INTERSTELLAR DUST PROPERTIES FROM A SURVEY OF X-RAY HALOS

For each source, the literature was scoured for measurements of A_V or reddening E(B–V), which has often been used to estimate A_V by the relation A_V = ${R}_{V}\times E(B-V)$, where ${R}_{V}\;\sim$ 3.1 for the typical Galactic sight line. For sources where E(B–V) was given, this was cast as A_V by assuming R_V = 3.1. In cases where no uncertainties were given, the average of the quoted uncertainties, 13%, was assumed.

There were 20 objects in the survey with known A_V. In order to increase the number in the sample, the HEASARC archive was searched for absorbed XRBs in globular clusters and stars with known A_V. These were bright enough to have a spectrum that could be fit well, but not bright enough to have a detectable halo. Three sources were found (EXO 1745–248, HD 245770, and NGC 6440). The parameters of their spectral fits are listed in Table 11. Values of A_V for all sources, with and without halos, are discussed in this section. The extinction values used in this work are summarized in Table 12. For ease of comparison, the hydrogen column densities obtained from the spectral fits (from Tables 4 and 11) are reprinted here.

Table 11.  Spectrum Fit Parameters for Absorbed Objects without Detectable Halos

Object	Fit (plus abs)	${N}_{{\rm{H}}}$ a	Parametersb	χ2
EXO 1745–248	DBB	1.72 ± 0.04	Tin = 2.76 ± 0.09	0.77
HD 245770	PL	0.32 ± 0.03	Γ = 0.51 ± 0.04	0.76
NGC 6440	PL	0.65 ± 0.02	Γ = 1.34 ± 0.03	0.91

Notes.

^aN_H is in units of 10²² cm⁻², T_in is the temperature of the inner disk in keV. ^bT_in is the temperature of the inner disk in keV.

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4U 1820–30. This LMXRB is in the globular cluster NGC 6624. A catalog of globular clusters (Harris 1996, 2010 edition) lists E(B–V) = 0.28 ± 0.03. Valenti et al.'s (2004) study of the cluster's color–magnitude diagram (CMD) and distance modulus yielded a slightly higher value, 0.34, although if the uncertainty is about 13%, these values are essentially the same. Nonetheless, Valenti et al. (2004) relied on Harris's value in their study and we do the same, leading to A_V = 0.87 ± 0.13.

Swift J1753.5–0127. This soft X-ray transient was found in hard X-rays in 2005 with the Swift BAT instrument, and ground-based follow-up quickly detected the optical counterpart (Halpern 2005). It was the subject of an extensive multiwavelength campaign by Cadolle Bel et al. (2007), who obtained optical spectra and measured the width of the IS Na i doublet. This led to an estimate of the reddening, E(B–V) = 0.34 ± 0.04, or A_V = 1.05 ± 0.12.

4U 1850–087. This LMXRB is in the globular cluster NGC 6712. Harris's catalog (1996, 2010 edition) listed E(B–V) = 0.45 ± 0.05, which is higher than that found by studies of the cluster's CMD by Ortolani et al. (2000; E(B–V) = 0.33) and Zinn (1980; E(B–V) = 0.39) but similar to that found by Webbink (1985; E(B–V) = 0.48) and Zinn (1985; E(B–V) = 0.48). Here we adopted Harris's value, and A_V = 1.40 ± 0.14.

IGR J18450–0435. This HMXRB was discovered by ASCA and follow-up optical and IR photometry and spectra were obtained (Coe et al. 1996). These revealed that the companion is O9.5 I, and based on its colors, the authors estimate E(B–V) = 2.45, although they also note that there is large uncertainty in the extinction law for this sight line. If R_V = 3.1, then A_V = 7.6.

4U 1908+005. Identifying the optical counterpart in this LMXRB was a challenge. Thorstensen et al. (1978) obtained photographic photometry and spectroscopy of what was thought to be the companion. They determined that it had a spectral type between G7 and K3, with indeterminate luminosity type; given its colors and assuming it was K0 V, they estimated E(B–V) ∼ 0.37. Later studies confirmed the spectral type to be early K (Shahbaz et al. 1997), but Callanan et al. (1999) was able to resolve the system in quiesence with K-band Keck photometry and found that it was a different star than had been examined by Thorstensen et al. (1978) or Shahbaz et al. (1997). Subsequent spectroscopy by Chevalier et al. (1999) found that the companion is likely to be K7 V with E(B–V) = 0.5 ± 0.1, or A_V = 1.55 ± 0.31.

4U 1957+11. Margon et al. (1978) identified the optical counterpart to this LMXRB and obtained spectra and photometry for both it and several nearby stars. From these field stars, Margon et al. estimated that A_V = 1.0–1.5. We therefore take A_V = 1.25 ± 0.25. As will be seen in Section 5.4, this source has an X-ray scattering optical depth (τ_sca) that is higher than expected for its optical extinction.

