Exploring the Interstellar Medium Using an Asymmetric X-Ray Dust Scattering Halo

SWIFT J1658.2−4242 is an X-ray transient whose detection was first reported on 2018 February 16 in Swift/BAT (Barthelmy et al. 2018; D'Avanzo et al. 2018; Lien et al. 2018). It was also detected by INTEGRAL on 2018 February 14 (Grebenev et al. 2018; Grinberg et al. 2018). Lien et al. (2018) refined the analysis of the Swift/XRT data and reported the source coordinates being R.A. = 16^h58^m1264, decl. = −42°41'544, with the 90% uncertainty being 16. This position corresponds to the Galactic coordinates l = 343.25153, b = +0.05387, indicating that the source should be in the Galactic plane, at an angular separation of 16.693° from Sgr A^⋆. They also found that the Swift/XRT spectrum of SWIFT J1658.2−4242 was well fitted by an absorbed power-law model, with the photon index being 1.7 ± 1.5 and a large neutral hydrogen column density for the X-ray absorption: N_H,abs = (1.9 ± 0.5) × 10²³ cm⁻². These spectral properties were also confirmed by Beri et al. (2018) using an AstroSat observation of 20 ks exposure time on 2018 February 20. They found that the photon index was 1.76 ± 0.06 and N_H,abs = (1.6 ± 0.2) × 10²³ cm⁻².

Russell et al. (2018b) reported radio observation of the source on 2018 February 17 using Australia Telescope Compact Array (ATCA). They found that the source position in the radio band was R.A. = 16^h58^m12700 (±0.004), decl. = −42°41'5609 (±0.25). This radio position is consistent with the X-ray position. Russell et al. (2018a) reported optical observations between 2018 February 22 and 25 in the SDSS i and r bands, using a 1 m telescope in the Las Cumbres Observatory. An optical source was detected at the radio position, with the i band AB magnitude being 19.07 ± 0.06 mag, which was the only source within 8 arcsec of the radio source. However, no significant optical variability was found in this optical source during the X-ray outburst of the transient, so they concluded that this optical source was likely to be a foreground star, rather than being the true optical counterpart.

Most recently, Xu et al. (2018) reported results from a full spectral-timing analysis of 33.3 ks NuSTAR exposure on 2018 February 16. They found that the broadband X-ray continuum could be well fitted by a cutoff power law plus a Compton reflection. In their best-fit model 4, they reported N_H,abs = (1.80 ± 0.08) × 10²³ cm⁻², the photon index was 1.63 ± 0.02, and the coronal temperature was 22 ± 1 keV. The black hole spin was found to be larger than 0.96. The binary system was found to have a large inclination angle of ${64}_{-3}^{+2}$°, which was consistent with the detection of dips in the NuSTAR X-ray light curve. The N_H,abs during the dips increased to ${1.00}_{-0.07}^{+0.08}$ × 10²⁴ cm⁻². Type C quasi-periodic oscillation signals were also detected in the X-ray power spectrum. All the above results suggest that SWIFT J1658.2−4242 should be a typical black hole X-ray binary in the hard state and is viewed at a high inclination angle.

Dust grains in the interstellar medium (ISM) can scatter X-ray photons with small scattering angles. This phenomenon was predicted half a century ago (Overbeck 1965; Trümper & Schönfelder 1973). The scattering can be calculated by the Mie scattering theory. Provided that there is an X-ray pointlike source and a dust layer in front of it, dust scattering will create a small halo around the source (Mathis & Lee 1991). There are also calculations about the time delay of the scattered photons in the halo due to different light paths from those photons coming directly from the line of sight (LOS) (Xu et al. 1986). Since the first observational discovery of a dust scattering halo around the source GX339-4 by the Einstein satellite (Rolf 1983), this effect has been repeatedly observed in several tens of X-ray sources (e.g., Predehl & Schmitt 1995; Xiang et al. 2005; Valencic & Smith 2015). The timing effects of dust scattering have also been observed in several X-ray sources, with short bursts of X-ray emission, therefore showing ring-like structures around them (e.g., Beardmore et al. 2016; Heinz et al. 2016; Vasilopoulos & Petropoulou 2016), as well as sources undergoing eclipses showing typical eclipse light curves (Jin et al. 2018).

It was also noticed long time ago that because of the existence of a halo, the radial profile of a pointlike X-ray source should be different from the standard point-spread function (PSF) of an instrument (Predehl et al. 1992). However, dust scattering opacity is often much smaller than the X-ray absorbing opacity; thus, it was often ignored in previous X-ray spectral studies. For example, dust scattering opacity is not considered in the widely used xspec (v12.10.1, Arnaud 1996) X-ray absorbing models such as phabs and tbabs (Wilms et al. 2000). Corrales et al. (2016) reported that ignoring the effects of dust scattering opacity could lead to an overestimate of N_H,abs by a baseline level of 25%. Smith et al. (2016) pointed out that a proper treatment of the dust scattering should consider both the type of the dust grains and the source extraction region. Jin et al. (2017) showed that for the X-ray binary AX J1745.6−2901 in the Galactic Center (GC) with N_H,abs ∼ 3 × 10²³ cm⁻² (Ponti et al. 2018), dust scattering created severe spectral biases in terms of both spectral shape and flux. These biases depended on the shape of the source extraction region and the instrumental PSF. It is also clear that dust scattering significantly affect the spectra of most (likely all) sources at the GC (C. Jin et al. 2019, in preparation).

Because SWIFT J1658.2−4242 lies in the Galactic plane and its N_H,abs is on the order of 10²³ cm⁻², X-ray dust scattering in its LOS can be strong and complex. Therefore, it is both important and interesting to study the X-ray dust scattering halo and determine whether it can lead to severe spectral biases. In this paper, we use the latest Chandra and XMM-Newton observations to study the properties of the X-ray dust scattering halo around SWIFT J1658.2−4242, and explore the significance of the spectral biases. The paper is organized as follows. We first describe the observation and data reduction in Section 2, and then present detailed study of the dust scattering halo in Section 3. The analysis of the halo asymmetry is presented in Section 4. Then in Section 5 we discuss the foreground ISM distribution, the source distance, the azimuthal asymmetry of the halo shape, and the spectral biases. The final section summarizes the main conclusions of our study.

