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

Chichuan Jin; Gabriele Ponti; Guangxing Li; David Bogensberger

arXiv:1903.08099·astro-ph.HE·May 1, 2019

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

Chichuan Jin, Gabriele Ponti, Guangxing Li, David Bogensberger

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TL;DR

This study uses Chandra and XMM-Newton data to analyze an asymmetric X-ray dust scattering halo around the transient SWIFT J1658.2-4242, revealing dust layer distributions, source distance, and spectral biases caused by dust scattering.

Contribution

It introduces a detailed analysis of an asymmetric dust scattering halo, estimates the source distance, and develops a correction model for spectral biases in X-ray observations.

Findings

01

Dust layers account for 85-90% of intervening material.

02

Estimated source distance is approximately 10 kpc.

03

Developed the Xspec dscor model to correct spectral biases.

Abstract

SWIFT J1658.2-4242 is an X-ray transient discovered recently in the Galactic plane, with severe X-ray absorption corresponding to an equivalent hydrogen column density of $N_{H, abs} \sim 2 \times 1 0^{23}$ cm $^{- 2}$ . Using new Chandra and XMM-Newton data, we discover a strong X-ray dust scattering halo around it. The halo profile can be well fitted by the scattering from at least three separated dust layers. During the persistent emission phase of SWIFT J1658.2-4242, the best-fit dust scattering $N_{H, sca}$ based on the COMP-AC-S dust grain model is consistent with $N_{H, abs}$ . The best-fit halo models show that 85-90 percent of the intervening gas and dust along the line of sight of SWIFT J1658.2-4242 are located in the foreground ISM in the Galactic disk. The dust scattering halo also shows significant azimuthal asymmetry, which appears consistent with the inhomogeneous…

Tables6

Table 1. Table 1: List of Chandra and XMM-Newton DDT observations on SWIFT J1658.2-4242.

Satellite	OBSID	Obs-Date	Instrument	Exp	$θ_{offaxis}$	$E_{2 - 4 k e V}$	$E_{4 - 6 k e V}$	$E_{6 - 10 k e V}$	$F_{2 - 10 k e V}$
				(ks)	(arcmin)	(keV)	(keV)	(keV)	(erg cm^-2 s^-1)
Chandra	21083	2018-04-28	ACIS-S	28.9	0.391	3.3	4.9	6.9	$0.62 \times 10^{- 9}$
XMM-Newton	0811213401	2018-02-27	MOS1	25.0	1.702	3.1	4.8	6.9	$2.62 \times 10^{- 9}$
XMM-Newton	0805200201a	2018-03-04	MOS2	7.9	1.704	3.2	4.8	7.0	$3.72 \times 10^{- 9}$
XMM-Newton	0805200201b	2018-03-04	MOS2	8.7	1.704	3.2	4.8	7.0	$2.50 \times 10^{- 9}$
XMM-Newton	0805200301	2018-03-11	MOS2	44.5	1.690	3.2	4.8	6.9	$1.48 \times 10^{- 9}$
XMM-Newton	0805200401	2018-03-15	MOS2	36.5	1.733	3.2	4.8	6.9	$1.72 \times 10^{- 9}$
XMM-Newton	0805201301	2018-03-28	MOS2	31.5	1.700	3.2	4.8	6.9	$1.61 \times 10^{- 9}$

Table 2. 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	x_low,1	0.000 ${}_{l}^{+ 0.001}$	0.990 ${}_{- 0.002}^{u}$	0.990 ${}_{- 0.003}^{u}$	0.990 ${}_{- 0.002}^{u}$	0.990 ${}_{- 0.003}^{u}$
	x_high,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 ${}_{- 0.010}^{u}$
	$f_{nH, 1}$	100.0^u	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	x_low,2	–	0.000 ${}_{l}^{+ 0.001}$	0.666 ${}_{- 0.062}^{+ 0.062}$	0.867 ${}_{- 0.037}^{+ 0.037}$	0.7-fixed
	x_high,2	–	0.911 ${}_{- 0.005}^{+ 0.005}$	0.906 ${}_{- 0.019}^{+ 0.019}$	0.867 ${}_{- 0.037}^{+ 0.037}$	0.9-fixed
	$f_{nH, 2}$	–	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	x_low,3	–	–	0.000 ${}_{l}^{+ 0.390}$	0.697 ${}_{- 0.095}^{+ 0.095}$	0.5-fixed
	x_high,3	–	–	0.401 ${}_{- 0.052}^{+ 0.052}$	0.697 ${}_{- 0.095}^{+ 0.095}$	0.7-fixed
	$f_{nH, 3}$	–	–	60.9 ${}_{- 9.2}^{+ 9.2}$	17.7 ${}_{- 4.6}^{+ 4.6}$	0.0 ${}_{l}^{+ 21.6}$	%
Layer-4	x_low,4	–	–	–	0.007 ${}_{- 0.007}^{+ 0.064}$	0.3-fixed
	x_high,4	–	–	–	0.335 ${}_{- 0.226}^{+ 0.226}$	0.5-fixed
	$f_{nH, 4}$	–	–	–	57.8 ${}_{- 6.2}^{+ 6.2}$	17.7 ${}_{- 4.4}^{+ 4.4}$	%
Layer-5	x_low,5	–	–	–	–	0.1-fixed
	x_high,5	–	–	–	–	0.3-fixed
	$f_{nH, 5}$	–	–	–	–	26.6 ${}_{- 8.9}^{+ 8.9}$	%
Layer-6	x_low,6	–	–	–	–	0.0-fixed
	x_high,6	–	–	–	–	0.1-fixed
	$f_{nH, 6}$	–	–	–	–	18.7 ${}_{- 3.0}^{+ 3.0}$	%
	$N_{H, tot}$	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 ${}_{- 0.40}^{+ 0.40}$	$10^{23}$ cm^-2
	$χ_{ν}^{2}$	348.3/96	214.3/93	108.0/90	107.3/87	108.1/91

Table 3. Table 3: Best-fit N H , sca subscript 𝑁 H sca N_{\rm H,sca} of each dust layer in Scenario-4 for different azimuthal subregions.