X Per. This HMXRB was studied in great detail by Telting et al. (1998). Using UV, optical, and IR data taken from the disk-free and near-disk-free states, they modeled the system and found that the companion was likely a O9.5-B0V star, similar to spectral types found by others (Hiltner 1956; Lesh 1968), and found that E(B–V) = 0.39, or A_V = 1.21.

4U 0614+091. Davidsen et al. (1974) obtained photographic photometry and spectrophotometry on this LMXRB system, and argued that the reddening from nearby stars suggested E(B–V) ∼ 0.3. This was supported by work by Machin et al. (1990), who found an upper limit on the equivalent width of the DIB at 4430 Å, which led to $E(B-V)\;\leqslant$ 0.3 ± 0.2. However, the most recent study on the ISM on this sight line that included spectroscopy on the IS Na i lines provided a lower limit of $E(B-V)\;\geqslant \;$ 0.4, and the strength of the DIB at 5780 Å led to E(B–V) = 0.88 ± 0.1 (Nelemans et al. 2004). We have adopted the most recent value for this work, and so A_V = 2.73 ± 0.31.

4U 0919–54. Chevalier & Ilovaisky (1987) obtained optical photometry on this LMXRB system and assumed the intrinsic colors of van Paradijs (1983) to find E(B–V) = 0.3 ± 0.1, which compared favorably with an estimate of the region's extinction, A_V = 1.0 (Neckel & Klare 1980). However, Nelemans et al. (2004) measured the equivalent widths of the IS Na D lines and the DIB at 5780 Å and found $E(B-V)\;\geqslant$ 0.4 and E(B–V) = 0.70 ± 0.15, respectively. For this work, we use A_V = 2.17 ± 0.47.

2S 0921–630. Shahbaz et al. (1999) obtained high resolution spectra of this LMXRB system and determined that the companion is a K0 III. In a subsequent study by Shahbaz & Watson (2007) of the star's equatorial rotational velocity, the authors noted that the IS Na i doublet was clearly detected, and used it to estimate E(B–V) = 0.33 ± 0.01 for this LOS, or A_V = 1.02 ± 0.03.

4U 1119–603 = Cen X-3 = V779 Cen. Krzeminski (1974) identified the optical companion in this system as a reddened O9-O9.5 V or B0 I-III based on the observed color indices. Later work by Hutchings et al. (1979) relied on spectra to suggest the companion's spectral type to be O6-O9 I. Hutchings et al. (1979) also noted the presence of DIBs at 4430, 5780, and 6254 Å, but did not use them to estimate the reddening; rather, with the star's color index and brightness, they estimate A_V = 4.2. More recent work by Ash et al. (1999) concluded that the companion was likely an O6-O7 II-III, and van der Meer et al. (2007) give E(B–V) ∼ 1.4, which leads to A_V = 4.3.

4U 1538–52. Cowley et al. (1977) examined Schmidt plates to find candidate optical counterparts and suggested that the counterpart was likely to be a reddened OB star. Follow-up studies by Crampton et al. (1978) and Parkes et al. (1978) confirmed that the counterpart likely had spectral type ∼B0 I, and was reddened. From the spectral type and color, Crampton et al. (1978) estimated E(B–V) = 2.4 ± 0.15, which is similar to what Parkes et al. (1978) found using the equivalent width of the DIB at 6283 Å, E(B–V) = 2.1. A study by Ilovaisky et al. (1979) also found E(B–V) = 2.16 from the counterpart's spectral type and colors. A subsequent study of the system's optical photometry by Pakull et al. (1983) suggested E(B–V) = 2.22. For this work, we adopt E(B–V) ∼ 2.2, or A_V = 6.8.

4U 1608–52. Grindlay & Liller (1978) obtained I-band photometry and identified the optical counterpart. They noted that the source was not visible in photographic plates taken by other workers, which placed a lower limit on the system's $B-I$ color. They then assumed that the source was similar in absolute luminosity and intrinsic colors to other X-ray transients, and set a lower limit of ${A}_{V}\geqslant 4.5$. Later, Wachter et al. (2002) obtained VRI photometry and found that the counterpart's spectral energy distribution made it most likely a late F or early G main-sequence star; this, combined with a distance estimate based from Nakamura et al. (1989) on type I X-ray bursts with photospheric radius expansion, led to an extinction estimate of 6 $\leqslant \;{A}_{V}\;\leqslant$ 8. Thus, for this work we let A_V = 7 ± 1.

4U 1659–487. Grindlay (1979) found the optical counterpart in this LMXRB system and used the equivalent widths of the IS Na D lines and several DIBs seen toward nearby stars to estimate E(B–V) ∼ 1.25. Later work by Cowley et al. (1987) found a similar value, E(B–V) ∼ 1.3, by measuring the strength of the DIB at 4430 Å along the 4U 1659–487 LOS. Zdziarski et al. (1998) used a weighted mean based on these earlier studies, E(B–V) ∼ 1.2 ± 0.1, or A_V = 3.7 ± 0.3. This is the value used in the current work.

