Characterizing the transition from diffuse atomic to dense molecular clouds in the Magellanic clouds with [CII], [CI], and CO

TL;DR

This study uses Herschel/HIFI observations of [CII], [CI], and CO lines to analyze the transition from atomic to molecular gas in the low-metallicity environments of the Magellanic Clouds, revealing the prevalence of CO-dark H2 and variations in X_CO.

Contribution

It provides detailed measurements of gas-phase carbon species and molecular fractions, offering new insights into the atomic-to-molecular transition in low-metallicity galaxies.

Findings

Most molecular gas is CO-dark H2 (77-89%) in the Magellanic Clouds.

The mean X_CO conversion factors are higher than in the Milky Way but closer after correction.

[CII] accounts for about 1% of the total far-infrared emission in the observed lines of sight.

Abstract

We present and analyze deep Herschel/HIFI observations of the [CII] 158um, [CI] 609um, and [CI] 370um lines towards 54 lines-of-sight (LOS) in the Large and Small Magellanic clouds. These observations are used to determine the physical conditions of the line--emitting gas, which we use to study the transition from atomic to molecular gas and from C^+ to C^0 to CO in their low metallicity environments. We trace gas with molecular fractions in the range 0.1<f(H2)<1, between those in the diffuse H2 gas detected by UV absorption (f(H2)<0.2) and well shielded regions in which hydrogen is essentially completely molecular. The C^0 and CO column densities are only measurable in regions with molecular fractions f(H2)>0.45 in both the LMC and SMC. Ionized carbon is the dominant gas-phase form of this element that is associated with molecular gas, with C^0 and CO representing a small fraction, implying that most (89% in the LMC and 77% in the SMC) of the molecular gas in our sample is CO-dark H2. The mean X_CO conversion factors in our LMC and SMC sample are larger than the value typically found in the Milky Way. When applying a correction based on the filling factor of the CO emission, we find that the values of X_CO in the LMC and SMC are closer to that in the Milky Way. The observed [CII] intensity in our sample represents about 1% of the total far-infrared intensity from the LOSs observed in both Magellanic Clouds.

Figures

Tables

Table 1. Table 1 Derived Parameters for LMC and SMC Sample

LOS	R.A	Decl.	$N{\left(H^0\right)}^1$	$N{\left(H^{+}\right)}^2$	$N{\left(H_2\right)}^3$	$f{\left(H_2\right)}^4$	$A_V^5$	Total far–IR6
			log	log	log			log
	J2000	J2000	[cm-2]	[cm-2]	[cm-2]		[mag]	[erg s-1cm-2sr-1]
Large Magellanic Cloud
Diff1_NW8	5:31:59.2	-66:22:52.3	21.23$\pm$0.02	20.51$\pm$0.01	–	–	0.91$\pm$0.36	-2.61$\pm$0.04
Diff2_SE8	4:59:35.5	-70:11:04.6	21.39$\pm$0.01	20.48$\pm$0.01	${20.9}_{-0.1}^{+0.2}$	${0.4}_{-0.1}^{+0.1}$	0.70$\pm$0.28	-2.70$\pm$0.04
Diff3_RIDGE8	5:31:50.6	-71:12:41.6	21.53$\pm$0.01	19.61$\pm$0.10	–	–	2.00$\pm$0.80	-2.82$\pm$0.06
Diff4_NE8	5:01:47.7	-65:59:05.2	21.39$\pm$0.01	19.85$\pm$0.06	–	–	0.38$\pm$0.15	-2.91$\pm$0.07
Diff5_SE8	4:58:54.0	-69:08:29.9	21.47$\pm$0.01	19.67$\pm$0.09	–	–	0.42$\pm$0.17	-2.78$\pm$0.05
Diff6_NW8	5:43:34.9	-67:56:08.2	21.35$\pm$0.01	20.06$\pm$0.03	–	–	0.46$\pm$0.18	-2.95$\pm$0.08
Diff7_NW8	5:25:17.3	-67:08:03.6	21.48$\pm$0.01	19.91$\pm$0.05	20.9$\pm$0.1	${0.4}_{-{0.0}^7}^{+{0.0}^7}$	0.50$\pm$0.20	-2.68$\pm$0.04
LMC10_NE9	4:51:51.1	-67:05:45.0	21.58$\pm$0.01	20.84$\pm$0.16	–	–	2.23$\pm$0.89	-2.63$\pm$0.04
LMC11_Ridge9	5:25:33.8	-69:50:16.6	21.36$\pm$0.01	19.92$\pm$0.05	${21.3}_{-0.4}^{+0.3}$	${0.6}_{-0.2}^{+0.2}$	1.21$\pm$0.48	-1.77$\pm$0.01
LMC12_SE9	5:02:13.7	-69:02:16.4	21.40$\pm$0.01	20.25$\pm$0.02	${21.5}_{-0.5}^{+0.2}$	${0.7}_{-0.2}^{+0.1}$	2.94$\pm$1.18	-1.91$\pm$0.01
LMC_1_NW9	5:28:1.9	-67:25:14.0	21.43$\pm$0.01	21.14$\pm$0.007	${21.6}_{-0.1}^{+{0.0}^7}$	${0.8}_{-{0.0}^7}^{+{0.0}^7}$	5.05$\pm$2.02	-1.72$\pm$0.007
LMC2_NW9	5:25:16.3	-66:24:40.8	21.58$\pm$0.01	20.32$\pm$0.02	21.0$\pm$0.1	${0.3}_{-0.1}^{+0.1}$	0.91$\pm$0.36	-2.44$\pm$0.02
LMC3_NW9	5:20:44.8	-66:06:58.2	21.25$\pm$0.02	19.74$\pm$0.07	${20.5}_{-0.2}^{+0.3}$	${0.3}_{-0.1}^{+0.1}$	0.63$\pm$0.25	-2.85$\pm$0.06
LMC4_RIDGE9	5:28:22.5	-69:28:22.5	21.49$\pm$0.01	20.53$\pm$0.01	21.2$\pm$0.1	${0.5}_{-{0.0}^7}^{+{0.0}^7}$	1.79$\pm$0.72	-2.18$\pm$0.01
LMC5_SE9	5:06:23.1	-70:28:08.7	21.26$\pm$0.02	20.47$\pm$0.01	21.2$\pm$0.1	${0.6}_{-0.1}^{+{0.0}^7}$	1.35$\pm$0.54	-2.08$\pm$0.01
LMC7_RIDGE9	5:45:6.9	-69:50:42.6	21.74$\pm$0.01	20.49$\pm$0.01	21.2$\pm$0.1	${0.4}_{-{0.0}^7}^{+{0.0}^7}$	1.00$\pm$0.40	-2.20$\pm$0.01
LMC8_RIDGE9	5:47:11.8	-69:28:35.1	21.81$\pm$0.007	20.52$\pm$0.01	–	–	1.75$\pm$0.70	-2.20$\pm$0.01
LMC9_NE9	5:03:20.8	-67:11:44.2	21.61$\pm$0.01	20.17$\pm$0.03	${20.5}_{-0.2}^{+0.3}$	${0.1}_{-0.1}^{+0.1}$	1.56$\pm$0.62	-2.63$\pm$0.04
NT12710	5:24:19.8	-70:27:48.7	21.05$\pm$0.03	19.49$\pm$0.13	${21.1}_{-0.7}^{+0.4}$	${0.7}_{-0.2}^{+0.2}$	1.23$\pm$0.49	-2.74$\pm$0.05
NT2_NE10	4:47:36.8	-67:12:13.7	21.35$\pm$0.01		–	–	1.32$\pm$0.53	-3.01$\pm$0.09
NT7410	5:14:33.4	-70:10:51.9	21.33$\pm$0.01	20.87$\pm$0.15	${21.4}_{-0.3}^{+0.6}$	${0.7}_{-0.1}^{+0.3}$	1.11$\pm$0.45	-2.49$\pm$0.03
NT7710	5:15:9.4	-70:35:42.0	21.00$\pm$0.03	20.66$\pm$0.24	${21.3}_{-0.3}^{+0.2}$	${0.8}_{-0.1}^{+0.1}$	1.82$\pm$0.73	-1.56$\pm$0.007
NT9710	5:19:27.8	-71:13:52.4	21.03$\pm$0.03	19.52$\pm$0.12	–	–	0.44$\pm$0.18	-3.04$\pm$0.10
NT9910	5:19:57.6	-70:42:21.7	21.17$\pm$0.02	20.87$\pm$0.15	–	–	0.68$\pm$0.27	-2.83$\pm$0.06
PDR1_NW10	5:25:46.9	-66:13:41.6	21.71$\pm$0.01	20.40$\pm$0.01	${21.7}_{-0.6}^{+0.3}$	${0.6}_{-0.2}^{+0.2}$	3.27$\pm$1.31	-1.93$\pm$0.01
PDR2_NW10	5:35:22.4	-67:35:00.5	21.37$\pm$0.01	21.78$\pm$0.007	22.2$\pm$0.1	${0.9}_{-{0.0}^7}^{+{0.0}^7}$	3.38$\pm$1.35	-0.51$\pm$0.007
PDR3_NE10	4:52:8.3	-66:55:13.7	21.50$\pm$0.01	21.47$\pm$0.007	22.5$\pm$0.1	${1.0}_{-{0.0}^7}^{+{0.0}^7}$	8.84$\pm$3.54	-0.33$\pm$0.007
PDR4_RIDGE10	5:39:48.7	-71:09:27.4	21.65$\pm$0.01	20.43$\pm$0.01	${21.5}_{-0.4}^{+0.2}$	${0.6}_{-0.2}^{+0.1}$	11.70$\pm$4.68	-1.42$\pm$0.007
SK-66D3511	4:57:4.5	-66:34:38.0	21.49$\pm$0.01	20.64$\pm$0.007	${21.1}_{-0.2}^{+0.1}$	${0.6}_{-0.1}^{+0.3}$	1.40$\pm$0.56	-2.29$\pm$0.02
SK-67D211	4:47:4.4	-67:06:53.0	21.31$\pm$0.01	20.13$\pm$0.03	–	–	0.31$\pm$0.12	-2.61$\pm$0.04
SK-68D12911	5:36:26.8	-68:57:32.0	21.55$\pm$0.01	20.66$\pm$0.007	–	–	0.98$\pm$0.39	-2.34$\pm$0.02
SK-68D14011	5:38:57.3	-68:56:53.0	21.69$\pm$0.01	21.20$\pm$0.007	21.0$\pm$0.1	${0.3}_{-0.1}^{+0.1}$	0.45$\pm$0.18	-1.63$\pm$0.007
SK-68D15511	5:42:54.9	-68:56:54.0	21.76$\pm$0.01	20.81$\pm$0.007	21.4$\pm$0.0	${0.5}_{-{0.0}^7}^{+{0.0}^7}$	0.92$\pm$0.37	-1.77$\pm$0.01
SK-68D2611	5:01:32.2	-68:10:43.0	21.24$\pm$0.02	19.91$\pm$0.05	–	–	0.61$\pm$0.24	-2.86$\pm$0.06
SK-69D22811	5:37:9.2	-69:20:20.0	21.52$\pm$0.01	20.85$\pm$0.007	20.9$\pm$0.1	${0.3}_{-0.1}^{+0.1}$	0.48$\pm$0.19	-2.17$\pm$0.01
SK-69D27911	5:41:44.7	-69:35:15.0	21.62$\pm$0.01	20.41$\pm$0.01	–	–	0.64$\pm$0.26	-2.61$\pm$0.04
11footnotetext: H0 column density derived from the integrated intensity of the H i 21 cm line over the full velocity range (see Section 3.2). 22footnotetext: H+ column density derived from H$\alpha$ observations as described in Section 3.1. 33footnotetext: H2 column density derived from [C ii], [C i], and CO observations as described in Section LABEL:sec:h-h_2-transition. 44footnotetext: Molecular fraction, $f\left(H_2\right)=2N\left(H_2\right)/\left(N\left(H^0\right)+2N\left(H_2\right)\right)$ (Section LABEL:sec:h-h_2-transition). 55footnotetext: Visual extinction derived from dust continuum maps as described in Section 4.1. 66footnotetext: Total far–infrared intensity derived from Spitzer 24 $\mu$m and Herschel 100 $\mu$m maps as described in Section LABEL:sec:relat-betw-c. 77footnotetext: The uncertainty is below 0.005 or 0.05. 88footnotetext: H i Peak (See Section 2). 99footnotetext: 160 $\mu$m Peak (See Section 2). 1010footnotetext: CO Peak (See Section 2). 1111footnotetext: FUSE LOSs (See Section 2).