	$N_{H, sca}$	$f_{region - 1}$	$f_{region - 2}$	$f_{region - 3}$	$f_{region - 4}$	$f_{region - 5}$	$f_{region - 6}$	$f_{region - 7}$
	( $10^{22}$ cm^-2)
Layer-1	$2.2$	1.00-fixed	1.00-fixed	1.00-fixed	1.00-fixed	1.00-fixed	1.00-fixed	1.00-fixed
Layer-2	$1.9$	$0.41 \pm 0.08$	$1.18 \pm 0.09$	$1.17 \pm 0.08$	$1.39 \pm 0.09$	$1.37 \pm 0.09$	$0.30 \pm 0.09$	$0.95 \pm 0.11$
Layer-3	$3.0$	$1.16 \pm 0.07$	$0.74 \pm 0.08$	$0.34 \pm 0.07$	$1.00 \pm 0.08$	$1.19 \pm 0.08$	$1.68 \pm 0.08$	$0.88 \pm 0.10$
Layer-4	$9.6$	1.00-fixed	1.00-fixed	1.00-fixed	1.00-fixed	1.00-fixed	1.00-fixed	1.00-fixed
All Layers	$16.7$	$0.96 \pm 0.02$	$0.97 \pm 0.02$	$0.90 \pm 0.02$	$1.04 \pm 0.02$	$1.08 \pm 0.02$	$1.04 \pm 0.02$	$0.97 \pm 0.02$

Table 4. 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	x_low,1	0.990 ${}_{- 0.002}^{+ 0.002}$
	x_high,1	1.000 ${}_{- 0.019}^{u}$
	$N_{H, 1}$	2.1 ${}_{- 0.2}^{+ 0.2}$	$10^{22}$ cm^-2
Layer-2	x_low,2	0.857 ${}_{- 0.042}^{+ 0.042}$
	x_high,2	0.857 ${}_{- 0.104}^{+ 0.104}$
	$N_{H, 2, ave}$	1.8 ${}_{- 0.5}^{- 0.5}$	$10^{22}$ cm^-2
	$N_{H, 2, region - 4}$	1.1 ${}_{- 0.2}^{- 0.2}$	$10^{22}$ cm^-2
Layer-3	x_low,3	0.765 ${}_{- 0.065}^{+ 0.065}$
	x_high,3	0.766 ${}_{- 0.065}^{+ 0.065}$
	$N_{H, 3}$	1.8 ${}_{- 0.5}^{- 0.5}$	$10^{22}$ cm^-2
	$N_{H, 3, region - 4}$	1.0 ${}_{- 0.5}^{+ 0.5}$	$10^{22}$ cm^-2
Layer-4	x_low,4	0.000 ${}_{l}^{+ 0.075}$
	x_high,4	0.458 ${}_{- 0.090}^{+ 0.090}$
	$N_{H, 4}$	10.5 ${}_{- 1.4}^{+ 1.4}$	$10^{22}$ cm^-2
	$N_{H, 4, region - 4, inner}$	18.8 ${}_{- 1.8}^{+ 1.8}$	$10^{22}$ cm^-2
	$R_{break}$	27.0 ${}_{- 0.1}^{+ 0.1}$	arcsec
	$N_{H, 4, region - 4, outer}$	8.5 ${}_{- 0.8}^{+ 0.8}$	$10^{22}$ cm^-2
$χ_{ν, ave}^{2}$ = 110.5/87		$χ_{ν, region - 4}^{2}$ = 111.1/70

Table 5. 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	x_low,1	0.338 ${}_{- 0.014}^{+ 0.014}$	0.990 ${}_{- 0.001}^{u}$	0.990 ${}_{- 0.001}^{u}$	0.990 ${}_{- 0.001}^{u}$	0.900 ${}_{l}^{+ 0.003}$
	x_high,1	0.958 ${}_{- 0.002}^{+ 0.002}$	1.000 ${}_{- 0.020}^{u}$	1.000 ${}_{- 0.013}^{u}$	1.000 ${}_{- 0.019}^{u}$	1.000 ${}_{- 0.008}^{u}$
	$f_{nH, 1}$	100.0^u	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	x_low,2	–	0.383 ${}_{- 0.012}^{+ 0.012}$	0.901 ${}_{- 0.045}^{+ 0.045}$	0.917 ${}_{- 0.027}^{+ 0.027}$	0.7-fixed
	x_high,2	–	0.950 ${}_{- 0.001}^{u}$	0.929 ${}_{- 0.031}^{+ 0.031}$	0.917 ${}_{- 0.027}^{+ 0.027}$	0.9-fixed
	$f_{nH, 2}$	–	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	x_low,3	–	–	0.319 ${}_{- 0.034}^{+ 0.034}$	0.764 ${}_{- 0.118}^{+ 0.118}$	0.5-fixed
	x_high,3	–	–	0.850 ${}_{- 0.026}^{+ 0.026}$	0.765 ${}_{- 0.117}^{+ 0.117}$	0.7-fixed
	$f_{nH, 3}$	–	–	74.6 ${}_{- 7.9}^{+ 7.9}$	30.4 ${}_{- 5.3}^{+ 5.3}$	8.8 ${}_{- 5.4}^{+ 5.4}$	%
Layer-4	x_low,4	–	–	–	0.453 ${}_{- 0.238}^{+ 0.238}$	0.3-fixed
	x_high,4	–	–	–	0.453 ${}_{- 0.238}^{+ 0.238}$	0.5-fixed
	$f_{nH, 4}$	–	–	–	44.5 ${}_{- 10.2}^{+ 10.2}$	42.6 ${}_{- 5.1}^{+ 5.1}$	%
Layer-5	x_low,5	–	–	–	–	0.1-fixed
	x_high,5	–	–	–	–	0.3-fixed
	$f_{nH, 5}$	–	–	–	–	0.0 ${}_{l}^{+ 2.9}$	%
Layer-6	x_low,6	–	–	–	–	0.0-fixed
	x_high,6	–	–	–	–	0.1-fixed
	$f_{nH, 6}$	–	–	–	–	0.0 ${}_{l}^{+ 1.8}$	%
	$N_{H, tot}$	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 ${}_{- 0.13}^{+ 0.13}$	$10^{23}$ cm^-2
	$χ_{ν}^{2}$	261.8/96	175.0/93	124.5/90	122.1/87	254.4/91