4U 1746–37. This LMXRB is located in the globular cluster NGC 6441. The cluster is at low Galactic latitude and near the Galactic Center. Harris (1996, 2010 edition) gives E(B–V) = 0.47 for the cluster, and Bonatto et al. (2013) showed that it exhibits differential reddening, with E(B–V) ranging from $\sim 0.40\;\mathrm{to}\;0.54$ over the 200'' × 200'' FOV of the HST/WFC, due to the Galactic foreground ISM. For this study, we use E(B–V) = 0.47 ± 0.07, or A_V = 1.46 ± 0.22.

4U 1724–307. This LMXRB is located in the globular cluster Terzan 2. Christian & Friel (1992) relied on the metallicity measurement of Armandroff & Zinn (1988) and IR photometery to find the distance modulus and reddening toward this cluster, E(B–V) = 1.25 ± 0.15. However, later work by Ortolani et al. (1997) and Valenti et al. (2009) found notably higher values, E(B–V) = 1.54 and 1.87, respectively. Harris (1996, 2010 edition) lists E(B–V) = 1.87 ± 0.19 (A_V = 5.80 ± 0.59), and we use this value.

Cyg X-2. The optical counterpart in this LMXRB was suggested by Cowley et al. (1979) to be an F2 III-IV; later work by Casares et al. (1998) found that it was best described as A9 III. Goranskij & Lyutyj (1988) relied on spectra and photometry to estimate E(B–V) = 0.22 ± 0.05. This is notably lower than the reddening given by McClintock et al. (1984), who estimated E(B–V) = 0.40 ± 0.07 by essentially "ironing out" the 2175 Å bump, which was in agreement with Chiappetti et al. (1981) who also found 0.4 $\lt \;E(B-V)\;\lt$ 0.5 via the same method. However, these values are much higher than the rest of the stars within ∼25 of Cyg X-2 (Cathey & Hayes 1968). To investigate further, the dust maps of Schlafly & Finkbeiner (2011) were consulted, which gave E(B–V) = 0.25, which is in agreement with that found by Goranskij & Lyutyj (1988). In this work, we take E(B–V) = 0.22 ± 0.05 (A_V = 0.68 ± 0.16).

XTE J1720–318. The near-infrared (NIR) counterpart to this LMXRB was found by Nagata et al. (2003), who used the dust maps of Schlegel et al. (1998) and Dutra et al. (2003) to estimate ${A}_{V}\;\sim$ 6–7. Chaty & Bessolaz (2006) confirmed Nagata's counterpart in the optical regime, and used optical and NIR photometry to analyze the CMD and model the spectral energy distribution. They found that the companion is most likely a main-sequence star, ranging in spectral type from late B to early G, with A_V ranging from 6 to 8 mag. We therefore take A_V = 7 ± 1.

IGR J17544–2619. Rodriguez (2003) announced that a likely counterpart had been detected by 2MASS, and later work by Pellizza et al. (2006) confirmed it, by obtaining the optical and NIR photometry and optical spectra of the source. The spectroscopy indicated that it is likely an O9 I. Further, several DIBs were present, and the equivalent width of the one at 5780 Å indicated E(B–V) = 1.97 ± 0.15; this is in agreement with the reddening they found with the counterpart's spectral type and color, 2.07 ± 0.11. The authors take the reddening to the system to be the average, E(B–V) = 2.02 ± 0.13, or A_V = 6.26 ± 0.40.

NGC 6440. A bright LMXRB is located in this globular cluster, which is at low Galactic latitude and near the Galactic Center. The cluster has high foreground reddening, with E(B–V) = 1–1.1 (Zinn 1980; Bica & Pastoriza 1983; Ortolani et al. 1994). Harris (1996, 2010 edition) lists E(B–V) = 1.07 ± 0.11, or A_V = 3.32 ± 0.34.

EXO 1745–248. This LMXRB is located in the globular cluster Terzan 5, which is known to have differential foreground reddening (Ortolani et al. 1996). Armandroff & Zinn (1988) used the DIB at 8621 Å to estimate E(B–V) = 1.65, but studies with optical or NIR photometry indicate much higher average reddenings: from 2.16 (Cohn et al. 2002) to 2.49 (Ortolani et al. 1996). Barbuy et al. (1998) and Valenti et al. (2007) estimated the reddening to be about 2.38–2.39, whereas according to Harris (1996, 2010 edition), E(B–V) = 2.28. However, Massari et al. (2012) used Hubble Space Telescope (HST) photometry to produce a high resolution extinction map of the cluster and found the reddening to be even more severe: 2.15 $\;\leqslant \;E(B-V)\;\leqslant$ 2.82; further, they estimate that R_V = 2.83, leading to 6.09 $\;\leqslant \;{A}_{V}\;\leqslant$ 7.98. We therefore let A_V = 7.04 ± 0.95.