Table 2. Table 2 Derived Parameters for LMC and SMC Sample

LOS	R.A	Decl.	$N{\left(H^0\right)}^1$	$N{\left(H^{+}\right)}^2$	$N{\left(H_2\right)}^3$	$f{\left(H_2\right)}^4$	$A_V^5$	Total far–IR6
			log	log	log			log
	J2000	J2000	[cm-2]	[cm-2]	[cm-2]		[mag]	[erg s-1cm-2sr-1]
Small Magellanic Cloud
AzV1811	0:47:13.1	-73:06:25.0	22.10$\pm$0.007	20.54$\pm$0.007	21.9$\pm$0.1	${0.5}_{-{0.0}^7}^{+0.1}$	0.55$\pm$0.22	-1.88$\pm$0.01
AzV45611	1:10:55.8	-72:42:55.0	21.64$\pm$0.007	20.52$\pm$0.01	–	–	0.09$\pm$0.04	-3.15$\pm$0.12
AzV46211	1:11:25.9	-72:32:21.0	21.62$\pm$0.007	19.77$\pm$0.07	–	–	0.00$\pm$0.007	-3.54$\pm$0.30
SMC_HI_18	0:58:40.5	-72:34:52.4	21.99$\pm$0.007	20.10$\pm$0.03	–	–	0.28$\pm$0.11	-3.04$\pm$0.10
SMC_HI_28	0:57:35.7	-72:48:56.3	21.99$\pm$0.007	20.11$\pm$0.03	–	–	0.40$\pm$0.16	-2.98$\pm$0.08
SMC_HI_38	0:53:2.0	-73:15:27.9	22.02$\pm$0.007	20.27$\pm$0.02	–	–	0.58$\pm$0.23	-2.82$\pm$0.06
SMC_HI_48	0:48:41.5	-73:06:08.3	22.13$\pm$0.007	20.36$\pm$0.01	21.8$\pm$0.1	${0.5}_{-{0.0}^7}^{+{0.0}^7}$	0.85$\pm$0.34	-2.11$\pm$0.01
SMC_HI_58	0:47:20.4	-73:18:28.4	22.05$\pm$0.007	20.63$\pm$0.01	–	–	0.73$\pm$0.29	-2.73$\pm$0.05
SMC_HI_68	0:49:53.2	-72:56:15.6	22.05$\pm$0.007	20.48$\pm$0.01	–	–	0.58$\pm$0.23	-2.76$\pm$0.05
SMC_HI_78	0:49:38.1	-73:01:14.2	22.06$\pm$0.007	20.16$\pm$0.03	–	–	0.35$\pm$0.14	-2.80$\pm$0.06
SMC_B2_610	0:47:57.2	-73:17:16.4	22.00$\pm$0.007	20.98$\pm$0.007	22.2$\pm$0.1	${0.7}_{-{0.0}^7}^{+{0.0}^7}$	0.48$\pm$0.19	-1.79$\pm$0.01
SMC_LIRS3610	0:46:40.3	-73:06:10.5	22.04$\pm$0.007	20.96$\pm$0.007	22.2$\pm$0.2	${0.7}_{-0.1}^{+0.1}$	0.60$\pm$0.24	-1.53$\pm$0.007
SMC_LIRS4910	0:48:21.1	-73:05:29.0	22.12$\pm$0.007	20.53$\pm$0.007	${22.5}_{-0.2}^{+0.1}$	${0.8}_{-0.1}^{+{0.0}^7}$	0.90$\pm$0.36	-1.69$\pm$0.007
SMC_NE_1a10	0:59:43.8	-71:44:47.0	21.60$\pm$0.007	20.23$\pm$0.02	${21.5}_{-0.2}^{+0.1}$	${0.6}_{-0.1}^{+0.1}$	0.41$\pm$0.16	-2.38$\pm$0.02
SMC_NE_3c10	1:03:30.0	-71:57:00.0	21.78$\pm$0.007	20.48$\pm$0.01	${21.5}_{-0.8}^{+0.3}$	${0.5}_{-0.4}^{+0.2}$	0.46$\pm$0.19	-2.70$\pm$0.04
SMC_NE_3g10	1:03:9.9	-72:03:46.9	21.79$\pm$0.007	20.84$\pm$0.007	${21.4}_{-0.2}^{+0.1}$	${0.5}_{-0.1}^{+0.1}$	0.82$\pm$0.33	-2.29$\pm$0.02
SMC_NE_4a_hi10	0:57:0.0	-72:22:40.0	21.86$\pm$0.007	20.21$\pm$0.02	${22.1}_{-1.9}^{+0.6}$	${0.8}_{-0.2}^{+0.3}$	1.13$\pm$0.45	-2.77$\pm$0.05
SMC_NE_4c_low10	0:58:40.0	-72:27:40.0	21.93$\pm$0.007	20.39$\pm$0.02	22.2$\pm$0.7	${0.8}_{-0.2}^{+0.4}$	0.67$\pm$0.27	-2.63$\pm$0.04
11footnotetext: H0 column density derived from the integrated intensity of the H i 21 cm line over the full velocity range (see Section 3.2). 22footnotetext: H+ column density derived from H$\alpha$ observations as described in Section 3.1. 33footnotetext: H2 column density derived from [C ii], [C i], and CO observations as described in Section LABEL:sec:h-h_2-transition. 44footnotetext: Molecular fraction, $f\left(H_2\right)=2N\left(H_2\right)/\left(N\left(H^0\right)+2N\left(H_2\right)\right)$ (Section LABEL:sec:h-h_2-transition). 55footnotetext: Visual extinction derived from dust continuum maps as described in Section 4.1. 66footnotetext: Total far–infrared intensity derived from Spitzer 24 $\mu$m and Herschel 100 $\mu$m maps as described in Section LABEL:sec:relat-betw-c. 77footnotetext: The uncertainty is below 0.005 or 0.05. 88footnotetext: H i Peak (See Section 2). 99footnotetext: 160$\mu$m Peak (See Section 2). 1010footnotetext: CO Peak (See Section 2). 1111footnotetext: FUSE LOSs (See Section 2).