We used the Chandra Interactive Analysis of Observations (CIAO) software (v4.10, Fruscione et al. 2006) and the latest Calibration Data Base (CALDB, v4.7.9) to perform the data reduction. First the chandra_repro script was used to reprocess the data. Then we followed the thread on the Chandra website to remove all the background flaring periods using the deflare script.⁵ This resulted in a new event file with totally 28.9 ks clean exposure time.

Then the acisreadcorr script was used to remove artificial features due to the readout streak produced by out-of-time events. To ensure a clean removal of these features, the streak width was chosen to be 5 pixels, instead of the default value of 2 pixels, as shown in Figure 1. The remaining out-of-time events from the halo were negligible compared to the primary halo emission even at large radii, so that no extra steps were taken to remove them. Because the source was on the back-illuminated ACIS-S3 CCD chip, we excluded the data on the two nearby front-illuminated CCD chips (i.e., ACIS-S2 and S4) because of their different background count rates. Then the fluximage script was used to create flux image and exposure maps. The wavdetect script was used to perform point-source detection within the field of view. The off-axis angle of SWIFT J1658.2−4242 relative to the optical axis was found to be 0.391 arcmin during the observation. We extracted the light curve of SWIFT J1658.2−4242 and found that during this Chandra observation the source did not show any flip-flop behavior, as seen in XMM-Newton observations (see Section 2.2); thus, it was not necessary to exclude any data for the variability issue. By using the pileup_map script, we found that the central circular region around the source with 2.5 arcsec radius had more than 1% pile-up level.

Zoom In Zoom Out Reset image size

Moreover, bright features along the HETG arms that arise from the dispersion of source photons could seriously contaminate the primary halo intensity. We visually inspected the counts image of the chip and masked out large areas around these features to minimize their contamination, as shown in Figure 1. Then the funtools in ds9 (v7.5, Joye & Mandel 2003) was used to extract values within a set of annuli around the source in order to obtain the radial profile. This azimuthal averaging also helps to smear out remaining contaminations.

Similar to Jin et al. (2017, 2018), we studied the halo profile in three energy bands: 2–4, 4–6, and 6–10 keV. This band division could reveal the energy dependence of the halo, meanwhile keeping enough signal-to-noise ratio (S/N) in every band. Then we calculated the spectral-weighted effective energy in every band (Table 1), which was used to calculate the halo model in that band. The central 20 arcsec of the PSF was obtained from simulations using the Chandra online ChaRT PSF simulator. The PSF wing outside 20 arcsec was calculated using the analytical formulas in Gaetz (2010). These PSF profiles were added to the radial profile modeling and to be convolved with the dust scattering halo.

We used the XMM-Newton (Jansen et al. 2001) Science Analysis Software (SAS, v17.0.0, Gabriel et al. 2004), especially the Extended Source Analysis Software (ESAS; Snowden & Kuntz 2014), and the latest calibration files to perform the data reduction. Because SWIFT J1658.2−4242 was bright enough to cause severe pile-up, the EPIC-pn camera and one MOS camera were put in the Timing mode, while the other MOS camera was operating in the full frame mode in order to detect the dust scattering halo. In this work about the dust scattering halo, we only made use of the MOS data in the imaging mode. The data reduction was conducted as follows. First, the odfingest, emchain, and mos-filter scripts were run in sequence to reprocess the data and obtain a new event file. Then both the source and background light curves were extracted to check the high background periods and source variability. The source showed intriguing flux jumps and dips during the XMM-Newton observations. These phenomena are not related to the topic of this work (see D. Bogensberger et al. 2019, in preparation for detailed analysis), but they may cause some variability in the halo shape (Jin et al. 2018). Therefore, we excluded all the dips, and carefully chose time intervals to avoid flux jumps in order to ensure the stability of the halo. Because the source was very bright (F_{2–10 keV} ∼ 10⁻⁹ erg cm⁻² s⁻¹ observed during all the observations in Table 1), S/N was not a problem for the XMM-Newton data even for a short exposure time of only a few kiloseconds.

In OBSID: 0805200201, the source showed a flip-flop behavior appearing as high-flux and low-flux platforms, the flux difference between them was ≳20% in 2–10 keV. We decided to extract halo profiles from the two platforms separately. The first time interval contained 7.9 ks clean exposure in the high-flux platform, and the second interval contained 8.7 ks clean exposure in the low-flux platform. In OBSID: 0805201301, the first 11 ks and the interval within 18–21 ks showed significant flux drops of ∼10% in 2–10 keV, while the final 13 ks showed enhanced variability of ∼10% in the same band; thus, these periods were excluded, and only the remaining 25.0 ks clean exposure was used. In OBSID: 0811213401, the first 26 ks and last 3 ks contained dramatic flux jumps of more than a factor of 1.5 in 2–10 keV, so these periods were excluded, and the total clean exposure left for the halo extraction was 31.5 ks (see Table 1, light curves and detailed spectral-timing analysis can be found in D. Bogensberger et al. 2019, in preparation). There was no flip-flop behavior in the remaining two XMM-Newton observations, so all the data were used.

For the clean data within these time intervals, we used mos-spectra and mos_back scripts to create counts images, flux images, and exposure maps in the 2–4, 4–6, and 6–10 keV bands. Then the cheese script was run to detect serendipitous point sources in the field of view to be masked out. Finally, the funtools in ds9 was used to obtain the radial profiles of SWIFT J1658.2−4242 in the three energy bands. Within each energy band, we calculated the spectral-weighted effective energy (Table 1), which was used as input for the halo modeling and PSF production. As in Jin et al. (2017, 2018), we used the Ghizzardi (2002) analytical PSF profiles for the halo model convolution and radial profile analysis.

Both Chandra ACIS and XMM-Newton MOS observed a strong halo around SWIFT J1658.2−4242, but the MOS data were heavily contaminated by the pile-up effect, so we present the results from MOS in Appendix A, and used only the ACIS data of much higher angular resolution for more detailed halo profile analysis. First we created the flux image of SWIFT J1658.2−4242 in ACIS-S in 0.5–7 keV band (the default "broad" energy band in the fluximage script), as shown in Figure 2. The source does not appear exactly like a point source; instead. it is surrounded by bright pixels with the intensity decreasing toward large radii. This is a clear indication for the existence of a strong halo. Azimuthal variation of the halo intensity is also apparently visible in the figure, which we discuss in more detail in Section 4.

