The gas-to-extinction ratio and the gas distribution in the Galaxy

TL;DR

This study quantifies the gas-to-extinction ratio across the Galaxy, finds it to be largely invariant, and models the hydrogen distribution vertically and radially, providing key parameters for Galactic gas structure.

Contribution

It provides a comprehensive measurement of the N_H/A_V ratio across the Galaxy and models the vertical hydrogen distribution with new scale height and density estimates.

Findings

N_H/A_V ratio is approximately 2.08×10^{21} H cm^{-2} mag^{-1} with little variation across the Galaxy.

Vertical hydrogen distribution follows a Gaussian with a scale height of about 75.5 pc.

N_H/A_V ratio increases by ~20% when using subsolar abundances instead of solar abundances.

Abstract

We investigate the relation between the optical extinction ($A_V$) and the hydrogen column density ($N_H$) determined from X-ray observations of a large sample of Galactic sightlines toward 35 supernova remnants, 6 planetary nebulae, and 70 X-ray binaries for which $N_H$ was determined in the literature with solar abundances. We derive an average ratio of ${N_H}/{A_V}=(2.08\pm0.02)\times10^{21}{\rm H\, cm^{-2}\, mag^{-1}}$ for the whole Galaxy. We find no correlation between ${N_H}/{A_V}$ and the number density of hydrogen, the distance away from the Galactic centre, and the distance above or below the Galactic plane. The ${N_H}/{A_V}$ ratio is generally invariant across the Galaxy, with ${N_H}/{A_V}=(2.04\pm0.05)\times10^{21}{\rm H\, cm^{-2}\, mag^{-1}}$ for the 1st and 4th Galactic quadrants and ${N_H}/{A_V}=(2.09\pm0.03)\times10^{21}{\rm H\, cm^{-2}\, mag^{-1}}$ for the 2nd and 3rd Galactic quadrants. We also explore the distribution of hydrogen in the Galaxy by enlarging our sample with additional 74 supernova remnants for which both $N_H$ and distances are known. We find that, between the Galactic radius of 2 kpc to 10 kpc, the vertical distribution of hydrogen can be roughly described by a Gaussian function with a scale height of $h=75.5\pm12.4\,{\rm pc}$ and a mid-plane density of $n_{H}(0)=1.11\pm0.15\,{\rm cm^{-3}}$, corresponding to a total gas surface density of ${\sum}_{gas}{\sim}7.0\,{M_{\bigodot}}\,{\rm pc^{-2}}$. We also compile $N_H$ from 19 supernova remnants and 29 X-ray binaries for which $N_H$ was determined with subsolar abundances. We obtain ${N_H}/{A_V}=(2.47\pm0.04)\times10^{21}{\rm H\, cm^{-2}\, mag^{-1}}$ which exceeds that derived with solar abundances by $\sim$20%. We suggest that in future studies one may simply scale $N_H$ derived from subsolar abundances by a factor of $\sim$1.2 when converting to $N_H$ of solar abundances.

Tables

Table 1. Table 1: N H / A V subscript 𝑁 H subscript 𝐴 𝑉 N_{\rm H}/A_{V} Ratios Determined from the HI and H 2 UV Absorption Spectra.

Hydrogen	$N_H/A_V$	Sample	Reference	Comments
Type	(${10}^{21}{\mathrm{cm}}^{-2}{\mathrm{mag}}^{-1}H$)	Size
HI+H2	2.15$\pm$0.14	17	Rachford et al. (2009)	FUSE observations of stars with
HI	1.59$\pm$0.09	393	Diplas & Savage (1994)	IUE observations of stars with
HI+H2	1.9	12	Whittet (1981)	Copernicus observations of stars with
HI+H2	1.87	75	Bohlin et al. (1978)	Copernicus observation of stars with
HI+H2	2.0	95	Jenkins & Savage (1974)	OAO-2 observations of stars with

Table 2. Table 2: N H / A V subscript 𝑁 H subscript 𝐴 𝑉 N_{\rm H}/A_{V} Ratios Determined from the HI 21 cm Emission and/or CO emission.

Hydrogen	$N_H/A_V$	Sample	Reference	Comments
Type	(${10}^{21}{\mathrm{cm}}^{-2}{\mathrm{mag}}^{-1}H$)	Size
HI	2.68	–	Liszt (2014)	Galactic latitudes $\left|b\right|\stackrel{>}{\sim }{20}^{\circ }$ and
HI	1.56	76	Heiles (1976)	stars and globular clusters with
HI	1.6	81	Knapp & Kerr (1974)	globular clusters with
HI	$\sim$1.3–1.6	40	Sturch (1969)	RR Lyrae stars with
HI+H2	2.4	–	Chen et al. (2015)	Galactic latitudes $\left|b\right|\stackrel{>}{\sim }{10}^{\circ }$ and

Table 3. Table 3: N H / A V subscript 𝑁 H subscript 𝐴 𝑉 N_{\rm H}/A_{V} Ratios Previously Determined from Interstellar X-Ray Absorption Data.

$N_H/A_V$	Sample	Interstellar Abundance	O/H	Mg/H	Si/H	Fe/H	Reference	Comments
(${10}^{21}H{\mathrm{cm}}^{-2}{\mathrm{mag}}^{-1}$)	Size	Standard	(ppm)	(ppm)	(ppm)	(ppm)
2.87$\pm$0.12	17	Wilms et al. (2000)	4.90	2.51	1.86	2.69	Foight et al. (2016)	SNRs with
2.08$\pm$0.30	23	Anders & Grevesse (1989)	8.51	3.80	3.55	4.68	Valencic & Smith (2015)	XBs with
2.2${}_{-0.4}{}^{}{}_{}{}^{+0.3}$	$>$100	Anders & Grevesse (1989)	8.51	3.80	3.55	4.68	Watson (2011)	$\gamma$-ray bursts
2.21$\pm$0.09	22	Anders & Grevesse (1989)	8.51	3.80	3.55	4.68	Guver & Ozel (2009)	SNRs with
$\sim$1	20	Anders & Ebihara (1982)	7.39	3.95	3.68	3.31	Vuong et al. (2003)	SF regions with distances0.5 kpc
1.79$\pm$0.03	26	Anders & Ebihara (1982)	7.39	3.95	3.68	3.31	Predehl & Schmitt (1995)	SNRs and XBs with
2.19$\pm$0.52	5	-	-	-	-	-	Ryter et al. (1975)	SNRs with
2.22$\pm$0.14	7	-	-	-	-	-	Gorenstein (1975)	SNRs with
1.85	4	-	-	-	-	-	Reina & Tarenghi (1973)	XBs, extended sources with $E\left(B-V\right)$10$\mathrm{mag}$

Table 4. Table 4: Optical extinction A V subscript 𝐴 𝑉 A_{V} and hydrogen column density N H subscript 𝑁 H N_{\rm H} compiled from the literature (see Appendix for details).

Object	Gla	Gba	$N_H{\left(\mathrm{KBH}\right)}^b$	$N_H{\left(\mathrm{DL}\right)}^c$	$N_H{\left(\mathrm{AG89}\right)}^d$	$N_H{\left(\mathrm{W00}\right)}^e$	$A_V$	$D^f$	$N_H\left(\mathrm{AG89}\right)$/$A_V$	$N_H\left(\mathrm{W00}\right)$/$A_V$
Name	(degree)	(degree)	(${10}^{21}H{\mathrm{cm}}^{-2}$)	(${10}^{21}H{\mathrm{cm}}^{-2}$)	(${10}^{21}H{\mathrm{cm}}^{-2}$)	(${10}^{21}H{\mathrm{cm}}^{-2}$)	($\mathrm{mag}$)	(kpc)	(${10}^{21}H{\mathrm{cm}}^{-2}{\mathrm{mag}}^{-1}$)	(${10}^{21}H{\mathrm{cm}}^{-2}{\mathrm{mag}}^{-1}$)
Supernova remnants
G4.5+6.8 north	4.5	6.8	2.12	2.38	5.1$\pm$0.3	5.4$\pm$0.1	3.0$\pm$0.4	5.1	1.89$\pm$0.27	1.93$\pm$0.28
G6.4-0.1 central	6.4	-0.1	11.40	14.40	4.3$\pm$0.1	6.3$\pm$1.9	3.3$\pm$0.3	1.9	1.30$\pm$0.12	1.91$\pm$0.60
G6.4-0.1 northeast	6.4	-0.1	11.40	14.40	7.7$\pm$0.2		4.0$\pm$0.5	2.0	1.93$\pm$0.25
G11.2-0.3 southeast	11.2	0.3	12.70	17.50	15.7$\pm$1.5		13.0$\pm$1.7	4.4	1.21$\pm$0.20
G13.3-1.3	13.3	-1.3	8.05	8.11	5.5$\pm$4.5		0.5$\pm$0.1	3.0	11.00$\pm$9.26
G39.7-2.0 east jet	39.7	-2.0	6.49	7.63	5.2$\pm$0.1		2.3$\pm$0.3	5.5	2.26$\pm$0.30
G53.6-2.2 central	53.6	-2.2	5.48	6.69	6.1$\pm$0.1		3.1$\pm$0.4	2.3	1.97$\pm$0.26
G53.6-2.2 southwest	53.6	-2.2	5.48	6.69	4.8$\pm$0.8	6.7$\pm$0.3	4.0$\pm$0.5	2.3	1.20$\pm$0.25	1.68$\pm$0.22
G54.1+0.3	54.1	0.3	11.90	14.30	18.1$\pm$0.5	25.5$\pm$0.4	7.3$\pm$0.1	6.2	2.48$\pm$0.08	3.49$\pm$0.07
G67.7+1.8 north	67.7	1.8	9.42	10.50	4.1$\pm$0.9		1.7$\pm$0.4		2.41$\pm$0.78
G69.0+2.7 central	69	2.7	6.59	7.92	3.0$\pm$0.1	4.5$\pm$0.2	2.5$\pm$0.3	1.5	1.20$\pm$0.15	1.80$\pm$0.23
G74.0-8.5	74.0	-8.5	1.60	1.68	0.34$\pm$0.03		0.25$\pm$0.06	0.54	1.36$\pm$0.25
G78.2+2.1	78.2	2.1	12.10	13.80	7.6$\pm$0.7		3.4$\pm$0.6	2.0	2.24$\pm$0.44
G82.2+5.3	82.2	5.3	6.87	8.30	4.7$\pm$0.5		2.8$\pm$0.1	2.0	1.68$\pm$0.19
G85.9-0.6	85.9	-0.6	7.59	9.45	6.9$\pm$0.3		0.7$\pm$0.1	5.0	9.86$\pm$1.47
G89.0+4.7 northwest	89.0	4.7	6.83	7.64	3.0$\pm$0.4		1.6$\pm$0.3	1.7	1.88$\pm$0.43
G109.1-1.0	109.1	-1.0	6.39	7.50	7.1$\pm$0.7	9.0$\pm$1.4	3.1$\pm$0.6	3.2	2.29$\pm$0.50	2.90$\pm$0.72
G111.7-2.1 north	111.7	-2.1	3.94	6.70	13.6$\pm$0.3	11.7$\pm$1.6	4.8$\pm$0.7	3.4	2.83$\pm$0.42	2.44$\pm$0.49
G116.9+0.2	116.9	0.2	6.32	6.77	5.9$\pm$0.8	9.2$\pm$0.7	2.6$\pm$0.1	3.0	2.27$\pm$0.32	3.54$\pm$0.30
G119.5+10.2	119.5	10.2	2.06	2.17	2.1$\pm$0.4	3.8$\pm$1.1	1.3$\pm$0.2	1.4	1.62$\pm$0.40	2.92$\pm$0.96
G120.1+1.4	120.1	1.4	8.24	9.22	5.8$\pm$0.4	8.0$\pm$1.0	1.8$\pm$0.1	3.0	3.22$\pm$0.29	4.44$\pm$0.61
G130.7+3.1	130.7	3.1	5.57	5.72	4.1$\pm$0.1	5.4$\pm$0.1	2.1$\pm$0.2	2.0	1.95$\pm$0.19	2.57$\pm$0.25
G132.7+1.3	132.7	1.3	7.98	9.00	8.3$\pm$0.3		2.2$\pm$0.1	2.5	3.91$\pm$0.22
G166.0+4.3	166.0	4.3	3.86	5.67	2.0$\pm$0.2		1.7$\pm$0.2	4.5	1.18$\pm$0.18
G180.0-1.7	180.0	-1.7	4.93	6.30	3.1$\pm$0.2		0.7$\pm$0.2	1.3	4.43$\pm$1.30
G184.6-5.8	184.6	-5.8	3.26	3.79	3.2$\pm$0.1	4.1$\pm$0.1	1.5$\pm$0.1	2.0	2.13$\pm$0.16	2.73$\pm$0.19
G189.1+3.0	189.1	3.0	4.85	6.09	5.2$\pm$0.5	6.0$\pm$0.5	2.8$\pm$0.6	1.5	1.86$\pm$0.44	2.14$\pm$0.49
G260.4-3.4	260.4	-3.4	7.45	9.46	3.1$\pm$0.1	3.5$\pm$1.5	1.5$\pm$0.2	2.2	2.07$\pm$0.28	2.33$\pm$1.05
G263.9-3.3	263.9	-3.3	7.38	9.10	0.19$\pm$0.02	0.3$\pm$0.1	0.31$\pm$0.05	0.29	0.61$\pm$0.12	0.97$\pm$0.36
G292.0+1.8	292	1.8	5.52	6.21	3.8$\pm$0.3	5.0$\pm$0.4	2.2$\pm$0.2	6.0	1.73$\pm$0.21	2.27$\pm$0.28
G296.1-0.5 north	296.1	-0.5	13.20	16.20	0.6$\pm$0.2		1.9$\pm$0.3	2.0	0.32$\pm$0.12
G296.5+10.0	296.5	10.0	1.13	1.27	1.2$\pm$0.1		0.5$\pm$0.1	2.1	2.40$\pm$0.52
G315.4-2.3southwest	315.4	-2.3	7.19	9.06	4.0$\pm$0.2		1.7$\pm$0.2	2.3	2.35$\pm$0.30
G320.4-1.2	320.4	-1.2	14.80	14.70	10.9$\pm$0.1	11.5$\pm$0.3	3.6$\pm$0.4	5.2	3.03$\pm$0.34	3.19$\pm$0.36
G327.6+14.6	327.6	14.7	0.75	0.68	0.68$\pm$0.10	1.6$\pm$0.1	0.32$\pm$0.10	2.2	2.13$\pm$0.73	5.00$\pm$1.59
G332.4-0.4	332.4	-0.4	20.70	22.80	7.0$\pm$0.7	8.7$\pm$3.5	4.7$\pm$0.7	3.1	1.49$\pm$0.27	1.85$\pm$0.79
G332.5-5.6	332.5	-5.6	2.47	2.84	1.4$\pm$0.4		0.8$\pm$0.3	3.0	1.75$\pm$0.83
Planetary nebulae
G37.7-34.5	37.7	-34.5	0.50	0.47	0.81$\pm$0.85		0.19$\pm$0.02	1.1	4.26$\pm$4.50
G64.7+5.0	64.7	5.0	3.03	3.10	2.5$\pm$0.1		1.0$\pm$0.1	1.2	2.50$\pm$0.27
G84.9-3.4	84.9	-3.4	4.68	5.58	4.1$\pm$0.2		2.9$\pm$0.3	0.7	1.41$\pm$0.16
G94.0+27.4	94.0	27.4	0.34	0.41	0.12$\pm$0.02		0.09$\pm$0.03	1.0	1.33$\pm$0.50
G197.8+17.3	197.8	17.3	0.54	0.57	0.8$\pm$0.6		0.5$\pm$0.1	1.2	1.60$\pm$1.24
G331.7-1.0	331.7	-1.0	16.70	17.60	5.0$\pm$0.8		4.1$\pm$0.4	1.1	1.22$\pm$0.23
X-ray Binaries
2E 0236.6+6101	135.7	1.1	7.57	9.02	5.9$\pm$0.2		2.8$\pm$0.3	2.4	2.11$\pm$0.24
2E 1118.7-6138	292.5	-0.9	12.00	14.10	8.1$\pm$0.1	13.2$\pm$0.3	2.9$\pm$0.3	5.0	2.79$\pm$0.29	4.55$\pm$0.48
2S 0620-003	209.6	-6.5	3.66	4.10	2.4$\pm$1.1		1.2$\pm$0.1	1.2	2.00$\pm$0.93
2S 0921-63	281.8	-0.9	1.70	2.13	2.3$\pm$0.1		1.02$\pm$0.03	8.5	2.25$\pm$0.12
4U 0352+30	163.1	-17.1	7.09	9.39	2.5$\pm$1.1		1.2$\pm$0.1	1.0	2.08$\pm$0.19
4U 0538+26	181.4	-2.6	4.50	5.90	3.9$\pm$0.1	7.0$\pm$0.3	2.4$\pm$0.2	2.5	1.63$\pm$0.08	2.92$\pm$0.17
4U 0614+09	200.9	-3.4	4.48	5.47	3.5$\pm$0.1	3.3$\pm$0.1	1.2$\pm$0.1		2.92$\pm$0.26	2.75$\pm$0.24
4U 0919-54	275.9	-3.8	6.16	7.30	3.1$\pm$0.1	3.0$\pm$0.1	1.0$\pm$0.1	4.8	3.10$\pm$0.33	3.00$\pm$0.32
4U 1036-56	285.4	1.4	9.02	10.10	2.8$\pm$0.9		2.3$\pm$0.8	5.0	1.22$\pm$0.58
4U 1118-60	292.1	0.3	9.95	12.00	11.0$\pm$0.1		4.0$\pm$0.5	9.0	2.75$\pm$0.34
4U 1258-61	304.1	1.2	10.9	10.6	10.0$\pm$0.2		5.5$\pm$0.7	2.4	1.82$\pm$0.23
4U 1254-69	303.5	-6.4	2.16	2.91	2.6$\pm$0.1	2.2$\pm$0.1	1.2$\pm$0.1	13	2.17$\pm$0.55	1.83$\pm$0.47
4U 1456-32	332.2	23.9	0.91	0.84	0.7$\pm$0.1	0.9$\pm$0.1	0.31$\pm$0.15	1.2	2.26$\pm$1.14	2.90$\pm$1.44
4U 1516-56	322.1	0.0	15.90	19.80	18.4$\pm$1.2		12.2$\pm$1.6	5.5	1.51$\pm$0.22
4U 1538-52	327.4	2.2	9.14	9.70	16.2$\pm$0.5	20.6$\pm$0.5	7.1$\pm$0.7	5.5	2.28$\pm$0.24	2.90$\pm$0.29
4U 1543-47	330.9	5.4	3.51	4.00	3.8$\pm$0.2		1.6$\pm$0.2	7.5	2.38$\pm$0.32
4U 1543-62	321.8	-6.3	2.43	2.96	3.2$\pm$0.1	3.4$\pm$0.1	1.0$\pm$0.3	7.0	3.20$\pm$0.97	3.40$\pm$1.02
4U 1608-52	330.9	-0.9	18.10	19.20	10.7$\pm$0.2	10.8$\pm$2.2	6.2$\pm$1.7	3.9	1.73$\pm$0.47	1.74$\pm$0.60
4U 1636-53	332.9	-4.8	2.76	3.58	2.9$\pm$0.1	3.7$\pm$0.1	2.5$\pm$0.3	6.0	1.16$\pm$0.14	1.48$\pm$0.18
4U 1658-48	338.9	-4.3	3.74	5.26	5.0$\pm$0.1	8.1$\pm$0.2	3.7$\pm$0.4		1.35$\pm$0.15	2.19$\pm$0.24
4U 1704-30	353.8	7.3	1.82	1.82	2.3$\pm$0.2		0.9$\pm$0.1	10.0	2.56$\pm$0.36
4U 1724-307	356.3	2.3	5.70	6.57	6.6$\pm$0.5		4.9$\pm$0.6	7.4	1.35$\pm$0.19