HD 245770. Wade & Oke (1977) obtained optical spectra of the system and examined the counterpart as well as the reddening along the sight line. They found that the companion was likely a B0 III, and estimated E(B–V) = 0.8, based on the strengths of DIBs at 4430 and 5790 Å and the Na i D lines. This is in agreement with that found by Giangrande et al. (1980; E(B–V) = 0.83 ± 0.08), also obtained via the 4430 Å DIB, and similar to what was found in Steele et al.'s (1998) examination of this sight line, where the strengths of the Na i D₂ line and the DIBs at 5780, 5797, 6269, and 6613 Å led to an average E(B–V) ∼ 0.7 ± 0.2. In Lyuty & Zaitseva's (2000) comprehensive study of the system's photometry over the span of 100 years, the authors concluded that in the system's quiescent phase E(B–V) = 0.74, which compares well with the values found by the others. For this work, we take the average, with E(B–V) = 0.74 ± 0.11, or A_V = 2.29 ± 0.34.

Vel X-1 = HD 77581 = 4U 0900–40. The optical counterpart in this system was identified by Hiltner et al. (1972) as a star with spectral type B0.5 Ib. Optical photometry by van Genderen (1981) suggested $E(B-V)\;\lt$ 0.77, which is consistent with E(B–V) = 0.73, as found by Zuiderwijk et al. 1977 photometry. Snow et al.'s (1977) compilation of diffuse DIB measurements lists two values for the depth of the feature at 4430 Å; taking the average of these measurements and using their relation between band strength and reddening, a lower value was found: E(B–V) = 0.64. Here we have adopted E(B–V) = 0.7, or A_V = 2.2. As will be seen in Section 5.4, this source has an X-ray scattering optical depth (τ_sca) that is higher than expected for its optical extinction.

First, the relation between A_V and N_H from the X-ray spectral fits was considered. Figure 5 shows A_V plotted against N_H found by fitting the X-ray spectrum. The best-fit line is given by A_V = (0.48 ± 0.06)$\;\times \;{N}_{{\rm{H}}}$ (10²¹ cm⁻²). Many others have examined the ratio of optical extinction to N_H. For comparison, their results are summarized in Table 13, as well as discussed later. Prior to the launch of ROSAT in 1990, X-ray data for these studies came from detectors on sounding rockets or the Uhuru X-ray satellite. Reina & Tarenghi (1973) used the N_H of five objects reported in the literature to find A_V = 0.54 × N_H (10²¹ cm⁻²). Gorenstein (1975) used a sample of seven objects with N_H in the literature and found A_V = (0.45 ± 0.03) × N_H (10²¹ cm⁻²).

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Twenty years later, Predehl & Schmitt (1995) examined ROSAT data and fitted the spectra of 29 objects with absorbed thermal BR, BB, and PL models. For some sources, the BR models provided better fits, while for others, the BB models were better; for all, however, the PL provided fits that were consistent with the better of the two other models. This was probably due to ROSAT's narrow bandpass (0.1–2.4 keV). The authors used the values of N_H that were yielded by the PL fits, and found A_V = (0.56 ± 0.01) × N_H (10²¹ cm⁻²).

More recently, Güver & Özel (2009) examined the spectra of 22 supernova (SN) remnants with Chandra, Suzaku, and XMM-Newton. The spectra were fit from 0.2 to 8 keV, with typical successful fits being provided by absorbed thermal plasma, BB, BR, or PL models. Values of E(B–V) were found in the literature, where they had been determined by measuring the Balmer decrement, S ii or Fe[ ii] line ratios; A_V was then found by assuming the standard Galactic reddening law. For four of their objects, these optical data did not exist, so A_V was estimated by finding the extinction for nearby stars in the field with known distances. This led the authors to find A_V = (0.45 ± 0.02)$\;\times \;{N}_{{\rm{H}}}$ (10²¹ cm⁻²).

It is worth noting that the results found here, and those found in the earlier works mentioned previously, are also in reasonable agreement with those found in other wavelength regimes; Bohlin et al. (1978) used Copernicus data to examine Lyα absorption along 100 lines of sight, and found A_V = (0.53 ± 0.03) $\;\times \;{N}_{{\rm{H}}}$ (10²¹ cm⁻²).

The X-ray scattering optical depth τ_sca was found for all sight lines and models that produced good fits. As N_H was large for many of the sight lines, multiple scattering (i.e., a single photon being scattered more than once) was a concern. Multiple scattering broadens the halo, and Mathis & Lee (1991) showed that at ${\tau }_{\mathrm{sca}}\;\gt$ 1.3, multiply scattered photons dominate over singly scattered, and for models like MRN and Draine & Lee (1984), the scattering cross section ${\sigma }_{\mathrm{sca}}$ = 9.03 $\times {10}^{-23}{[E(\mathrm{keV})]}^{-2}$ H⁻¹. Thus, at an energy of 1 keV, multiple scattering will overtake single scattering in importance when N_H = 1.4 × 10²² cm⁻², which is comparable to the IS N_H along many of these sight lines. In contrast, at an energy of 2.5 keV, single scattering still dominates over multiple scattering up to N_H = 9 × 10²² cm⁻². This is about twice as large as the largest value of IS N_H for objects in the sample, so multiple scattering should not affect the results at that energy. The values of τ_sca(2.5 keV) were normalized to τ_sca(1.0 keV) for ease of comparison with results from previous workers by noting that τ_sca(1.0 keV) = τ_sca/[E (keV)]² (Predehl & Schmitt 1995) assuming the RG approximation.