Table 3. Table 3 Integrated Intensities of Spectral Line for LMC Sample

LOS	$V_{\mathrm{LSR}}$	$I_{\left[\mathrm{HI}\right];\mathrm{CNM}}^1$	$I_{\left[\mathrm{CII}\right]}$	$I_{\left[\mathrm{CI}\right]\left(1-0\right)}$	$I_{\left[\mathrm{CI}\right]\left(2-1\right)}$	$I_{\mathrm{CO}\left(1-0\right)}$	$I_{\mathrm{CO}\left(3-2\right)}$	$I_{\mathrm{CO}\left(7-6\right)}$	$I_{{}_{}{}^{13}\mathrm{CO}\left(1-0\right)}$	$I_{{}_{}{}^{13}\mathrm{CO}\left(3-2\right)}$
	[km s-1]	[K km s-1]
Large Magellanic Cloud
Diff1_NW_1	288.8	510$\pm$8	2.4$\pm$0.3	–	–	–	–	–	–	–
Diff2_SE_1	233.3	169$\pm$6	2.8$\pm$0.6	0.9$\pm$0.3	–	–	–	–	–
Diff3_RIDGE_1	–	–	–	–	–	0.7$\pm$0.2	–	–	–
Diff5_SE_1	245.0	405$\pm$7	0.9$\pm$0.2	–	–	–	–	–	–	–
Diff6_NW_1	–	–	–	–	–	1.0$\pm$0.1	0.3$\pm$0.1	–	–	–
Diff7_NW_1	288.1	253$\pm$6	2.7$\pm$0.2	–	–	–	–	–	–	–
LMC10_NE_1	275.4	496$\pm$7	1.8$\pm$0.2	0.3$\pm$0.1	–	1.7$\pm$0.2	–	–	–
LMC11_Ridge_1	250.3	341$\pm$7	7.9$\pm$0.1	0.6$\pm$0.1	0.4$\pm$0.1	4.1$\pm$0.2	3.4$\pm$0.1	–	–	0.3$\pm$0.1
LMC12_SE_1	265.7	224$\pm$6	6.4$\pm$0.2	0.1$\pm$0.1	–	1.9$\pm$0.2	2.8$\pm$0.1	–	–	0.2$\pm$0.1
LMC12_SE_2	270.6	288$\pm$6	5.3$\pm$0.2	1.1$\pm$0.1	0.9$\pm$0.1	4.7$\pm$0.2	7.4$\pm$0.1	–	0.4$\pm$0.1	0.5$\pm$0.1
LMC_1_NW_1	293.1	288$\pm$7	6.6$\pm$0.02	0.6$\pm$0.1	0.4$\pm$0.02	1.8$\pm$0.3	1.3$\pm$0.2	1.5$\pm$0.1	–	0.3$\pm$0.02
LMC_1_NW_2	287.6	341$\pm$7	6.1$\pm$0.02	0.9$\pm$0.1	0.6$\pm$0.1	2.3$\pm$0.3	2.5$\pm$0.3	0.4$\pm$0.1	–	0.3$\pm$0.1
LMC_1_NW_3	288.0	890$\pm$12	10.1$\pm$0.02	–	–	–	–	–	–	–
LMC2_NW_1	290.5	716$\pm$8	4.7$\pm$0.4	0.5$\pm$0.1	0.4$\pm$0.1	2.3$\pm$0.2	–	–	–
LMC3_NW_1	289.7	257$\pm$6	1.6$\pm$0.3	–	–	–	–	–	–	–
LMC4_RIDGE_1	246.6	618$\pm$9	5.7$\pm$0.3	–	–	0.6$\pm$0.2	–	–	–
LMC5_SE_1	219.0	75$\pm$4	9.7$\pm$0.1	0.7$\pm$0.1	0.8$\pm$0.2	2.5$\pm$0.2	3.2$\pm$0.1	–	–	0.4$\pm$0.1
LMC7_RIDGE_1	232.7	745$\pm$9	6.2$\pm$0.5	–	–	1.9$\pm$0.2	0.5$\pm$0.2	–	–	–
LMC8_RIDGE_1	238.5	688$\pm$9	3.7$\pm$0.4	–	–	–	–	–	–	–
LMC9_NE_1	274.2	310$\pm$7	2.0$\pm$0.3	–	–	3.3$\pm$0.3	1.3$\pm$0.1	–	–	–
NT127_1	235.0	73$\pm$4	0.6$\pm$0.1	1.1$\pm$0.1	0.2$\pm$0.02	3.7$\pm$0.2	4.2$\pm$0.1	–	–	0.3$\pm$0.1
NT2_NE_1	–	–	–	1.2$\pm$0.2	–	8.2$\pm$0.2	–	–	0.9$\pm$0.1
NT74_1	236.1	310$\pm$8	1.6$\pm$0.4	2.6$\pm$0.1	0.5$\pm$0.1	17.1$\pm$0.3	11.0$\pm$0.1	–	2.5$\pm$0.2	0.6$\pm$0.1
NT77_1	217.4	59$\pm$4	8.3$\pm$0.1	1.0$\pm$0.2	1.0$\pm$0.1	8.1$\pm$0.2	15.5$\pm$0.1	1.1$\pm$0.1	1.5$\pm$0.1	2.7$\pm$0.1
NT97_1	–	–	–	0.4$\pm$0.1	–	3.8$\pm$0.1	–	–	0.7$\pm$0.1
NT99_1	227.0	270$\pm$7	1.3$\pm$0.3	–	–	5.0$\pm$0.1	–	–	0.6$\pm$0.1
PDR1_NW_1	285.8	775$\pm$9	13.7$\pm$0.3	3.1$\pm$0.2	1.7$\pm$0.1	13.6$\pm$0.2	23.0$\pm$0.1	–	1.6$\pm$0.1	1.6$\pm$0.1
PDR1_NW_2	293.3	287$\pm$6	1.0$\pm$0.2	–	–	–	–	–	–	–
PDR2_NW_1	291.4	184$\pm$7	3.1$\pm$0.2	–	0.4$\pm$0.02	2.1$\pm$0.5	3.9$\pm$0.1	1.5$\pm$0.1	–
PDR2_NW_2	284.3	144$\pm$7	47.0$\pm$0.3	0.8$\pm$0.1	1.8$\pm$0.1	7.1$\pm$0.6	11.8$\pm$0.1	5.9$\pm$0.2	–	1.0$\pm$0.2
PDR2_NW_3	279.6	203$\pm$8	21.0$\pm$0.2	1.2$\pm$0.1	0.5$\pm$0.02	4.2$\pm$0.3	2.8$\pm$0.1	–	–	–
PDR2_NW_4	301.4	173$\pm$11	13.6$\pm$0.5	–	–	–	–	–	–	–
PDR3_NE_1	275.8	737$\pm$9	42.7$\pm$1.4	0.9$\pm$0.4	0.4$\pm$0.1	3.7$\pm$0.5	14.7$\pm$0.3	5.0$\pm$0.2	0.3$\pm$0.3	2.6$\pm$0.1
PDR3_NE_2	271.4	391$\pm$7	34.1$\pm$0.2	2.5$\pm$0.4	4.0$\pm$0.1	15.1$\pm$0.5	32.0$\pm$0.3	7.6$\pm$0.2	2.1$\pm$0.3	5.3$\pm$0.02
PDR3_NE_3	276.6	1370$\pm$13	36.6$\pm$1.4	–	–	–	–	–	–	–
PDR4_RIDGE_1	228.0	602$\pm$9	9.3$\pm$0.1	4.2$\pm$0.2	2.2$\pm$0.1	33.9$\pm$0.3	34.2$\pm$0.1	2.4$\pm$0.1	5.4$\pm$0.2	4.0$\pm$0.1
SK-66D35_1	–	–	–	1.0$\pm$0.3	0.3$\pm$0.1	0.7$\pm$0.1	2.0$\pm$0.1	0.5$\pm$0.1	–	0.3$\pm$0.02
SK-66D35_2	279.5	584$\pm$9	5.9$\pm$0.4	–	–	–	0.4$\pm$0.1	–	–	–
SK-67D2_1	–	–	–	–	–	0.7$\pm$0.1	0.3$\pm$0.02	–	–	–
SK-68D129_1	259.0	708$\pm$10	2.2$\pm$0.5	–	–	0.6$\pm$0.2	–	–	–
SK-68D140_1	250.0	635$\pm$9	7.0$\pm$0.6	–	–	–	–	–	–	–
SK-68D140_2	273.9	809$\pm$14	6.2$\pm$1.5	–	–	–	–	–	–	–
SK-68D140_3	262.0	590$\pm$9	5.4$\pm$1.2	–	–	–	–	–	–	–
SK-68D155_1	246.1	383$\pm$8	8.0$\pm$0.5	–	–	–	–	–	–	–
SK-68D155_2	256.6	374$\pm$7	1.8$\pm$0.4	–	–	–	–	–	–	–
SK-68D26_1	251.3	476$\pm$9	2.2$\pm$0.5	–	–	–	–	–	–	–
SK-69D228_1	247.0	314$\pm$9	6.1$\pm$0.3	–	–	–	–	–	–	–

Table 4. Table 4 Integrated Intensities of Spectral Line for SMC Sample

LOS	$V_{\mathrm{LSR}}$	$I_{\left[\mathrm{HI}\right];\mathrm{CNM}}^1$	$I_{\left[\mathrm{CII}\right]}$	$I_{\left[\mathrm{CI}\right]\left(1-0\right)}$	$I_{\left[\mathrm{CI}\right]\left(2-1\right)}$	$I_{\mathrm{CO}\left(1-0\right)}$	$I_{\mathrm{CO}\left(3-2\right)}$	$I_{\mathrm{CO}\left(7-6\right)}$	$I_{{}_{}{}^{13}\mathrm{CO}\left(1-0\right)}$	$I_{{}_{}{}^{13}\mathrm{CO}\left(3-2\right)}$
	[km s-1]	[K km s-1]
Small Magellanic Cloud
AzV18_1	122.0	1709$\pm$11	5.9$\pm$0.6	–	–	–	–	–	–	–
AzV18_2	136.7	764$\pm$8	3.4$\pm$0.5	–	–	–	–	–	–	–
SMC_B2_6_1	120.9	731$\pm$4	15.6$\pm$0.4	0.9$\pm$0.1	0.8$\pm$0.1	5.5$\pm$0.2	5.6$\pm$0.1	0.8$\pm$0.1	0.8$\pm$0.1	0.7$\pm$0.1
SMC_B2_6_2	125.3	1273$\pm$5	5.3$\pm$0.4	–	–	–	–	–	–	–
SMC_HI_2_1	–	–	–	0.7$\pm$0.2	–	–	–	–	–
SMC_HI_3_1	145.4	2347$\pm$8	4.4$\pm$0.8	0.6$\pm$0.1	–	–	–	0.4$\pm$0.1	–
SMC_HI_4_1	123.3	1103$\pm$4	5.5$\pm$0.4	–	–	–	–	–	–	–
SMC_HI_4_2	114.8	508$\pm$3	2.3$\pm$0.3	–	–	–	–	–	–	–
SMC_HI_6_1	149.7	431$\pm$4	1.3$\pm$0.3	–	–	–	–	–	–	–
SMC_LIRS36_1	126.4	383$\pm$3	16.4$\pm$0.1	2.0$\pm$0.1	1.8$\pm$0.1	7.6$\pm$0.2	18.9$\pm$0.1	1.5$\pm$0.1	0.7$\pm$0.1	2.8$\pm$0.2
SMC_LIRS36_2	–	–	–	–	–	0.5$\pm$0.1	–	–	–
SMC_LIRS49_1	110.4	448$\pm$3	5.6$\pm$0.02	–	–	–	0.8$\pm$0.1	–	–	–
SMC_LIRS49_2	115.0	502$\pm$3	14.3$\pm$0.02	2.5$\pm$0.2	1.3$\pm$0.1	8.6$\pm$0.2	18.1$\pm$0.1	0.6$\pm$0.1	0.6$\pm$0.1	2.0$\pm$0.2
SMC_LIRS49_3	125.9	1173$\pm$5	5.2$\pm$0.02	–	–	1.3$\pm$0.2	2.4$\pm$0.1	–	–	0.3$\pm$0.1
SMC_LIRS49_4	137.2	191$\pm$2	1.4$\pm$0.02	–	–	–	–	–	–	–
SMC_NE_1a_1	148.9	496$\pm$4	4.5$\pm$0.1	0.5$\pm$0.1	0.5$\pm$0.1	4.0$\pm$0.1	4.3$\pm$0.1	0.6$\pm$0.1	0.4$\pm$0.02
SMC_NE_3c_1	175.1	170$\pm$2	1.1$\pm$0.1	1.2$\pm$0.1	0.7$\pm$0.1	4.2$\pm$0.2	4.1$\pm$0.1	–	0.7$\pm$0.02	0.4$\pm$0.1
SMC_NE_3g_1	169.1	690$\pm$4	4.0$\pm$0.1	0.6$\pm$0.2	0.6$\pm$0.1	4.3$\pm$0.1	3.2$\pm$0.1	0.5$\pm$0.1	0.4$\pm$0.02	0.5$\pm$0.1
SMC_NE_4a_hi_1	–	–	–	–	–	–	0.7$\pm$0.1	–	–	0.2$\pm$0.1
SMC_NE_4a_hi_2	153.9	131$\pm$2	1.6$\pm$0.2	0.5$\pm$0.1	–	3.1$\pm$0.1	2.1$\pm$0.1	–	0.2$\pm$0.02
SMC_NE_4a_hi_3	122.2	551$\pm$4	1.3$\pm$0.3	–	–	–	–	–	–	–
SMC_NE_4c_low_1	121.6	780$\pm$4	2.1$\pm$0.4	0.7$\pm$0.1	–	5.8$\pm$0.1	1.7$\pm$0.1	0.2$\pm$0.1	0.7$\pm$0.02