4U 1728-16	8.5	9.0	1.96	2.08	2.4$\pm$0.1		0.8$\pm$0.5	4.2	3.00$\pm$1.88
4U 1728-34	354.3	0.2	12.40	16.00	29.3$\pm$0.5		10.8$\pm$1.8	5.2	2.71$\pm$0.45
4U 1730-335	354.8	-0.2	12.20	16.70	17.4$\pm$0.3		10.1$\pm$1.9	8.0	1.72$\pm$0.19
4U 1746-37	353.5	-5.0	2.63	2.95	4.0$\pm$0.3		1.5$\pm$0.2	11.0	2.67$\pm$0.41
4U 1820-30	2.8	-7.9	1.29	1.50	2.7$\pm$0.1	2.6$\pm$0.3	0.9$\pm$0.1	7.6	3.00$\pm$0.35	2.89$\pm$0.46
4U 1822-37	356.9	-11.3	1.04	1.24	1.2$\pm$0.2		0.5$\pm$0.3	2.5	2.40$\pm$1.49
4U 1837+04	36.1	4.8	4.14	4.71	5.2$\pm$0.2		1.3$\pm$0.1	8.4	4.00$\pm$0.34
4U 1850-08	25.4	-4.3	2.36	2.78	3.8$\pm$0.1	4.8$\pm$0.2	1.2$\pm$0.2	8.2	3.17$\pm$0.53	4.00$\pm$0.69
4U 1908+00	35.7	-4.1	2.84	3.37	4.4$\pm$0.1	4.1$\pm$0.1	1.2$\pm$0.1	5.0	3.67$\pm$0.32	3.42$\pm$0.30
4U 1915-05	31.4	-8.5	2.31	2.60	3.9$\pm$0.1	5.6$\pm$40.7	2.2$\pm$0.9	8.9	1.77$\pm$0.73	2.55$\pm$1.09
4U 1956+35	71.3	3.1	7.21	7.21	4.4$\pm$0.1	5.4$\pm$0.1	3.3$\pm$0.1	2.14	1.33$\pm$0.05	1.64$\pm$0.06
4U 1957+11	51.3	-9.3	1.21	1.27	1.6$\pm$0.1	1.1$\pm$0.1	0.9$\pm$0.1		1.78$\pm$0.23	1.22$\pm$0.18
4U 2129+47	91.6	-3.0	3.30	3.82	2.4$\pm$0.7	3.6$\pm$0.1	1.2$\pm$0.2	7.0	2.00$\pm$0.67	3.00$\pm$0.51
4U 2135+57	99	3.3	8.18	9.19	7.8$\pm$0.3		4.0$\pm$0.3	3.8	1.95$\pm$0.16
4U 2142+38	87.3	-11.3	1.87	2.17	1.9$\pm$0.1	2.9$\pm$0.1	1.1$\pm$0.1	7.2	1.73$\pm$0.18	2.64$\pm$0.26
EXO 0331+530	146.1	-2.2	6.91	8.54	9.0$\pm$1.0		5.8$\pm$0.2		1.55$\pm$0.18
EXO 0748-676	280.0	-19.8	1.01	1.14	0.8$\pm$0.1	0.6$\pm$0.1	0.2$\pm$0.1	6.8	4.00$\pm$2.06	3.00$\pm$1.58
EXO 1745-248	3.8	1.7	6.33	5.81	13.2$\pm$3.5		7.2$\pm$1.0	8.7	1.83$\pm$0.55
EXO 2030+375	77.2	-1.2	8.80	10.30	20.5$\pm$0.1		11.7$\pm$0.7	7.1	1.75$\pm$0.11
GRO J1719-24	0.1	7.0	2.56	2.84	4.0$\pm$0.4		2.8$\pm$0.6	1.2	1.43$\pm$0.34
GRO J0422+32	165.9	-11.9	1.55	1.66	1.6$\pm$0.9		0.8$\pm$0.1		2.00$\pm$1.15
GRO J1008-57	283	-1.8	13.50	15.10	12.7$\pm$0.1		6.1$\pm$0.2	2.0	2.08$\pm$0.07
GRO J1655-40	345	2.5	5.33	6.86	7.4$\pm$0.3	7.4$\pm$0.2	3.7$\pm$0.3		2.00$\pm$0.18	2.00$\pm$0.17
GRO J1944+26	63.2	1.4	9.43	10.20	13.0$\pm$0.1	16.3$\pm$0.3	6.5$\pm$0.3	9.5	2.00$\pm$0.09	2.51$\pm$0.12
GRO J2058+42	83.5	-2.7	6.22	7.1	9.5$\pm$2.3		4.3$\pm$0.4	9.0	2.21$\pm$0.57
GRS 1009-45	275.9	9.3	1.05	1.16	0.4$\pm$0.1		0.6$\pm$0.2	4.5	0.67$\pm$0.28
GS 0834-43	262.0	-1.5	10.10	11.80	21.2$\pm$2.3		12.3$\pm$3.7	4.0	1.72$\pm$0.29
Gu Mus	295.3	-7.1	1.91	2.50	2.3$\pm$0.1		0.9$\pm$0.1	5.9	2.56$\pm$0.30
IGR J17544-2619	3.2	-0.3	11.80	14.40	11.2$\pm$1.2		6.3$\pm$0.4	3.7	1.78$\pm$0.22
IGR J22534+6243	110.0	2.9	8.96	9.98	18.1$\pm$1.9		5.7$\pm$0.4		3.18$\pm$0.40
KS 1947+300	66.1	2.1	8.90	10.40	5.1$\pm$0.2		3.4$\pm$0.4	10.0	1.50$\pm$0.19
LS 2883	304.2	-1.0	14.50	16.20	4.0$\pm$0.3		3.3$\pm$0.4	2.7	1.21$\pm$0.17
LS 5039	16.9	-1.3	8.87	8.71	6.4$\pm$0.1		3.7$\pm$0.3	2.9	1.73$\pm$0.14
ALS 19596	33.0	1.7	10.10	10.10	23.0$\pm$1.3		8.1$\pm$0.9		2.84$\pm$0.35
MXB 1746-20	7.7	3.8	3.30	2.92	6.7$\pm$0.3	5.7$\pm$0.1	3.2$\pm$0.3	8.5	2.13$\pm$0.22	1.78$\pm$0.17
SAX J1748.9-2021	7.7	3.8	3.30	2.92	7.0$\pm$1.0		3.2$\pm$0.4	8.5	2.19$\pm$0.42
RX J0146.9+6121	129.5	-0.8	7.58	8.49	4.9$\pm$0.5		2.9$\pm$0.1	2.3	1.69$\pm$0.18
RX J0440.9+4431	159.8	-1.3	5.45	6.64	3.4$\pm$0.1		2.2$\pm$0.2	3.3	1.55$\pm$0.15
RX J1829.4-2347	9.3	-6.1	1.71	1.88	2.6$\pm$1.7		1.2$\pm$0.4	6.0	2.17$\pm$0.73
RX J1832-33	1.5	-11.4	0.92	1.23	0.55$\pm$0.22	0.58$\pm$0.06	0.3$\pm$0.1	9.3	1.83$\pm$0.95	1.93$\pm$0.67
Swift J1753.5-0127	24.9	12.2	1.74	1.69	2.2$\pm$0.1	2.7$\pm$0.1	1.3$\pm$0.1	6.0	1.69$\pm$0.15	2.08$\pm$0.18
V404 Cyg	73.1	-2.1	6.66	8.10	8.1$\pm$0.3	8.6$\pm$0.6	3.6$\pm$0.5	3.5	2.25$\pm$0.32	2.39$\pm$0.37
XTE J1550-564	325.9	-1.8	10.10	8.97	6.6$\pm$0.1	6.6$\pm$0.6	2.9$\pm$0.2	5.3	2.28$\pm$0.16	2.28$\pm$0.16
XTE J1720-318	354.6	3.1	4.77	5.25	15.1$\pm$0.2		6.6$\pm$0.6		2.29$\pm$0.21
XTE J1808-369	355.4	-8.1	1.13	1.34	1.4$\pm$0.1	1.4$\pm$0.1	0.8$\pm$0.3	3.0	1.75$\pm$0.67	1.75$\pm$0.67
XTE J1819-254	6.8	-4.8	1.81	2.34		2.4$\pm$0.1	0.8$\pm$0.1	9.5		3.00$\pm$0.63
XTE J1859+226	54.0	8.6	2.16	2.21	3.6$\pm$0.4		1.8$\pm$0.4	7.6	2.00$\pm$0.50
XTE J2103+457	87.1	-0.7	6.64	7.78	7.6$\pm$0.1		4.2$\pm$0.3	6.5	1.81$\pm$0.13
XTE J2123-058	46.5	-36.2	0.54	0.57	0.8$\pm$2.3		0.37$\pm$0.15	8.5	2.16$\pm$6.28

Table 6. Table 5: A summary of the final N H subscript 𝑁 H N_{\rm H} - A V subscript 𝐴 𝑉 A_{V} fitting.

Sample	Coefficient	Zero Offset
	(${10}^{21}H{\mathrm{cm}}^{-2}{\mathrm{mag}}^{-1}$)	(${10}^{21}H{\mathrm{cm}}^{-2}$)
	AG89
Whole	2.08$\pm$0.02	0 (fixed)
Whole	2.12$\pm$0.03	$-0.11\pm 0.04$
SNRs	2.06$\pm$0.05	0 (fixed)
XBs	2.09$\pm$0.03	0 (fixed)
	W00
Whole	2.47$\pm$0.04	0 (fixed)
Whole	2.59$\pm$0.07	$-0.23\pm 0.10$
SNRs	2.51$\pm$0.10	0 (fixed)
XBs	2.46$\pm$0.05	0 (fixed)

Table 7. Table 6: Hydrogen column density N H subscript 𝑁 H N_{\rm H} and distance D 𝐷 D compiled from the literature.

Objects	Gl	Gb	$N_H$	$D$	References
Name	(degree)	(degree)	(${10}^{21}H{\mathrm{cm}}^{-2}$)	(kpc)
G1.0-0.1	1.0	-0.1	75	8.5	1,2
G1.9+0.3	1.9	0.3	58	8.5	3,4
G5.4-1.2	5.4	-1.2	35	5.2	1,5
G8.7-0.1	8.7	-0.1	12	4.5	6
G12.0-0.1	12.0	-0.1	49	10.9	7,8
G12.8-0.0	12.8	0.0	100	4.8	7,9
G15.9+0.2	15.9	0.2	39	8.5	7,10
G16.7+0.1	16.7	0.1	47.4	14.0	11,12
G18.9-1.1	18.9	-1.1	8.3	2.0	13,14
G21.5-0.9	21.5	-0.9	22.4	4.8	15,16
G21.8-0.6	21.8	-0.6	28	5.5	15,17
G27.4+0.0	27.4	0.0	26	8.7	18,19
G28.6-0.1	28.6	-0.1	37	7.0	20,21
G28.8+1.5	28.8	1.5	20	4.0	22
G29.7-0.3	29.7	-0.3	29	10.6	23-30
G31.9+0.0	31.9	0.0	28	7.9	31-36
G32.4+0.1	32.4	0.1	52	17.0	37
G32.8-0.1	32.8	-0.1	8.1	4.8	38,39
G33.6+0.1	33.6	0.1	15	7.5	40-44
G34.7-0.4	34.7	-0.4	13	2.7	43,45-48
G41.1-0.3	41.1	-0.3	32	10.3	49,50
G43.3-0.2	43.3	-0.2	50	10.0	51-55
G49.2-0.7	49.2	-0.7	17	5.2	56-61
G65.7+1.2	65.7	1.2	2	0.9	62-64
G76.9+1.0	76.9	1.0	16	10.0	65,66
G85.4+0.7	85.4	0.7	8.3	3.8	67,68
G148.1+0.8	148.1	0.8	4.9	1.0	69-71
G156.2+5.7	156.2	5.7	3.2	2.0	72-75
G195.1+4.3	195.1	4.3	0.11	0.25	71,76
G201.1+8.3	201.1	8.3	0.25	0.28	71,77-79
G266.2-1.2	266.2	-1.2	3.5	0.75	80-84
G272.2-3.2	272.2	-3.2	10	10.0	85-89
G284.0-1.8	294.0	-1.8	5	3.0	90,91
G284.2-0.4	284.2	-0.4	15	9.0	92,93
G284.3-1.8	284.3	-1.8	6.6	2.9	94,95
G287.4+0.6	287.4	0.6	9	3.0	96,97
G290.1-0.8	290.1	-0.8	7.3	7.0	98,99
G291.0-0.1	291.0	-0.1	6.7	3.5	100,101
G292.2-0.5	292.2	-0.5	14.6	8.4	102-104
G296.7-0.9	296.7	-0.9	12.4	9.8	105
G296.8-0.3	296.8	-0.3	6.4	9.6	106,107
G299.2-2.9	299.2	-2.9	3.5	5.0	108,109
G304.1-0.2	304.1	-0.2	27	7.0	93,110
G304.6+0.1	304.6	0.1	38.7	10.0	89,111,112
G306.3-0.9	306.3	-0.9	19.5	8.0	113
G308.3-1.4	308.3	-1.4	10	9.8	114,115
G309.2-0.6	309.2	-0.6	6.5	4.0	116
G309.8-2.6	309.8	-2.6	3.9	2.5	117,118
G310.6-1.6	310.6	-1.6	20.9	10.0	93,119
G311.5-0.3	311.5	-0.3	27.7	13.8	89,112,120
G313.3+0.1	313.3	0.1	18.5	3.0	93,121
G313.6+0.3	313.6	0.3	35.4	5.6	121-123
G326.3-1.8	326.3	-1.8	3.5	5.1	124,125
G327.1-1.1	327.1	-1.1	18.8	9.0	126-128
G327.4+0.4	327.4	0.4	24	4.3	129,130
G330.2+1.0	330.2	1.0	26	7.8	89,130,131
G337.2+0.1	337.2	0.1	83	11.0	132-134
G337.2-0.7	337.2	-0.7	32.3	9.0	89,135
G337.8-0.1	337.8	-0.1	67.5	12.3	136,137
G338.3-0.0	338.3	0.0	150	12.8	138,139
G343.7-2.3	343.7	-2.3	5	2.6	71,140,141
G344.7-0.1	344.7	-0.1	45	6.3	142
G346.6-0.2	346.6	-0.2	22.7	11.0	120,137,143-146