The results are shown in Figure 6 for a representative selection of models (MRN, WD, ZBAF, ZBGF). The number of sources that a model could fit, the best fit τ_sca(1.0 keV)/N_H with 1σ uncertainties, and the Pearson correlation coefficients r are listed in Table 14. Three things are immediately noticeable: First, the number of sources that a model could fit varied greatly. The ZDA COMP-AC models, in particular, had difficulty fitting the halos successfully. Second, values of τ_sca(1.0 keV)/N_H from the more successful models tended to be similar, ranging from about 0.02 to 0.03. For comparison, Predehl & Schmitt (1995) found τ_sca(1.0 keV)/N_H = 0.05. Part of this discrepancy may be due to the fact that Predehl & Schmitt (1995) fit all their spectra with the absorbed PL model, because the narrow ROSAT bandpass allowed that model to consistently provide the best fits for their sources. It is also likely due to our choice of halo energy bandpass, as Smith & Dwek (1998) showed that RG overestimates halo intensities at low energies ($E\;\lt$ 2 keV) compared to the Mie solution. Third, values of τ_sca(1.0 keV)/N_H showed appreciable variability among sources for a single dust model. This may be due circumstellar material around the source, and is discussed further in Section 5.4. The intent of these fits and tables is not to suggest there are significant differences between the models that can be inferred from these data, but rather to show the range of possible values and show the agreement between the data and a simple linear model.

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The ratio of τ_sca/A_V for each model was also examined. Of the 27 sources with halos that were well fit, 15 had values of A_V from the literature. The MRN and ZDA BARE- models had the most, whereas the ZDA COMP-AC models had the least (<10); with such few data points, the ZDA COMP-AC models were not considered further. In cases where no uncertainties were given with reddening estimates, the average of the quoted uncertainties, 13%, was again assumed. The values of τ_sca(1.0 keV) and A_V are plotted in Figure 7 for a representative selection of models (MRN, WD, ZBAS, and ZBGS). Again, these fits are shown simply to demonstrate the range of possible values obtained from different dust models.

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All models had sources with notably high or low τ_sca for its A_V, with Vel X-1 being one of the most common. This LOS is discussed further in Section 6.3. The values of τ_sca(1.0 keV)$/{A}_{V}$ found without such sources, their 1σ uncertainties, and the correlation coefficients for all models are listed in Table 15. The values of τ_sca(1.0 keV)/A_V ranged from 0.04 to 0.05. For comparison, Predehl & Schmitt (1995) found τ_sca(1.0 keV)/A_V ∼ 0.06.

It is interesting to compare the values of the correlation coefficients for each model's τ_sca/N_H (Table 14) and of τ_sca/A_V (Table 15). Values of τ_sca/A_V showed far less variability among sources for a single dust model than τ_sca/N_H. This may be because the values for A_V were obtained independently of the X-ray source, via examination of the optical counterpart, IS absorption lines, or the cluster's characteristics (if the system was in a globular cluster). In contrast, N_H was obtained by fitting the X-ray spectrum and therefore includes contributions from both the ISM and any circumstellar material that may be at the X-ray source. This suggests that the A_V–N_H correlation seen in Figure 5 may be used to gauge how much local absorption a system has, because a value of A_V/N_H that is much lower than expected may indicate the presence of excess absorbing material at the X-ray source.

Values of τ_sca(2.5 keV)/A_V were compared to that expected from the theoretical values listed in Table 1. For brevity, the quantity $\varepsilon \equiv {[{\tau }_{\mathrm{sca}}(2.5\mathrm{keV})/{A}_{V}]}^{\mathrm{empirical}}/{[{\tau }_{\mathrm{sca}}(2.5\mathrm{keV})/{A}_{V}]}^{\mathrm{theory}}$. The values of are shown in Figure 8.

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Eight LOS had dust halos that could not be fit with any model. An in-depth analysis of these halos is beyond the scope of this work, but they are each discussed generally below; some are known to have unusual dust properties, while others are not. Nonetheless, it is interesting to contrast these sources with the ones with successful fits. The scale heights of the objects with successful fits varied between ∼40 and 3000 pc. Ten were in the thin disk ($| z| \;\lesssim$ 330 pc, Chen et al. 2001) where most of the dust is. Of these 10, eight were relatively nearby, with $d\;\leqslant$ 5 kpc. Twelve well-fit sources had $| z| \;\gt$ 330 pc; of these, 11 had $d\;\gt$ 5 kpc. In contrast, seven of the eight sources with unsuccessful fits had $d\;\gt$ 5 kpc, and seven were to sources where all or most of the sight line passed through the thin disk. Thus, halos tended to have successful fits when (a) the sight lines were short, or (b) the sight lines were long, but to sources that were out of the Galaxy's plane. Halos around sources that were both distant and in the thin disk usually could not be fit, suggesting that either the dust does not have properties similar to those described in the models, or the cloud distribution is not well described by those used here. We describe these sources in more detail below.