Table 5. Table 5 Derived Parameters for LMC and SMC Sample

LOS	$N{\left(H^0\right)}_{\mathrm{CNM}}^1$	$T_{\mathrm{kin}}^{C^{+};2}$	$n_{H_2}^{C^{+};3}$	$N{\left(C^{+}\right)}_{H_2}^4$	$T_{\mathrm{kin}}^{C^0;2}$	$n_{H_2}^{C^0;3}$	$N{\left(C^0\right)}^4$	$T_{\mathrm{kin}}^{\mathrm{CO};2}$	$n_{H_2}^{\mathrm{CO};3}$	$N{\left(\mathrm{CO}\right)}^4$	filling5
	log		log	log		log	log		log	log	factor
	[cm-2]	[K]	[cm-3]	[cm-2]	[K]	[cm-3]	[cm-2]	[K]	[cm-3]	[cm-2]
Large Magellanic Cloud
Diff2_SE_1	20.56	49	2.8	${17.1}_{-0.1}^{+0.2}$	--	--	--	--	--	--	--
Diff7_NW_1	20.76	49	2.8	17.1$\pm$0.1	--	--	--	--	--	--	--
LMC11_Ridge_1	20.86	40$\pm$10	${3.4}_{-0.3}^{+{0.0}^6}$	17.5$\pm$0.3	40$\pm$10	${3.9}_{-0.6}^{+0.2}$	${15.9}_{-0.7}^{+0.3}$	20$\pm$10	4.5$\pm$0.1	${15.9}_{-0.7}^{+0.3}$	${0.10}_{-0.32}^{+0.04}$
LMC12_SE_1	20.66	30$\pm$10	3.7$\pm$0.06	${17.5}_{-0.6}^{+0.3}$	30$\pm$10	4.4$\pm$0.1	${15.3}_{-0.3}^{+0.2}$	40$\pm$10	4.4$\pm$0.1	${16.0}_{-0.3}^{+0.2}$	${0.10}_{-0.05}^{+0.02}$
LMC12_SE_2	20.76	60$\pm$10	3.1$\pm$0.06	${17.1}_{-0.2}^{+0.1}$	60$\pm$10	3.5$\pm$0.1	${16.2}_{-0.4}^{+0.2}$	30$\pm$10	${4.6}_{-0.1}^{+0.3}$	${16.3}_{-0.4}^{+0.2}$	${0.34}_{-0.32}^{+0.09}$
LMC_1_NW_1	20.76	120$\pm$20	2.6$\pm$0.06	17.2$\pm$0.1	120$\pm$20	2.7$\pm$0.1	${16.3}_{-0.4}^{+0.2}$	${50}_{-20}^{+10}$	${6.0}_{-0.1}^{+1.9}$	${16.2}_{-0.5}^{+0.4}$	${0.01}_{-0.02}^{+{0.00}^7}$
LMC_1_NW_2	20.86	160$\pm$10	2.6$\pm$0.06	16.9$\pm$0.1	160$\pm$10	2.9$\pm$0.1	${16.1}_{-0.3}^{+0.2}$	60$\pm$10	4.0$\pm$0.1	${15.8}_{-0.3}^{+0.2}$	${0.02}_{-0.01}^{+{0.00}^7}$
LMC_1_NW_3	21.26	49	2.8	17.6$\pm$0.06	--	--	--	--	--	--	--
LMC2_NW_1	21.16	49	2.8	17.2$\pm$0.1	--	--	--	--	--	--	--
LMC3_NW_1	20.76	49	2.8	${16.7}_{-0.2}^{+0.3}$	--	--	--	--	--	--	--
LMC4_RIDGE_1	21.16	49	2.8	17.4$\pm$0.1	--	--	--	--	--	--	--
LMC5_SE_1	20.16	${170}_{-20}^{+10}$	2.8	17.3$\pm$0.06	${170}_{-20}^{+10}$	3.3$\pm$0.1	${16.0}_{-0.4}^{+0.2}$	30$\pm$10	${4.6}_{-0.1}^{+0.2}$	${15.9}_{-0.4}^{+0.2}$	${0.09}_{-0.07}^{+0.02}$
LMC7_RIDGE_1	21.16	49	2.8	17.4$\pm$0.1	--	--	--	--	--	--	--
LMC9_NE_1	20.86	49	2.8	${16.7}_{-0.2}^{+0.3}$	--	--	--	--	--	--	--
NT127_1	20.16	30$\pm$10	2.6$\pm$0.06	${17.2}_{-0.7}^{+0.5}$	30$\pm$10	2.1$\pm$0.1	${16.7}_{-0.4}^{+0.3}$	30$\pm$10	4.3$\pm$0.1	${16.0}_{-0.4}^{+0.3}$	${0.16}_{-0.15}^{+0.05}$
NT77_1	20.06	${190}_{-10}^{+20}$	2.7$\pm$0.06	${17.3}_{-0.1}^{+{0.0}^6}$	${190}_{-10}^{+20}$	3.2$\pm$0.1	${16.1}_{-0.2}^{+0.6}$	50$\pm$20	${4.3}_{-0.4}^{+0.6}$	${16.9}_{-0.6}^{+1.1}$	${0.74}_{-0.26}^{+0.49}$
PDR1_NW_1	21.16	30$\pm$10	3.7$\pm$0.06	${17.8}_{-0.7}^{+0.3}$	30$\pm$10	${4.4}_{-0.1}^{+0.2}$	${16.6}_{-0.2}^{+0.3}$	30$\pm$10	${4.4}_{-0.1}^{+0.2}$	${16.8}_{-0.2}^{+0.7}$	${0.79}_{-0.21}^{+0.24}$
PDR2_NW_2	20.46	40$\pm$10	4.4$\pm$-0.0	${17.9}_{-0.3}^{+0.2}$	40$\pm$10	5.9$\pm$0.1	16.1$\pm$0.2	40$\pm$10	5.9$\pm$0.1	16.5$\pm$0.2	${0.11}_{-0.03}^{+0.02}$
PDR2_NW_3	20.66	49	2.8	18.0$\pm$0.06	--	--	--	--	--	--	--
PDR2_NW_4	20.56	49	2.8	17.6$\pm$0.06	--	--	--	--	--	--	--
PDR3_NE_1	21.16	150$\pm$10	2.3$\pm$0.06	18.4$\pm$0.1	150$\pm$10	2.3$\pm$0.1	${16.2}_{-0.3}^{+0.2}$	${60}_{-20}^{+10}$	${4.2}_{-0.3}^{+0.2}$	${16.8}_{-0.3}^{+0.2}$	${0.09}_{-0.04}^{+0.02}$
PDR3_NE_2	20.96	170$\pm$10	3.4$\pm$0.06	17.5$\pm$0.06	170$\pm$10	4.5$\pm$0.1	${16.6}_{-0.3}^{+0.2}$	40$\pm$10	4.5$\pm$0.4	${17.3}_{-0.3}^{+0.2}$	${0.38}_{-0.28}^{+0.08}$
PDR3_NE_3	21.46	49	2.8	18.3$\pm$0.06	--	--	--	--	--	--	--
PDR4_RIDGE_1	21.06	80$\pm$20	2.7$\pm$0.06	${17.5}_{-0.2}^{+0.1}$	80$\pm$20	2.8$\pm$0.1	${16.7}_{-0.5}^{+0.3}$	30$\pm$10	${4.6}_{-0.4}^{+0.7}$	${17.2}_{-0.6}^{+0.4}$	${0.40}_{-0.60}^{+0.16}$
SK-66D35_2	21.06	49	2.8	17.1$\pm$0.1	--	--	--	--	--	--	--
SK-68D140_1	21.16	49	2.8	17.2$\pm$0.1	--	--	--	--	--	--	--
SK-68D155_1	20.86	49	2.8	17.6$\pm$0.06	--	--	--	--	--	--	--
SK-69D228_1	20.86	49	2.8	17.1$\pm$0.1	--	--	--	--	--	--	--
Small Magellanic Cloud
AzV18_1	21.56	49	3.3	17.1$\pm$0.1	--	--	--	--	--	--	--
AzV18_2	21.16	49	3.3	16.9$\pm$0.1	--	--	--	--	--	--	--
SMC_B2_6_1	21.16	160$\pm$10	2.9$\pm$0.06	17.4$\pm$0.1	160$\pm$10	3.1$\pm$0.1	${16.1}_{-0.5}^{+0.3}$	--	${4.1}_{-0.2}^{+0.3}$	${16.4}_{-0.6}^{+0.4}$	${0.06}_{-0.07}^{+0.03}$
SMC_B2_6_2	21.46	49	3.3	17.1$\pm$0.1	--	--	--	--	--	--	--
SMC_HI_4_1	21.36	49	3.3	17.1$\pm$0.06	--	--	--	--	--	--	--
SMC_HI_4_2	21.06	49	3.3	16.7$\pm$0.1	--	--	--	--	--	--	--
SMC_LIRS36_1	20.86	60$\pm$10	3.5$\pm$0.06	17.5$\pm$0.1	60$\pm$10	3.8$\pm$0.1	${16.4}_{-0.1}^{+0.4}$	--	${4.3}_{-0.2}^{+0.4}$	${16.9}_{-0.3}^{+0.8}$	${0.89}_{-0.11}^{+0.42}$
SMC_LIRS49_1	20.96	49	3.3	17.2$\pm$0.06	--	--	--	--	--	--	--
SMC_LIRS49_2	21.06	50$\pm$10	3.1$\pm$0.06	${17.8}_{-0.2}^{+0.1}$	50$\pm$10	3.0$\pm$0.1	16.5$\pm$0.4	--	4.4$\pm$0.3	${16.8}_{-0.6}^{+0.8}$	${0.51}_{-0.49}^{+0.26}$
SMC_LIRS49_3	21.36	50$\pm$10	${3.8}_{-{0.0}^6}^{+0.1}$	${16.8}_{-0.2}^{+0.1}$	--	--	--	--	${4.3}_{-0.1}^{+0.3}$	${16.3}_{-0.5}^{+0.4}$	${0.15}_{-0.24}^{+0.03}$
SMC_LIRS49_4	20.56	49	3.3	16.6$\pm$0.06	--	--	--	--	--	--	--
SMC_NE_1a_1	21.06	110$\pm$10	3.3	16.7$\pm$0.1	110$\pm$10	3.6$\pm$0.1	${15.8}_{-0.2}^{+0.1}$	--	${3.9}_{-0.2}^{+0.3}$	${16.6}_{-0.2}^{+0.3}$	${0.12}_{-0.05}^{+{0.00}^7}$
SMC_NE_3c_1	20.56	40$\pm$10	3.3$\pm$-0.0	${16.6}_{-0.4}^{+0.2}$	40$\pm$10	3.3$\pm$0.1	${16.3}_{-1.0}^{+0.3}$	--	${3.5}_{-0.1}^{+0.7}$	${16.5}_{-1.0}^{+0.4}$	${0.06}_{-0.42}^{+0.03}$
SMC_NE_3g_1	21.16	190$\pm$10	3.0$\pm$0.06	16.6$\pm$0.1	190$\pm$10	3.3$\pm$0.1	15.9$\pm$0.3	--	3.4$\pm$0.1	16.4$\pm$0.3	0.03$\pm$0.01
SMC_NE_4a_hi_2	20.46	20$\pm$10	${3.8}_{-0.1}^{+{0.0}^6}$	${17.5}_{-2.0}^{+0.7}$	20$\pm$10	4.0$\pm$0.1	${15.9}_{-0.2}^{+0.1}$	--	4.0$\pm$0.1	${16.2}_{-0.2}^{+0.1}$	${0.10}_{-0.02}^{+{0.00}^7}$
SMC_NE_4a_hi_3	21.06	49	3.3	${16.3}_{-0.2}^{+0.3}$	--	--	--	--	--	--	--
SMC_NE_4c_low_1	21.26	${30}_{-20}^{+10}$	2.8$\pm$0.06	${17.4}_{-0.8}^{+0.7}$	${30}_{-20}^{+10}$	${2.1}_{-0.2}^{+0.1}$	${16.4}_{-0.4}^{+0.5}$	--	${2.1}_{-0.2}^{+0.1}$	${17.1}_{-0.5}^{+0.6}$	${0.15}_{-0.17}^{+0.09}$
11footnotetext: H0 column density derived from the integrated intensity of the H i 21 cm line over the velocity range defined by the FWHM of the [C ii] velocity components (see Section 3.2). 22footnotetext: Kinetic temperature of the H2 gas associated with C+ (Section LABEL:sec:c-sc-i), C0 (Section LABEL:sec:ci_excitation), and CO (Section LABEL:sec:co-emission) . 33footnotetext: Volume density of the H2 gas associated with C+ (Section LABEL:sec:c-sc-i), C0 (Section LABEL:sec:ci_excitation), and CO (Section LABEL:sec:co-emission) . 44footnotetext: C+ (Section LABEL:sec:c-sc-i), C0 (Section LABEL:sec:ci_excitation), and CO (Section LABEL:sec:co-emission) column densities associated with H2 gas. 55footnotetext: Filling factor of the [C i] and CO--emitting layers derived from 13CO observations in Section 4.4. 66footnotetext: The uncertainty is below 0.05. 77footnotetext: The uncertainty is below 0.005. We constrained the properties of the CO and [C i]--emitting gas by comparing line intensity ratios and absolute intensities of [C i], 12CO, and 13CO with the results of a radiative transfer code. We used the RADEX non--LTE radiative transfer code (vanderTak2007), using the uniform sphere approximation, to calculate line intensities as a function of the kinetic temperature, H2 volume density, and the column density per velocity interval $N$/$\Delta$v of the species of interest. The collisional rate coefficients were taken from the Leiden Atomic and Molecular Database (LAMDA; Schoeier2005). In the PDRs located at the borders of molecular clouds, the innermost region is at higher density, deeper in the cloud, and the outermost region is at lower density. Thus, the physical conditions of the C0 layer are not necessarily the same as those at the CO layer. Since we will be modelling spheres with uniform volume density and kinetic temperature, we analyzed the [C i] and CO data separately. We nevertheless assume that the [C i] and CO emission originate from the same regions with identical filling factors. This assumption is justified considering that the CO and [C i] emission arise from the FUV illuminated surfaces of clouds that are unresolved at the scale of our observations. For optically thin clumps (or for clumps with moderate opacity), the observed--to--model integrated intensity ratio gives the ratio of the beam--averaged column density to the clump intrinsic column density, assuming that the total integrated intensity is proportional to the number of clumps, i.e. no velocity crowding is present. We therefore determined the beam filling factor by comparing the observed absolute intensity of an optically thin line ( 13CO $J=3\to 2$ or 13CO $J=1\to 0$) with a constrained model. We compared the observed line intensity ratios with the predictions from a grid of RADEX models. The model grids predict line ratios for the kinetic temperatures ranging from 10 K to 200 K in steps of 10 K as a function of the CO or C0 column densities per velocity interval, $N_{\mathrm{CO}}/\Delta v$ (or $N_{C^0}/\Delta v$), and H2 volume density, $n_{H_2}$. The coverage in $N_{\mathrm{CO}}/\Delta v$ and $N_{C^0}/\Delta v$ is ${10}^{15}-{10}^{19}$ cm-2 (km s-1)-1 and in $n_{H_2}$ is ${10}^2-{10}^6$  cm-3, both in steps of 0.1 dex. In our calculations, we initially assumed $\Delta v=$1 km s-1, but later converted the constrained $N_{C^0}/\Delta v$ and $N_{\mathrm{CO}}/\Delta v$ to total C0 and CO column density by multiplying by the line FWHM resulting from the Gaussian fit in each velocity component. For velocity components where the lines in the numerator of the line ratios are not detected but those in the denominator are, we use the 3$\sigma$ upper limits of the lines in the numerator to calculate line ratios which are used to discard solutions in the RADEX grids (Figure 9). In Table 5, we summarize the physical parameters derived in the LMC and SMC. We only list velocity components where the [C ii] line is detected. We quantified how a RADEX model $M$($T_{\mathrm{kin}}$, $N_{C^0}/\Delta v$, $n_{H_2}$) reproduces a given line ratio $R$ with uncertainty ${\sigma }_R$ by calculating ${\chi }_R^2={\sum }_i{\left(R-M_i\right)}^2/{\sigma }_R^2$ over the entire model grid. We later added the resulting ${\chi }_R^2$ for all line ratios available in a given velocity component to determine a total ${\chi }_{\mathrm{total}}^2$. We then identified the best matching model by searching for the minimum ${\chi }_{\mathrm{total}}^2$ in the model grid, ${\chi }_{\mathrm{total},\min }^2$. To determine the uncertainties in the derived parameters, we defined a region in the parameter space where models have a ${\chi }_{\mathrm{total}}^2$ that is within three times the minimum ${\chi }_{\mathrm{total},\min }^2$. We then determined the range of possible values of a given parameter within this region when the other two are fixed. For well constrained models, ${\chi }_{\mathrm{total},\min }^2$ can be very small and the adjacent models in the parameter space often have ${\chi }_{\mathrm{total}}^2$ that are higher than $3{\chi }_{\mathrm{total},\min }^2$. In this case the accuracy in which a model parameter can be determined is given by the step size of the model grid. We studied the effect of beam dilution in the line ratios used our analysis in Appendix LABEL:sec:beam-dilut-corr. Note that we do not correct the line ratios for beam dilution effects in our analysis, due to the uncertainties of whether dust continuum emission traces the distribution of gas. In Table 6, we present the effect of beam dilution in the line ratios that are calculated using observations at different angular resolutions. We find that these line ratios typically show a 10% variation. This small variation suggest that the observed structures are relatively extended at the resolution of our observations. In Table 7, we summarize the impact of the variation in the line ratios due to beam dilution in the derived physical properties of the C0 and CO layers. The kinetic temperature, column density, and filling factor of the C0 and CO layers are typically affected by factors between 1.1 to 1.6. The largest impact of the variation in the line ratios is in the derived H2 volume density with variations between 1.5 and 4. Note that the largest variation we see, in the resulting H2 volume density of CO gas in the LMC, is dominated by three sources, PDR4_RIDGE_1, PDR3_NW, and NT77, which vary by factors of 25, 8, and 8, respectively. Without these three sources we find typical variations of a factor 1.6 for $n_{H_2}^{\mathrm{CO}}$ in the LMC.