Zoom In Zoom Out Reset image size

Then we extracted the azimuthal-averaged radial profiles from 2 to 4, 4 to 6, and 6 to 10 keV bands separately. Because there was no archival Chandra observation on the same position of SWIFT J1658.2−4242 before its outburst, it was not possible to directly measure the X-ray background, including both X-ray diffuse emission and detector background underneath the halo of SWIFT J1658.2−4242, as was done for another transient AX J1745.6−2901 in the GC (Jin et al. 2017). Therefore, we assumed a flat background underneath the halo profile. The background flux was derived from the average intensity outside the radius where the radial profile becomes flat, which is about 220, 150, and 120 arcsec in 2–4, 4–6, and 6–10 keV band, respectively (Figure 3). The subtraction of this background has little effect on the radial profile within ∼30 arcsec, where the source is more than one order of magnitude brighter than the background. However, because of the limitation of background subtraction and source brightness, the halo profile is significantly detectable only at ≲200 arcsec. Thus, it is not possible to check the existence of an extended halo wing as seen in AX J1745.6−2901 (Jin et al. 2017, 2018).

Zoom In Zoom Out Reset image size

Figure 4 shows the background-subtracted radial profiles of SWIFT J1658.2−4242 within the three energy bands. The PSF profile, renormalized to the source flux within 3 arcsec, is overplotted for comparison. Note that a dust component local to the source will create a scattering halo with a similar profile as the PSF even within 3 arcsec, which is difficult to disentangle using halo profile study alone (Jin et al. 2018). Excess flux is clearly observed outside 3.5 arcsec, and the excess decreases with the increasing energy. This is strong evidence for the presence of an X-ray dust scattering halo. For comparison, we also overplot the composite radial profile observed in Chandra ACIS for X-ray sources within 2 square degrees of Sgr A^⋆ in the GC (C. Jin et al. 2019, in preparation), where the N_H,abs is also on the order of 10²³ cm⁻². By renormalizing them to the profile of SWIFT J1658.2−4242 within the radial range of 60–80 arcsec, we see that the halo of SWIFT J1658.2−4242 appears very different from the GC composite halo. This implies that the foreground dust distribution toward SWIFT J1658.2−4242 should be quite different from the GC direction. Thus, although the dust distribution may be relatively uniform within the central 2° around Sgr A^⋆ (C. Jin et al. 2019, in preparation), it is significantly different on scales of 10°–20°.

Zoom In Zoom Out Reset image size

3.1.1. Modeling the Azimuthal-averaged Halo Profile

In order to model the halo of SWIFT J1658.2−4242, we applied the method in Jin et al. (2017), which used several dust scattering components from multiple geometrically thick foreground dust layers to fit the halo profile. We used the dimensionless fractional distance (x) to calculate the halo shape; thus, the halo modeling is not affected by the source distance, which might be uncertain (see Section 5.1). x is defined between 0 and 1, with the observer being at 0 and source being at 1. Because there is no knowledge about the number of major dust layers along the LOS, we tried five different model scenarios for the LOS dust distribution. The type of dust grain is also a major source of uncertainty. We chose three typical dust grain populations reported in Zubko et al. (2004). The first one is the COMP-AC-S dust grain population, which has been recommended for the GC direction (Fritz et al. 2011). Because SWIFT J1658.2−4242 is only 16° from Sgr A^⋆, it is possible that COMP-AC-S is also a reasonably good approximation for it. The other two are BARE-GR-B and COMP-NC-B. Jin et al. (2017) showed that among all the 19 dust grain populations tried in their work, these two populations could create the most extended and most compact halos, separately. Thus, the best-fit parameters based on these two grain populations can reflect the range of parameter dispersion because of the choice of different grain populations. The Minuit algorithm in the Python iminuit (v1.3.3, James & Roos 1975) interface was used to perform the minimum χ² fitting. The best-fit parameters are given in Tables 2, 5 and 6.

Table 2.  Best-fit Parameters for Different Scenarios of Foreground Dust Distribution (see Section 3.1.1)

Layer	Parameter	Scenario 1	Scenario 2	Scenario 3	Scenario 4	Scenario 5	Unit
Layer 1	xlow,1	${0.000}_{l}^{+0.001}$	${0.990}_{-0.002}^{u}$	${0.990}_{-0.003}^{u}$	${0.990}_{-0.002}^{u}$	${0.990}_{-0.003}^{u}$
	xhigh,1	${0.888}_{-0.005}^{+0.005}$	${1.000}_{-0.019}^{u}$	${0.996}_{-0.002}^{+0.002}$	${1.000}_{-0.020}^{+0.020}$	${1.000}_{-0.010}^{u}$
	fnH,1	100.0u	${14.1}_{-5.2}^{+5.2}$	${13.3}_{-1.3}^{+1.3}$	${13.2}_{-1.3}^{+1.3}$	${13.3}_{-1.3}^{+1.3}$	%
Layer 2	xlow,2	⋯	${0.000}_{l}^{+0.001}$	${0.666}_{-0.062}^{+0.062}$	${0.867}_{-0.037}^{+0.037}$	0.7-fixed
	xhigh,2	⋯	${0.911}_{-0.005}^{+0.005}$	${0.906}_{-0.019}^{+0.019}$	${0.867}_{-0.037}^{+0.037}$	0.9-fixed
	fnH,2	⋯	${85.9}_{-2.8}^{+2.8}$	${25.8}_{-3.0}^{+3.0}$	${11.3}_{-1.0}^{+1.0}$	${23.7}_{-3.8}^{+3.8}$	%
Layer 3	xlow,3	⋯	⋯	${0.000}_{l}^{+0.390}$	${0.697}_{-0.095}^{+0.095}$	0.5-fixed
	xhigh,3	⋯	⋯	${0.401}_{-0.052}^{+0.052}$	${0.697}_{-0.095}^{+0.095}$	0.7-fixed
	fnH,3	⋯	⋯	${60.9}_{-9.2}^{+9.2}$	${17.7}_{-4.6}^{+4.6}$	${0.0}_{l}^{+21.6}$	%
Layer 4	xlow,4	⋯	⋯	⋯	${0.007}_{-0.007}^{+0.064}$	0.3-fixed
	xhigh,4	⋯	⋯	⋯	${0.335}_{-0.226}^{+0.226}$	0.5-fixed
	fnH,4	⋯	⋯	⋯	${57.8}_{-6.2}^{+6.2}$	${17.7}_{-4.4}^{+4.4}$	%
Layer 5	xlow,5	⋯	⋯	⋯	⋯	0.1-fixed
	xhigh,5	⋯	⋯	⋯	⋯	0.3-fixed
	fnH,5	⋯	⋯	⋯	⋯	${26.6}_{-8.9}^{+8.9}$	%
Layer 6	xlow,6	⋯	⋯	⋯	⋯	0.0-fixed
	xhigh,6	⋯	⋯	⋯	⋯	0.1-fixed
	fnH,6	⋯	⋯	⋯	⋯	18.7 ${}_{-3.0}^{+3.0}$	%
	NH,tot	${1.03}_{-0.01}^{+0.01}$	${1.55}_{-0.09}^{+0.09}$	${1.66}_{-0.16}^{+0.16}$	${1.66}_{-0.13}^{+0.13}$	${1.65}_{-0.40}^{+0.40}$	1023 cm−2
	${\chi }_{\nu }^{2}$	348.3/96	214.3/93	108.0/90	107.3/87	108.1/91