Table 6. 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	x_low,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 ${}_{- 0.002}^{+ 0.002}$
	x_high,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 ${}_{- 0.009}^{u}$
	$f_{nH, 1}$	100.0^u	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	x_low,2	–	0.000 ${}_{l}^{+ 0.001}$	0.470 ${}_{- 0.032}^{+ 0.032}$	0.851 ${}_{- 0.097}^{+ 0.097}$	0.7-fixed
	x_high,2	–	0.864 ${}_{- 0.006}^{+ 0.006}$	0.905 ${}_{- 0.008}^{+ 0.008}$	0.851 ${}_{- 0.097}^{+ 0.097}$	0.9-fixed
	$f_{nH, 2}$	–	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	x_low,3	–	–	0.000 ${}_{l}^{+ 0.025}$	0.627 ${}_{- 0.133}^{+ 0.133}$	0.5-fixed
	x_high,3	–	–	0.000 ${}_{l}^{+ 0.025}$	0.627 ${}_{- 0.133}^{+ 0.133}$	0.7-fixed
	$f_{nH, 3}$	–	–	53.1 ${}_{- 4.1}^{+ 4.1}$	22.3 ${}_{- 4.7}^{+ 4.7}$	14.1 ${}_{- 1.4}^{+ 1.4}$	%
Layer-4	x_low,4	–	–	–	0.000 ${}_{- 0.022}^{+ 0.022}$	0.3-fixed
	x_high,4	–	–	–	0.000 ${}_{- 0.022}^{+ 0.022}$	0.5-fixed
	$f_{nH, 4}$	–	–	–	55.4 ${}_{- 10.0}^{+ 10.0}$	0.0 ${}_{l}^{+ 2.9}$	%
Layer-5	x_low,5	–	–	–	–	0.1-fixed
	x_high,5	–	–	–	–	0.3-fixed
	$f_{nH, 5}$	–	–	–	–	0.0 ${}_{l}^{+ 3.1}$	%
Layer-6	x_low,6	–	–	–	–	0.0-fixed
	x_high,6	–	–	–	–	0.1-fixed
	$f_{nH, 6}$	–	–	–	–	55.3 ${}_{- 1.9}^{+ 1.9}$	%
	$N_{H, tot}$	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 ${}_{- 0.14}^{+ 0.14}$	$10^{23}$ cm^-2
	$χ_{ν}^{2}$	610.0/96	504.4/93	114.1/90	111.1/87	119.6/91

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Full text

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

Chichuan Jin

National Astronomical Observatories, Chinese Academy of Sciences, A20 Datun Road, Beijing 100101, China

Gabriele Ponti

INAF, Osservatorio Astronomico di Brera Merate, via E. Bianchi 46, I-23807 Merate, Italy

Max-Planck-Institut für Extraterrestrische Physik, Giessenbachstrasse, D-85748 Garching, Germany

Guangxing Li

South-Western Institute for Astronomy Research, Yunnan University, Kunming 650500, China

David Bogensberger

Max-Planck-Institut für Extraterrestrische Physik, Giessenbachstrasse, D-85748 Garching, Germany

(Accepted for Publication in ApJ)

Abstract

SWIFT J1658.2-4242 is an X-ray transient discovered recently in the Galactic plane, with severe X-ray absorption corresponding to an equivalent hydrogen column density of $N_{\rm H,abs}\sim 2\times 10^{23}$ cm*-2*. Using new Chandra and XMM-Newton data, we discover a strong X-ray dust scattering halo around it. The halo profile can be well fitted by the scattering from at least three separated dust layers. During the persistent emission phase of SWIFT J1658.2-4242, the best-fit dust scattering $N_{\rm H,sca}$ based on the COMP-AC-S dust grain model is consistent with $N_{\rm H,abs}$ . The best-fit halo models show that 85-90 percent of the intervening gas and dust along the line of sight of SWIFT J1658.2-4242 are located in the foreground ISM in the Galactic disk. The dust scattering halo also shows significant azimuthal asymmetry, which appears consistent with the inhomogeneous distribution of foreground molecular clouds. By matching the different dust layers to the distribution of molecular clouds along the line of sight, we estimate the source distance to be $\sim$ 10 kpc, which is also consistent with the results given by several other independent methods of distance estimation. The dust scattering opacity and the existence of a halo can introduce a significant spectral bias, the level of which depends on the shape of the instrumental point spread function and the source extraction region. We create the xspec dscor model to correct for this spectral bias for different X-ray instruments. Our study reenforces the importance of considering the spectral effects of dust scattering in other absorbed X-ray sources.

(ISM:) dust, extinction — X-rays: ISM — X-rays: binaries — Galaxy: disk — ISM: clouds

††facilities: Chandra(ACIS), XMM-Newton(EPIC)††software: ciao (v4.10; Fruscione et al. 2006), sas (v17.0.0; Gabriel et al. 2004), esas (Snowden & Kuntz 2014), ds9 (v7.5; Joye & Mandel 2003), iminuit (v1.3.3, James & Roos 1975), xspec (v12.10.1; Arnaud 1996)

1 Introduction

1.1 X-ray Transient: SWIFT J1658.2-4242

SWIFT J1658.2-4242 is an X-ray transient whose first detection was reported on 2018 February 16 in Swift/BAT (Barthelmy et al. 2018; D’Avanzo, Melandri & Evans 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 Ra= $16^{\rm h}58^{\rm m}12^{\rm s}.64$ , Dec= $-42\arcdeg 41^{\prime}54.4^{\prime\prime}$ , with the 90% uncertainty being 1.6”. 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 degree 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 $1.7\pm 1.5$ and a large neutral hydrogen column density for the X-ray absorption: $N_{\rm H,abs}~{}=~{}(1.9\pm 0.5)\times 10^{23}$ 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 $1.76\pm 0.06$ and $N_{\rm H,abs}=(1.6\pm 0.2)~{}\times 10^{23}$ cm*-2*.