G347.3-0.5	347.3	-0.5	7.8	1.0	146-149
G348.5+0.1	348.5	0.1	35	7.9	120,150,151
G348.7+0.3	348.7	0.3	38	13.2	151-153
G349.7+0.2	349.7	0.2	64	11.5	154,155
G350.1-0.3	350.1	-0.3	33	9.0	154
G352.7-0.1	352.7	-0.1	32	7.6	156,157
G353.6-0.7	353.6	-0.7	18.2	3.2	158-160
G355.6-0.0	355.6	0.0	55	13.0	145,161
G357.7-0.1	357.7	-0.1	100	11.8	31,162
G359.0-0.9	359.0	-0.9	16	3.7	89,163,164
G359.1-0.5	359.0	-0.5	25	7.6	163-165

Object

Type

$D$

References

$N_H\left(\mathrm{AG89}\right)$

References

Accept “A”

$N_H\left(\mathrm{AG89}\right)$

$N_H\left(\mathrm{W00}\right)$

References

Accept “A”

$N_H\left(\mathrm{W00}\right)$

$A_V$

References

Accept “A”

$A_V$ (mag)

(kpc)

for $D$

(${10}^{21}H{\mathrm{cm}}^{-2}$)

for $N_H\left(\mathrm{AG89}\right)$

or Reject “R”

This Work

(${10}^{21}H{\mathrm{cm}}^{-2}$)

for $N_H\left(\mathrm{W00}\right)$

or Reject “R”

This Work

(mag)

for $A_V$

or Reject “R”