GRS 1915+105 is a low mass X-ray binary and a known Galactic microquasar. The system is composed of a 14 ± 4 ${M}_{\odot }$ black hole and a K-M III companion (Greiner et al. 2001). It has notably variable X-ray emission; Greiner et al. (1996) examined several RXTE observations taken between 1996 February and 1996 June, and found that its brightness varies on timescales ranging from seconds to days. GRS 1915+105 lies in the plane of the Galaxy ($l=45\buildrel{\circ}\over{.} 37,b=-0\buildrel{\circ}\over{.} 22$) at a distance of ∼9–12.5 kpc (Mirabel & Rodriguez 1994; Fender et al. 1999; Dhawan et al. 2000; Chapuis & Corbel 2004). Chapuis & Corbel (2004) used radio and millimeter observations to measure N_H along the LOS, and thus the optical extinction A_V. They found N_H = (3.5 ± 0.3) × 10²² cm⁻², which agrees with our value of (3.43 ± 0.03) × 10²² cm⁻², which was derived from the X-ray spectral fit. They note that an AGB star is only 18'' away, and place it at a maximum distance from the Sun of about 6 kpc. Such stars can eject material up to 1 pc, or 36'' on this scale. For the halo to be free of any effect from the AGB star, the inner radius of the halo measurement must be greater than 54''. The halo was fitted from 50 to 800''. Out of an abundance of caution, we checked for any influence from the AGB dust by refitting it from 60 to 800'' for the MRN model, using both the single-cloud and smooth distributions. The results were not significantly different from those obtained when fitting from 50 to 800'', so we believe that the halo fits are minimally influenced by the AGB's ejecta.

4U 1538–52 (QV Nor) is a well-studied eclipsing high mass X-ray binary system composed of a pulsar and a highly reddened (${A}_{V}\sim 6$) B0Iab companion (e.g., Crampton et al. 1978; Pakull et al. 1983; Reynolds et al. 1992). The dust along this LOS has also been examined in detail (Clark et al. 1994; Clark 2004), with the result that the halo can be fit when the source is at 4.5 kpc and there are three MRN-like clouds, two at distances corresponding to concentrations of atomic H, and the third closer to the source. Our attempts to reproduce this result were not sucessful. It has also been suggested that the halo intensity is less than expected given the B0Iab's extinction, leading to the suggestion that it may exhibit porous dust (Clark et al. 1994). However, as discussed in Section 6.2, the results of the present work indicate that porous grains are not required to fit halos.

4U 1820–30 (Sgr X-4) is a low mass X-ray binary in the globular cluster NGC 6624, at a distance of about 8 kpc (Harris 1996, 2010 edition). It is an intriguing system, and has been the subject of many studies. It is composed of a neutron star primary with an He-rich white dwarf companion that has filled its Roche lobe. Of all known binaries with a neutron star or black hole primary, it is the most compact, having an orbital period of 11.4 minutes (Stella et al. 1987; Chou & Grindlay 2001). It has been suggested that this system formed through a collision between the neutron star and a giant, which has since lost its outer layers to mass transfer so that all that remains is its He-rich core (Verbunt 1987; Ivanova et al. 2005). An additional periodicity in the system's luminosity suggests the presence of a third body in the system, orbiting the neutron star-white dwarf inner binary (Zdziarski et al. 2007; Wang & Chakrabarty 2010). The IS medium along this LOS has been examined by Costantini et al. (2012), who studied absorption features in its soft X-ray spectrum and found a slight overabundance of O and underabundance of Fe (with respect to the solar nebula values of Lodders & Palme 2009).

XTE J1720–318 (V1228 Sco) is a low mass X-ray binary that is believed to harbor a radio-quiet black hole. It was examined in detail in the optical and near-IR by Chaty & Bessolaz (2006), who determined that the companion is most likely a main-sequence star, with spectral type ranging from late B to early G. They found that the system is likely at a distance of 3–10 kpc. Values for A_V range from about 6 to 8 mag (Nagata et al. 2003).

IGR J17544–2619 is a super fast X-ray transient that was discovered in 2003 (Sunyaev et al. 2003). Data taken during an outburst in 2004 clearly show a complicated time-dependent halo structure, an examination of which suggests that there are two clouds along this sight line (Mao et al. 2014).