Russell et al. (2018) 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 Ra= $16^{\rm h}58^{\rm m}12^{\rm s}.700$ ( $\pm 0.004$ ), Dec= $-42\arcdeg 41^{\prime}56.09^{\prime\prime}$ ( $\pm 0.25$ ). This radio position is consistent with the X-ray position. Russell, Lewis & Zhang (2018) reported optical observations between 2018 February 22 and 25 in the SDSS $\sc i$ and $\sc r$ bands, using an one-meter telescope in the Las Cumbres Observatory. An optical source was detected at the radio position, with the $i$ band AB magnitude being 19.07 $\pm$ 0.06 $mag$ , which was the only source within 8 arcsec of the radio source. But 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 cut-off power law plus a Compton reflection. In their best-fit model 4, they reported $N_{\rm H,abs}=(1.80\pm 0.08)~{}\times 10^{23}$ cm*-2*, photon index was $1.63\pm 0.02$ and the coronal temperature was $22\pm 1$ 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 $64^{+2}_{-3}$ degree, which was consistent with the detection of dips in the NuSTAR X-ray light curve. The $N_{\rm H,abs}$ during the dips increased to $1.00^{+0.08}_{-0.07}~{}\times 10^{24}$ cm*-2*. Type-C Quasi-Periodic Oscillation (QPO) 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.

1.2 X-ray Dust Scattering Halo

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 point-like 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, McCray & Kelley 1986). Since the first observational discovery of a dust scattering halo around the source GX339-4 by the Einstein satellite (Rolf 1983), such effect has been repeatedly observed in several tens of X-ray sources (e.g. Predehl & Schmitt 1995; Xiang, Zhang & Yao 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 point-like X-ray source should be different from the standard point spread function (PSF) of an instrument (Predehl, Schmitt & Trümper 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, Allen & McCray 2000). Corrales et al. (2016) reported that ignoring the effects of dust scattering opacity could lead to an over-estimate of $N_{\rm H,abs}$ by a baseline level of 25%. Smith, Valencic & Corrales (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 Centre (GC) with $N_{\rm H,abs}\sim 3\times 10^{23}$ 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 (Jin et al. in preparation).

Since SWIFT J1658.2-4242 lies in the Galactic plane and its $N_{\rm H,abs}$ is on the order of $10^{23}$ 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 check if 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.

2 Observation and Data Reduction

This work is based on the data from a 29.9 ks Chandra Director’s Discretionary Time (DDT) observation conducted on 28th April 2018, using the spectroscopic array of the Advanced CCD Imaging Spectrometer (ACIS-S) instrument with the High-Energy Transmission Grating (HETG). It also uses data from 5 XMM-Newton DDT observations conducted between 27th February and 28th March 2018 (Table 1), each with one Metal-Oxide-Silicon (MOS) camera in the Full Frame mode (Medium filter) and the other two European Photon Imaging Cameras (EPIC) in the Timing mode (Bogensberger et al. in preparation). The data reduction procedures are described below.

2.1 Chandra

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. Firstly 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 script111http://cxc.cfa.harvard.edu/ciao/threads/flare/. 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. Since 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 behaviour 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.

Moreover, bright features along the HETG arms 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 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 modelling and to be convolved with the dust scattering halo.

2.2 XMM-Newton

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. Since 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. Firstly, 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 Bogensberger et al. 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. Since the source was very bright ( $F_{\rm 2-10~{}keV}\sim 10^{-9}$ erg cm*-2* s*-1* observed during all the observations in Table 1), signal-to-noise was not a problem for the XMM-Newton data even for a short exposure time of only a few kilo-seconds.

In OBSID: 0805200201, the source showed a flip-flop behaviour appearing as high-flux and low-flux platforms, the flux difference between them was $\gtrsim$ 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 $\sim$ 10% in 2-10 keV, while the final 13 ks showed enhanced variability of $\sim$ 10% in the same band, thus these periods were excluded, 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 Bogensberger et al. in preparation). There was no flip-flop behaviour in the rest 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 modelling 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.

3 Analysis of the X-ray Dust Scattering Halo

3.1 Shape of the Azimuthal-averaged Halo

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 only used the ACIS data of much higher angular resolution for more detailed halo profile analysis. Firstly 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 towards 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.

Then we extracted the azimuthal-averaged radial profiles from 2-4, 4-6 and 6-10 keV bands, separately. Since 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 $\sim$ 30 arcsec, where the source is more than one order of magnitude brighter than the background. But due to the limitation of background subtraction and source brightness, the halo profile is significantly detectable only at $\lesssim$ 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).

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 over-plotted 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 a strong evidence for the presence of an X-ray dust scattering halo. For comparison, we also over-plot the composite radial profile observed in Chandra ACIS for X-ray sources within 2 square degrees of Sgr A⋆ in the GC (Jin et al. in preparation), where the $N_{\rm H,abs}$ is also on the order of $10^{23}$ 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 towards 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 degrees around Sgr A⋆ (Jin et al. in preparation), it is significantly different on scales of 10-20 degrees.

3.1.1 Modelling 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 modelling 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. Since 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, Dwek & Arendt (2004). The first one is the COMP-AC-S dust grain population, which has been recommended for the GC direction (Fritz et al. 2011). Since SWIFT J1658.2-4242 is only 16 degree 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 due to 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 $\chi^{2}$ fitting. The best-fit parameters are given in Tables 2, 5 and 6.