Note. Error bars indicate 1σ parabolic errors. Scenarios 1, 2, 3, 4, and 5 comprise 1, 2, 3, 4, and 6 dust layers, respectively. All dust layers adopt the COMP-AC-S dust grain population. u and l signify that the parameter pegged at its upper and lower limit during the minimal χ² run. "Fixed" indicates that the parameter value was fixed during the halo profile fitting.

Download table as:  ASCIITypeset image

We began the halo profile modeling with the COMP-AC-S grain population. In Scenario 1, which contains only one geometrically thick dust layer, the lower and upper boundaries and the N_H,sca (the equivalent hydrogen column density for the dust scattering) of the layer are all free parameters. The best-fit model shows that the layer distributes within 0 ≤ x ≤ 0.888, with the total N_H,sca being (1.03 ± 0.01) × 10²³ cm⁻². However, the χ² is only 348.3 for 96 degrees-of-freedom (dof). The bad χ² is confirmed by the significant residuals shown in the Panels (a1), (b1) and (c1) in Figure 5.

Zoom In Zoom Out Reset image size

Zoom In Zoom Out Reset image size

Then we tried Scenario 2, which contains two dust layers. Layer 1 is closer to the binary system and layer 2 is closer to Earth. The best-fit model gives ${\chi }_{\nu }^{2}=214.3/93$, indicating a significant improvement compared to Scenario 1. Layer 1 is found to distribute within 0.99 ≤ x ≤ 1 and contains (14.1 ± 5.2)% LOS dust. The remaining dust is contained in layer 2, which is located within 0 ≤ x ≤ 0.911. The total N_H,sca is found to be (1.55 ± 0.09) × 10²³ cm⁻². According to the Panels (a2), (b2), and (c2) in Figure 5, the main improvement is in the central 5 arcsec region, where the halo contribution is more significant in Scenario 2, but there are still severe residuals outside 40 arcsec radius.

Then a third layer was added, namely Scenario 3. In this scenario, the best-fit χ² is 105.4 for 90 dof, indicating a further significant improvement. The best-fit model shows that (13.3 ± 1.3)% LOS dust is in layer 1 at 0.990 ≤ x ≤ 0.996, (25.8 ± 3.0)% LOS dust is in layer 2 at 0.666 ≤ x ≤ 0.906, and the remaining (60.9 ± 9.2)% LOS dust is in layer 3 at 0 ≤ x ≤ 0.401. The total N_H,sca is (1.66 ± 0.16) × 10²³ cm⁻², which is consistent with the result from Scenario 2. According to the Panels (a3), (b3), and (c3) in Figure 5, the main model improvement is in the radial range outside 40 arcsec, with the new χ² being 108.0 for 90 dof.

Scenario 4 contains four dust layers. The best-fit halo decomposition is shown in the Panels (a4), (b4), and (c4) in Figure 5. However, the χ² only improves by 0.7 for three additional free parameters; thus, adding more layers cannot bring further improvement in the halo fitting. The best-fit total N_H,sca is also consistent with the result of Scenario 3.

As a further test, we tried Scenario 5 with six layers, as shown by the Panels (a5), (b5), and (c5) in Figure 5. Layer 1 is still local to the source, with another five foreground layers distributing within the fractional distance ranges of 0.0–0.1, 0.1–0.3, 0.3–0.5, 0.5–0.7, and 0.7–0.9, respectively. The boundaries of these five layers were fixed during the fitting; only their N_H,sca values were allowed to vary. In the best-fit model of this scenario, (13.3 ± 1.3)% LOS dust is contained in layer 1 at 0.99 ≤ x ≤ 1. For the remaining five layers, (23.7 ± 3.8)% LOS dust is located within 0.7 ≤ x ≤ 0.9, 0% within 0.5 ≤ x ≤ 0.7, (17.7 ± 4.4)% within 0.3 ≤ x ≤ 0.5, (26.6 ± 8.9)% within 0.1 ≤ x ≤ 0.3, and (18.7 ± 3.0)% within 0.0 ≤ x ≤ 0.1. The best-fit χ² is 108.1 for 91 dof, and the total N_H,sca is (1.65 ± 0.40) × 10²³ cm⁻²; both are consistent with the results in Scenarios 3 and 4.

All the error bars come from the 1σ parabolic error returned by the iminuit code. However, we emphasize that this statistical uncertainty, even derived from the more robust Monte Carlo simulation as done in Jin et al. (2018), cannot reflect the true uncertainty of the halo profile fitting. This is because most of the uncertainty should arise from the lack of knowledge about the properties of dust grains, such as their grain type, metallicity, and spatial and size distribution. All these physical properties can lead to a significant change of the best-fit values. To assess this uncertainty, we also tried BARE-GR-B and COMP-NC-B grain populations for all the model scenarios. We found that despite the change of best-fit parameters the resultant relative distribution of LOS dust did not change significantly, and Scenario 4 always gave the best χ² (see Appendix B). This is also consistent with Jin et al. (2017), who tried 19 different dust grain populations and found that the conclusion for the general LOS dust distribution did not change.

Consequently, we can conclude that the observed average halo profile requires at least three dust layers to fit, and adding more dust layers cannot bring further improvement. In all the scenarios with more than two layers, the one local to SWIFT J1658.2−4242 contains (10–15)% LOS dust regardless of the number of layers or the type of dust grains. The majority of LOS dust is in the foreground layers significantly far away from the source and located along the Galactic disk. However, it must be emphasized that this relative dust distribution is still based on the assumption that the dust grain population does not change along the LOS.