GX 13+1 is a low mass X-ray binary with a neutron star primary. Bandyopadhyay et al. (1999) determined the companion star to have spectral type K5III, and placed the system at a distance of 7 kpc in the Galactic bulge. The N_H found for the source, (2.75 ± 0.06) × 10²²cm⁻², is slightly lower than that found by Ueda et al. (2004; N_H = $3.2\times {10}^{22}$ cm⁻²) and implies an optical extinction of ∼15 mag. Smith (2008) examined the halo using simultaneous RXTE and Chandra HRC-I data and could not find a dust model that fit adequately.

GX 5–1 is a heavily absorbed (${N}_{H}\sim 3\times {10}^{22}$ cm⁻²) low mass X-ray binary near the Galactic Center. In Smith et al.'s (2006) examination of its halo using Chandra ACIS data, they found that the single-cloud distribution was more successful than a smooth distribution, as seen in this work. However, they also found that their best-fit model, ZBGB, had ${\chi }^{2}\sim 2$ in the E = 2.4–2.6 keV band. This contrasts with the fits from this work, all of which had values of ${\chi }^{2}\gt 6$ around this energy and differences between the fits and the data that were larger than 3σ. The broader bandpass used in this work and the extreme brightness of the source are likely the cause of the discrepancy.

4U 1119–603 (Cen X-3) is a high-mass X-ray binary is composed of a neutron star and O6 II, at a distance of about 6–8 kpc. Its dust halo was examined by Thompson & Rothschild (2009), who used data from the Chandra HETG to fit its halo over radial distances from the source <100''. In contrast, in this work, data from XMM's MOS camera were used over a much larger radial extent (<600''). They found that a good fit was provided using four clouds of WD-type dust. Our attempts to reproduce this result were not successful.

Porous conglomerate (silicate+carbonaceous) grains were proposed by Mathis & Whiffen (1989) to be a more realistic grain population than two seperate populatons of pure graphite and silicate, as proposed by MRN. Porous grains also are more efficient scatterers and absorbers at UV/optical wavelengths than non-porous (compact) grains, and so may help to solve the problem of having IS abundances that were too low to account for IS extinction (Mathis 1996), although this is not undisputed (Li 2005). In X-rays, porous grains are less efficient scatterers than compact grains, so if there are porous grains in the ISM, halo fits using models that do not explicitly contain them should produce values of τ_sca that are lower than expected for a given A_V. The potential detection of porous grains in the ISM has been controversial. Woo et al. (1994) found that the halo of Cen X-3 could be fit with MRN when the grains were ∼50% porous. Similarly, Predehl & Schmitt (1995) fitted their halo sample with variants of the MRN PL grain size distribution ($f(a)\cong {a}^{-q}$, solving for q and maximum radius a_max) and found values of q and a_max that were similar to those of the standard MRN, though they also calculated that for grains with radius = 0.1 μm, if the grain-forming elements are largely depleted, then grains must be up to 70% voids in order to not exceed the observed halo intensities.

However, these works examined halos at low energies ($E\lt 2$ keV) and relied on the RG approximation of the differential scattering cross section. Smith & Dwek (1998) showed that Rayleigh–Gans substantially overestimates halo intensity at these energies, compared to results from the Mie solution. Further, they assume cosmic abundances that are much higher than are currently indicated. For instance, Predehl & Schmitt (1995) relied on the work of Morrison & McCammon (1983), whose cosmic abundances are notably higher than those of more recent works (e.g., Nieva & Przybilla 2012). If ISM abundances are indeed much lower, fewer voids are needed to avoid overly bright halos (Mathis 1996).

Our results indicate that porous grains are not necessary to fit halos. They do this in two ways. First, the models that contain them (the ZDA COMP- families) performed markedly worse than those without, as can be seen from Table 14, where the number of sources a model could fit is listed. Second, of the models that did not have porous grains (MRN, WD, and the ZDA BARE- families), values of τ_sca/A_V were similar to their expected theoretical values with $\varepsilon \sim 1$. Halo intensity depends strongly on grain size, so the general ability or inability of a model to fit a halo relies heavily on the large end of its grain size distribution. The most successful models (MRN and ZDA BARE-) had similar maximum grain sizes, ${a}_{\mathrm{max}}\;\sim$ 0.25–0.4 μm, which were notably smaller than those of the less successful ones, which had a_max = 0.5–0.9 μm.

Successful models also had fewer large grains, which can be seen in ZDA's Figures 4–17. The number of large grains a model had tracked closely with its halo fitting success. Of the models tested here, the COMP-AC family had the most large grains. COMP-GR-FG and COMP-GR-S had fewer, and the BARE- family had the least. The large end of the grain size distribution of the COMP-GR-B model was more similar to that of MRN and the BARE- families, although a_max was larger (0.52 μm); it was also the most successful member of the COMP- family. WD does not contain porous grains, but its large grain size distribution is comparable to that of the COMP- family, so it is not surprising that it performed in a similar way. Dwek et al. (2004) also noted that the BARE- models tended to fit halos better than COMP- models, again, because of the grain size distribution.