This Work

G4.5+6.8

SNR

5.1

Sankrit et al. 2016

5.3$\pm$0.4

Bamba et al. 2005

A

5.3$\pm$0.1

5.4$\pm$0.1

Foight et al. 2016

A

5.4$\pm$0.1

2.8$\pm$0.3

Blair et al. 1991

A

3.0$\pm$0.4

north

3.5$\pm$0.2

Cassam-Chenai et al. 2004

A

2.5$\pm$0.9

Oliva et al. 1989

A

5.7$\pm$0.1

Kinugasa & Tsunemi 1999

A

3.5

Leibowitz & Danziger 1983

A

3.3

Dennefeld 1982

A

2.2$\pm$0.6

van den Bergh & Kamper 1977

A

G6.4-0.1

SNR

1.9

Velázquez et al. 2002

4.1$\pm$0.1

Zhou et al. 2014

A

4.3$\pm$0.1

6.3$\pm$1.9

Foight et al. 2016

A

6.3$\pm$1.9

3.4$\pm$0.3

Mavromatakis et al. 2004a

A

3.3$\pm$0.3

Central

4.7$\pm$0.2

Sawada & Koyama 2012

A

3.1

Long et al. 1991

A

5.1$\pm$0.5

Kawasaki et al. 2005

A

6.6$\pm$0.6

Rho & Borkowski 2002

A

G6.4-0.1

SNR

1.9

Velázquez et al. 2002

7.9$\pm$0.2

Zhou et al. 2014

A

7.7$\pm$0.2

4.0

Long et al. 1991

A

4.0$\pm$0.5

northeast shell

7.6$\pm$0.2

Nakamura et al. 2014

A

7.7$\pm$0.8

Rho & Borkowski 2002

A

G11.2-0.3

SNR

4.4

Kilpatrick et al. 2016

17.1$\pm$3.3

Roberts et al. 2003

A

15.7$\pm$1.5

13.0

Koo et al. 2007

A

13.0$\pm$1.7

southeast

15.9$\pm$1.1

Vasisht et al. 1996

A

13$\pm$3

Reynolds et al. 1994

A

G13.3-1.3

SNR

3.0

Seward et al. 1995a

5.5$\pm$4.5

Seward et al. 1995a

A

5.5$\pm$4.5

0.5

Seward et al. 1995a

A

0.5$\pm$0.1

G39.7-2.0

SNR

5.5

Blundell & Bowler 2004

5.2$\pm$0.1

Brinkmann et al. 2007

A

5.2$\pm$0.1

2.3$\pm$0.3

Boumis et al. 2007

A

2.3$\pm$0.3

east jet

2.2$\pm$0.6

Brinkmann et al. 1996

R

3.3$\pm$0.6

Yamauchi et al. 1994

R

G53.6-2.2

SNR

2.3

Giacani et al. 1998

6.1$\pm$0.1

Broersen & Vink 2015

A

6.1$\pm$0.1

3.1

Long et al. 1991

A

3.1$\pm$0.4

central

6.2$\pm$1.1

Yoshita et al. 2001

A

G53.6-2.2

SNR

2.3

Giacani et al. 1998

4.8$\pm$0.7

Broersen & Vink 2015

A

4.8$\pm$0.8

6.7$\pm$0.3

Foight et al. 2016

A

6.7$\pm$0.3

4.0

Long et al. 1991

A

4.0$\pm$0.5

southwest

4.8$\pm$1.1

Yoshita et al. 2001

A

G54.1+0.3

SNR

6.2

Leahy et al. 2008

19.5$\pm$0.4

Temim et al. 2010

A

18.1$\pm$0.5

25.5$\pm$0.4

Foight et al. 2016

A

25.5$\pm$0.4

7.3$\pm$0.1

Kim et al. 2013

A

7.3$\pm$0.1

15.7$\pm$0.6

Bocchino et al. 2010

A

8.0$\pm$0.7

Koo et al. 2008

A

16$\pm$1

Lu et al. 2002

A

17.9$\pm$2.7

Lu et al. 2001

A

G67.7+1.8

SNR

4.1$\pm$0.9

Hui & Becker 2009

A

4.1$\pm$0.9

1.0-2.5

Gök et al. 2008

A

1.7$\pm$0.4

north rim

1.7$\pm$0.3

Mavromatakis et al. 2001

A

G69.0+2.7

SNR

1.5

Leahy & Ranasinghe 2012

3.0$\pm$0.1

Li et al. 2005

A

3.0$\pm$0.1

4.5$\pm$0.2

Foight et al. 2016

A

4.5$\pm$0.2

2.4

Hester & Kulkarni 1989

A

2.5$\pm$0.3

central

2.9$\pm$0.5

Mavromatakis et al. 2001

A

2.4

Blair et al. 1984a

A

3.1-4.3

Angerhofer et al. 1980

A

G74.0-8.5

SNR

1.5

Blair et al. 2005

0.95$\pm$0.13

Oakley et al. 2013

R

0.34$\pm$0.03

0.25

Miller 1974

A

0.25$\pm$0.04

0.34$\pm$0.02

Leahy & Hassan 2013

A

0.25$\pm$0.06

Parker 1967

A

0.35$\pm$0.05

Kimura et al. 2009

A

0.01-1.47

Nemes et al. 2008

R

0.4$\pm$0.1

Uchida et al. 2008

A

0.5$\pm$0.1

Miyata et al. 2007

A

G78.2+2.1

SNR

2.0

Leahy et al. 2013

7.4$\pm$0.6

Hui et al. 2015

A

7.6$\pm$0.7

3.4$\pm$0.6

Mavromatakis 2003

A

3.4$\pm$0.6

east

12$\pm$2

Uchiyama et al. 2002

R

9.2$\pm$1.8

Leahy et al. 2013

A

for central

G82.2+5.3

SNR

2.0

Uyaniker et al. 2003

4.7$\pm$0.5

Mavromatakis et al. 2004b

A

4.7$\pm$0.5

2.8$\pm$0.1

Mavromatakis et al. 2004b

A

2.8$\pm$0.1

G85.9-0.6

SNR

5.0

Kothes et al. 2001

6.9$\pm$0.3

Jackson et al. 2008

A

6.9$\pm$0.3

0.7$\pm$0.1

Gök et al. 2009

A

0.7$\pm$0.1

G89.0+4.7

SNR

1.7

Byun et al. 2006

2.6$\pm$0.5

Pannuti et al. 2010b

A

3.0$\pm$0.4

1.6$\pm$0.3a

Mavromatakis et al. 2007

A

1.6$\pm$0.3

3.2$\pm$0.3

Lazendic & Slane 2006

A

G109.1-1.0

SNR

3.2

Kothes & Foster 2012

5-7

Sasaki et al. 2004

A

7.1$\pm$0.7

9.0$\pm$1.4

Foight et al. 2016

A

9.0$\pm$1.4

3.1$\pm$0.6

Fesen & Hurford 1995

A

3.1$\pm$0.6

6.9$\pm$0.8

Parmar et al. 1998

A

7.7$\pm$0.6

Rho & Petre 1997

A

G111.7-2.1

SNR

3.4

Reed et al. 1995

12.7$\pm$0.3

Laming et al. 2006

A

13.6$\pm$0.3

11.7$\pm$1.6

Foight et al. 2016

A

11.7$\pm$1.6

4.6-6.2

Hurford & Fesen 1996

A

4.8$\pm$0.7

north

14.2$\pm$0.2

Laming & Hwang 2003

A

4.4

Searle 1971

A

15$\pm$8

Willingale et al. 2002

A

10$\pm$1

Gotthelf et al. 2001

A

G116.9+0.2

SNR

3.0

Yar-Uyaniker et al. 2004

6.3$\pm$1.2

Pannuti et al. 2010b

A

5.9$\pm$0.8

9.2$\pm$0.7

Foight et al. 2016

A

9.2$\pm$0.7

2.6$\pm$0.1

Fesen et al. 1997

A

2.6$\pm$0.1

5.7$\pm$0.7

Lazendic & Slane 2006

A

G119.5+10.2

SNR

1.4

Pineault et al. 1993

1.8$\pm$0.3

Caraveo et al. 2010

A

2.1$\pm$0.4

3.8$\pm$1.1

Foight et al. 2016

A

3.8$\pm$1.1

1.27$\pm$0.14

Mavromatakis et al. 2000

A

1.3$\pm$0.2

2.8$\pm$0.6

Slane et al. 1997

A

1.5

Fesen et al. 1981

A

2.3$\pm$0.6

Seward et al. 1995b

A

G120.1+1.4

SNR

3.0

Zhou et al. 2016

6.6$\pm$0.4

Cassam-Chenai et al. 2007

A

5.8$\pm$0.4

8.0$\pm$1.0

Foight et al. 2016

A

8.0$\pm$1.0

1.9$\pm$0.1

Ruiz-Lapuente 2004

A

1.8$\pm$0.1

Tian & Leahy 2011

6.4$\pm$0.5

Warren et al. 2005

A

$\sim$1.6

Ghavamian et al. 2000

A

4.7$\pm$0.3

Hwang et al. 2002

A

2.1$\pm$0.5

Chevalier et al. 1980

A

8.3

Decourchelle et al. 2001

A

G130.7+3.1

SNR

2.0

Kothes 2013

4.2$\pm$0.1

Gotthelf et al. 2007

A

4.1$\pm$0.1

5.4$\pm$0.1

Foight et al. 2016

A

5.4$\pm$0.1

2.1$\pm$0.2

Fesen et al. 1988

A

2.1$\pm$0.2

4.5$\pm$0.1

Slane et al. 2004

A

1.9$\pm$0.9

Fesen 1983

A

3.8$\pm$0.1

Slane et al. 2002

A

3.3$\pm$0.4

Torii et al. 2000

A

3.3$\pm$0.7

Helfand et al. 1995

A

G132.7+1.3

SNR

2.5

Routledge et al. 1991; Landecker et al. 1987

8.6$\pm$0.3

Lazendic & Slane 2006

A

8.6$\pm$0.3

2.2$\pm$0.1

Fesen et al. 1995

A

2.2$\pm$0.1

G166.0+4.3

SNR

4.5

Landecker et al. 1989

$\sim$1.9

Bocchino et al. 2009

A

2.0$\pm$0.2

1.7

Fesen et al. 1985

A

1.7$\pm$0.2

$\sim$2.1

Guo & Burrows 1997

A

$\pm$2

Burrows & Guo 1994

A

G180.0-1.7

SNR

1.3

Chatterjee et al. 2009

2.9$\pm$0.1

Ng & Romani 2007

A

3.1$\pm$0.2

0.7$\pm$0.2

Fesen et al. 1985

A

0.7$\pm$0.2

3.9$\pm$0.2

Romani & Ng 2003

A

G184.6-5.8

SNR

2.0

Trimble 1968

$\sim$3.5

Seward et al. 2006

A

3.2$\pm$0.1

3.0$\pm$0.2

Foight et al. 2016

A

4.1$\pm$0.1

1.6$\pm$0.2

Miller 1973, Sollerman et al. 2000

A

1.5$\pm$0.1

2.7$\pm$0.1

Kirsch et al. 2006

R

4.4$\pm$0.1

Weisskopf et al. 2004

A

1.6

Sollerman et al. 2000

A

3.6$\pm$0.1

Weisskopf et al. 2004

A

1.4$\pm$0.1

Veron-Cetty & Woltjer 1993

A

3.5$\pm$0.1

Willingale et al. 2001

A

1.6$\pm$0.1

Blair et al. 1992

A

1.6$\pm$0.1

Wu 1981

A

G189.1+3.0

SNR

1.5

Frail 2011

$\sim$4.1

Bocchino et al. 2009

A

5.2$\pm$0.5

$\sim$6

Yamaguchi et al. 2014

A

6$\pm$0.5

$\sim$2-5

Kokusho et al. 2013

A

2.8$\pm$0.6

5.2$\pm$0.4

Troja et al. 2006

A

2.6$\pm$0.7

Welsh & Sallmen 2003

A

7.2$\pm$0.6

Gaensler et al. 2006

A

2.9$\pm$0.5

Fesen & Kirshner 1980

A

8.0$\pm$1.5

Bocchino & Bykov 2001

A

G260.4-3.4

SNR

2.0

Reynoso et al. 1995

2.7$\pm$0.1

Katsuda et al. 2012

A

3.1$\pm$0.1

3.5$\pm$1.5

Foight et al. 2016

A

3.5$\pm$1.5

1.7$\pm$0.6

Blair et al. 1995

A

1.5$\pm$0.2

Sakhibov & Smirnov 1983

4.3$\pm$0.2

Katsuda et al. 2008

A

1.5

Winkler & Kirshner 1985

A

4.5$\pm$0.5

Hui & Becker 2006

A

0.6

Dopita et al. 1977

R

G263.9-3.3

SNR

$\sim$0.29

Verbiest et al. 2012

0.13$\pm$0.09

Yamaguchi & Katsuda 2009

A

0.19$\pm$0.02

0.3$\pm$0.1

Foight et al. 2016

A

0.3$\pm$0.1

0.31

Sankrit et al. 2003

A

0.32$\pm$0.04

0.23$\pm$0.09

Miceli et al. 2008

A

0.1

Bocchino et al. 2000

R

0.16$\pm$0.03

Lamassa et al. 2008

A

0.56

Raymond et al. 1997

R

0.14$\pm$0.02

Katsuda & Tsunemi 2006

A

0.31

Wallerstein & Balick 1990

A

0.24$\pm$0.03

Katsuda & Tsunemi 2005

A

0.15$\pm$0.25

Miceli et al. 2005

A

0.37

Manchester et al. 1978

A

0.19$\pm$0.1

Lu & Aschenbach 2000

A

0.03-0.3

Bocchino et al. 1994

A

0.35$\pm$0.08

Tsunemi et al. 1999

A

G292.0+1.8

SNR

6.0

Gaensler et al. 2003

4.3$\pm$0.2

Kamitsukasa et al. 2014

A

3.8$\pm$0.3

$\sim$5

Yamaguchi et al. 2014

A

5$\pm$0.4

1.9

Winkler & Long 2006

A

2.2$\pm$0.2

5.4$\pm$0.6

Lee et al. 2010

A

2.8$\pm$0.3

Goss et al. 1979

A

5.2$\pm$0.6

Park et al. 2004

A

5$\pm$1

Gonzalez & Safi-Harb 2003

A

3.1$\pm$0.4

Hughes et al. 2003

A

3.2$\pm$0.2

Hughes et al. 2001

A

G296.1-0.5

SNR

$\sim$2.0

Castro et al. 2011

0.75$\pm$0.05

Gök & Sezer 2012

A

0.6$\pm$0.2

1.9$\pm$0.3

Longmore et al. 1977

A

1.9$\pm$0.3

north

0.2$\pm$0.1

Castro et al. 2011

A

G296.5+10.0

SNR

$\sim$2.1

Giacani et al. 2000

1.2$\pm$0.1

De Luca et al. 2004

A

1.2$\pm$0.1

0.5

Ruiz 1983

A

0.5$\pm$0.1

1.5$\pm$0.4

Zavlin et al. 1998

A

G315.4-2.3

SNR

2.3

Sollerman et al. 2003

5.1$\pm$0.4

Helder et al. 2011

A

4.0$\pm$0.2

1.7

Leibowitz & Danziger 1983

A

1.7$\pm$0.2

southwest

4.3$\pm$0.6

Bamba et al. 2005

A

4.3$\pm$0.2

Rho et al. 2002

A

2.7$\pm$1.0

Borkowski et al. 2001

A

3.2$\pm$0.5

Bamba et al. 2000

A

$\sim$2.8

Bocchino et al. 2000

A

2.0$\pm$0.4

Vink et al. 1997

A

1.8$\pm$0.4

Lemoine-Goumard et al. 2012

A

4.8$\pm$0.1

Broersen et al. 2014

A

G320.4-1.2

SNR

5.2

Gaensler et al. 1999

8.6$\pm$0.2

DeLaney et al. 2006

A

10.9$\pm$0.1

11.5$\pm$0.3

Schock et al. 2010

A

11.5$\pm$0.3

5.5

Seward et al. 1983

A

3.6$\pm$0.4

11.7$\pm$0.1

Yatsu et al. 2005

A

3.0-3.6

Dopita et al. 1977

A

9.5$\pm$0.3

Gaensler et al. 2002

A

12.7$\pm$2.3

Marsden et al. 1997

A

5.9$\pm$0.6

Tamura et al. 1996

A

G327.6+14.6

SNR

2.2

Winkler et al. 2003

0.68$\pm$0.01

Uchida et al. 2013

A

0.68$\pm$0.10

1.6$\pm$0.1

Foight et al. 2016

A

1.6$\pm$0.1

0.32$\pm$0.1

Schweizer & Middleditch 1980

A

0.32$\pm$0.1

0.42$\pm$0.08

Broersen et al. 2013

A

0.90$\pm$0.05

Bamba et al. 2003

A

0.56$\pm$0.06

Allen et al. 2001

A

G332.4-0.4

SNR

3.1

Caswell et al. 1975

7

Gotthelf et al. 1997

A

7$\pm$0.7

8.7$\pm$3.5

Foight et al. 2016

A

8.7$\pm$3.5

4.5

Leibowitz & Danziger 1983

A

4.7$\pm$0.7

A

$\sim$5.0

Ruiz 1983

A

4.7$\pm$0.9

Oliva et al. 1989

A

G332.5-5.6

SNR

3.0

Zhu et al. 2015

1.4$\pm$0.4

Zhu et al. 2015

A

1.4$\pm$0.4

0.83

Stupar et al. 2007

A

0.8$\pm$0.3

0.83

Stupar et al. 2007

R

G37.7-34.5

PN

1.1

Gaensler et al. 1999

0.81$\pm$0.85

Guerrero et al. 2002

A

0.81$\pm$0.85

0.29$\pm$0.23

Rubin et al. 2001

A

0.19$\pm$0.02

0.70$\pm$0.18

Lame & Pogge 1996

R

0.19

Mendez et al. 1988

A

G64.7+5.0

PN

5.2

Gaensler et al. 1999

2.5$\pm$0.1

Maness et al. 2003

A

2.5$\pm$0.1

1.1

Bernard-Salas et al. 2003

A

1.0$\pm$0.1

0.9

Aller & Hyung 1995

A

0.9

Rudy et al. 1991

A

0.9

Torres-Peimbert & Pena 1981

A

G84.9-3.4

PN

0.7

Yang et al. 2016

4.1$\pm$0.2

Maness et al. 2003

A

4.1$\pm$0.2

2.6

Salas et al. 2001

A

2.9$\pm$0.3

2.9$\pm$0.2

Aller & Keyes 1988

A

2.9

Pottasch et al. 1982

A

3.0

Shaw & Kaler 1982

A

3.0$\pm$0.3

Atherton et al. 1979

A

G94.0+27.4

PN

1.0

Cahn et al. 1992

0.12$\pm$0.02

Montez & Kastner 2013

A

0.12$\pm$0.02

0.09$\pm$0.03

Kaler & Feibelman 1985

A

0.09$\pm$0.03

G197.8+17.3

PN

1.2

Bensby & Lundstrom 2001

0.8$\pm$0.5

Montez et al. 2015

A

0.8$\pm$0.6

0.5$\pm$0.1

Pottasch et al. 2008

A

0.5$\pm$0.1

0.8$\pm$0.9

Guerrero et al. 2005

A

G331.7-1.0

PN

1.1

Ortiz et al. 2011

5.0$\pm$0.8

Kastner et al. 2003

A

5.0$\pm$0.8

3.2

Smith 2003

A

4.1$\pm$0.4

4.6$\pm$0.3

Zhang & Liu 2002

A

4.4

Tylenda et al. 1992

A

2E 0236.6+6101

HMXB

2.4

Liu et al. 2006

6.1$\pm$0.1

Rea et al. 2010

A

5.9$\pm$0.2

3.5

Paredes & Figueras 1986

A

2.8$\pm$0.3

5.1$\pm$0.4

Albert et al. 2008

A

2.3

Howarth 1983

A

5.7$\pm$0.3

Esposito et al. 2007

A

2.8$\pm$0.2

Maraschi et al. 1981

A

7.0$\pm$0.6

Paredes et al. 2007

A

2.9

Hutchings & Crampton 1981a

A

4.9$\pm$0.2

Chernyakova et al. 2006a

A

6$\pm$1

Sidoli et al. 2006

A

6.0$\pm$0.5

Leahy et al. 1997

A

2E 1118.7-6138

HMXB

5.0

Liu et al. 2006

8.1$\pm$0.1

Maitra et al. 2012

A

8.1$\pm$0.1

13.2$\pm$0.3

Suchy et al. 2011