Moreover, it is necessary to emphasize that the halo model used in this work does not include multiple scattering. Mathis & Lee (1991) shows that multiple scattering can dominate over single scattering when the scattering optical depth τ_sca is larger than 1.3. The major effect of multiple scattering is causing the halo profile to be more extended (Mathis & Lee 1991; Xiang et al. 2007; Jin et al. 2017). Because we know τ_sca ∝ E⁻² where E is the photon energy (Predehl & Schmitt 1995), it is clear that multiple scattering is much more important at lower energies. Adopting N_H,sca = 16.6 × 10²³ cm⁻² from the best-fit halo model in Table 2, we can calculate τ_sca to be 0.90, 0.41, and 0.21 in the 2–4, 4–6, and 6–10 keV band, respectively; thus, single scattering should dominate in these bands. This is further supported by the fact that our single-scattering-based halo models can already reproduce the observed halo profile and its energy dependence reasonably well. Therefore, we can conclude that multiple scattering should not affect our results.

Figure 2 shows that there is apparent azimuthal asymmetry in the halo. To investigate this, the region surrounding SWIFT J1658.2−4242 was divided evenly into six subregions, each having an opening angle of 60°. The seventh region was defined with a 30° angular width where the nonuniformity of the halo is most significant. Then a radial profile was extracted from each subregion. A flat background was subtracted in the same way as described in Section 3.1. Figure 6 shows radial profiles in every subregion. The halo nonuniformity is most severe in regions 3, 4, 7. Region 3 shows lower halo intensity than the azimuthal-averaged halo within 20–40 arcsec radii. Region 4 shows higher intensity within 10–30 arcsec radii. Region 7 is a subregion of region 4, where the halo intensity drops sharply by a factor of 2–3 at the viewing angle of ∼30 arcsec.

Zoom In Zoom Out Reset image size

To quantify this azimuthal asymmetry, we used the best-fit halo model from Scenario 4 with the COMP-AC-S grain population to fit the radial profile in every subregion, by fixing the location of each layer but allowing the N_H,sca of layers 2 and 3 to vary. We also fixed the N_H,sca of layer 1 and layer 4, because they dominate the regions within 3 arcsec and outside 100 arcsec where the data quality is poor in subregions (see Figure 5). The best-fit N_H,sca in every subregion as a fraction of the azimuthal-averaged halo value is given in Table 3. We find that the N_H,sca of layer 2 can change by as much as a factor of 4 in different subregions, while the N_H,sca of layer 3 can change by a factor of 3, but the total N_H,sca in different subregions change by only ∼10%.

However, simply changing the N_H,sca in layers 2 and 3 is not enough to account for all the halo asymmetry. For example, the flux drop in Figure 6 Panel (a7) at ∼30 arcsec is clearly too sharp to be fitted by any halo components. An obvious explanation is that the dust distribution is not uniform at all viewing angles in at least one of the foreground layers. This effect can potentially be associated with the distribution of molecular clouds in the source direction, which we discuss in more detail in Section 5.2.

In order to understand the flux drop in region 7, we created a toy model based on Scenario 4. From previous results, layer 4 has the largest contribution at large radii, so we assumed that its N_H,sca has a sudden change at a specific radius (R_break, a free parameter) in region 7, then the sharp flux drop can be reproduced. We also allowed the N_H,sca of layers 2, 3, and 4 in region 7 to be different from the azimuthal-averaged values. Then a simultaneous halo profile fitting to the azimuthal-averaged halo and the one in region 7 was performed, and the results are shown in Figure 7 and Table 4.

Zoom In Zoom Out Reset image size

Table 4.  Best-fit Parameters from Fitting the Radial Profiles in Region 4 Using Scenario 4, but Assuming an Inhomogeneous Dust Distribution in Layer 4

Layer	Parameter	Value	Unit
Layer 1	xlow,1	${0.990}_{-0.002}^{+0.002}$
	xhigh,1	${1.000}_{-0.019}^{u}$
	NH,1	${2.1}_{-0.2}^{+0.2}$	1022 cm−2
Layer 2	xlow,2	${0.857}_{-0.042}^{+0.042}$
	xhigh,2	${0.857}_{-0.104}^{+0.104}$
	NH,2,ave	${1.8}_{-0.5}^{-0.5}$	1022 cm−2
	NH,2,region-4	${1.1}_{-0.2}^{-0.2}$	1022 cm−2
Layer 3	xlow,3	${0.765}_{-0.065}^{+0.065}$
	xhigh,3	${0.766}_{-0.065}^{+0.065}$
	NH,3	${1.8}_{-0.5}^{-0.5}$	1022 cm−2
	NH,3,region-4	${1.0}_{-0.5}^{+0.5}$	1022 cm−2
Layer 4	xlow,4	${0.000}_{l}^{+0.075}$
	xhigh,4	${0.458}_{-0.090}^{+0.090}$
	NH,4	${10.5}_{-1.4}^{+1.4}$	1022 cm−2
	NH,4,region-4,inner	${18.8}_{-1.8}^{+1.8}$	1022 cm−2
	Rbreak	${27.0}_{-0.1}^{+0.1}$	arcsec
	NH,4,region-4,outer	${8.5}_{-0.8}^{+0.8}$	1022 cm−2
${\chi }_{\nu ,\mathrm{ave}}^{2}$ = 110.5/87		${\chi }_{\nu ,\mathrm{region} \mbox{-} 4}^{2}$ = 111.1/70

Note. Error bars indicate the 1σ parabolic errors. See Figure 7 for the corresponding halo decomposition.

Download table as:  ASCIITypeset image

First, the best-fit values from fitting the azimuthal-averaged halo and the halo in region 7 are very similar to the results of fitting only the azimuthal-averaged halo, only that the fraction of N_H,sca in layer 4 increases slightly to (64.8 ± 8.6)%, and its upper limit increases to 0.458 ± 0.090. Second, the flux drop can be well modeled with R_break = 27.0 ± 0.1 arcsec. Within this radius, the N_H,sca of layer 4 is (18.8 ± 1.8) × 10²² cm⁻², which is about 1.8 times as high as the average value, but it drops significantly to (8.5 ± 0.8) × 10²² outside R_break, as required by fitting the sharp flux drop. The residuals in region 7, e.g., seen in Figure 7 Panel (b1), is likely caused by more detailed radial variation of N_H,sca in foreground dust layers.