Equations

$$I_{[\mathrm{C}\mathrm{II}]}=I_{[\mathrm{C}\mathrm{II}]}^{{\mathrm{H}}^0}+I_{[\mathrm{C}\mathrm{II}]}^{{\mathrm{H}}_2}+I_{[\mathrm{C}\mathrm{II}]}^{{\mathrm{e}}^{-}}.$$

$$\begin{gathered} I_{[\mathrm{CII}]}= \\ {N}_{{\mathrm{C}}^{+}}{\left[3.05\times 10^{15}\left(1+0.5\left(1+\frac{A_{ul}}{R_{ul}n}\right)e^{\frac{91.21}{T_{\mathrm{kin}}}}\right)\right]}^{-1}, \end{gathered}$$

$$EM=\int n_e^{2}dl.$$

$$EM=⟨n_e⟩N_e\simeq ⟨n_e⟩N_{{\mathrm{H}}^{+}}.$$

$$\left(\frac{EM}{{\mathrm{pc}\mathrm{cm}}^{-6}}\right)=2.75{\left(\frac{T_{\mathrm{kin}}}{10^4\mathrm{K}}\right)}^{0.9}\left(\frac{I_{\mathrm{H}\alpha }}{\mathrm{R}}\right).$$

$$I_{[\mathrm{CII}]}^{e^{-}}=n_e{N}_{{\mathrm{C}}^{+}}{\left[1.52\times 10^{15}{n}_{\mathrm{cr}}{e}^{\frac{91.21}{T_{\mathrm{kin}}}}\right]}^{-1}.$$

$$I_{[\mathrm{CII}]}^{e^{-}}=X_{{\mathrm{C}}^{+}}EM{\left[1.52\times 10^{15}{n}_{\mathrm{cr}}{e}^{\frac{91.21}{T_{\mathrm{kin}}}}\right]}^{-1},$$

$${\tau }_{160\mu \mathrm{m}}=\frac{I_{160\mu \mathrm{m}}}{B_{\nu }(T_{\mathrm{dust}},160\mu \mathrm{m})},$$

$$N({\mathrm{C}}^{+}{)}_{\mathrm{total}}=N({\mathrm{C}}^{+}{)}_{{\mathrm{H}}^0}+N({\mathrm{C}}^{+}{)}_{{\mathrm{H}}_2}+N({\mathrm{C}}^{+}{)}_{{\mathrm{e}}^{-}}.$$

$$A_{\mathrm{V}}^{\mathrm{total}}=A_{\mathrm{V}}^{{\mathrm{H}}_2}+A_{\mathrm{V}}^{{\mathrm{H}}^0,\mathrm{CNM}}+A_{\mathrm{V}}^{{\mathrm{H}}^0,\mathrm{WNM}}+A_{\mathrm{V}}^{{\mathrm{H}}^{+}}.$$

$$p_{\mathrm{th}}/k_{\mathrm{B}}=n_{\mathrm{H}}{T}_{\mathrm{kin}}^{{\mathrm{H}}^0}=n_{{\mathrm{H}}_2}{T}_{\mathrm{kin}}^{{\mathrm{H}}_2}.$$

Full text

††slugcomment: To appear in the Astrophysical Journal

1. Introduction

Understanding the life cycle of the interstellar medium in galaxies is a primary goal in the study of galaxy evolution and star formation. The formation of molecular clouds, their subsequent evolution to initiate star formation, and the radiative and mechanical feedback of stars into their progenitor molecular gas that terminates or reignites star formation are fundamental aspects determining how galaxies evolve over cosmic time. Most of the star formation at early cosmological times took place in environments with reduced gas metallicity and dust–to–gas ratio. With the implementation of ALMA it is now possible to study a large number of high–redshift systems (e.g. Carilli2013). To interpret these observations of poorly resolved high redshift galaxies it is necessary to understand local templates of the low–metallicity interstellar medium (ISM), that can be spatially and spectrally resolved in a detail that is not achievable for distant galaxies.

The best local templates for studying the life cycle of the ISM and star formation in low–metallicity environments are the Large and Small Magellanic clouds (LMC; $Z$=0.5 Z*⊙* and SMC, $Z$=0.2 Z*⊙*; Westerlund97). Due to their proximity (LMC: $D=50$ kpc; SMC: $D=60$ kpc; Schaefer2008; Hilditch2005), the Magellanic clouds provide a unique opportunity to resolve individual clouds, allowing us to conduct detailed studies of the different phases of the ISM in low–metallicity environments using various gas and dust tracers.

The interstellar medium plays the critical role of fueling star formation in galaxies. Obtaining a complete census of the mass of the different phases of the interstellar medium is thus key for understanding star formation and its effect in the evolution of galaxies. Traditionally, the distribution of the ISM phases in galactic disks has been studied in H$\alpha$ or radio continuum emission to trace the ionized gas (e.g. Haffner2009), in the H i 21 cm line which traces atomic gas (e.g. Kalberla2009), and in the CO line to trace shielded molecular gas (e.g. Heyer2015). The total dust mass of the interstellar medium has been traced by modeling the spectral energy distribution of dust continuum, but the conversion from dust mass to hydrogen mass is often complicated by finding appropriate values for the dust to gas ratio, dust emissivity and dust temperature, parameters that can vary with environmental conditions (Roman-Duval2014). We lack, however, observations of very important ISM phases constituting the transition between diffuse atomic clouds and dense molecular clouds. This missing link between diffuse atomic and dense molecular gas can be isolated and characterized with observations of the [C ii] 158 $\mu$m line that traces the diffuse ionized medium, warm and cold atomic clouds, clouds in transition from atomic to molecular form, and dense and warm photon dominated regions (PDRs). In particular, the [C ii] line is a tracer of the CO–dark H2 gas (Madden1997; Grenier2005; Wolfire2010; Langer2010; Langer2014a), which is gas in which hydrogen is molecular but carbon is ionized and thus not traced by CO but by [C ii]. The CO–dark H2 gas represents $\sim$30% of the molecular mass of the Milky Way and this fraction increases with galactocentric distance, which is an effect of the metallicity gradient of the Galaxy (Pineda2013).