We began the halo profile modelling 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 $N_{\rm H,sca}$ (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 $0\leq x\leq 0.888$ , with the total $N_{\rm H,sca}$ being $(1.03\pm 0.01)~{}\times 10^{23}$ cm*-2*. But the $\chi^{2}$ is only 348.3 for 96 degrees-of-freedom (DOFs). The bad $\chi^{2}$ is confirmed by the significant residuals shown in the Panels a1, b1 and c1 in Figure 5.

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 $\chi^{2}_{\rm\nu}=214.3/93$ , indicating a significant improvement compared to Scenario-1. Layer-1 is found to distribute within $0.99\leq x\leq 1$ and contains ( $14.1\pm 5.2$ )% LOS dust. The remaining dust is contained in layer-2, which is located within $0\leq x\leq 0.911$ . The total $N_{\rm H,sca}$ is found to be $(1.55\pm 0.09)~{}\times 10^{23}$ 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 $\chi^{2}$ is 105.4 for 90 DOF, indicating a further significant improvement. The best-fit model shows that (13.3 $\pm 1.3$ )% LOS dust is in layer-1 at $0.990\leq x\leq 0.996$ , ( $25.8\pm 3.0$ )% LOS dust is in layer-2 at $0.666\leq x\leq 0.906$ , and the remaining ( $60.9\pm 9.2$ )% LOS dust is in layer-3 at $0\leq x\leq 0.401$ . The total $N_{\rm H,sca}$ is $(1.66\pm 0.16)~{}\times 10^{23}$ 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 $\chi^{2}$ being 108.0 for 90 DOFs.

Scenario-4 contains 4 dust layers. The best-fit halo decomposition is shown in the Panels a4, b4 and c4 in Figure 5. However, the $\chi^{2}$ only improves by 0.7 for 3 additional free parameters, thus adding more layers cannot bring further improvement in the halo fitting. The best-fit total $N_{\rm H,sca}$ is also consistent with the result of Scenario-3.

As a further test, we tried Scenario-5 with 6 layers, as shown by the Panels a5, b5 and c5 in Figure 5. Layer-1 is still local to the source, and another 5 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, 0.7-0.9, respectively. The boundaries of these 5 layers were fixed during the fitting, only their $N_{\rm H,sca}$ values were allowed to vary. In the best-fit model of this scenario, ( $13.3\pm 1.3$ )% LOS dust is contained in layer-1 at $0.99\leq x\leq 1$ . For the rest 5 layers, ( $23.7\pm 3.8$ )% LOS dust is located within $0.7\leq x\leq 0.9$ , 0% within $0.5\leq x\leq 0.7$ , ( $17.7\pm 4.4$ )% within $0.3\leq x\leq 0.5$ , ( $26.6\pm 8.9$ )% within $0.1\leq x\leq 0.3$ , and ( $18.7\pm 3.0$ )% within $0.0\leq x\leq 0.1$ . The best-fit $\chi^{2}$ is 108.1 for 91 DOFs, and the total $N_{\rm H,sca}$ is $(1.65\pm 0.40)~{}\times 10^{23}$ cm*-2*, both are consistent with the results in Scenario-3 and 4.

All the error bars come from the 1 $\sigma$ 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, 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 $\chi^{2}$ (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 3 dust layers to fit, and adding more dust layers cannot bring further improvement. In all the scenarios with more than 2 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 $\tau_{sca}$ is larger than 1.3. The major effect of multiple-scattering is causing the halo profile to be more extended (Mathis & Lee 1991; Xiang, Lee & Nowak 2007; Jin et al. 2017). Since we know $\tau_{sca}\propto E^{-2}$ where $E$ is the photon energy (Predehl & Schmitt 1995), it is clear that multiple scattering is much more important at lower energies. Adopting $N_{\rm H,sca}=16.6\times 10^{23}$ cm*-2* from the best-fit halo model in Table 2, we can calculate $\tau_{sca}$ 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.

4 Halo Azimuthal Asymmetry Analysis

4.1 Comparison of Halo Profiles in Subregions

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 6 sub-regions, each having an opening angle of 60 degrees. The 7th region was defined with a 30-degree angular width where the non-uniformity 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 sub-region. The halo non-uniformity is most severe in region-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 sub-region of region-4, where the halo intensity drops sharply by a factor of 2-3 at the viewing angle of $\sim$ 30 arcsec.

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 sub-region, by fixing the location of each layer but allowing the $N_{\rm H,sca}$ of layers-2 and 3 to vary. We also fixed the $N_{\rm H,sca}$ 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 sub-regions (see Figure 5). The best-fit $N_{\rm H,sca}$ in every subregion as a fraction of the azimuthal-averaged halo value is given in Table 3. We find that the $N_{\rm H,sca}$ of layer-2 can change by as much as a factor of 4 in different subregions, while the $N_{\rm H,sca}$ of layer-3 can change by a factor of 3, but the total $N_{\rm H,sca}$ in different subregions change by only $\sim$ 10%.

However, simply changing the $N_{\rm H,sca}$ in layer-2 and 3 is not enough to account for all the halo asymmetry. For example, the flux drop in Figure 6 Panel a7 at $\sim$ 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.

4.2 Halo Model with Inhomogeneous Dust Distribution

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 $N_{\rm H,sca}$ has a sudden change at a specific radius ( $R_{\rm break}$ , a free parameter) in region-7, then the sharp flux drop can be reproduced. We also allowed the $N_{\rm H,sca}$ 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 Figures 7 and Table 4.

Firstly, 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 $N_{\rm H,sca}$ in layer-4 increases slightly to (64.8 $\pm$ 8.6)%, and its upper limit increases to 0.458 $\pm$ 0.090. Secondly, the flux drop can be well modelled with $R_{\rm break}=27.0\pm 0.1$ arcsec. Within this radius, the $N_{\rm H,sca}$ of layer-4 is ( $18.8\pm 1.8$ ) $\times$ 1022 cm*-2* which is about 1.8 times as high as the average value. But it drops significantly to ( $8.5\pm 0.8$ ) $\times$ 1022 outside $R_{\rm break}$ , 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 $N_{\rm H,sca}$ in foreground dust layers.