5.1.1. Results from the Halo Profile Study

SWIFT J1658.2−4242 is a heavily absorbed X-ray transient with N_H,abs ≃ 2 × 10²³ cm⁻² during the persistent phase (i.e., the time period out of dips, Xu et al. 2018). We discover a strong X-ray dust scattering halo around it, which can be decomposed into several dust scattering components. Figure 8 shows the amount of dust, as indicated by the N_H,sca, in every layer along the LOS from different best-fit halo models. It is clear that most of the X-ray scattering dust should be in the foreground layers far from SWIFT J1658.2−4242. We also tried some other dust grain populations, but found that they had a only small impact on the resultant relative dust distribution.

Zoom In Zoom Out Reset image size

However, a potential uncertainty is associated with the fact that the halo profile modeling cannot fully constrain the intensity of the dust scattering component local to the binary system. This is because as the dust layer becomes closer to the primary X-ray source, the halo size also becomes smaller, and eventually its size can be smaller than the pixel size if the dust layer is close enough to the X-ray source. In this extreme case, the source plus the local halo would still appear pointlike, and the radial profile is indistinguishable from the instrumental PSF, i.e., the halo component is not "visible" in the observed radial profile even if the N_H,sca is large. Therefore, it is possible for the fraction of N_H,sca in the other foreground dust layers to be overestimated.

5.1.2. Results from the Molecular Cloud (MC) Study

The distribution of MCs can reflect the distribution of ISM in the LOS of SWIFT J1658.2−4242. To determine the number of velocity-coherent components along the LOS, we use ¹³CO(1−0) data from the Mopra Southern Galactic Plane CO survey (Burton et al. 2013). The spectrum is integrated over the circular region of 1 arcmin radius around SWIFT J1658.2−4242. To increase the S/N, we also smoothed the spectrum, reaching an effective velocity resolution of 1.2 km s⁻¹. The velocity resolution is adequate for identifying different MC components.

The ¹³CO(1−0) spectrum is plotted in Figure 9. First, we identified components and measured their velocities. The distances of these components can be determined on the basis of their velocities using the Galactic model described in Reid et al. (2016), where their displacements from the plane and proximities to individual parallax sources are automatically considered. We identified four components and estimated their distances. These are indicated in Figure 9, and are summarized as follows:

• 1.  
  A intensive component (C1) at −25 km s⁻¹, which sits at a distance of 2.5 ± 0.6 kpc.
• 2.  
  A intensive component (C2) at −118 km s⁻¹, which sits at a distance of 8.0 ± 0.8 kpc.
• 3.  
  A weaker component (C3) at −11 km s⁻¹, with a relatively low surface densities, which sits at a distance of 1.5 ± 0.6 kpc.
• 4.  
  A component (C4) at −72 km s⁻¹, with a relatively large velocity dispersion, which sits at a distance of either 5 or 10 kpc.

C1 and C2 have integrated intensities of ∼12 K km s⁻¹ and 24 K km s⁻¹, respectively. Using the standard conversion in Simon et al. (2001), these correspond to column densities of 1.2 × 10²² cm⁻² and 2.4 × 10²² cm⁻², respectively. Note that these are the mean column densities estimated by integrating over a large region, and they are not necessarily identical to the column density derived using dust scattering. We also note that C1 and C2 have well-defined emission peaks, and they probably correspond to dense MCs in the Galactic disk. C3 is much weaker might correspond to a cloud of a lower surface density. C4 consists of several peaks and is wide in velocity (dv ≈ 20 km s⁻¹). It probably corresponds to diffuse gas that lingers around in one of the the Galactic spiral arms.

Zoom In Zoom Out Reset image size

Conventionally, the distance of a Galactic source can be determined using its velocity and its H i 21 cm spectrum, where its distance can be determined using its velocity with the help of a Galactic rotation model. In most cases, distance estimated using the Galactic rotation method has two solutions, where the H i 21 cm emission line can be used to distinguish between these two solutions, e.g., if a source stays close to us, it can produce an absorption feature visible in the spectrum. In this work, our distances are mostly determined with the help of the Galactic model of Reid et al. (2016) where the H i 21 cm data is not used. Although this is already considered as accurate, we still plotted the H i 21 cm emission presented in McClure-Griffiths et al. (2005) as a reference, where C1 and C3 do exhibit corresponding absorption features, implying that they presumably stay at the near distances. Components C2 and C4 show very little self-absorption, indicating that they probably stay at the far distances. These are broadly consistent with the result from the galactic model described in Reid et al. (2016). If the source is located at a distance of ∼10 kpc (see Section 5.3), then most of the MCs in its LOS will be located in the Galactic disk.

5.1.3. More Evidences for the ISM Distribution

The azimuthal asymmetry of the X-ray dust scattering halo has been reported in some sources (e.g., Seward & Smith 2013; Valencic & Smith 2015). The halo can become nonuniform for at least two reasons. One reason is the partial alignment of nonspherical dust grains with the magnetic field. This type of halo azimuthal asymmetry can reach 10% at the same radius, as calculated by Draine & Allaf-Akbari (2006). Another reason is the nonuniform distribution of foreground dust, which can cause different scattering opacity at different viewing angles and azimuthal angles. The halo asymmetry observed in SWIFT J1658.2−4242 changed by a factor of 2–3 at the radius of 30 arcsec in region 7, as shown in Figure 2, which is much larger than the asymmetry that can be caused by the magnetic field. The change of dust grain population cannot explain the asymmetry, because the profile of any dust scattering halo cannot reproduce the sharp flux drop in region 7. Thus, the most likely explanation is the inhomogeneous distribution of foreground dust. Indeed, in Section 4 we have shown that a sudden N_H,sca drop at the viewing angle of 27 arcsec in layer 4 can account for most of the observed flux drop in region 7.

The two-dimensional (2D) azimuthal asymmetry of the halo can also be visualized. To do this, we first reran the acisreadcorr script to remove the readout streak but keeping a set of photons whose spectrum is similar to pixels at the same radius,⁷ so that the region of the readout streak was no longer black after the removal. Note that this step is only for the purpose of creating nicer images of the halo, because it is not possible to fully recover the primary halo intensity underneath the readout streak. Then we renormalized the ChaRT-simulated 4–6 keV PSF image to the intensity of the reextracted 4–6 keV flux image within the 2–4 arcsec annulus, and subtracted the PSF image from the flux image, leaving only the dust scattering halo. Figure 10(a) shows the smoothed halo image, where complex azimuthal inhomogeneity of the halo is clearly revealed by yellow contours.