The reduced dust–to–gas ratio and lower abundance of species responsible for gas cooling (e.g. C and O) in metal poor environments impacts the relative distributions of different ISM phases and their thermal balance. In low dust–to–gas ratio environments, the dust column density required to form enough H2 to self–shield efficiently against photo–destruction, enabling the transition from atomic to molecular gas, is achieved at larger gas column densities compared with larger dust–to–gas ratio environments (e.g. Gnedin2009; Krumholz2009; Sternberg2014). Additionally, due to the reduced attenuation of FUV photons by dust in low metallicity gas, the CO molecule is more readily photo–dissociated pushing the C+/C0/CO transition to higher molecular hydrogen column densities compared to higher metallicity systems (vanDishBlack88). This effect results in an enhanced CO–to–H2 conversion factor in the Magellanic Clouds (Cohen88; Rubio91; Israel97; Israel2000; Bolatto2013). Observations of the distribution of [C ii], [C i], and CO line emission in the Magellanic clouds are thus important tools for studying how metallicity affects the properties of the different phases of the interstellar medium.

The [C ii] line has been imaged in the entire Large Magellanic cloud with the BICE balloon by Mochizuki1994, with 15′ angular resolution and 175 km s*-1* velocity resolution. These observations showed an enhanced [C ii]/CO ratio compared with the Milky Way and that [C ii] constitutes about 1.32% of the far–infrared luminosity of the LMC (Rubin2009). A handful of star forming regions in the LMC and SMC have been studied with the Kuiper Airborne Observatory both with low (Poglitsch95; Israel96; Israel2011) and with high (Boreiko91) velocity resolution observations. The 30 Doradus region in the LMC has been studied in detail with the PACS instrument on Herschel (Chevance2016). High velocity resolution [C ii] images of H ii regions in the LMC and SMC are starting to become available using SOFIA (Okada2015; Requena-Torres2016).

The [C ii] 158 $\mu$m, [C i] 609 $\mu$m and 370 $\mu$m fine structure, and 12CO and 13CO rotational, transitions are diagnostics of the physical conditions of PDRs (e.g. Kim2006; Minamidani2007; Minamidani2011; Pineda2008; Pineda2012; Okada2015; Lee2016; Chevance2016). When compared with predictions from PDR models, the [C ii] line constrains the strength of the FUV field and volume density. The excitation of the [C i] 609 $\mu$m and 370 $\mu$m lines can give independent estimates of the kinetic temperature and H2 volume density (Stutzki1997). The ionized gas component can be characterized with the [N ii] 122 and 205 $\mu$m fine structure line emission (Goldsmith2015, Langer2016) as well as with hydrogen recombination lines and free–free continuum emission in the cm wavelength regime. Characterizing the physical conditions of the gas is key for our understanding to the origin of the [C ii] emission in the Magellanic clouds and will have implications in the interpretation of observations of distant galaxies.

In this paper we present deep observations of the [C ii] 158 $\mu$m, [C i] 609 $\mu$m, [C i] 370 $\mu$m, and 12CO $J=7\to 6$ lines towards 54 LMC and SMC lines-of-sight (LOS). These data were obtained using the HIFI (deGraauw2010) instrument onboard the Herschel Space Observatory111Herschel is an ESA space observatory with science instruments provided by European-led Principal Investigator consortia and with important participation from NASA. (Pilbratt2010). We complement this data set with observations of the $J=1\to 0$ and $J=3\to 2$ transitions of 12CO and 13CO from the Mopra and APEX telescopes, respectively. We base our target selection on maps of H i, 160 $\mu$m dust continuum emission, and CO emission as well as on results from the FUSE survey of H2 absorption towards the Magellanic Clouds (Cartledge2005). The targets are distributed throughout the LMC and SMC in order to study spatial variations of the properties of their ISM. By studying clouds with different physical conditions we aim to determine the key factors that characterize the evolution of the interstellar matter in the Magellanic clouds.

This paper is organized as follows. In Section 2 we describe our sample selection and observations. We discuss the determination of the contributions of the different phases of the interstellar medium to the observed [C ii] emission in Section 3 and we estimate in Section 4 the physical parameters of different ISM components. In Section LABEL:sec:discussion, we study the H0 to H2 as well as the C+/C0/CO transitions in the LMC and SMC. We also discuss the CO–to–H2 conversion factor, the relationship between [C ii] and far–infrared dust emission in our sample, and we compare our single dish observations with pencil beam FUV and optical studies to characterize the substructure of the ISM in the Magellanic clouds. We present our conclusions in Section LABEL:sec:conclusions.

2. Sample Selection and Observations

2.1. Sample Selection

To characterize the transition from diffuse atomic to dense molecular clouds in the Magellanic clouds we need to study many different clouds having different physical conditions in their low metallicity environments. Therefore our work results in statistical properties of the sample of clouds rather than full understanding of an individual region. This strategy also allows us to search for locations that could be followed up with current or future observatories (e.g. SOFIA, STO2).

Our sample consists of 36 LOSs in the LMC and 18 in the SMC. We show the locations used in our analysis in Figure 1. The locations of our LOSs were selected to be as uniformly distributed as possible over the LMC and SMC, and they do not necessarily represent the brightest emission peaks in these galaxies. We present sample spectra representing diffuse and dense photon dominated regions (PDRs) in Figure 2. The full spectral line data set used in this paper including images of the spectra in each LOS is available as a Herschel User Provided Data Product222http://www.cosmos.esa.int/web/herschel/user-

provided-data-products . In Table 1 and 2, we show the observational parameters in our sample, including H2 column densities and molecular fractions derived in our analysis and discussed in Section LABEL:sec:h-h_2-transition. By fitting Gaussians to the observed [C ii], [C i], and CO spectra we identified 49 velocity components in the LMC and 28 velocity components in the SMC. We show the integrated intensities of the spectral lines detected in our survey in Table 3 for the LMC and in Table 4 for the SMC.

Our selection of positions to sample was initially based on H i (LMC; Kim2003, SMC; Stanimirovic1999) and CO (LMC; Wong2011, SMC; Muller2010; Rubio93) maps of the LMC and SMC. In the case of the LMC, we also used Spitzer 160 $\mu$m continuum emission (Meixner06)333The 160 $\mu$m continuum map, used as a proxy for higher column density, warmer gas, was only available for the LMC when the sample was originally selected.. We included 7 H i peaks in both the LMC and SMC that have faint or no associated CO line emission or, in the case of the LMC, 160 $\mu$m continuum. These peaks represent atomic hydrogen–dominated LOSs. We also included 12 H i peaks in the LMC that are associated with 160 $\mu$m continuum emission but are undetected in the CO maps. This sample is likely tracing clouds that are in transition from diffuse molecular to dense molecular clouds. We also included 10 CO peaks in the LMC and 7 in the SMC representing regions that have enough column density to show CO emission. They might still have a large fraction of H2 gas traced by [C ii] if they are clumpy and the volume filling factor of CO cores is low. Finally, our sample also includes 8 lines–of–sight in the LMC and 3 in the SMC studied in UV absorption with FUSE by Cartledge2005. With these sources we have a priori knowledge of the H2 column density, and thus they can be used to compare with our determination of the H2 column densities from spectral line data.

We studied whether the physical conditions derived in our sample are representative of the average conditions in the LMC and SMC. For that purpose, we compared the ratio of the total far–infrared intensity (TIR; Section LABEL:sec:relat-betw-c) to the H0 column density (Section 3.2) as a function of the visual extinction in our sample with that derived in maps over the entire LMC and SMC. In Figure 3, we show the TIR/$N$(H0) ratio as a function of $A_{\rm V}$ for both the entire LMC and SMC and for the locations of our sample. The color scale in Figure 3 represents the number of pixels at a given TIR/$N$(H0) and $A_{\rm V}$ bin, with contour lines representing 2, 10, 100, and 1000 pixels. The TIR/$N$(H0) ratio is an approximate measure of the FUV radiation field per unit hydrogen atom, and therefore it is sensitive to how closely a LOS is associated with star formation, while the $A_{\rm V}$ is a measure of the total column density. Thus, a diffuse LOS away from star formation would be in the lower left corner of the plot, while a warm and dense photon dominated region close to newly formed stars would be in the upper right corner of the plot. The TIR and $A_{\rm V}$ maps used here were smoothed to 60″ to match the resolution of the H i data. The bulk of the LOSs have TIR/$N$(H0) $\simeq 10^{-25}-10^{-23}$ erg s*-1* sr*-1* and $A_{\rm V}\lesssim 2$ mag in the LMC, and $\simeq 10^{-25.5}-10^{-24.5}$ erg s*-1* sr*-1* and $\lesssim 0.5$ mag in the SMC. In the LMC, a large fraction (90%) of our sample have TIR/$N$(H0) and $A_{\rm V}$ values that are similar to those of the bulk of the pixels in this galaxy. This correspondence suggests that the properties derived in our sample are representative of the average properties in the LMC. There are four LOSs that have larger TIR/$N$(H0) and $A_{\rm V}$ values, corresponding to CO peaks associated with dense photon dominated regions, which represent a small volume fraction in the LMC. In the SMC, half the LOSs have conditions that are similar to the bulk of the pixels in this galaxy while the other half tend to have larger values of TIR/$N$(H0) and $A_{\rm V}$. However, most of the [C ii] emission is detected in the latter half of the sample. Thus, the conditions derived in our sample in the SMC might represent those of more active regions compared with the bulk of the SMC.

2.2. [C ii] and [C i] observations

We surveyed the Magellanic Clouds in the [C i] 3P1–3P0, [C i] ${}^{3}{\rm P}_{2}-^{3}$P1, and [C ii] 2P${}_{3/2}-^{2}$P1/2 fine–structure lines at 492.1607 GHz, 809.3420 GHz, and 1900.5469 GHz (rest frequency), respectively, with the HIFI (deGraauw2010) instrument aboard the Herschel Space Observatory (Pilbratt2010). These observations are part of the Herschel Open Time 1 Project OT1_jpineda_1. The 12CO $J=7\to 6$ (806.6518 GHz) rotational line was observed simultaneously with the [C i] 3P2–3P1 line. There are 9 LOS where only the 12CO $J=7\to 6$ was observed due to an error in the frequency configuration. These LOS correspond to diffuse LOS where the [C i] 3P1–3P0 line was not detected and therefore we do not expect a detection of the usually weaker [C i] 3P2–3P1 line.

The [C ii] 1.9 THz observations were carried out with the HIFI Band 7b receiver, which is employs Hot Electron Bolometer (HEB) mixers, in the LoadChop with reference observing mode. The HEB bands in HIFI show prominent electrical standing waves that are produced between the HEB mixing element and the first low noise amplifier. The standing wave shape is not a standard sinusoid and is difficult to remove from the resulting spectrum using standard fitting methods (Higgins2009). To remove these standing waves we used a procedure available in HIPE (Ott2006) version 12, which uses a library of standing wave shapes to find the best fit to correct the observed spectrum (see Higgins2011 for a detailed description of this method). In HIPE we also removed residual standing waves by fitting a single sinusoidal function using the FitHIFIFringe() procedure. After all standing waves are removed, we exported our data to the CLASS90444http://www.iram.fr/IRAMFR/GILDAS data analysis software, which we used to combine the two polarization, fit the data with polynomial baselines (typically of order 3), and smooth in velocity.

The angular resolution of the [C ii] observations is 12″. We divided the data by a factor of 0.61 to transform the data from an antenna temperature to a main-beam temperature scale555The beam efficiencies of all HIFI bands are presented in http://herschel.esac.esa.int/twiki/pub/Public/

HifiCalibrationWeb/HifiBeamReleaseNote_Sep2014.pdf. The data were produced by the wide band spectrometer (WBS), which has a channel width of 1 MHz (0.16 km s*-1* at 1.9 THz). We later smoothed the data to a resolution of 0.8 km s*-1*. For this resolution the average rms noise of our data is666 For the typical [C ii] FWHM line width of about 3 km s*-1*, this sensitivity limit corresponds to $1.1\times 10^{-6}$ erg s*-1* cm*-2* sr*-1*. The integrated intensity in units of K km s*-1* can be converted that in units of erg s*-1* cm*-2* sr*-1* using $I$[K km s*-1*]=1.43\times 10^{5}$$I[erg s*-1* cm*-2* sr*-1*] (Goldsmith2012). 0.1 K.