5 Discussion

5.1 ISM Distribution along the Source Sightline

5.1.1 Results from the Halo Profile Study

SWIFT J1658.2-4242 is a heavily absorbed X-ray transient with $N_{\rm H,abs}~{}\simeq~{}2~{}\times 10^{23}$ 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 $N_{\rm H,sca}$ , 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 only had a small impact on the resultant relative dust distribution.

However, a potential uncertainty is associated with the fact that the halo profile modelling 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, 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 point-like, and the radial profile is undistinguishable from the instrumental PSF, i.e. the halo component is not ‘visible’ in the observed radial profile even if the $N_{\rm H,sca}$ is large. Therefore, it is possible for the fraction of $N_{\rm H,sca}$ in the other foreground dust layers to be over-estimated.

5.1.2 Results from the Molecular Cloud Study

The distribution of molecular clouds (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 ratio, 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. Firstly, we identified components and measured their velocities. The distances of these components can be determined based on 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:

•

A intensive component (C1) at -25 km s*-1*, which sits at a distance of $2.5\pm 0.6$ kpc.

•

A intensive component (C2) at -118 km s*-1*, which sits at a distance of 8.0 $\pm$ 0.8 kpc.

•

A weaker component (C3) at -11 km s*-1*, with a relatively low surface densities, which sits at a distance of 1.5 $\pm$ 0.6 kpc.

•

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 $\sim$ 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 $1.2\times 10^{22}$ cm*-2* and $2.4\times 10^{22}$ 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 ( ${\rm d}v\approx$ 20 km s*-1*). It probably corresponds to diffuse gas that lingers around in one of the the Galactic spiral arms.

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 $\sim$ 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

There are other clues to support the fact that a large fraction of the gas and dust along the LOS of SWIFT J1658.2-4242 should be located in the Galactic disk, which are described separately below:

•

The total $N_{\rm H,sca}$ of SWIFT J1658.2-4242 is found to be $(1.66\pm 0.16)\times 10^{23}$ cm*-2* (see Table 2, Scenario-3). The dust grain model adopts the Solar abundances from Holweger (2001), which is also consistent with the Asplund et al. (2009) abundances. In comparison, the $N_{\rm H,abs}=(1.8\pm 0.08)~{}\times 10^{23}$ cm*-2* for the persistent phase outside the dips222The $N_{\rm H,abs}$ of SWIFT J1658.2-4242 can reach $10^{24}$ cm*-2* during the dips (Xu et al. 2018). In this case most of the X-ray absorption should be intrinsic to the binary system, likely due to the matter transferred from the companion star. (Xu et al. 2018) is based on the interstellar medium (ISM) abundances from Wilms, Allen & McCray (2000), which is $\sim 20$ % lower than the Solar abundances. Then $N_{\rm H,abs}$ based on the Holweger (2001) Solar abundances will be $(1.99\pm 0.19)~{}\times 10^{23}$ cm*-2*. Thus $N_{\rm H,abs}$ is consistent with $N_{\rm H,sca}$ , which implies that the detected LOS dust in the halo can already fully account for the observed X-ray absorption.

•

The $N_{\rm H,abs}$ of SWIFT J1658.2-4242 has a baseline level on the order of $10^{23}$ cm*-2* in all the observations taken at different times and different source flux levels (Bogensberger et al. in preparation). This underlying $N_{\rm H,abs}$ is most likely to be associated with the ISM in the Galactic disk, which should not vary as rapid as the ISM local to the binary system of SWIFT J1658.2-4242 since its discovery.

•

According to the Schlafly & Finkbeiner (2011) reddening map, the Galactic extinction in the LOS of SWIFT J1658.2-4242 is $A_{\rm v}\sim 58.6$ mag (Pessev 2018), which, using the Zhu et al. (2017) gas-to-dust relation, corresponds to $N_{\rm H,abs}~{}=~{}1.22~{}\times 10^{23}$ cm*-2* (Russell, Lewis & Zhang 2018). This value is also consistent with the observed lower limit of $N_{\rm H,abs}$ . Thus the strong Galactic reddening towards SWIFT J1658.2-4242 also implies a large fraction of foreground gas and dust in the Galactic disk.

•

SWIFT J1658.2-4242 is in the Galactic plane at 16.693 degree from Sgr A⋆, its underlying $N_{\rm H,abs}$ is very similar to Sgr A⋆ (Ponti et al. 2017) and the GC magnetar SGR J1745-2900 (e.g. Kennea et al. 2013; Mori et al. 2013; Rea et al. 2013; Coti Zelati et al. 2017; Jin et al. 2017). It has been reported that most of the GC foreground gas and dust should be located in the Galactic disk, probably distributed along the spiral arms (e.g. Bower et al. 2014; Wucknitz 2015; Sicheneder & Dexter 2017; Jin et al. 2017, 2018). Thus it is possible that the same intervening spiral arms also create significant X-ray absorption opacity and dust scattering opacity towards SWIFT J1658.2-4242.

According to all the above clues, we conclude that most of the gas and dust in the LOS of SWIFT J1658.2-4242 is likely to be located in the Galactic disk, and they correspond to an $N_{\rm H}$ of the order of $10^{23}$ cm*-2*.

5.2 Asymmetric Halo and Inhomogeneous Distribution of Foreground ISM

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 non-uniform because of at least two reasons. One reason is the partial alignment of non-spherical 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 non-uniform 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 $N_{\rm H,sca}$ drop at the viewing angle of 27 arcsec in layer-4 can account for most of the observed flux drop in region-7.

The 2-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 radius333http://cxc.harvard.edu/ciao/ahelp/acisreadcorr.html, 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 re-extracted 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.

Since 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 $\rightarrow$ 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.