Of course, these results do not completely exclude the possibility of porous grains; they only place limits on how large they (and compact grains) can be, and how many there are. It seems unlikely that very large grains (${a}_{\mathrm{max}}\gt 0.5\;\mu$m) are present in any significant quantity in the diffuse ISM or most cold clouds.

As noted in Section 5.4, some models produced scattering optical depths that were larger or smaller than expected for the sight lines' optical extinctions. After verifying the values of A_V in the literature, possible issues with the empirical values of τ_sca(2.5 keV) were considered. If the source is projected near a region of ISM that is not uniform (for example, near the edge of an intervening cloud), it is possible that the A_V that is measured on the source's LOS is not consistent with the τ_sca in different regions of the halo. In that case, one might expect that $\varepsilon \sim 1$ only for parts of the halo.

To investigate halo non-uniformity, all halos were divided into quadrants according to Galactic latitude and longitude. This is a similar approach to that used in the detailed study of halo azimuthal variation by Seward & Smith (2013), although the detailed data used in their analysis was not available here. Only the sources with at least 3,000 counts in each quadrant were analyzed further to ensure a solid measurement of τ_sca. Six sources met this requirement in the E = 2.5 keV bandpass; Vel X-1 did not, but it did in the E = 4.0 keV bandpass, so that band was used instead. These bright quadrants were then fitted with the MRN model, and was found. These are listed in Table 16, along with the standard deviation from the mean of the quadrants, and the number of models for which these halos deviated from their expected values by more than a factor of two when the entire halo was fitted. (Again, the 4.0 keV bandpass was used for Vel X-1.) Several points are of note.

Table 16.  Values of $\varepsilon$ for Sources With >3000 Counts per Quadrant

Source	Quadrant	Quadrant	Quadrant	Quadrant	Standard	No. of Models With
	1	2	3	4	Deviation	Discrepant ${\varepsilon }^{\mathrm{totalhalo}}$
4U 1608–52	1.68 ± 0.24	0.96 ± 0.14	1.00 ± 0.14	1.80 ± 0.26	0.4	0
Cyg X-2	2.27 ± 0.31	1.10 ± 0.17	1.67 ± 0.24	1.33 ± 0.19	0.5	0
4U 1659–487	1.45 ± 0.12	0.49 ± 0.04	0.53 ± 0.06	1.35 ± 0.11	0.5	2
Vel X-1	3.38 ± 0.49	6.49 ± 0.90	7.53 ± 1.04	1.98 ± 0.30	2.6	11
Swift J1753.5–0127	1.44 ± 0.38	11.5 ± 1.4	8.32 ± 1.04	12.7 ± 1.5	5.1	2
4U 1957+11	16.7 ± 3.4	⋯	1.31 ± 0.29	3.69 ± 0.76	7.5	7
4U 1746–37	41.7 ± 6.3	35.3 ± 5.4	6.96 ± 1.21	3.50 ± 0.67	19	6

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First, some sources show large differences between the $\varepsilon$ found for each quadrant, often having the expected $\varepsilon \sim 1$ for one or two quadrants, and an $\varepsilon$ that was significantly larger or smaller for the remainder. This suggests that the A_V on the source's LOS is consistent with the τ_sca only for parts of the halo. Second, sources with larger deviations between quadrants were more likely to have empirical values of τ_sca(2.5 keV)/A_V from the whole-halo fits be significantly different from their theoretical values. It is interesting to consider that the source with the highest deviation, 4U 1746–37, is in a globular cluster that is known to have differential Galactic reddening with $E(B-V)=0.4-0.54$ over its central 200'' (see Section 5.1). In this work, the halo was examined over an angular distance of 600'', with the regions of highest [τ_sca(2.5 keV)/A_V]^empirical corresponding to quadrants that were closest to the Galactic plane. For 4U 1957+11, which had the second highest deviation between quadrants, the reddening of several stars within an 800'' radius was found to range from ∼0.1 to 0.5. Vel X-1 had only a modest deviation, but the largest number of discrepant $\varepsilon$ values; in the 4.0 keV band, no model could produce [τ_sca/A_V] within a factor of two of the expected value. This source is located in the Vel OB1 association, which has reddening that ranges between 0.3 and 1.4 (Reed 2000). An image of Vel X-1 made with the DSS and Wide-field Infrared Survey Explorer (WISE) 12 and 22 μm survey data is shown in Figure 9. An arc-shaped region of emission is clearly visible, at a distance of about 50'' from the source, as is patchy nebulosity over the entire region. If such a structure is also associated with X-ray-scattering dust in the region of halo extraction, it supports the possibility that inhomogeneities in the ISM give rise to discrepant halos. In contrast, sources with lower deviations and fewer discrepant values had a narrower range of reddenings: within 800'' of Cyg X-2, 4U 1608–52, and 4U 1659–487, E(B–V) ranged from $\sim 0.1\ \mathrm{to}\ 0.3$, $\sim 0.0\ \mathrm{to}\ 0.3$, and $\sim 0.1\ \mathrm{to}\ 0.2$, respectively.

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