We observed the [C i] 3P1--3P0 line using HIFI Band 1, while the [C i] 3P2--3P1 and 12CO $J=7\to 6$ lines were observed simultaneously using HIFI Band 3. The angular resolutions are 44″ and 26.5″ for Bands 1 and 3, respectively. We applied main-beam efficiencies of 0.651 and 0.645, respectively, to convert these data from an antenna temperature to a main-beam temperature scale. The typical rms noise for the [C i] 3P1--3P0 line was 0.035 K in a 0.91 km s*-1* channel width. For the [C i] 3P2--3P1 and 12CO $J=7\to 6$ lines the typical rms noise was 0.02 K in a 1.1 km s*-1* channel width.

2.3. CO observations

To complement the Herschel data, we observed the $J=1\to 0$ transitions of 12CO, 13CO, and C18O with the ATNF Mopra777The Mopra radio telescope is part of the Australia Telescope which is funded by the Commonwealth of Australia for operation as a National Facility managed by CSIRO. Telescope (project M580). The Mopra 22m telescope has an angular resolution of 33″ at 115 GHz. Typical system temperatures were 600, 300, and 250 K for 12CO, 13CO, and C18O, respectively. To convert from antenna to main--beam temperature scale, we used a main-beam efficiency of 0.42 (Ladd05). All lines were observed simultaneously with the MOPS spectrometer in zoom mode. The spectra were smoothed in velocity to 0.87 km s*-1* for 12CO and to 0.91 km s*-1* for 13CO. The typical rms noise is 0.06 K for 12CO and 0.05 K for 13CO. The C18O line was detected only in a small number of LOSs, and we will not use these observations in the present analysis. We checked pointing accuracy every 60 minutes using a nearby SiO maser.

We used the APEX888This publication is based in part on data acquired with the Atacama Pathfinder Experiment (APEX). APEX is a collaboration between the Max-Planck-Institut für Radioastronomie, the European Southern Observatory, and the Onsala Space Observatory 12m telescope (Guesten2006) to observe the 12CO $J=3\to 2$ and 13CO $J=3\to 2$ lines in 25 LOS in the LMC and SMC that have been detected in our low--$J$ observations (project M0036_93). The angular resolution of the APEX telescope is 17.5″ at 345 GHz. We converted from antenna to main--beam temperature scale using an efficiency of 0.69 for 345 GHz. The typical rms noise in the 12CO $J=3\to 2$ data is 0.08 K for a 0.33 km s*-1* channel width and in the 13CO $J=3\to 2$ data is 0.05 K for a 0.33 km s*-1* channel width.

2.4. H i, H$\alpha$, H66$\alpha$, and Dust Continuum data

We used the H i 21 cm maps of the entire LMC and SMC presented by Kim2003 and Stanimirovic1999 (see also Staveley-Smith2003), respectively. These maps of the Magellanic clouds were made by combining interferometric (ATCA) and single dish (Parkes) observations. The map of the LMC has an angular resolution of 60″, corresponding to a spatial resolution of 15 pc, while the SMC map has an angular resolution of 98″ corresponding to a spatial scale of 29 pc. The rms noise in the LMC map is 2.4 K in a 1.65 km s*-1* channel width and in the SMC map is 1.3 K over a 1.65 km s*-1* channel width.

To estimate the contribution to the [C ii] emission from ionized gas, we used the H$\alpha$ map from Southern Halpha Sky Survey Atlas survey (SHASSA; Gaustad2001). The SHASSA maps cover the entire LMC and SMC with an angular resolution of 48″ and a sensitivity level of 0.5 Rayleigh (R=$10^{6}$/4$\pi$ photons cm*-2*  s*-1* sr*-1*). We also used the NASA 70--m Deep Space Network telescope (DSS--43) to observe the H66$\alpha$ hydrogen radio recombination line at 22.364 GHz in one of our sources with the aim to test the effect of dust extinction on the H$\alpha$ observations. The angular resolution of the DSS--43 at 22.364 GHz is 48″. We converted the data from an antenna temperature to a main beam temperature scale using a main--beam efficiency of 0.50. The H66$\alpha$ spectrum has a rms noise of 5.4 mK in a 3.5 km s*-1* channel width.

We also compared our Herschel spectral line observations with dust continuum maps of the LMC and SMC taken using the PACS and SPIRE instruments on Herschel. These maps are part of the HERITAGE survey (Meixner2013) which provides images at 100 $\mu$m, 160 $\mu$m (PACS), 250 $\mu$m, and 350 $\mu$m, and 500 $\mu$m (SPIRE). The angular resolution of these maps are 7.7″ (100 $\mu$m), 12″ (160 $\mu$m), 18″ (250 $\mu$m), 25″ (350 $\mu$m), and 40″ (500 $\mu$m). The foreground dust emission originating from the Milky Way was subtracted using a linear baseline (Meixner2013). We also used the Spitzer 24 $\mu$m MIPS maps observed as part of the SAGE survey (Meixner06) and has an angular resolution of 6″.

2.5. Angular Resolution

The analysis presented in this paper uses a multi--wavelength data set from different telescopes. Therefore, the angular resolution of the observations is not uniform. While maps can be convolved to a uniform resolution, this is not the case for pointed [C ii], [C i], and CO observations, with angular resolutions ranging from 12″ for [C ii] and 60″ for H i. Therefore, absolute intensities and line ratios used in our analysis can be affected by beam dilution effects.

We studied the effect of beam dilution in our observations by smoothing the 12″ angular resolution 160 $\mu$m HERITAGE dust continuum map, which is assumed to be a proxy for the distribution of gas in the LMC and SMC. We then compared the resulting intensities at different angular resolutions. In the case of ionized gas traced by H$\alpha$ observations, we used the Spitzer 24 $\mu$m images of the Magellanic clouds which is a proxy for hot dust emission associated with ionized gas. Details of this study are presented in Appendix LABEL:sec:beam-dilut-corr. The effects of beam dilution in our results will be discussed as they are presented throughout the paper. In general, we find that beam dilution has a minor effect in our results for most of our sample, with the exception of a handful of point--like, unresolved PDR sources. Note that the data used in our analysis is not corrected for beam dilution effects, due to the uncertainty on whether the 24 $\mu$m or 160 $\mu$m are good tracers of the ionized and neutral gas components, respectively.

3. The Origin of the [C ii] emission in the Magellanic Clouds

The observed [C ii] emission arises from gas associated with hydrogen in the form of H0, H2, and H+. In the latter gas component, the collisions are mainly with electrons due to their higher speeds, so we refer to it as $\mathrm{e^{-}}$ gas. Thus, the observed [C ii] emission is given by,

[TABLE]

For optically thin emission, the [C ii] intensity (in units of K km s*-1*) is related to the C+ column density, $N_{\rm C^{+}}$ (cm*-2*), and volume density of the collisional partner (assumed to be uniform along the line of sight), $n$ (e-, H0, or H2; cm*-3*), as (see e.g. Goldsmith2012)

[TABLE]

where $A_{ul}=2.3\times 10^{-6}$ s*-1* is the Einstein spontaneous decay rate and $R_{ul}$ is the collisional de--excitation rate coefficient at a kinetic temperature $T_{\rm kin}$, with $u$ and $l$ denoting the upper and lower energy levels. Values of $R_{ul}$ for collisions with H0, H2, and $e^{-}$ as a function of the kinetic temperature are available from Barinovs2005, Wiesenfeld2014, and Wilson2002, respectively. For example, at $T_{\rm kin}=100$ K, $R_{ul}=7.58\times 10^{-10}$ and $5.12\times 10^{-10}$ cm3 s*-1* for collisions with atomic and molecular hydrogen999Assuming an ortho–to–para H2 ratio, OPR=1. See discussion in Wiesenfeld2014., respectively, while at $T_{\rm kin}=8000$ K, $R_{ul}=5.2\times 10^{-8}$ cm3 s*-1* for collisions with electrons.

Dufour1982 studied the carbon abundance in H ii regions in the Magellanic clouds deriving 12+log(C/H)=7.9 for the LMC and 12+log(C/H)=7.16 for the SMC. Relative to the gas--phase carbon fractional abundance of [C/H]=1.4$\times 10^{-4}$ determined in the Milky Way (Sofia1997), the carbon abundances in the LMC and SMC are 1.8 and 10 times lower, respectively. We used the fractional carbon abundances derived by Dufour1982 in the analysis presented here.

In the following we study the relative contribution to the observed [C ii] emission from ionized, atomic, and molecular gas. In Figure 4 we show an example of the decomposition of the [C ii] emission originating from different ISM components. The derived [C ii] emission fractions as a function of the observed [C ii] intensity for the entire sample are summarized in Figure 5.

3.1. Ionized gas

We estimated the [C ii] intensity originating from ionized gas ($\mathrm{e^{-}}$ gas) using the Southern Halpha Sky Survey Atlas survey (SHASSA; Gaustad2001) H$\alpha$ emission maps of the LMC and SMC. A commonly defined quantity used to relate the properties of the ionized gas and the observed H$\alpha$ emission is the emission measure (EM), defined as the integral of the electron volume density squared along the line of sight,

[TABLE]

Assuming that the electron density is constant along the line of sight, this equation can be simplified to

[TABLE]

The emission measure is related to the intensity of the H$\alpha$ line, in units of Rayleigh (R), as (e.g. Reynolds1991)

[TABLE]

The critical density, $n_{\rm cr}\equiv A_{\rm ul}/R_{\rm ul}$, is the density at which the collisional de--excitation rate is equal to the effective spontaneous decay rate, and for collisions of C+ with electrons at $T_{\rm kin}=8000$ K is equal to 44 cm*-3*. For electron densities much smaller than the critical density $n_{e}\ll n_{\rm cr}$, Equation (2) can be written as

[TABLE]

The term $n_{e}N_{{\rm C}^{+}}$ can be written in terms of the fractional abundance of ionized carbon, $X_{\rm C^{+}}=N_{\rm C^{+}}/N_{\rm H^{+}}$, as $X_{\rm C^{+}}n_{e}N_{{\rm H}^{+}}=X_{\rm C^{+}}EM$. Paradis2011 estimated typical electron densities for regions emitting different regimes of H$\alpha$ emission. For the range of H$\alpha$ intensities in our sample, electron densities vary from 0.05 to 3.98 cm*-3*, thus validating the assumption that $n_{e}\ll n_{\rm cr}$. Equation (6) can thus be rewritten in terms of the emission measure as,

[TABLE]

and can be used to estimate the contribution of ionized gas to the observed [C ii] emission from H$\alpha$ observations.

In Figure 5, we show the fraction of the [C ii] emission we estimate arises from ionized gas as a function of the observed [C ii] emission in the LMC and SMC. We assumed $T_{\rm kin}=8000$ K for the kinetic temperature of the ionized gas. In LOSs with multiple velocity components, we assumed that each component contributes equally to the derived [C ii] emission from ionized gas, as suggested by the H$66\alpha$ spectrum in Figure 6 that shows two [C ii] velocity components with varying peak intensities but uniform recombination line emission. We find that ionized gas tends to contribute a small fraction of the [C ii] emission, with typical fractions around 19% in the LMC and 5% in the SMC. These contributions from ionized gas to the observed [C ii] emission are in agreement with those estimated using the unobscured [N ii] fine structure lines by Chevance2016 and Okada2015 in the 30 Dor and N159 regions in the LMC, respectively, and by Requena-Torres2016 in several star forming regions in the SMC. The derived contributions from ionized gas to the observed [C ii] emission in the LMC and SMC are also consistent with those estimated in the Galactic plane (Pineda2013).