Zoom In Zoom Out Reset image size

Because the dust distribution in the ISM is likely to be linked to the distribution of MCs, it is possible to find this inhomogeneity in the MC distribution in the same direction. Figure 10(b) shows the 0.87 mm intensity map, which is an indicator for the intensity map of the CO $3\to 2$ emission line, from the Atacama Pathfinder EXperiment (APEX) Telescope's large Area Survey of the Galaxy (ATLASGAL) (Schuller et al. 2009) in the direction of SWIFT J1658.2−4242. The yellow contours from the halo intensity image is copied to the ATLASGAL image for comparison. This shows that there is an evident correlation between the X-ray halo intensity and the intensity of the 0.87 mm emission. Therefore, it is most likely that the asymmetric X-ray dust scattering halo is due to the inhomogeneous distribution of foreground ISM.

SWIFT J1658.2−4242 is a heavily extincted source in the Galactic plane. The strong dust reddening and X-ray absorption require the source to be far from Earth, so that its LOS can pass through enough ISM in the Galactic disk to produce such severe extinction. Soon after the discovery of SWIFT J1658.2−4242, Russell et al. (2018b) compared its radio and X-ray luminosities and suggested that at a distance of d > 3 kpc the source appear like a black hole X-ray binary, while at closer distances it would be more consistent with a neutron star X-ray binary. Then the following study of Xu et al. (2018) showed that the spectral-timing properties of SWIFT J1658.2−4242 look like a black hole binary, which seems to support d > 3 kpc. However, it is not possible to get better constraints on the source distance on the basis of this argument alone. Below we discuss several other methods of estimating the source distance.

5.3.1. Distance Estimated from the State Transition Luminosity

5.3.2. Distance Estimated from the Halo Profile

Valencic & Smith (2015) used a single foreground dust layer to fit the halo profiles of 35 X-ray sources with a large range of LOSs. They discovered that for X-ray sources whose LOSs traversed more than 5 kpc in the Galactic plane, their halo profiles could not be well fitted by a single foreground dust layer. SWIFT J1658.2−4242 also requires at least three dust layers to fit its halo, so it is likely to have d > 5 kpc. However, because all the distances in the model are fractional, and they are also degenerated to the dust grain population to some extent (see Tables 2, 5, 6), it is not possible to obtain further constraints on the source distance using only the halo profile study. The fractional distances must be mapped to the real distribution of ISM in order to determine the source distance more precisely.

Table 5.  Best-fit Halo Models in Different Scenarios Using the BARE-GR-B Dust Grain Population

Layer	Parameter	Scenario 1	Scenario 2	Scenario 3	Scenario 4	Scenario 5	Unit
Layer 1	xlow,1	${0.338}_{-0.014}^{+0.014}$	${0.990}_{-0.001}^{u}$	${0.990}_{-0.001}^{u}$	${0.990}_{-0.001}^{u}$	${0.900}_{l}^{+0.003}$
	xhigh,1	${0.958}_{-0.002}^{+0.002}$	${1.000}_{-0.020}^{u}$	${1.000}_{-0.013}^{u}$	${1.000}_{-0.019}^{u}$	${1.000}_{-0.008}^{u}$
	fnH,1	100.0u	${8.6}_{-1.5}^{+1.5}$	${9.4}_{-1.0}^{+1.0}$	${9.5}_{-1.0}^{+1.0}$	${9.0}_{-0.8}^{+0.8}$	%
Layer 2	xlow,2	⋯	${0.383}_{-0.012}^{+0.012}$	${0.901}_{-0.045}^{+0.045}$	${0.917}_{-0.027}^{+0.027}$	0.7-fixed
	xhigh,2	⋯	${0.950}_{-0.001}^{u}$	${0.929}_{-0.031}^{+0.031}$	${0.917}_{-0.027}^{+0.027}$	0.9-fixed
	fnH,2	⋯	${91.4}_{-2.3}^{+2.3}$	${16.0}_{-1.7}^{+1.7}$	${15.6}_{-1.9}^{+1.9}$	${39.6}_{-1.5}^{+1.5}$	%
Layer 3	xlow,3	⋯	⋯	${0.319}_{-0.034}^{+0.034}$	${0.764}_{-0.118}^{+0.118}$	0.5-fixed
	xhigh,3	⋯	⋯	${0.850}_{-0.026}^{+0.026}$	${0.765}_{-0.117}^{+0.117}$	0.7-fixed
	fnH,3	⋯	⋯	${74.6}_{-7.9}^{+7.9}$	${30.4}_{-5.3}^{+5.3}$	${8.8}_{-5.4}^{+5.4}$	%
Layer 4	xlow,4	⋯	⋯	⋯	${0.453}_{-0.238}^{+0.238}$	0.3-fixed
	xhigh,4	⋯	⋯	⋯	${0.453}_{-0.238}^{+0.238}$	0.5-fixed
	fnH,4	⋯	⋯	⋯	${44.5}_{-10.2}^{+10.2}$	${42.6}_{-5.1}^{+5.1}$	%
Layer 5	xlow,5	⋯	⋯	⋯	⋯	0.1-fixed
	xhigh,5	⋯	⋯	⋯	⋯	0.3-fixed
	fnH,5	⋯	⋯	⋯	⋯	${0.0}_{l}^{+2.9}$	%
Layer 6	xlow,6	⋯	⋯	⋯	⋯	0.0-fixed
	xhigh,6	⋯	⋯	⋯	⋯	0.1-fixed
	fnH,6	⋯	⋯	⋯	⋯	${0.0}_{l}^{+1.8}$	%
	NH,tot	${1.35}_{-0.25}^{+0.25}$	${1.73}_{-0.05}^{+0.05}$	${1.92}_{-0.16}^{+0.16}$	${1.94}_{-0.23}^{+0.23}$	${1.57}_{-0.13}^{+0.13}$	1023 cm−2
	${\chi }_{\nu }^{2}$	261.8/96	175.0/93	124.5/90	122.1/87	254.4/91

Download table as:  ASCIITypeset image

Table 6.  Best-fit Halo Models in Different Scenarios Using the COMP-NC-B Dust Grain Population