A

13.2$\pm$0.3

2.9$\pm$0.4

Coe et al. 1994a

A

2.9$\pm$0.3

2.8$\pm$0.2

Coe & Payne 1985

A

3.7$\pm$0.6

Janot-Pacheco et al. 1981

A

2S 0620-003

LMXB

1.2

Liu et al. 2007

2.4$\pm$1.1

Kong et al. 2002

A

2.4$\pm$1.1

1.1$\pm$0.1

Wu et al. 1983

A

1.2$\pm$0.1

1.2

Greenstein 1979

A

1.2$\pm$0.1

Maraschi et al. 1981

A

2S 0921-63

LMXB

8.5

Liu et al. 2007

2.3$\pm$0.1

Valencic & Smith 2015

A

2.3$\pm$0.1

1.02$\pm$0.03

Shahbaz & Watson 2007

A

1.02$\pm$0.03

4U 0115+63

HMXB

17.5$\pm$12.3

Li et al. 2012

R

5.1$\pm$0.2

Negueruela et al. 2001

A

5.1$\pm$0.2

17.4$\pm$1.8

Campana et al. 2001

R

4.7

Hutchings & Crampton 1981b

A

4U 0352+30

HMXB

1.0

Liu et al. 2006

2.5$\pm$0.1

Valencic & Smith 2015

A

2.5$\pm$0.1

1.2

Telting et al. 1998

A

1.2$\pm$0.1

3.4$\pm$0.2

La Palombara & Mereghetti 2007

A

1.2$\pm$0.1

Fabregat et al. 1992

A

1.5$\pm$0.2

Di Salvo et al. 1998

A

1.1

Bernacca et al. 1983

A

1.2$\pm$0.1

Ferrari-Toniolo et al. 1978

A

4U 0538+26

HMXB

2.5

Liu et al. 2006

3.5$\pm$0.1

Doroshenko et al. 2014

A

3.9$\pm$0.1

7.0$\pm$0.3

Caballero et al. 2013

A

7.0$\pm$0.3

2.3

Lyuty & Zaitseva 2000

A

2.4$\pm$0.1

5.3$\pm$0.2

Maitra & Paul 2013

A

2.2$\pm$0.1

Steele et al. 1998

A

6.7$\pm$1.5

Mukherjee & Paul 2005

A

2.3

De Loore et al. 1984

A

2.2

Wu et al. 1983

A

2.5$\pm$0.1

Giangrande et al. 1980

A

2.5

Wade & Oke 1977

A

2.5

Stier & Liller 1976

A

4U 0614+09

LMXB

3.4$\pm$0.3

Migliari et al. 2010

A

3.5$\pm$0.1

3.3$\pm$0.1

Schulz et al. 2010

A

3.3$\pm$0.1

2.7$\pm$0.3

Nelemans et al. 2004

A

1.2$\pm$0.1

1.5-2.0

Paerels et al. 2001

R

1.0

Davidsen et al. 1974

A

3.8$\pm$0.1

Juett et al. 2001

A

3.2$\pm$0.1

Piraino et al. 1999

A

4U 0919-54

LMXB

2.8$\pm$0.1

Valencic & Smith 2015

A

3.1$\pm$0.1

3.0$\pm$0.1

Juett & Chakrabarty 2003

A

3.0$\pm$0.1

2.2$\pm$0.5

Nelemans et al. 2004

R

1.0$\pm$0.1

3.0$\pm$0.3

in’t Zand et al. 2005

A

1.0$\pm$0.3

Chevalier & Ilovaisky 1987

A

3.5$\pm$0.1

Juett et al. 2001

A

1.2

Chevalier & Ilpvaisky 1985

A

1.0

Neckel et al. 1980

A

4U 1036-56

HMXB

5.0

Liu et al. 2007

22$\pm$8

Cusumano et al. 2013

R

2.8$\pm$0.9

2.3$\pm$0.8

Motch et al. 1997

A

2.3$\pm$0.8

$>$14

Li et al. 2012

R

2.8$\pm$0.9

La Palombara et al. 2009

A

4U 1118-60

HMXB

9.0

Liu et al. 2006

11.2$\pm$0.1

Naik et al. 2011a

A

11.0$\pm$0.1

4.3

van der Meer et al. 2007

A

4.0$\pm$0.5

9.5$\pm$0.3

Wojdowski et al. 2001

A

2.8

Coe & Payne 1985

R

3.7$\pm$0.6

Janot-Pacheco et al. 1981

A

4.2

Hutchings et al. 1979

A

3.3

Genderen 1975

A

4.2

Mauder 1975

A

4.4

Krzeminski 1974

A

4.2

Vidal et al. 1974

A

4U 1258-61

HMXB

2.4

Liu et al. 2007

10.0$\pm$0.2

Jaisawal & Naik 2015

A

10.0$\pm$0.2

5.3$\pm$0.6

Parkes et al. 1980

5.5$\pm$0.7

5.9

Menzies et al. 1981

4U 1254-69

LMXB

13.0

Liu et al. 2007

2.0$\pm$0.1

Iaria et al. 2007

A

2.6$\pm$0.1

2.2$\pm$0.1

Trigo et al. 2008

A

2.2$\pm$0.1

1.2$\pm$0.3

Motch et al. 1987

A

1.2$\pm$0.3

3.2$\pm$0.1

Boirin & Parmer 2003

A

3.5$\pm$0.5

Iaria et al. 2001

A

4U 1456-32

LMXB

1.2

Liu et al. 2007

0.5$\pm$0.1

Cackett et al. 2010

A

0.7$\pm$0.1

0.9$\pm$0.1

Chakrabarty et al. 2014

A

0.9$\pm$0.1

0.31$\pm$0.15

Blair et al. 1984b

A

0.31$\pm$0.15

3$\pm$1

Asai et al. 1998

R

0.8$\pm$0.4

Campana et al. 2004

A

0.8$\pm$0.1

Bernardini et al. 2013

A

4U 1516-56

HMXB

5.5

Liu et al. 2007

18$\pm$1

Heinz et al. 2013

A

18.4$\pm$1.2

12.2

Jonker et al. 2007

A

12.2$\pm$1.6

20.3$\pm$2.3

Sell et al. 2010

A

12.1

Whelan et al. 1977

A

4U 1538-52

HMXB

5.5

Liu et al. 2006

14.3$\pm$2.6

Valencic & Smith 2015

A

16.2$\pm$0.5

20.6$\pm$0.5

Hemphill et al. 2016

A

20.6$\pm$0.5

6.9

Pakull et al. 1983

A

7.1$\pm$0.7

46

Clark 2004

R

6.8

Ilovaisky et al. 1979

A

16.3$\pm$0.4

Robba et al. 2001

A

7.4$\pm$0.5

Parkes et al. 1978

A

6.8

Crampton et al. 1978

A

4U 1543-47

LMXB

7.5

Liu et al. 2007

3.8$\pm$0.2

La Palombara & Mereghetti 2005

A

3.8$\pm$0.2

1.6$\pm$0.2

Orosz et al. 1998

A

1.6$\pm$0.2

A

4U 1543-62

LMXB

7.0

Liu et al. 2007

2.6$\pm$0.9

Farinelli et al. 2003

A

3.2$\pm$0.1

3.4$\pm$0.1

Juett & Chakrabarty 2003

A

3.4$\pm$0.1

1.0$\pm$0.3

Nelemans et al. 2004

A

1.0$\pm$0.3

3.3$\pm$0.7

Schultz 2003

A

1.4$\pm$0.3

Asai et al. 2000

A

3.4$\pm$0.1

Juett et al. 2001

A

4U 1608-52

LMXB

3.9

Liu et al. 2007

13.6$\pm$0.4

Valencic & Smith 2015

A

10.7$\pm$0.2

10.8$\pm$2.2

Guver et al. 2010a

A

10.8$\pm$2.2

$>$2

Wachter et al. 2002

R

6.2$\pm$1.7

9$\pm$6

Asai et al. 1996

A

6.2$\pm$1.7

Grindlay & Liller 1978

A

10.5$\pm$0.1

Armas Padilla et al. 2017

A

4U 1636-53

LMXB

6.0

Liu et al. 2007

4.4$\pm$1.4

Cackett et al. 2009a

A

2.9$\pm$0.1

3.5$\pm$0.6

Sanna et al. 2013

A

3.7$\pm$0.1

2.5$\pm$0.3

Lawrence et al. 1983

A

2.5$\pm$0.3

2.9$\pm$0.1

Lyu et al. 2014

A

3.7$\pm$0.2

Pandel et al. 2008

A

3.7$\pm$0.1

Lyu et al. 2015

A

4U 1658-48

LMXB

2.9$\pm$0.1

Plant et al. 2015

R

5.0$\pm$0.1

7.7$\pm$0.2

Parker et al. 2016

A

8.1$\pm$0.2

3.3$\pm$0.5

Gandhi et al. 2011

A

3.7$\pm$0.4

5.4$\pm$0.1

Shidatsu et al. 2011b

A

8.5$\pm$0.2

Furst et al. 2015

A

3.9

Casella et al. 2010

A

5.3$\pm$0.1

Miller et al. 2008

A

6.5$\pm$1.2

Garcia et al. 2015

A

3.4$\pm$0.6

Buxton & Vennes 2003

A

5.2$\pm$0.1

Reis et al. 2008

A

3.7$\pm$0.3

Zdziarski et al. 1998

A

4.0$\pm$0.1

Miller et al. 2004a

A

4.0

Cowley et al. 1987

A

5.3$\pm$0.1

Miller et al. 2004b

A

2.2$\pm$0.3

Ilovaisky et al. 1986

R

5.1$\pm$1.5

Kong et al. 2000a

A

3.9$\pm$0.8

Grindlay 1979

A

4.5$\pm$0.1

Shidatsu et al. 2011a

4U 1704-30

LMXB

10.0

Liu et al. 2006

2.0$\pm$0.2

Cackett et al. 2006

A

2.3$\pm$0.2

0.9

Wachter & Smale 1998

A

0.9$\pm$0.1

2.4$\pm$0.8

Wijnands et al. 2003

A

3.5$\pm$0.2

Sidoli et al. 2001a

A

1.3$\pm$0.2

Oosterbroek et al. 2001a

A

4U 1724-307

LMXB

7.4

Liu et al. 2007

6.6$\pm$0.5

Valencic & Smith 2015

A

6.6$\pm$0.5

5.8$\pm$0.6

Harris 2010 and 1996

A

4.9$\pm$0.6

6.5$\pm$0.5

Valencic et al. 2009

A

5.8

Valenti et al. 2010

A

11.0$\pm$0.7

Barret et al. 1999

R

4.8

rtolani et al. 1997

A

3.9$\pm$0.5

Christian & Friel 1992

A

4U 1728-16

LMXB

4.2b

Green et al. 2014

2.4$\pm$0.2

Xiang et al. 2005

A

2.4$\pm$0.1

0.8$\pm$0.5

Shahbaz et al. 1996

A

0.8$\pm$0.5

2.4$\pm$0.1

Church & Balucinska-Church 2001

A

4U 1728-34

LMXB

5.2

Liu et al. 2007

23.4$\pm$1.0

Egron et al. 2011

A

29.3$\pm$0.5

7.8$\pm$1.7

Di Salvo et al. 2000

A

10.8$\pm$1.8

25.1$\pm$0.8

D’Ai et al. 2006

A

15.0

Glass 1978

A

31.3$\pm$0.3

Narita et al. 2001

A

28.6$\pm$1.0

Di Salvo et al. 2000

A

27.3$\pm$0.5

Piraino et al. 2000

A

22.9$\pm$2.5

Misanovic et al. 2010

A

4U 1730-335

LMXB

$\sim$8

Liu et al. 2007

17.4$\pm$0.3

Marshall et al. 2001

A

17.4$\pm$0.3

9.5

Harris 2010 and 1996

A

10.1$\pm$1.1

9.3

Homer et al. 2001

A

11$\pm$1

Kleinmann et al. 1976

A

4U 1746-37

LMXB

11.0

Liu et al. 2007

4.0$\pm$0.3

Gavriil et al. 2012

A

4.0$\pm$0.3

1.5$\pm$0.3

Bonatto et al. 2013

A

1.5$\pm$0.2

2.8$\pm$0.4

Parmar et al. 1999

R

1.5$\pm$0.2

Harris 2010 and 1996

A

1.6

Deutsch et al. 1998

A

1.4$\pm$0.5

Hesser & Hartwick 1976

A

4U 1820-30

LMXB

7.6

Liu et al. 2007

2.9$\pm$0.1

Valencic & Smith 2015

A

2.7$\pm$0.1

2.5$\pm$0.3

Guver et al. 2010b

A

2.6$\pm$0.3

0.9$\pm$0.1

Harris 2010 and 1996

A

0.9$\pm$0.1

2.0

Yao & Wang 2006

A

1.9$\pm$0.1

Mondal et al. 2016

R

1.1

Valenti et al. 2004

A

2.7$\pm$0.4

Juett et al. 2004

A

1.0

Heasley et al. 2000

A

0.9

Reed et al. 1988

A

0.8

Zinn 1980

A

4U 1822-37

LMXB

2.5

Liu et al. 2007

1.2$\pm$0.2

Iaria et al. 2001

A

1.2$\pm$0.2

0.4$\pm$0.4

Mason et al. 1982

A

0.5$\pm$0.3

0.8$\pm$0.7

Heinz & Nowak 2001

A

0.6$\pm$0.3

Mason & Cordova 1982

A

4U 1837+04

LMXB

4.9$\pm$0.2

Xiang et al. 2005

A

5.2$\pm$0.2

8.9$\pm$0.1

Matranga et al. 2017

A

2.5$\pm$1.2

Hynes et al. 2004

A

1.3$\pm$0.1

5.0$\pm$0.3

Oosterbroek et al. 2001b

A

1.3$\pm$0.1

Shahbaz et al. 1996

A

6.5$\pm$1.4

Seon & Min 2002

A

$>$1.2

Thorstensen, Charles & Bowyer 1980

A

4U 1850-08

LMXB

8.2

Liu et al. 2007

4.0$\pm$0.1

Valencic & Smith 2015

A

3.8$\pm$0.1

4.8$\pm$0.2

Sidoli et al. 2005a

A

4.8$\pm$0.2

1.4$\pm$0.2

Harris 2010 and 1996

A

1.2$\pm$0.2

4$\pm$2

Sidoli et al. 2006

A

1.0$\pm$ 0.2

Paltrinieri et al. 2001

A

3.9$\pm$0.3

Sidoli et al. 2001b

A

1.0

Ortolani et al. 2000

A

2.9$\pm$0.2

Juett et al. 2001

A

1.4

Peterson 1993

A

1.3

Cudworth 1988

A

1.5

Webbink 1985 and Zinn 1985

A

1.2

Zinn 1980

A

4U 1908+00

LMXB

5.0

Liu et al. 2007

5.0$\pm$0.1

Valencic & Smith 2015

A

4.4$\pm$0.1

4.0$\pm$0.1

Campana et al. 2014

A

4.1$\pm$0.1

1.6$\pm$0.3

Chevalier et al. 1999

A

1.2$\pm$0.1

3.8$\pm$0.1

Cackett et al. 2011

A

5.9$\pm$0.4

Coti Zelati et al. 2014

A

1.1

Shahbaz et al. 1996

A

3.4$\pm$0.7

Campana & Stella 2003

A

1.3$\pm$0.2

Thorstensen et al. 1978

A

4U 1915-05

LMXB

8.9

Liu et al. 2007

4.4$\pm$0.1

Iaria et al. 2006

A

3.9$\pm$0.1

5.6$\pm$0.7

Juett & Chakrabarty 2006

5.6$\pm$0.7

2.2$\pm$0.9

Schmidtke 1988

A

2.2$\pm$0.9

5.8$\pm$0.2

Boirin et al. 2004

A

3.0$\pm$0.1

Ko et al. 1999

A

3.2$\pm$0.2

Church et al. 1998

A

4U 1956+35

HMXB

2.14

Liu et al. 2006

4.4$\pm$0.2

Xiang et al. 2005

A

4.4$\pm$0.1

6.4$\pm$0.2

Tomsick et al .2014

A

5.4$\pm$0.1

3.4$\pm$0.1

Caballero-Nieves et al. 2009

A

3.3$\pm$0.1

4.4$\pm$0.1

Cui et al. 1998

A

5.1$\pm$0.1

Parker et al. 2015

A

3.4

Ziolkowski 2005

A

5.4$\pm$0.1

Miskovicova et al. 2016

A

3.3

Bradt & McClintock 1983

A

2.9$\pm$0.2

Wu et al. 1982

A

4U 1957+11

LMXB

2.2$\pm$0.1

Valencic & Smith 2015

A

1.6$\pm$0.1

1.1$\pm$0.1

Nowak et al. 2008

A

1.1$\pm$0.1

0.9

Margon et al. 1978

A

0.9$\pm$0.1

1.2$\pm$0.1

Maitra et al. 2014

A

1.3$\pm$0.1

Nowak & Wilms 1999

A

4.4$\pm$2.9

Singh et al. 1994

R

4U 2129+47

LMXB

7.0

Liu et al. 2007

2.4$\pm$0.7

Bozzo et al. 2007

A

2.4$\pm$0.7

3.6$\pm$0.1

Lin et al. 2009

A

3.6$\pm$0.1

1.6$\pm$0.3

Shahbaz et al. 1996

A

1.2$\pm$0.2

3.2$\pm$0.6

Nowak et al. 2002

A

1.2

Deutsch et al. 1996

A

0.9

Cowley & Schmidtke 1990

A

1.6

Chevalier et al. 1989

A

1.2

Thorstensen et al. 1988

A

4U 2135+57

HMXB

3.8

Liu et al. 2006

7.8$\pm$0.3

Jaisawal et al. 2016

A

7.8$\pm$0.3

4.0$\pm$0.3

Bonnet-Bidaud & Mouchet 1998

A

4.0$\pm$0.3

4U 2142+38

LMXB

7.2

Liu et al. 2007

1.8$\pm$0.3

Seward & Smith 2013

A

1.9$\pm$0.1

3.6$\pm$0.1

Balucinska-Church et al. 2011

A

2.9$\pm$0.1

1.1

Shahbaz et al. 1996

A

1.1$\pm$0.1

2.2$\pm$0.4

Xiang et al. 2005

A

2.2$\pm$0.1

Costantini et al. 2005

A

0.7$\pm$0.2

Goranskij & Lyutyj 1988

A

2.0$\pm$0.1

Piraino et al. 2002

A

2.3$\pm$0.5

Juett et al. 2004

A

1.2$\pm$0.2

McClintock et al. 1984

A

1.9$\pm$0.1

Di Salvo et al. 2002

A

1.4$\pm$0.2

Chiappetti et al. 1983

A

EXO 0331+530

HMXB

16$\pm$6

Pottschmidt et al. 2005

A

9.0$\pm$1.0

5.9

Coe et al. 1987

A

5.8$\pm$0.2

9.1$\pm$1.3

Unger et al. 1992

A

5.8$\pm$0.3

Corbet et al. 1986

A

$\sim$10-13

Tsygankov et al. 2016

A

6.8$\pm$0.8

Stocke et al. 1985

A

8.3$\pm$0.7

Caballero-Garcia et al. 2016

A

6.0$\pm$0.2

Honeycut & Schlegel 1985

A

10.7$\pm$4.3

Elshamouty et al. 2016

A

5.6$\pm$0.2

Kodaira et al. 1985

A

EXO 0748-676

LMXB

6.8

Liu et al. 2006

0.7$\pm$0.1

Degenaar et al. 2011

A

0.8$\pm$0.1

0.6$\pm$0.1

Degenaar et al. 2014

A

0.6$\pm$0.1

0.48$\pm$0.26

Pearson et al. 2006

A

0.2$\pm$0.1

1.3$\pm$0.3

Degenaar et al. 2009

A

0.6$\pm$0.1

Diaz Trigo et al. 2011

A

0.2$\pm$0.1

Hynes et al. 2006

A

1.1$\pm$0.4

Sidoli et al. 2005b

A

1.3$\pm$0.1

Schoembs & Zoeschinger 1990

R

EXO 1745-248

LMXB

8.7

Liu et al. 2007

13$\pm$3

Degenaar & Wijnands 2012

A

13.2$\pm$3.5

7.0$\pm$1.0

Massari et al. 2012

A

7.2$\pm$1.0

14$\pm$5

Wijnands et al. 2005

A

7.1

Harris 2010 and 1996

A

7.4

Valenti et al. 2007

A

6.7

Cohn et al. 2002

A

7.4

Barbuy et al. 1998

A

7.7

Ortolani et al. 1996

A

5.1

Armandroff & Zinn 1988

