007) display such red NIR spectra. For most NS-LMXBs it is unclear at which frequency the break between optically thick and thin synchrotron emission occurs. In 1RXS J180408.9–342058, the outburst NIR/optical emission at frequencies as high as the SDSS r band showed a flat spectrum when the source was in an X-ray hard state (Baglio et al. 2016). For 4U 0614+091 the break lies in the mid-IR (Migliari et al. 2010), with the optically thin component declining toward the NIR, at which point it is dominated by thermal emission.

In cases like 4U 0614+091, or when a jet is absent to begin with, thermal emission from an X-ray-heated or viscously heated accretion disk, or from the (possibly X-ray-heated) secondary, gives rise to a positive α. Specifically, emission dominated by X-ray reprocessing results in $0.5\lesssim \alpha \lesssim 2$, whereas for a viscously heated disk the expected α is 1/3 or 2 (Frank et al. 1992; Hynes 2005; Russell et al. 2007). With the exception of GX 17+2 (Harrison et al. 2011), thermal emission typically dominates the NIR spectra of the Z sources (Russell et al. 2007; Harrison et al. 2014), all of which have been detected as radio-jet sources¹⁰ (Fender & Hendry 2000). Emission from an irradiated disk can also explain the NIR spectrum of the two luminous atolls 4U 1705-44 and GX 3+1 (Homan et al. 2009; van den Berg et al. 2014), for which a radio jet has never been detected.

To uncover the origin of the NIR emission in GX 9+1, we have fitted the dereddened FIRE spectrum with a power-law shape (see Figure 4). Taking the suggested range in N_H at face value, we find that the spectral index is poorly constrained; the possible range in ${N}_{{\rm{H}}}/{A}_{V}$ ratios only makes it worse. Fits to the spectrum that is dereddened using the Nishiyama et al. (2009) extinction law, give $\alpha \approx -0.40\pm 0.12$ for ${N}_{{\rm{H}}}=8\times {10}^{21}$ cm⁻², and $\alpha \approx 0.87\pm 0.16$ for ${N}_{{\rm{H}}}=1.5\times {10}^{22}$ cm⁻² for the Predehl & Schmitt (1995) ${N}_{{\rm{H}}}/{A}_{V}$ ratio.¹¹ For the Güver & Özel (2009) ratio, the spectral index is smaller, viz. $\alpha \approx -0.65\pm 0.12$ and $\alpha \approx 0.32\pm 0.15$ for the low and high N_H value, respectively. The Nishiyama NIR extinction law is appropriate toward the Galactic center. Since GX 9+1 is located about 10° away from this direction, we have also considered the Cardelli et al. (1989) extinction law. The effect is to increase the values of α (see the last column in Table 4).

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Table 4.  Results for the NIR Spectral Index α

NH	AV	α (N09)	α (CCM89)
(cm−2)
8 × 1021	4.5 (PS)	−0.40 ± 0.12	−0.08 ± 0.13
	3.6 (GO)	−0.65 ± 0.12	−0.38 ± 0.12
$1.5\times {10}^{22}$	8.4 (PS)	0.87 ± 0.16	1.56 ± 0.18
	6.8 (GO)	0.32 ± 0.15	0.9 ± 0.1

Note.

Summary of the values of the spectral index α that result from fits to the FIRE spectrum of GX 9+1. The spectrum was dereddened using different assumptions about N_H, ${N}_{{\rm{H}}}/{A}_{V}$ (PS—Predehl & Schmitt 1995, GO—Güver & Özel 2009), and the NIR extinction law (N09—Nishiyama et al. 2009, CCM89—Cardelli et al. 1989).

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As discussed in Section 4.1, we consider the lower N_H values less likely as they imply a rather small distance and low X-ray luminosity for GX 9+1. If the actual N_H toward GX 9+1 is indeed on the high end of the range considered, the positive slope of the NIR spectrum of GX 9+1 points at thermal emission. Given the uncertainties in the extinction law and ${N}_{{\rm{H}}}/{A}_{V}$ ratios, we refrain from trying to distinguish between viscous heating and heating by X-ray reprocessing. The positive slope is inconsistent with a dominant contribution from jet synchrotron emission in this wavelength region. In this respect, GX 9+1 is similar to the other two bright atolls and most Z sources that have been studied in the NIR, which also have NIR spectra with positive slopes. For GX 9+1 and the other bright atolls, there is no indication for the presence of a strong jet given that these sources have not been detected at radio wavelengths (Berendsen et al. 2000). This is not surprising as jets are commonly associated with NS-LMXBs that are in relatively hard X-ray spectral states. The bright atolls, on the contrary, are typically found in an X-ray–soft state. Therefore, we can also turn the argument around: the assumption that there is no jet in GX 9+1, implies that α must be positive. This can be used as another argument in favor for the higher N_H values toward the system.

If the thermal NIR emission is mainly coming from the outer disk, where X-ray heating dominates over viscous heating, there should be a connection between the K_s-band luminosity, the X-ray luminosity, and the orbital period (which sets the size of the disk). The existence of such a correlation has been demonstrated by Revnivtsev et al. (2012), analogously to the work by van Paradijs & McClintock (1994) for the case of the optical emission of X-ray binaries. We have used their empirical formula to constrain the orbital period of GX 9+1 based on its X-ray luminosity and estimated absolute K_s magnitude. We assume that ∼70% of the X-ray luminosity in the 0.12–18 keV band is emitted in the 2–10 keV band¹² , for which Revnivtsev et al. derived their relation. The resulting range is not very restrictive: for d = 4 kpc and ${N}_{{\rm{H}}}=8\times {10}^{21}$ cm⁻² we find ${P}_{b}\approx 1.0\,\mathrm{hr}$, whereas $d=8.3\,\mathrm{kpc}$ and ${N}_{{\rm{H}}}=1.5\times {10}^{22}$ cm⁻² give ${P}_{b}\approx 4.0\,\mathrm{hr}$. Again, the choice of ${N}_{{\rm{H}}}/{A}_{V}$ ratio has a small (≲5%) effect. Follow-up photometric monitoring of the NIR counterpart may reveal the actual orbital period of GX 9+1. The long-term variation in the X-ray light curve that is clearly visible in Figure 1 is unlikely to be related to the orbit but could reflect very-low frequency noise or solar-like magnetic-activity cycles (Durant et al. 2010; Kotze & Charles 2010)