5.3 Distance to SWIFT J1658.2-4242

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. (2018) 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 based on this argument alone. Below we discuss several other methods of estimating the source distance.

5.3.1 Distance Estimated from the State Transition Luminosity

An independent method to estimate the source distance is to use the soft-to-hard state transition Eddington ratio, i.e. the transition luminosity in the unit of Eddington luminosity. Maccarone (2003) studied the transition luminosity of 10 X-ray binaries (XRBs), including 6 black hole XRBs and 4 neutron-star XRBs. They found that for black hole XRBs the soft to hard transition luminosity is typically within 1-4% of the Eddington Luminosity, with an average value of 2%; while for neutron-star XRBs it is within 0.4-5%. Thus the transition luminosity can be used as a rough estimate of the source distance, provided that the mass of the accreting source is known.

Following the hardness ratio evolution of SWIFT J1658.2-4242 as monitored by Swift satellite, the soft to hard transition flux in the 2-10 keV band was observed to be $\sim 1.5\times 10^{-10}$ erg s*-1* cm*-2* (Bogensberger et al. in preparation). Then the bolometric transition flux from 0.5 keV to 10 MeV can be estimated to be $\sim 1.4\times 10^{-9}$ erg s*-1* cm*-2*, assuming a power law model with the photon index 1.8, $N_{\rm H,abs}=1.66\times 10^{23}$ cm*-2* and an exponential cutoff at 200 keV (Maccarone 2003). If SWIFT J1658.2-4242 contains a 1.5 M*⊙* neutron star, then for the transition Eddington ratio of 0.4-5%, $d$ would be 2.2-7.6 kpc. However, SWIFT J1658.2-4242 is more likely to be a black hole XRB (Xu et al. 2018). Then for a black hole mass of 5-15 M*⊙*, and for the average transition Eddington ratio of 2%, $d$ would be 8.8-15.3 kpc. We can also calculate that $d$ changes to 6.2-10.8 kpc and 10.8-18.7 kpc for the transition Eddington ratio of 1% and 4%, separately.

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 3 dust layers to fit its halo, so it is likely to have $d>$ 5 kpc. However, since 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.

5.3.3 Distance Estimated from the LOS MC Distribution

Since a large fraction of interstellar dust is likely to be contained in MCs, the distribution of MCs in the LOS can be used to compare with different dust scattering components, and thus help to determine the source distance. In Section 5.1.2 we have shown that there are at least 4 major MC components in the LOS of SWIFT J1658.2-4242. Comparing with the best-fit dust distribution in Scenarios-3, 4 and 5, C2 can be associated with the layers within $0.7\leq x\leq 0.9$ where $\sim$ 25% LOS dust is located. This allows us to estimate a source distance of 9 $\lesssim d\lesssim$ 11 kpc. This distance also put C1 and C3 in the fractional distance range of $0.0\leq x\leq 0.4$ where $\sim$ 50% LOS dust is located. Moreover, if C4 is located at 10 kpc away and is associated with layer-1 which is intrinsic to SWIFT J1658.2-4242, then the source distance will also be 10 kpc.

Considering all the independent distance estimates discussed above, we conclude that SWIFT J1658.2-4242 is most likely to be located at $d\sim$ 10 kpc.

5.4 Spectral Bias Caused by the Dust Scattering Halo

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, Valencic & Corrales 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. Due to 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 $\chi^{2}$ . It must be emphasized that an accurate correction factor only requires the halo model to fit the halo shape accurately in every energy band, 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 Fig.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. Based on these model calculations, we create xspec models, named dscor, for different instruments and different source extraction regions444The model package will be made available at http://blog.jinchichuan.cn/dscor-model and submitted to the xspec website. It can also be downloaded directly from https://www.dropbox.com/s/mvpvvas0i9y3hcs/dscor.tar.gz?dl=0..

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. Firstly, this requirement is difficult to be met for heavily absorbed X-ray sources like SWIFT J1658.2-4242 and GC sources (Jin et al. in preparation), because their dust scattering opacity is not negligible. Secondly, 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), 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.

6 Summary and Conclusions

SWIFT J1658.2-4242 is a bright X-ray transient in the Galactic plane at 16.693 degrees away from Sgr A⋆. Its X-ray emission was heavily absorbed with $N_{\rm H,abs}\sim 2\times 10^{23}$ cm*-2*. Given the X-ray brightness and the large amount of LOS dust as inferred from $N_{\rm H,abs}$ , we carry out a detailed study of the X-ray dust scattering halo around it. The main results of this work are summarized below:

•

We discovered a strong X-ray dust scattering halo around SWIFT J1658.2-4242 in the data of the latest Chandra and XMM-Newton observations.

•

The azimuthal-averaged halo was well modelled by at least 3 dust layers along the LOS. The best-fit halo model with the COMP-AC-S dust grain population had a total $N_{\rm H,sca}$ which is consistent with the $N_{\rm H,abs}$ of the X-ray spectrum observed during the persistent emission phase. Our halo modelling also suggested that 85-90 percent gas and dust in the LOS of SWIFT J1658.2-4242 should be located in the Galactic disk far from the source.

•

The halo showed significant azimuthal asymmetry, with one of the azimuthal sub-regions exhibiting a sharp flux drop in the halo profile. This feature was well explained as a sudden change of dust column in the major halo component nearby at the viewing angle of $27.0\pm 0.1$ arcsec.

•

We found that the 2D halo shape is broadly correlated with the 2D intensity map of CO ( $3\rightarrow 2$ ) 0.87 mm emission, suggesting that the halo asymmetry should be due to the inhomogeneous distribution of dust in the foreground ISM.

•

Several methods were used to obtain independent estimates of the source distance. The most direct constraints came from the comparison between the distributions of halo components and MC components. Our results indicated that SWIFT J1658.2-4242 is most likely to be at $d\sim$ 10 kpc.

•

The strong dust scattering halo introduced strong spectral biases for different instruments with conventional source extraction regions. We produced xspec models to correct for the spectral biases.