R

EXO 2030+375

HMXB

7.1

Liu et al. 2006

19.9$\pm$0.2

Naik & Jaisawal 2015

A

20.5$\pm$0.1

29.8$\pm$0.3

Ferrigno et al. 2016

A

11.2$\pm$0.9

Janot-Pacheco et al. 1988

A

11.7$\pm$0.7

20.6$\pm$0.1

Naik et al. 2013

A

11.6

Coe et al. 1988

A

11.8$\pm$0.5

Motch & Janot-Pacheco 1987

A

GRO J1719-24

LMXB

1.2b

Green et al. 2014

$\sim$4.0

Tanaka 1993

A

4$\pm$0.4

2.8$\pm$0.6

della Valle et al. 1994

A

2.8$\pm$0.6

GRO J0422+32

LMXB

2.49

Liu et al. 2007

1.6$\pm$0.9

Shrader et al. 1997

A

1.6$\pm$0.9

0.74$\pm$0.09

Gelino & Harrison 2003

A

0.8$\pm$0.1

0.9$\pm$0.3

Callanan et al. 1995

A

1.25$\pm$0.10

Chevalier & Ilovaisky 1995

A

0.72$\pm$0.05

Shrader et al. 1994

A

0.9$\pm$0.6

Shrader et al. 1993

A

0.9$\pm$0.3

Castro-Tirado et al. 1993

A

GRO J1008-57

HMXB

5.0

Liu et al. 2006

9.6$\pm$0.5

Yamamoto et al. 2014

A

12.7$\pm$0.1

6.1$\pm$0.2

Coe et al. 1994b

A

6.1$\pm$0.2

12.9$\pm$0.1

Naik et al. 2011b

A

GRO J1655-40

LMXB

7.1$\pm$0.3

Kubota et al. 2005

A

7.4$\pm$0.3

7.1$\pm$0.3

Sala et al. 2007

A

7.4$\pm$0.2

3.7$\pm$0.2

Hynes et al. 1998

A

3.7$\pm$0.3

7.1$\pm$0.8

Yamaoka et al. 2001

A

7.7$\pm$0.2

Diaz Trigo 2007

A

3.5

Bianchini et al. 1997

A

7.6$\pm$0.2

Gierlinski et al. 2001

A

4.0

Horne et al. 1996

A

7.4$\pm$0.3

Ueda et al. 1998

A

3.6

Bailyn et al. 1995

A

GRO J1944+26

HMXB

9.5

Liu et al. 2007

13.0$\pm$0.1

Maitra & Paul 2013

A

13.0$\pm$0.1

16.3$\pm$0.3

Marcu-Cheatham et al. 2015

A

16.3$\pm$0.3

6.5$\pm$0.3

Verrecchia et al. 2002

A

6.5$\pm$0.3

GRO J2058+42

HMXB

9.0

Liu et al. 2007

21.0$\pm$10.0

Wilson et al. 2005

A

9.5$\pm$2.3

4.3$\pm$0.3

Wilson et al. 2005

A

4.3$\pm$0.4

9$\pm$2

Krimm et al. 2008

A

4.3

Reig et al. 2005a

A

GRS 1009-45

LMXB

4.5

Liu et al. 2007

0.4$\pm$0.1

Kubota et al. 1998

A

0.4$\pm$0.1

0.6$\pm$0.2

della Valle et al. 1997

A

0.6$\pm$0.2

GS 0834-43

HMXB

4.0

Liu et al. 2006

24$\pm$3

Belloni et al. 1993

A

21.2$\pm$2.3

12.3

Israel et al. 2000

A

12.3$\pm$1.6

20$\pm$2

Aoki et al. 1992

A

GS 1124-684

LMXB

5.9

Liu et al. 2007

2.3$\pm$0.1

Greiner et al. 1994

A

2.3$\pm$0.1

0.93$\pm$0.16

Shrader & Gonzalez-Riestra 1993

A

0.90$\pm$0.1

0.90$\pm$0.03

Cheng et al. 1992

A

0.9$\pm$0.3

della Valle et al. 1991

A

HD 259440

HMXB

3.2$\pm$1.1

Rea & Torres 2011

R

2.6

Aragona et al. 2010

A

2.6$\pm$0.3

3.3$\pm$0.2

Falcone et al. 2010

R

3.1$\pm$0.3

Hinton et al. 2009

R

IGR J11215-5952

HMXB

$\sim$8.0

Liu et al. 2006

22.0$\pm$13.0

Romano et al. 2011

R

2.2

Lorenzo et al. 2014

A

2.3$\pm$0.3

10.4$\pm$2.5

Romano et al. 2007

R

2.4

Masetti et al. 2006

A

10.2$\pm$4.2

Mangano et al. 2007

R

12$\pm$3

Esposito et al. 2009

R

IGR J17544-2619

HMXB

3.7b

Marshall et al. 2006

11.2$\pm$0.8

Valencic & Smith 2015

A

11.2$\pm$1.2

6.3$\pm$0.4

Pellizza et al. 2006

A

6.3$\pm$0.4

12$\pm$2

Romano et al. 2015

A

14$\pm$3

Drave et al. 2014

A

11$\pm$2

Sidoli et al. 2009a

A

18$\pm$10

Sidoli et al. 2009b

A

19$\pm$5-43$\pm$2

Gonzalez-Riestra et al. 2004

R

IGR J18450-0435

HMXB

14.0b

Marshall et al. 2006

11.8$\pm$0.8

Valencic & Smith 2015

R

7.6

Coe et al. 1996

A

7.6$\pm$1.0

16$\pm$1.8-36.0$\pm$3.0

Goossens et al. 2013

R

26.0$\pm$2.0

Sguera et al. 2007

R

IGR J2000.6+3210

HMXB

6.0b

Marshall et al. 2006

13.6$\pm$2.0

Pradhan et al. 2013

R

$\sim$4

Masetti et al. 2008

A

4.0$\pm$0.5

Sale et al. 2014

22$\pm$2.0

Morris et al. 2009

R

IGR J21343+4738

HMXB

10.8$\pm$1.5

Reig & Zezas 2014

R

2.4$\pm$0.1

Reig & Zezas 2014

A

2.4$\pm$0.1

IGR J22534+6243

HMXB

18.1$\pm$1.9

Esposito et al. 2013

A

18.1$\pm$1.9

5.6$\pm$0.3

Esposito et al. 2013

A

5.7$\pm$0.4

6.7

Masetti et al. 2013

A

KS 1947+300

HMXB

10.0

Liu et al. 2006

5.1$\pm$0.2

Epili et al. 2016

A

5.1$\pm$0.2

3.4

Negueruela et al. 2003

A

3.4$\pm$0.4

LS 2883

HMXB

2.7b

Marshall et al. 2006

5.8$\pm$0.6

Tam et al. 2015

A

4.0$\pm$0.3

3.25

Westerlund & Garnier 1989

A

3.3$\pm$0.4

4.2$\pm$0.3

Pavlov et al. 2015

A

3.0$\pm$0.3

Kargaltsev et al. 2014

A

2.5$\pm$0.6

Pavlov et al. 2011

A

3.2$\pm$0.3

Chernyakova et al. 2006b

A

5.0$\pm$0.3

Hirayama et al. 1999

A

5.6$\pm$0.6

Hirayama et al. 1996

A

LS 5039

HMXB

2.9$\pm$0.3

Ribo et al. 2002

6.4$\pm$0.6

Durant et al. 2011

A

6.4$\pm$0.1

3.8$\pm$0.2

Ribo et al. 2002

A

3.7$\pm$0.3

7.1$\pm$0.4

Rea et al. 2011

A

3.7$\pm$0.3

Clark et al. 2001

A

6.8$\pm$0.2

Zabalza et al. 2011

A

3.2$\pm$0.7

Motch et al. 1997

A

6.3$\pm$0.1

Bosch-Ramon et al. 2007

A

10$\pm$4

Reig et al. 2003

A

LS 992

HMXB

5$\pm$3

Reig & Roche 1999

R

2.0$\pm$0.2

Reig & Roche 1999

A

2.1$\pm$0.2

2.5$\pm$0.6

Motch et al. 1997

A

ALS 19596

HMXB

23.0$\pm$1.3

Piraino et al. 2000

A

23.0$\pm$1.3

8.1$\pm$0.9

Israel et al. 2001

A

8.1$\pm$0.9

MXB 1746-20

LMXB

8.5$\pm$0.4

Liu et al. 2006

6.5$\pm$0.2

Valencic & Smith 2015

A

6.7$\pm$0.3

A

5.7$\pm$0.1

3.3$\pm$0.3

Harris 2010 and 1996

A

3.2$\pm$0.3

7.4$\pm$0.4

Walsh et al. 2015

A

3.2$\pm$0.3

Minniti 1995

A

SAX J1748.9-2021

HMXB

8.5$\pm$0.4

Liu et al. 2006

7$\pm$1

Cackett et al. 2005

A

7$\pm$1

5.7$\pm$0.1

Pintore et al. 2016

3.1$\pm$0.3

Ortolani et al. 1994a

A

3.2$\pm$0.4

3.3

Armandroff 1989

A

3.6

Harris & van den Bergh 1974

A

RX J0146.9+6121

HMXB

2.3

Liu et al. 2006

4.9$\pm$0.5

La Palombara & Mereghetti 2006

A

4.9$\pm$0.5

2.9$\pm$0.1

Reig et al. 1997

A

2.9$\pm$0.1

9.4$\pm$1.2

Haberl et al. 1998a

R

3.4

Motch et al. 1997

A

7.8$\pm$1.9

Haberl et al. 1998b

R

2.9

Coe et al. 1993

A

RX J0440.9+4431

HMXB

3.3

Liu et al. 2006

3.3$\pm$0.1

Ferrigno et al. 2013

A

3.4$\pm$0.1

2.0$\pm$0.2

Reig et al. 2005b

A

2.2$\pm$0.2

7.3$\pm$1.5

La Palombara et al. 2012

A

2.8

Motch et al. 1997

A

4.7$\pm$0.4

Tsygankov et al. 2012

A

3.1$\pm$0.4

Usui et al. 2012

A

RX J1829.4-2347

LMXB

6

Liu et al. 2006

2.2$\pm$0.1

Filippova et al. 2014

A

2.6$\pm$0.1

1.2

Barret et al. 1995

A

1.2$\pm$0.4

1.6$\pm$0.5

Thompson et al. 2005

A

4.0$\pm$0.4

Kong et al. 2000b

A

1.1$\pm$0.2

in’t Zand et al. 1999

A

3.4$\pm$0.1

Thompson et al. 2008

A

RX J1832-33

LMXB

9.3

Liu et al. 2006

0.46$\pm$0.18

Parmar et al. 2001

A

0.55$\pm$0.22

0.58$\pm$0.06

Sidoli et al. 2008

A

0.58$\pm$0.06

0.3

Harris 2010 and 1996

A

0.3$\pm$0.1

0.89$\pm$0.35

Mukai & Smale 2000

A

0.3$\pm$0.1

Ortolani et al. 1994b

A

Swift J1753.5-0127

LMXB

$\sim$6

Liu et al. 2007

2.5$\pm$0.1

Valencic & Smith 2015

A

2.2$\pm$0.1

2.8

Yoshikawa et al. 2015

A

2.7$\pm$0.1

1.4$\pm$0.1

Rahoui et al. 2015

A

1.3$\pm$0.1

2.7$\pm$0.1

Froning et al. 2014

A

4.1$\pm$1.4

Rushton et al. 2016

R

1.4$\pm$0.2

Froning et al. 2014

A

2.3$\pm$0.1

Reynolds et al. 2010

A

2.6$\pm$0.1

Tomsick et al. 2015

A

1.3$\pm$0.1

Durant et al. 2009

A

1.5$\pm$0.1

Reis et al. 2009

A

2.8$\pm$0.1

Mostafa et al. 2013

A

1.1$\pm$0.1

Cadolle Bel et al. 2007

A

2.3$\pm$0.2

Durant et al. 2009

A

1.7$\pm$0.1

Hiemstra et al. 2009

A

2.3$\pm$0.1

Miller et al. 2006

A

V404 Cyg

LMXB

3.5

Liu et al. 2007

7.4$\pm$0.7

Bernardini & Cackett 2014

A

8.1$\pm$0.3

8.6$\pm$0.6

Rana et al. 2016

A

8.6$\pm$0.6

4.0

Hynes et al. 2009

A

3.6$\pm$0.5

6.1$\pm$0.6

Kong et al. 2002

A

3.1$\pm$0.9

Shahbaz et al. 2003

A

8.4$\pm$0.2

Plotkin et al. 2017

A

4.0

Casares et al. 1993

A

6.1$\pm$0.7

Hynes et al. 2009

A

3.4$\pm$0.6

Gotthelf et al. 1992

A

8.8$\pm$0.6

Bradley et al. 2007

A

3.2

Wagner et al. 1991

A

XTE J1550-564

LMXB

5.3

Liu et al. 2007

8.8$\pm$1.1

Corbel et al. 2006

A

6.6$\pm$0.1

6.6$\pm$0.1

Steiner et al. 2011

A

6.6$\pm$0.1

3.2$\pm$0.2

Curran & Chaty 2013

A

2.9$\pm$0.2

6.8$\pm$0.2

Kubota & Done 2004

A

2.2$\pm$0.3

Sanchez-Fernandez et al. 1999

A

6.5$\pm$0.1

Gierlinski & Done 2003

A

8.0$\pm$0.4

Miller et al. 2003

A

8.5$\pm$2.3

Tomsick et al. 2001

A

XTE J1720-318

LMXB

17.8$\pm$0.2

Valencic & Smith 2015

A

15.1$\pm$0.2

7$\pm$1

Chaty & Bessolaz 2006

A

6.6$\pm$0.6

12.4$\pm$0.2

Cadolle Bel et al. 2004

A

6.5$\pm$0.5

Nagata et al. 2003

A

XTE J1808-369

LMXB

3

Liu et al. 2007

2.1$\pm$0.1

Papitto et al. 2009

A

1.4$\pm$0.1

1.6$\pm$0.2

Patruno et al. 2009

A

1.4$\pm$0.1

0.8$\pm$0.3

Elebert et al. 2009

A

0.8$\pm$0.3

1.2$\pm$0.1

Heinke et al. 2009

A

1.3$\pm$0.1

Campana et al. 2008

A

0.7$\pm$0.3

Wang et al. 2001

A

0.9$\pm$0.1

Cackett et al. 2009b

1.5$\pm$0.4

Heinke et al. 2007

XTE?J1819-254

HMXB

9.5

Liu et al. 2006

2.4$\pm$0.4

Pahari et al. 2015

A

2.4$\pm$0.4

1.1$\pm$0.6

MacDonald et al. 2014

A

0.8$\pm$0.1

0.7$\pm$0.2 or 1.6$\pm$0.3

Lindstrom et al. 2005

A

0.8

Chaty et al. 2003

A

1.0$\pm$0.3

Orosz et al. 2001

A

0.7

Wagner 1999

A

XTE J1859+226

LMXB

7.6

Liu et al. 2007

$\sim$3

Wood et al. 1999

A

3.6$\pm$0.4

1.8$\pm$0.4

Hynes et al. 2002

A

1.8$\pm$0.4

$\sim$8

dal Fiume et al. 1999

A

XTE J2103+457

HMXB

6.5

Liu et al. 2006

7.6$\pm$0.1

Camero et al. 2014

A

7.6$\pm$0.1

4.2$\pm$0.3

Hynes et al. 2004

A

4.2$\pm$0.3

7.0$\pm$0.3

Inam et al. 2004

A

37.6$\pm$1.2

Baykal et al. 2002

R

XTE J2123-058

LMXB

8.5

Liu et al. 2007

0.7${}_{-0.7}{}^{}{}_{}{}^{+4.0}$-0.8${}_{-0.8}{}^{}{}_{}{}^{+3.8}$

Tomsick et al. 2004

A

0.8$\pm$2.3

0.37$\pm$0.15

Hynes et al. 1998

A

0.37$\pm$0.15

$>$7.9

Tomsick et al. 1999

R

Equations

$$M(E)=\exp \left\{N_{\mathrm{H}}{\sigma }_{\mathrm{eff}}(E)\right\},$$

$$N_{\mathrm{H}}(\mathrm{H}{\mathrm{cm}}^{-2})=\left(2.19\pm 0.02\right)\times 10^{21}{A}_V(\mathrm{mag}),$$

$$\begin{array}[]{l}N_{\rm H}({\rm H}\,{\rm cm}^{-2})=\left(2.25\pm 0.03\right)\times 10^{21}\,A_{V}({\rm mag})\\ \qquad\qquad\qquad-\left(0.11\pm 0.04\right)\times 10^{21}({\rm H}\,{\rm cm}^{-2})~{}~{}.\\ \end{array}$$

$$N_{\mathrm{H}}(\mathrm{H}{\mathrm{cm}}^{-2})=\left(2.51\pm 0.05\right)\times 10^{21}{A}_V(\mathrm{mag})$$

$$N_{\mathrm{H}}(\mathrm{H}{\mathrm{cm}}^{-2})=\left(2.09\pm 0.03\right)\times 10^{21}{A}_V(\mathrm{mag})$$

$$N_{\mathrm{H}}(\mathrm{H}{\mathrm{cm}}^{-2})=\left(2.06\pm 0.05\right)\times 10^{21}{A}_V(\mathrm{mag})$$

$$N_{\mathrm{H}}(\mathrm{H}{\mathrm{cm}}^{-2})=\left(2.08\pm 0.02\right)\times 10^{21}{A}_V(\mathrm{mag})$$

$$N_{\mathrm{H}}(\mathrm{H}{\mathrm{cm}}^{-2})=\left(2.04\pm 0.05\right)\times 10^{21}{A}_V(\mathrm{mag})$$

$$N_{\mathrm{H}}(\mathrm{H}{\mathrm{cm}}^{-2})=\left(2.09\pm 0.03\right)\times 10^{21}{A}_V(\mathrm{mag})$$

$$\frac{M_{\mathrm{gas}}}{M_{\mathrm{dust}}}=1.086\times 1.4{\mu }_{\mathrm{H}}{\kappa }_{\mathrm{ext}}(V)\left(\frac{N_{\mathrm{H}}}{A_V}\right),$$

$$N_{\mathrm{H}}(\mathrm{H}{\mathrm{cm}}^{-2})=\left(2.87\pm 0.04\right)\times 10^{21}{A}_V(\mathrm{mag}).$$

$$N_{\mathrm{H}}(\mathrm{H}{\mathrm{cm}}^{-2})=\left(3.30\pm 0.06\right)\times 10^{21}{A}_V(\mathrm{mag})$$

$$N_{\mathrm{H}}(\mathrm{H}{\mathrm{cm}}^{-2})=\left(2.46\pm 0.05\right)\times 10^{21}{A}_V(\mathrm{mag})$$

$$N_{\mathrm{H}}(\mathrm{H}{\mathrm{cm}}^{-2})=\left(2.51\pm 0.10\right)\times 10^{21}{A}_V(\mathrm{mag})$$

$$N_{\mathrm{H}}(\mathrm{H}{\mathrm{cm}}^{-2})=\left(2.47\pm 0.04\right)\times 10^{21}{A}_V(\mathrm{mag})$$

Full text

1 Introduction

Interstellar extinction results from the absorption and scattering of starlight by interstellar dust grains. The knowledge of the interstellar extinction ($A_{\lambda}$) at wavelength $\lambda$ per hydrogen column ($N_{\rm H}$), particularly in the ultraviolet (UV), visible, and near infrared, is crucial for correcting for the interstellar obscuration and restoring the true luminosity of astronomical objects, and for determining the dust-to-gas mass ratio and the photoelectric heating rates of interstellar gas. So far, the commonly adopted hydrogen-to-extinction ratio is that of Bohlin et al. (1978), $N_{\rm H}/E(B-V)=5.8\times 10^{21}\,{\rm H}\,{\rm cm}^{-2}\,{\rm mag}^{-1}$, where $E(B-V)\equiv A_{B}-A_{V}$, the colour excess, is the difference between the $B$ band extinction ($A_{B}$) and the $V$ band extinction ($A_{V}$). The colour excess $E(B-V)$ relates to $A_{V}$ through $R_{V}\equiv A_{V}/E(B-V)$, the total-to-selective extinction ratio.