Layer	Parameter	Scenario 1	Scenario 2	Scenario 3	Scenario 4	Scenario 5	Unit
Layer 1	xlow,1	${0.000}_{l}^{+0.001}$	${0.981}_{-0.003}^{+0.003}$	${0.988}_{-0.002}^{+0.002}$	${0.990}_{-0.026}^{u}$	${0.988}_{-0.002}^{+0.002}$
	xhigh,1	${0.840}_{-0.006}^{+0.006}$	${0.999}_{-0.003}^{+0.001}$	${1.000}_{-0.020}^{u}$	${0.995}_{-0.002}^{+0.002}$	${1.000}_{-0.009}^{u}$
	fnH,1	100.0u	${12.0}_{-2.5}^{+2.5}$	${14.0}_{-2.1}^{+2.1}$	${11.5}_{-1.8}^{+1.8}$	${14.2}_{-2.1}^{+2.1}$	%
Layer 2	xlow,2	⋯	${0.000}_{l}^{+0.001}$	${0.470}_{-0.032}^{+0.032}$	${0.851}_{-0.097}^{+0.097}$	0.7-fixed
	xhigh,2	⋯	${0.864}_{-0.006}^{+0.006}$	${0.905}_{-0.008}^{+0.008}$	${0.851}_{-0.097}^{+0.097}$	0.9-fixed
	fnH,2	⋯	${88.0}_{-2.8}^{+2.8}$	${32.9}_{-1.9}^{+1.9}$	${10.8}_{-1.7}^{+1.7}$	${16.4}_{-0.6}^{+0.6}$	%
Layer 3	xlow,3	⋯	⋯	${0.000}_{l}^{+0.025}$	${0.627}_{-0.133}^{+0.133}$	0.5-fixed
	xhigh,3	⋯	⋯	${0.000}_{l}^{+0.025}$	${0.627}_{-0.133}^{+0.133}$	0.7-fixed
	fnH,3	⋯	⋯	${53.1}_{-4.1}^{+4.1}$	${22.3}_{-4.7}^{+4.7}$	${14.1}_{-1.4}^{+1.4}$	%
Layer 4	xlow,4	⋯	⋯	⋯	${0.000}_{-0.022}^{+0.022}$	0.3-fixed
	xhigh,4	⋯	⋯	⋯	${0.000}_{-0.022}^{+0.022}$	0.5-fixed
	fnH,4	⋯	⋯	⋯	${55.4}_{-10.0}^{+10.0}$	${0.0}_{l}^{+2.9}$	%
Layer 5	xlow,5	⋯	⋯	⋯	⋯	0.1-fixed
	xhigh,5	⋯	⋯	⋯	⋯	0.3-fixed
	fnH,5	⋯	⋯	⋯	⋯	${0.0}_{l}^{+3.1}$	%
Layer 6	xlow,6	⋯	⋯	⋯	⋯	0.0-fixed
	xhigh,6	⋯	⋯	⋯	⋯	0.1-fixed
	fnH,6	⋯	⋯	⋯	⋯	${55.3}_{-1.9}^{+1.9}$	%
	NH,tot	${1.47}_{-0.02}^{+0.02}$	${2.15}_{-0.08}^{+0.08}$	${2.61}_{-0.13}^{+0.13}$	${2.56}_{-0.29}^{+0.29}$	${2.58}_{-0.14}^{+0.14}$	1023 cm−2
	${\chi }_{\nu }^{2}$	610.0/96	504.4/93	114.1/90	111.1/87	119.6/91

Download table as:  ASCIITypeset image

5.3.3. Distance Estimated from the LOS MC Distribution

The strong dust scattering halo around SWIFT J1658.2−4242 makes its radial profile different from the PSF profile in any instrument; thus, the normal PSF correction used to retrieve the intrinsic source flux is not accurate unless the flux in the halo is properly treated (Smith et al. 2016; Jin et al. 2017). As the photon energy decreases, the halo becomes more significant, and so the spectral bias caused by the halo also increases. Because of the PSF convolution, the spectral bias is also more significant for instruments with smaller PSF. The source extraction region also affects the level of the spectral bias. If the region covers the entire halo, then the loss of photons in the LOS due to the dust scattering opacity is fully compensated by the photons in the halo, and so there will be no spectral bias. However, a typical source extraction region has a limited size, and part of the central region is often excluded to avoid the pile-up effect; thus, the spectral bias induced by the halo is inevitable.

The correction factor required to remove the spectral bias can be calculated from the halo model at different energies for different source extraction regions and instrumental PSF profiles. We used the best-fit halo model in Scenario 4 to calculate the correction, as this model gives the smallest χ². It must be emphasized that an accurate correction factor only requires the halo model to fit the halo shape accurately in every energy band, and it does not depend on the detailed halo decomposition. This is because the shapes of all the halo components, except the PSF, have the same energy dependence (e.g., Mathis & Lee 1991; Predehl & Schmitt 1995). Therefore, all the uncertainties and model degeneracies associated with the best-fit halo parameters do not affect the spectral correction (e.g., see Figure 11 in Jin et al. 2017).

Figure 11 shows the correction factor as a function of energy for typical source extraction regions in different instruments. It is clear that instruments with smaller PSF need larger correction factors, and the factor increases rapidly as the energy decreases. On the basis of these model calculations, we create xspec models, named dscor, for different instruments and different source extraction regions.⁸

Zoom In Zoom Out Reset image size

Another method often used to correct for the spectral bias of dust scattering is to assume a gas-to-dust ratio and add the dust scattering opacity to the X-ray absorption model. This method requires that the halo intensity should be negligible compared to the PSF intensity in the source extraction region. First, this requirement is difficult to be met for heavily absorbed X-ray sources like SWIFT J1658.2−4242 and GC sources (C. Jin et al. 2019, in preparation), because their dust scattering opacity is not negligible. Second, in the case of lower X-ray absorption, if the dust is intrinsic to the source, the halo will have the same profile as the PSF (Mathis & Lee 1991), and then the effective dust scattering opacity in the extracted spectrum would be zero, i.e., the dust is not "visible" to the observer (Jin et al. 2017), and so there would be no need to consider it in the absorption model. Therefore, this alternative spectral correction method is problematic. We emphasize that it is a must to measure and model the profile of the dust scattering halo in order to properly correct for its spectral biases.