•

We explained why it is problematic to simply assume a gas-to-dust ratio to estimate and correct for the dust scattering opacity. Instead, it is a must to measure and model the halo profile in order to correct for it properly.

The results of our work also highlighted the importance of considering the dust scattering in other absorbed X-ray sources, especially those with $N_{\rm H,abs}\gtrsim 10^{23}$ cm*-2*. Since the halo shapes of different sources are very likely to be different, this spectral correction must be carried out on a source-by-source basis in order to achieve the highest accuracy.

We thank the anonymous referee for providing valuable comments and suggestions. CJ thanks Ligang Hou for insightful discussions about the molecular clouds in the Milky Way. GL thanks Xiaohui Sun for help with the 21cm data. The authors wish to thank the Chandra and XMM-Newton teams for approving and scheduling the DDT observations. CJ acknowledges the National Natural Science Foundation of China through grant 11873054. GP acknowledges financial support from the Bundesministerium fur Wirtschaft und Technologie/Deutsches Zentrum für Luft- und Raumfahrt (BMWI/DLR, FKZ 50 OR 1604, FKZ 50 OR 1715, FKZ 50 OR 1812) and the Max Planck Society. This work is mainly based on observations made by the Chandra X-ray Observatory, as well as data obtained from the Chandra Data Archive. We also used the data from XMM-Newton, an ESA science mission with instruments and contributions directly funded by ESA Member States and NASA. This research has made use of software provided by the Chandra X-ray Center (CXC) in the application packages CIAO, ChIPS, and Sherpa.

Appendix A Dust Scattering Halo Observed by XMM-Newton MOS

The halo profile observed by XMM-Newton MOS should be the convolution of the intrinsic halo shape with the MOS PSF, as shown by Jin et al. (2017) for the halo around AX J1745.6-2901. We extracted the radial profiles of SWIFT J1658.2-4242 from each of the time intervals as described in Section 2.2 within 2-4, 4-6 and 6-10 keV bands. Since SWIFT J1658.2-4242 was very bright during the XMM-Newton observations, it caused severe pile-up effect on the CCD array, thereby distorting the halo shape in MOS. This effect is confirmed by the obvious bending-down of the radial profile at inner radii as show in Figure 12.

In comparison, the photon pile-up in the Chandra ACIS observation is less than one percent outside 2.5 arcsec radius. It is possible for the dust layer local to SWIFT J1658.2-4242 to change its $N_{\rm H,sca}$ significantly within a short timescale. For example, $N_{\rm H,abs}$ has been observed to increase by one order of magnitude during the dipping periods (Xu et al. 2018). However, the timescale for the foreground dust layers in the Galactic disk to vary significantly may be much longer (see Section 5.1). Therefore, we can convolve the best-fit halo model from Scenario-3 (see Section 3.1.1) with the PSF of MOS to obtain the predicted pile-up-free radial profile in MOS. Then we used the halo model, together with a free constant to account for the background, to fit the observed radial profile outside 300 arcsec where the halo should be dominated by dust scattering components far from the source. Then we extrapolated the model down to smaller radii. Figure 12 shows the background-subtracted radial profiles and the corresponding halo models. We find that the observed halo profile in MOS has a consistent shape with the model at $\gtrsim$ 200 arcsec. Within 200 arcsec, the observed profile is always lower than the model extrapolation, and the discrepancy increases towards smaller radii, which is consistent with the expected behaviour of photon pile-up effect.

In order to further check that the apparent differences between the observed and model radial profiles in MOS are not due to the change of $N_{\rm H,sca}$ in any foreground dust layers, we also show individual dust scattering components (blue dotted lines) and the PSF profile (red dash line) in Figure 12. It is clear that the observed radial profile in MOS is flatter than any of the halo components, thus it cannot be fitted by any linear combination of these halo components, and so the change of $N_{\rm H,sca}$ cannot be the reason.

Since photon pile-up can reduce the fraction of single events and increase multiple-pixel events, we computed the fraction of single and double events in 7-10 keV. Figure 13 shows the results for every observation. The pile-up-free fraction can be determined from the data at large radii where there is no pile-up and the fraction is constant, as shown by the dash lines in the figure. As the pile-up effect becomes stronger at inner radii, the fraction of single events becomes smaller, while the fraction of double events becomes larger. Therefore, the outer radius of the pile-up region can be roughly estimated to be the radius where the observed fraction of single events begins to deviate from the pile-up-free value, as shown by the red dotted line in the figure. We found that this radius is within the range of 100-200 arcsec, which is consistent with the radius where the observed halo shape deviates from the prediction. Because of the severe pile-up effect in MOS, we cannot extract further information from the halo profile.

Appendix B Modelling the Azimuthal-Averaged Halo Profile with Different Dust Grain Populations

For the five halo model scenarios described in Section 3.1.1, we changed the dust grain population to BARE-GR-B and COMP-NC-B, and repeated the above analysis. The best-fit parameters are listed in Tables 5 and 6. For each grain population, the $\chi^{2}$ improves significantly from one layer to two and three, but only marginally as the number of layers reaches 4. Scenario-5 produces worse fit than Scenario-3 and 4. Since the BARE-GR-B population is characterized by dust grains with smaller sizes than COMP-AC-S, its halo profile is more extended, therefore the best-fit fractional distances are all closer to the source. In comparison, the COMP-NC-B population has a bigger fraction of large dust grains, so the best-fit fractional distances are all closer to Earth. The relative distribution of LOS dust for each scenario does not change significantly with the dust grain population. The total $N_{\rm H,sca}$ is $(1.92\pm 0.16)~{}\times 10^{23}$ cm*-2* for BARE-GR-B and $(2.61\pm 0.13)~{}\times 10^{23}$ cm*-2* for COMP-NC-B in Scenario-3. These values are larger than in COMP-AC-S, which is due to different grain metallicities and size distributions assumed in different grain populations.

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