Bohlin et al. (1978) derived the hydrogen-to-extinction ratio from a sample of 100 stars with $E(B-V)$ up to ${\sim}\,0.5\,{\rm mag}$ based on the ultraviolet (UV) absorption spectra of HI and H2 observed by the Copernicus satellite. With $R_{V}\approx 3.1$ for the Milky Way (MW) diffuse interstellar medium (ISM; Whittet 2003), the Bohlin et al. (1978) hydrogen-to-extinction ratio becomes $N_{\rm H}/A_{V}\approx 1.87\times 10^{21}\,{\rm H}\,{\rm cm}^{-2}\,{\rm mag}^{-1}$. Similarly, as summarized in Table 1, Jenkins & Savage (1974), Whittet (1981), Diplas & Savage (1994), and Rachford et al. (2009) derived the hydrogen-to-extinction ratio from the UV absorption spectra of HI and H2 measured by the Orbiting Astronomical Observatory 2 (OAO-2; Jenkins & Savage 1974), the Copernicus satellite (Whittet 1981), the International Ultraviolet Explorer (IUE; Diplas & Savage 1994), and the Far Ultraviolet Space Explorer (FUSE; Rachford et al. 2009). The $N_{\rm H}/A_{V}$ ratios have also been derived by Sturch (1969), Knapp & Kerr (1974), Heiles (1976), Liszt (2014), and Chen et al. (2015) based on the column densities of hydrogen measured by CO and the 21 cm emission of HI.

While the aforementioned studies directly measured the column densities of HI and H2 (see Table 2), an alternative way of determining $N_{\rm H}$ is to measure the X-ray absorption spectra of heavy elements such as O, Mg, Si and Fe. One derives the column densities of these heavy elements from the measured X-ray spectra and then converts to $N_{\rm H}$ by assuming an interstellar reference abundance standard which specifies the relative abundances of these heavy elements (i.e., O/H, Mg/H, Si/H, and Fe/H). This method take ionized, neutral and molecular hydrogen into consideration and has been applied to measure $N_{\rm H}$ toward supernova remnants (SNRs), X-ray binaries (XBs), star-forming (SF) regions, and extended sources (see Table 3).

However, the $N_{\rm H}/A_{V}$ ratios derived from the X-ray absorption data involves the unknown interstellar abundance X/H (where X = O, Mg, Si, Fe …), often expressed in units of ppm (i.e., parts per million). One often assumes the interstellar elemental abundance to be solar. However, the solar abundances of the key heavy elements such C, O, N, S, Mg, Si, and Fe reported in the literature have undergone substantial changes over the past four decades (see Li 2005, Asplund et al. 2009). Also, there are arguments that the interstellar abundances could be better represented by those of B stars (because of their young ages) which are just ${\sim}\,$60–70% of the widely adopted solar values (“subsolar”; see Snow & Witt 1995, 1996, Sofia & Meyer 2001). As shown in Table 3, from the same set of X-ray data one would derive a much higher (by $>30\%$) $N_{\rm H}/A_{V}$ ratio if one adopts the reference abundance of Wilms et al. (2000; hereafter W00) for O and Fe instead of that of Anders & Grevesse (1989; hereafter AG89). Also, these previous studies suffer from small sample sizes and/or limited space distributions of the sample sources.

To reduce the above-mentioned limitation and to obtain a more reliable $N_{\rm H}/A_{V}$ ratio, in this work we carefully compile $N_{\rm H}$ and $A_{V}$ from the literature by separating those with $N_{\rm H}$ derived from solar abundances (AG89) from those with $N_{\rm H}$ derived from subsolar abundances (W00). We finally arrive at a sample of 35 SNRs, 6 planetary nebulae (PNe), 70 XBs for which $N_{\rm H}$ was derived with solar abundances (AG89) and 19 SNRs, 29 XBs for which $N_{\rm H}$ was derived with subsolar abundances (W00). We present our sample in §2 and derive a renewed mean $\langle N_{\rm H}/A_{V}\rangle$ ratio in §3. Also in §3 we estimate the gas-to-dust mass ratio and explore the spatial variation of $\langle N_{\rm H}/A_{V}\rangle$ and the gas distribution in the Galaxy. The major results are summarized in §4.

2 Compilation of $A_{V}$ and $N_{\rm H}$

2.1 $A_{V}$

If a group of lines are from the transitions with the same upper level, their intensity ratios would only depend on the transition probabilities. Thus they can be employed to calculate the extinction toward extended objects, e.g., SNRs and PNe. The frequently used line ratios include H$\alpha$(6563$\,{\rm\AA}$)/H$\beta$(4861$\,{\rm\AA}$), known as the Balmer decrement (e.g., SNR G67.7+1.8, Mavromatakis et al. 2001), SII/SII (e.g., SNR G111.7-2.1, Hurford & Fesen 1996) and FII/FII (e.g., SNR G332.4-0.4, Oliva et al. 1989). However, caution needs to be taken when applying the Balmer decrement method to very young SNRs, because their intrinsic H$\alpha$/H$\beta$ ratios may be different from the canonical ratios used for nebulae under the “Case B” condition, in which the nebula is always optical thin except for Lyman-line photons (e.g., Tycho, Ghavamian et al. 2000). Other methods to estimate the extinction of SNRs include the use of existing extinction maps (e.g., SNR G119.5+10.2, Mavromatakis et al. 2000), and the association of the targets with extinction-known objects (e.g., SNR G260.4-3.4, Gorenstein 1975).

For XBs, four methods are usually adopted to estimate their extinction: (1) the relation between the colour excess or reddening $E(B-V)$ and the widths of the diffuse interstellar bands or Na doublet lines (e.g., 4U0614+091, Nelemans et al. 2004); (2) the colour-magnitude diagram for those in star clusters (e.g., 4U 1820-30 in NGC 6624, Valenti et al. 2004); (3) a comparison of the observed colour with the intrinsic colour derived from the stellar spectral type (e.g., 4U1908+005, Thorstensen et al. 1978); and (4) fitting the observed, reddened UV spectrum of a source (e.g., 2S 0620-003) to determine the excess extinction at 2175$\,{\rm\AA}$ ($\Delta A_{\rm bump}$) and assuming a constant $\Delta A_{\rm bump}/A_{V}$ ratio.

For each source in our sample we estimate its $A_{V}$ or $E(B-V)$111From $E(B-V)$ to $A_{V}$ we take $A_{V}=3.1\times E(B-V)$.

following these rules: (1) if a source has more than one measure of $A_{V}$ or $E(B-V)$, an error-weighted value will be adopted; (2) if a source has more than two measures of $A_{V}$ or $E(B-V)$ and one measure differs from the others by $\buildrel>\over{\sim}$30% or 3$\sigma$, this measure will be rejected; (3) if there is no error estimation for the $A_{V}$ or $E(B-V)$ measure, we will assign an uncertainty of ${\sim}\,$13% which is obtained by averaging over those sources for which the uncertainties on $A_{V}$ or $E(B-V)$ are known (see Column 13 in Table 7).

2.2 $N_{\rm H}$

The X-ray absorption factor is usually expressed as

[TABLE]

where $\sigma_{\rm eff}(E)$ represents the effective absorption cross section taking into account the composition of interstellar medium. Apparently, the interstellar X-ray absorption is affected by both $N_{\rm H}$ and $\sigma_{\rm eff}(E)$. To be self-consistent, it is necessary to seek $N_{\rm H}$ from the literature using similar heavy element abundances (e.g., O, Ne, Fe, Mg, Si). As mentioned earlier, different abundance selection (e.g., AG89 vs W00) may lead to a difference of $>30\%$ for the derived $N_{\rm H}$ (Foight et al. 2016). In this study, we will consider the hydrogen column densities derived either from solar abundances (AG89) or subsolar abundances (W00). If there is no mention in the literature about the abundance setting for the software XSPEC, we will assume that the AG89 abundance was used because it is the default setting at least back to XSPEC version 8.

We take the following approach for adopting $N_{\rm H}$: (1) if a source has more than one measure of $N_{\rm H}$, an error-weighted value will be adopted; (2) if there are more than one measure of $N_{\rm H}$ and these measures all differ from each other by $\buildrel>\over{\sim}$30% or 3$\sigma$, the one derived from the data with a higher quality at energy E\lower 2.15277pt\hbox{\buildrel<\over{\sim}}2\,{\rm keV} will be selected because this energy range is more sensitive to X-ray absorption; this means that those derived from Chandra, XMM-Newton and Suzaku have a higher priority than those from ROSAT, RXTE and other telescopes; (3) if there are two or three measures of $N_{\rm H}$ for the same source and they are all derived from Chandra, XMM-Newton or Suzaku, we will take the error-weighted value without considering their differences; (4) if there is no error estimation for a $N_{\rm H}$ measure, we will adopt an uncertainty of ${\sim}\,$9% for AG89 or ${\sim}\,$8% for W00 which are obtained by averaging over those sources for which the uncertainties on $N_{\rm H}$ are known (see Columns 5, 9 in Table 7); (5) for SNRs which are extended sources of which $A_{V}$ and $N_{\rm H}$ are known for a range of regions, we make sure that the adopted $A_{V}$ and $N_{\rm H}$ are from the same region, if possible. Note that for XBs, some of them are dipper sources and have intrinsic local absorptions. We try to avoid these local absorptions by taking the following procedure: (1) for low mass X-ray binaries (LMXBs), we examine the catalog of Liu et al. (2006) to see whether they are dipper sources or not; if yes, we will exclude them from our sample except those for which $N_{\rm H}$ was derived from the spectral fitting and no dipper shows up in the spectra or the interstellar $N_{\rm H}$ and local $N_{\rm H}$ are considered separately during the fitting (e.g., using the partial covering model); (2) for high mass X-ray binaries (HMXBs), we examine them one by one through the literature to see whether the interstellar $N_{\rm H}$ and local $N_{\rm H}$ are considered separately and whether the interstellar $N_{\rm H}$ varies during different phases and states to avoid the influence of local absorptions. With these selection procedures, seven XBs (4U 0115+63, HD 259440, IGR J11215-5952, IGR J18450-0435, IGR J2000.6+3210, IGR J21343+4738, and LS 992) are exclused due to the possible presence of local absorptions. For three XBs (GRO J2058+42, GS 0834-43, and ALS 19596), we find no evidence for or against the presence of considerable amounts of local absorption. As their $N_{\rm H}/A_{V}$ ratios are not much larger than those previously published, we decide to keep them in our sample. We also note that, although SNRs are treated as having little or no intrinsic absorption, some of them may actually have considerable local dust emission (e.g., Cas A [Dunne et al. 2009]).

In Table 4, we present the finally adopted data. For each source we also list the $N_{\rm H}$ value determined from the HI 21 cm observation toward their lines of sight. One can find all the compiled $N_{\rm H}$ and $A_{V}$ for each sources in Appendix.

3 Results and Discussion

As the AG89 sample (i.e., those sources for which $N_{\rm H}$ was derived from solar abundances) is nearly three times larger than the W00 sample (i.e., those sources for which $N_{\rm H}$ was derived from subsolar abundances), the former sample allows us not only to determine $N_{\rm H}/A_{V}$ but also to investigate the variation of $N_{\rm H}/A_{V}$ and the distribution of interstellar gas in our Galaxy. Therefore, in this section, we will first focus on the AG89 sample in §3.1–§3.4. We will consider the W00 sample in §3.5. The possible caveats of our study will be discussed in §3.6.

3.1 The mean $N_{\rm H}$–${A_{V}}$ relation

Figure 1 plots $N_{\rm H}$ against $A_{V}$ for all calibration points with abundance of AG89. We fit a linear relationship to the data using the MPFITXY routine (Williams, Bureau & Cappellari 2010) of the MPFIT package (Markwardt 2009):

[TABLE]

where the errors represent a 1$\sigma$ statistical uncertainty. The black solid lines in Figure 1 shows the best-fit result. To assess the influence of possible intrinsic absorption in our sample, we add a zero point offset to equation (2) and we then obtain a slightly steeper relation as shown as the red dashed line in Figure 1.

[TABLE]

Since the zero point offset in equation (4) is much smaller than the column density of most of our calibration points, it indicates that our sample is not affected significantly by the possible intrinsic absorption.

We also explore whether different kinds of calibrator affect the derived $N_{\rm H}$-$A_{V}$ relation. To this end, we fit the data of SNRs and XBs separately and obtain

[TABLE]

for SNRs, and

[TABLE]

for XBs. Surprisingly, they are inconsistent with each other and the mean $\langle N_{\rm H}/A_{V}\rangle$ ratio derived from SNRs is larger by ${\sim}\,$20% than that from XBs. To find what causes this difference, we show the $N_{\rm H}$–$A_{V}$ relations in Figure 2 for SNRs and XBs, separately. Apparently, those three SNRs (G54.1+0.3, G85.9-0.6, and G132.7+3.1) which lie well above the best-fit line (see Figure 2, right panel) lead to an overestimation of $N_{\rm H}/A_{V}$. Indeed, for G54.1+0.3, Kim et al. (2013) estimated $A_{V}\sim 7.3\pm 0.1\,{\rm mag}$ based on the extinction toward several stars associated with the SNR, while the extinction toward the majority of the stars is in the range from ${\sim}\,$6.9 to ${\sim}\,$7.5$\,{\rm mag}$ and for one star $A_{V}$ is as high as ${\sim}\,$7.8 $\,{\rm mag}$ (see their Table 3). Also, Koo et al. (2008) derived an extinction of 8.0$\pm$0.7$\,{\rm mag}$. Therefore, an uncertainty of 0.1$\,{\rm mag}$ may have been underestimated. For G85.9-0.6, Gök et al. (2009) obtained $A_{V}$=0.47$\pm$0.05$\,{\rm mag}$, 1.18$\pm$0.12$\,{\rm mag}$, and 1.40$\pm$0.14$\,{\rm mag}$ at three positions which are not fully overlapped with the X-ray bright region. Therefore, the error-weighted $A_{V}$ and the associated uncertainty that we used may be not a good estimation for the X-ray bright region. For G132.7+3.1, the optical spectroscopy was taken at the western filaments (Fesen et al. 1995). However, only its central and northern regions are bright at X-ray. While the size of G132.7+3.1 is about 80*′*, the space separation between the optical and the X-ray observations could be larger than 0.5o. Taking these concerns into consideration, we decide to exclude these three SNRs. We then obtain

[TABLE]

for SNRs, and

[TABLE]

for the whole AG89 sample. We present the best-fit lines in Figure 3. Table 5 summarizes the above results. Our results on the $N_{\rm H}/A_{V}$ ratio with AG89 abundance are compatible with those previously obtained from X-ray data with the same abundance.

3.2 A constant $N_{\rm H}/A_{V}$ ratio across the Galaxy?

Watson (2011) compared the HI column density with the extinction with data from the LAB HI survey (Kalberla et al. 2005) and the extinction map of Schlegel et al. (1998). He found that the ${N_{\rm H}}/{A_{V}}$ ratio seems to correlate with $N_{\rm H}$ toward the Galactic centre. To investigate the variation of $N_{\rm H}$/$A_{V}$ within our Galaxy, we plot the $N_{\rm H}/A_{V}$ ratio distribution projected on the Galactic longitude-latitude ($l$-$b$) plane and the Galactic disk in Figure 4. There is no clear indication for a large-scale variation of $N_{\rm H}/A_{V}$ within the Galaxy. In Figure 5 we show the $N_{\rm H}/A_{V}$ ratio against (i) $R_{g}$, the distance away from the Galactic centre, (ii) $z$, the distance away from the Galactic plane, (iii) $n_{\rm H}$, the average line-of-sight number density of hydrogen, and (iv) $N_{\rm H}$. It is apparent that the $N_{\rm H}/A_{V}$ ratio does not show any systematic variation with $R_{g}$, $z$, $n_{\rm H}$ or $N_{\rm H}$. We also investigate the $N_{\rm H}$–$A_{V}$ relation for the inner Galaxy (the Galactic first/fourth quadrants) and outer Galaxy (the second/third quadrants) separately. We derive

[TABLE]

for the first/fouth quadrants, and

[TABLE]

for the second/third quadrants (see Figure 6). They are consistent within each other. In summary, we can safely conclude that the X-ray derived $N_{\rm H}$/$A_{V}$ ratio is roughly a constant across the entire Galaxy.

We should note that it has been well known that the abundances of heavy elements in our Galaxy increase toward the Galactic centre (e.g., see Rolleston et al. 2000). Since AG89 assumed a uniform abundance for the ISM, at the Galactic centre $N_{\rm H}$ could have been overestimated while at the outer Galaxy $N_{\rm H}$ could have been underestimated. However, it is also well recognized that the dust grains in the Galactic centre could be much larger than that of the diffuse ISM (e.g., see Gao et al. 2010, Shao et al. 2017) and the visual extinction on a per unit mass basis could be smaller. Therefore, even the Galactic centre is rich in dust-forming heavy elements and more heavy elements have been tied up in dust grains one does not necessarily expect a lower $N_{\rm H}/A_{V}$.

3.3 The Gas-to-dust mass ratio

From the hydrogen-to-extinction ratio we can determine $M_{\rm gas}/M_{\rm dust}$, the gas-to-dust mass ratio:

[TABLE]

where $\mu_{\rm H}$ is the atomic mass of hydrogen and $\kappa_{\rm ext}(V)$ is the $V$-band mass extinction coefficient (i.e., extinction cross section per dust mass). The coefficient, 1.4, arises from the contribution of helium. Taking $\kappa_{\rm ext}(V)$ from Li & Draine (2001) and Draine & Li (2007), we obtain $M_{\rm gas}/M_{\rm dust}\approx 140$.

3.4 The gas distribution of the Galaxy

When both $N_{\rm H}$ and $D$ (the distance of the source to Earth) are known, we are able to study the distribution of the gas in the Galaxy. To this end, we enlarge the sample in Table 1 by including 74 SNRs with known $N_{\rm H}$ (AG89 abundance) and $D$ from the literature (see Table 6). The final sample includes 175 calibrators. Figure 7 shows the projection distribution of the sample on the Galactic plane.

The distribution of hydrogen away from the Galactic plane is usually described by one to three Gaussian and/or exponential functions, (e.g., see Bohlin, Savage & Drake 1978, Diplas & Savage 1994, Dickey & Lockman 1990, Kalberla & Kerp 2009). A commonly-used HI distribution between the Galactic radius 4 kpc and 8 kpc is given by Dickey & Lockman (1990): $n_{\rm H}(z)=n_{\rm H,1}(0)\,\exp\left(-z^{2}/2h_{1}^{2}\right)+n_{\rm H,2}(0)\,\exp\left(-z^{2}/2h_{2}^{2}\right)+n_{\rm H,3}(0)\,\exp\left(-z^{2}/2h_{3}^{2}\right)$, where the midplane densities are $n_{\rm H,1}(0)\approx 0.395\,{\rm cm}^{-3}$, $n_{\rm H,2}(0)\approx 0.107\,{\rm cm}^{-3}$, and $n_{\rm H,3}(0)\approx 0.064\,{\rm cm}^{-3}$, and the scale heights are $h_{1}\approx 90\,{\rm pc}$, $h_{2}\approx 225\,{\rm pc}$, and $h_{3}\approx 403\,{\rm pc}$. A more recent study for the Galactic radius between 5 kpc and 35 kpc suggested that the HI scale hight varies with the distance away from the Galactic centre: $h(R_{g})\approx 150\,\exp\left\{(R_{g}-R_{0})/9800\right\}\,{\rm pc}$, where $R_{0}$ is the Galactic radius of the Sun (Kalberla & Kerp 2009). Figure 8 shows $N_{\rm H}\sin(|b|)$ versus $z$. To avoid the influence of the Galactic bulge and wrap, we only make use of the data within 2\,{\rm kpc}\lower 2.15277pt\hbox{\buildrel<\over{\sim}}R_{g}\lower 2.15277pt\hbox{\buildrel<\over{\sim}}10\,{\rm kpc}. We use a one-component Gaussian model, $n_{\rm H}(z)=n_{\rm H}(0)\,\exp\left(-z^{2}/2h^{2}\right)$, to fit the data. The best-fit is given by $n_{\rm H}(0)=1.11\pm 0.15\,{\rm cm}^{-3}$ and $h=75.5\pm 12.4\,{\rm pc}$ (see Figure 8). Compared with that of Dickey & Lockman (1990), our results suggest a larger midplane density and a sightly smaller scale height. This might be caused by the fact that the $N_{\rm H}$ column densities adopted here are based on X-ray absorption data and contain the contribution of molecular and ionized ISM, while the 21 cm emission only presents atomic hydrogen. We are not able to estimate the scale heights of any other extended components, because the majority of our sample has $z<1000\,{\rm pc}$.

The neutral hydrogen surface density is nearly constant within the Galactic radius of ${\sim}\,$12.5 kpc (Kalberla & Kerp 2009). A mean surface density of ${\sim}\,$5$\,{M_{\rm\bigodot}}\,{\rm pc}^{-2}$ was given by Dickey & Lockman (1990). More recently, Kalberla & Dedes (2008) argued for a surface density two times larger than that of Dickey & Lockman (1990). Based on the best-fit $n_{\rm H}(0)$ and $h$ values, here we estimate a mean gas surface density of the Galaxy in the Galactic radius range of ${\sim}\,$2 kpc to ${\sim}\,$10 kpc to be $\sum_{\rm gas}{\sim}\,$1.4 $n_{\rm H}(0)\times 2.4\,h\approx 7.0\,{M_{\rm\bigodot}}\,{\rm pc}^{-2}$.

Due to the limited amount of data, we are not able to accurately determine the radial distribution of the midplane density, but only give an rough estimation of $n_{\rm H}\approx 4.33\pm 12.87\,{\rm cm}^{-3}$ for $2.0\,{\rm kpc}<R_{g}<4.5\,{\rm kpc}$, $n_{\rm H}\approx 1.15\pm 5.35\,{\rm cm}^{-3}$ for $4.5\,{\rm kpc}<R_{g}<6.5\,{\rm kpc}$, $n_{\rm H}\approx 1.18\pm 0.77\,{\rm cm}^{-3}$ for $6.5\,{\rm kpc}<R_{g}<8.5\,{\rm kpc}$, and $n_{\rm H}\approx 1.13\pm 0.81\,{\rm cm}^{-3}$ for $8.5\,{\rm kpc}<R_{g}<10\,{\rm kpc}$. All regions are limited to $|z|<75\,{\rm pc}$.

3.5 $N_{\rm H}/A_{V}$ from the W00 Sample

Since the X-ray-derived $N_{\rm H}$ is sensitive to the abundances of heavy elements (relative to H), one could expect a higher $N_{\rm H}/A_{V}$ for the W00 sources of which $N_{\rm H}$ is determined with subsolar abundances compared to that of the AG89 sources of which $N_{\rm H}$ is determined with solar abundances. By fitting the whole W00 sample which include both SNRs and XBs, we indeed obtain a larger $\langle N_{\rm H}/A_{V}\rangle$:

[TABLE]

We also obtain

[TABLE]

for the SNRs of the W00 sample, and

[TABLE]

for the XBs of the W00 sample. Again, the mean $\langle N_{\rm H}/A_{V}\rangle$ ratio from SNRs differs from that of XBs by ${\sim}\,$34%. If we exclude three SNRs (G54.1+0.3, G116.9+0.2, and G184.6-5.8) which appear to be outliers, we derive

[TABLE]

for SNRs, and

[TABLE]

for the whole W00 sample. Similar to the AG89 sample, with the three SNR outliers excluded, the $\langle N_{\rm H}/A_{V}\rangle$ of SNRs agree with that of XBs. We tabulate the best-fit results in Table 5.

The $\langle N_{\rm H}/A_{V}\rangle$ derived here is smaller by ${\sim}\,$15% than that of Foight et al. (2016) who assumed subsolar abundances for 17 SNRs (see Table 3) and appreciably larger than most of those derived from HI and/or H2 UV absorption and HI 21 cm emission (see Tables 1,2). Two factors might be responsible for the inconsistency. First, our sample is larger than previous ones and it includes 29 XBs which do not suffer the problem with which SNRs may be confronted (i.e., the measured $N_{\rm H}$ and $A_{V}$ may not be for the same region. Second, the $N_{\rm H}$ column derived from the UV absorption data of HI and/or H2 and the HI 21 cm emission data only counts neutral and/or molecular hydrogen, while the $N_{\rm H}$ value determined from the X-ray absorption data includes atomic, molecular and ionic hydrogen.

With $\langle N_{\rm H}/A_{V}\rangle\approx 2.5\times 10^{21}\,{\rm mag}\,{\rm cm}^{2}\,{\rm H}^{-1}$, we estimate the gas-to-dust mass ratio to be $M_{\rm gas}/M_{\rm dust}\approx 170$, again, based on the mass extinction coefficient of Li & Draine (2001) and Draine & Li (2007). As expected, the gas-to-dust mass ratio of the W00 sample exceeds that of the AG89 sample by ${\sim}\,$20%. In Figure 10, we plot $N_{\rm H}$ from the W00 sample against that from the AG89 sample. The fact that they are closely related with $N_{\rm H}({\rm W00})/N_{\rm H}({\rm W00})\approx 1.2$ suggests that in future studies one may simply scale $N_{\rm H}$ derived from subsolar abundances by a factor of ${\sim}\,$1.2 when converting to $N_{\rm H}$ derived from solar abundances.

3.6 Caveats

Even though in our analysis we have tried our best to avoid systematic uncertainties (e.g., for SNRs adopting $N_{\rm H}$ and $A_{V}$ determined from the same region if possible, excluding those XBs with intrinsic local X-ray absorptions), there may still be sources of potential uncertainty:

• •

Since we compile $N_{\rm H}$ and $A_{V}$ from the literature, for some SNRs the adopted $N_{\rm H}$ and $A_{V}$ may not be for the same region (e.g., SNR G132.7).

• •

Since a number of SNRs only have one or two measures of $N_{\rm H}$ and/or $A_{V}$, we are not able to take into account the uncertainties caused by spatial variations.

• •

For most SNRs, $A_{V}$ was measured from line ratios, e.g., H$\alpha$(6563$\,{\rm\AA}$)/H$\beta$(4861$\,{\rm\AA}$), SII/SII, and FII/FII. Taking the Balmer decrement as an example, the intrinsic ratio of H$\alpha$/H$\beta$ is commonly taken to be ${\sim}\,$3 under the “Case A” condition, in which the nebula is always optically thin even for Lyman-line photons. However, this may not be always true for SNRs. Previous studies have showed that H$\alpha$/H$\beta$ could vary from ${\sim}\,$2.9 to ${\sim}\,$4.2 and even up to ${\sim}\,$6 (e.g., see Raymond 1979, Shull & McKee 1979, Ghavamian et al. 2001).

• •

For some XBs, the optical extinction was estimated by comparing the observed colour with the intrinsic colour derived from the stellar spectral type. However, if the optical flux contribution of the accretion disk or the absorption of the stellar wind is not negligible, the derived spectral type of the primary star may be incorrect and this may result in an incorrect $A_{V}$ (e.g., for EXO 0748-676, Schoembs & Zoeschinger (1990) estimated $A_{V}\approx 1.3\pm 0.1\,{\rm mag}$ based on its stellar spectral type, while Pearson et al. (2006) estimated $A_{V}\approx 0.48\pm 0.26\,{\rm mag}$ from the widths of the sodium doublet absorption lines).

4 Summary

The $N_{\rm H}$–$A_{V}$ relation is explored based on the X-ray absorption data of a large AG89 sample of Galactic lines of sight toward 35 supernova remnants, 6 planetary nebulae, 70 X-ray binaries for which $N_{\rm H}$ was derived with solar abundances, as well as a smaller W00 sample of 19 supernova remnants and 29 X-ray binaries for which $N_{\rm H}$ was derived with subsolar abundances. For the AG89 sample, our principal results are as follows:

We derive a mean hydrogen-to-extinction ratio of $\langle N_{\rm H}/A_{V}\rangle=\left(2.08\pm 0.02\right)\times 10^{21}\,{\rm H}\,{\rm cm}^{-2}\,{\rm mag}^{-1}$ for the whole Galaxy. 2. 2.

The X-ray-derived $N_{\rm H}/A_{V}$ ratio is generally constant across the Galaxy. It does not appear to correlate with $n_{\rm H}$ (the line of sight mean number density of hydrogen), $R_{g}$ (the distance away from the Galactic centre), and $z$ (the distance above or below the Galactic plane). The $\langle N_{\rm H}/A_{V}\rangle$ ratio derived for the 1st and 4th galactic quadrants ($\langle N_{\rm H}/A_{V}\rangle=\left(2.04\pm 0.05\right)\times 10^{21}\,{\rm H}\,{\rm cm}^{-2}\,{\rm mag}^{-1}$) is consistent with that of the 2nd and 3rd galactic quadrants ($\langle N_{\rm H}/A_{V}\rangle=\left(2.09\pm 0.03\right)\times 10^{21}\,{\rm H}\,{\rm cm}^{-2}\,{\rm mag}^{-1}$). 3. 3.

We estimate a gas-to-dust mass ratio of $M_{\rm gas}/M_{\rm dust}\approx 140$ from $\langle N_{\rm H}/A_{V}\rangle=2.08\times 10^{21}\,{\rm H}\,{\rm cm}^{-2}\,{\rm mag}^{-1}$. 4. 4.

The distribution of hydrogen in the Galaxy is explored with the addition of an additional sample of 74 supernova remnants for which both $N_{\rm H}$ and distances are known. It is found that, between the Galactic radius of 2 kpc to 10 kpc, the vertical distribution of hydrogen can be roughly described by a Gaussian function with a mid-plane density of $n_{\rm H}(0)=1.11\pm 0.15\,{\rm cm}^{-3}$ and a scale hight of $h=75.5\pm 12.4\,{\rm pc}$. We also estimate a total gas surface density of $\sum_{\rm gas}\sim 7.0\,{M_{\rm\bigodot}}\,{\rm pc}^{-2}$.

Similarly, for the W00 sample we derive $N_{\rm H}/A_{V}=\left(2.47\pm 0.04\right)\times 10^{21}\,{\rm H}\,{\rm cm}^{-2}\,{\rm mag}^{-1}$ for the whole Galaxy which is higher by ${\sim}\,$20% than that of the AG89 sample. We also find that $N_{\rm H}$ derived from subsolar abundances exceeds that from solar abundances by ${\sim}\,$20%, suggesting that in future studies one may simply scale $N_{\rm H}$ of subsolar abundances by a factor of ${\sim}\,$1.2 when converting to $N_{\rm H}$ of solar abundances.

Acknowledgements

HZ and WWT acknowledge support from NSFC (10273025, 11473038, 11603039). AL is supported in part by NSF AST-1311804 and NASA NNX14AF68G. We thank Patrick Slane, Linli Yan, and the referee Tolga Güver for their very helpful comments and suggestions which substantially improve the quality of our paper. We also thank H. Su, S. Yao and D. Wu for their help during the preparation of this paper.

Appendix: A list of $N_{\rm H}$, $A_{V}$ and $D$ data

compiled from the literature