We estimated the H+ column density in our LOSs using $EM=n_{e}N_{{\rm H}^{+}}$ and the volume densities of the ionized gas suggested by Paradis2011 for different ranges of H$\alpha$ emission. Typical H+ column densities in our sample are $10^{20.8\pm 0.35}$ cm*-2* for the LMC and $10^{20.5\pm 0.14}$ cm*-2* for the SMC.

Note that the H$\alpha$ emission used here might be affected by extinction from dust grains making our estimate of the emission measure from H$\alpha$ observations a lower limit. We tested the effect of dust extinction in the H$\alpha$ observations by assuming that half of the visual extinction ($A_{\rm H\alpha}=0.81A_{\rm V}$, e.g. Viallefond1986; Parker1992) derived for each line--of--sight (Section 4.1) is in front of the H$\alpha$ sources. We find that the H$\alpha$ intensities would be underestimated by an average factor of 4.6 in the LMC and 1.4 in the SMC. In the LMC the large factor is dominated by three warm and dense PDRs, PDR4_RIDGE, PDR3_NW, and LMC_1_NW, which are bright in [C ii] and have the largest visual extinctions. Without these PDR regions, we find that the H$\alpha$ emission would be affected by a factor of 1.65 in the LMC. If a correction to the H$\alpha$ intensity for dust extinction is applied to the calculation of the contribution of ionized gas to the observed [C ii] emission, the fraction would increase by a similar factor. Note that for the warm and dense PDRs mentioned above, applying a correction to the contribution from ionized gas to the observed [C ii] emission would result in larger [C ii] intensities than observed, suggesting that less than $A_{\rm V}/2$ of extinction is in the foreground of these sources.

We tested the reliability of H$\alpha$ as a tracer of ionized gas by observing the unobscured H66$\alpha$ radio recombination line using the DSS--43 NASA Deep Space Network Telescope in one of our lines--of--sight (Figure 6). Following Alves2015, we converted the integrated intensity of the H66$\alpha$ line to the emission measure, assuming $T_{\rm kin}=8000$ K, to be 1.9$\times 10^{4}$ cm*-6* pc. For the same position we obtain $EM=7.8\times 10^{3}$ cm*-6* pc from H$\alpha$, a factor of $\sim$2.4 lower than that obtained from H66$\alpha$. The position we observed in H66$\alpha$ corresponds to a warm and dense photon dominated region likely associated with a large column of dust, so we expect a smaller effect in more diffuse regions in our sample.

3.2. Atomic Gas

We estimated the contribution from atomic gas to the observed [C ii] emission in our sample in the Magellanic Clouds using the H i 21 cm line observations. We calculated $N({\rm H^{0}})$ for each LOS, assuming optically thin emission, using $N({\rm H^{0}})=1.82\times 10^{18}I({\rm HI})$ cm*-2*, with $I({\rm HI})$ in units of ${\rm K\,km\,s^{-1}}$. We converted from $N({\rm H^{0}})$ to $N({\rm C^{+}})$ using the carbon fractional abundances of the LMC and SMC, assuming that all gas--phase carbon associated with atomic gas is in the form of C+.

We only considered H i emission that is associated in velocity space with [C ii] emission, and to calculate $I({\rm HI})$ we integrate the H i spectrum over a velocity range defined by the full width at half maximum (FWHM) of the [C ii] lines. Because the [C ii] emission is volume density sensitive for $n_{\rm H}<3000\,{\rm cm}^{-3}$, the critical density for collisions with H (Goldsmith2012), we expect that the [C ii] emission is associated with cold, dense H i (CNM;Wolfire2003) rather than diffuse, warm H i (WNM; see discussion in Pineda2013).) We therefore consider the H i emission that is associated in velocity with [C ii] to be CNM while the remaining H i emission is WNM. In the top panel of Figure 2, we illustrate this decomposition by showing the velocity range as a shaded region in which we assign H i to be CNM. Note that due to the typical complexity of the H i line profiles, it is difficult to separate reliably components in velocity for our entire data set.

Our method for calculating the H i column could be overestimating the column density of cold atomic hydrogen associated with [C ii] if a broad WNM component overlaps in velocity with the [C ii] emission. To quantify this effect, we attempted to fit multiple Gaussian components to the H i spectra of SMC_HI_4 and SMC_LIRS36 shown in Figure 2. For the Gaussian fitting, we fixed the LSR velocity of the [C ii] components (see Table 4) and left the peak main--beam temperature and line width as free parameters. We then subtracted all Gaussian components that are not associated with [C ii] to the observed spectra, in order to isolate the Gaussian component associated with [C ii]. In this component, we recalculated the integrated intensity by integrating over the velocity range defined by the FWHM of the [C ii] line, as above. We find that we would typically overestimate the H i intensity associated with CNM by a factor of about 2 in SMC_HI_4 and SMC_LIRS36. Note, however, that complex H i spectra such as those of SMC_HI_4 and SMC_LIRS36 are typically rare in our sample, and mostly correspond to SMC lines--of--sight. In the SMC there are 5 LOSs with such complexity out of 10 detected in [C ii]. In the LMC the H i spectra is mostly similar to those of Diff1_NW and PDR1_NW as shown in Figure 2.

To calculate the [C ii] intensity from atomic gas using Equation (2), we need to assume a gas volume density and a kinetic temperature. As discussed in Section 3.4, we adopted a kinetic temperature of $T_{\rm kin}=70$ K in the case of velocity components where H i and [C ii] are detected but 13CO $J=1\to 0$ and/or $J=3\to 2$ are not. In these LOSs, we were unable to determine the physical conditions of the C0 or CO layer. In LOSs with kinetic temperatures of the C0 and/or CO layers derived in the excitation analysis (Section LABEL:sec:c-sc-i), and with [C ii] and H i detected, we still assume 70 K if the kinetic temperature of the C0 layer is lower than 70 K. Otherwise, we assume the kinetic temperature of the C0 layer. The volume density is then derived by combining the kinetic temperatures with the thermal pressures of the diffuse ISM derived in Section 4.3.

In Figure 5, we show the fraction of the observed [C ii] emission from atomic gas as a function of the observed [C ii]. The contribution from atomic gas to the observed [C ii] emission shows a large scatter with average values of about 43% for the LMC and 28% for the SMC. These average contributions are consistent with the 20% contribution derived in the plane of the Milky Way by Pineda2013.

3.3. CO--dark H2 gas and dense Photon Dominated Regions (PDRs)

When we subtract the contribution from the ionized and atomic gas components to the observed total [C ii] emission, we typically find that there is residual [C ii] emission. This residual emission is produced in regions where carbon is ionized but hydrogen is molecular. The molecular hydrogen component where carbon is mainly ionized, so that it is traced by [C ii] and not by CO, is what we refer to as CO--dark H2 gas. The CO--dark H2 gas can either originate (1) from a diffuse cloud that has enough dust shielding to maintain only a trace amount of C0 and CO, thus with most of the carbon in the form of C+, or (2) from the envelopes of a warm and dense molecular cloud in which the inner parts have significant column densities of C0 and CO. In order to associate the observed [C ii] velocity components to either of these gas conditions, we use the detection limit of the 13CO lines observed in our survey to identify clouds that have enough shielding to maintain significant amounts of CO, and therefore are likely associated warm and dense molecular clouds with ongoing star formation. We assigned the [C ii] emission to warm and dense PDRs in velocity components with enough CO column density for the 13CO $J=1\to 0$ and/or 13CO $J=3\to 2$ lines to be detected. In LOSs where the 13CO lines are detected, we were able to perform an excitation analysis (Section 4.4) that confirms our assumption of warm and dense gas in these velocity components (see Table 5). In LOSs that are detected in [C ii] and H i, but not in 13CO $J=1\to 0$ and/or 13CO $J=3\to 2$, we assumed that the residual [C ii] emission arises from diffuse CO--dark H2 gas clouds. In LOSs associated with PDRs, the [C ii] emission from this ISM component tends to be brighter than the emission arising from other components, which is the result of the higher volume densities and temperatures of the gas. The typical contributions to the [C ii] emission associated with PDRs are 62% and 66% of the observed emission in LOS in the LMC and SMC, respectively. The fraction of the [C ii] emission arising from CO--dark H2 shows a large scatter, ranging from $\sim$10% to $\sim$80%. A similar range of CO--dark H2 fractions is found in clouds in the Milky Way (Langer2014a; Tang2016). This large scatter could be the result of clouds at different stages in the transition from diffuse to dense molecular gas, with clouds having varying fractions of CO--dark H2 gas.

Our separation between [C ii] from diffuse CO--dark H2 gas and from warm and dense PDRs is sensitive to our ability to detect the 13CO $J=1\to 0$ and/or 13CO $J=3\to 2$ lines. For the thermal pressure of the diffuse ISM in the LMC and SMC derived in Section 4.3 and a kinetic temperature of the CO--dark H2 of 49K (Section LABEL:sec:h-h_2-transition), we obtain $n$(H2)=694 cm*-3* in the LMC and 2040 cm*-3* in the SMC. For these conditions, the 13CO column density required for a $3\sigma$ detection of the 13CO $J=1\to 0$ and 13CO $J=3\to 2$ is 4$\times$1014 cm*-2* and 3$\times$1015 cm*-2* for the LMC and 4.5$\times$1014 cm*-2* and 1$\times$1015 cm*-2* of SMC, respectively.

3.4. Uncertainties

The main uncertainty in our decomposition originates from the assumption of the temperature of atomic and molecular gas. The assumed kinetic temperature is used in the derivation of thermal pressures (Section 4.3) and in the calculation of the contribution of atomic gas to the observed [C ii] emission. Observations of H i absorption against background continuum sources in the LMC and SMC suggest temperatures of the atomic gas as low as 10 K, with typical values of 30--40 K (Marx-Zimmer2000; Dickey2000). Note that H i absorption features are stronger the lower the kinetic temperature of the H i gas, thus there might be a systematic tendency to detect colder atomic gas in absorption. At these low temperatures, most of the gas--phase carbon is likely to be in the form of CO rather than in C+, as suggested by the detection of the 12CO $J=1\to 0$ line in several H i absorption sources in the LMC (Marx-Zimmer1999). While it is possible that the H i temperatures are lower in the Magellanic clouds compared with our Galaxy, we consider it unlikely that [C ii] will be detected for temperatures below 40 K, as the [C ii] intensity is significantly reduced for kinetic temperatures below this value. We therefore assume a temperature of 70 K for the atomic gas in our calculations, which is an intermediate value between the temperature derived from H i absorption in the Magellanic Clouds and the 100 K typically assumed in the Milky Way (Pineda2013). For the temperature of the H2 gas, we assume that $T^{\rm H_{2}}_{\rm kin}=0.7T^{\rm H^{0}}_{\rm kin}$, which is based on results in the Milky Way that suggest a temperature of 70 K for the CO--dark H2 layer (Goldsmith2013), and which is in agreement with PDR models calculations (e.g. Goldsmith2016). The temperature of the CO--dark H2 gas corresponds to 49 K for our assumed H i temperature of 70K.

We estimated the uncertainty associated with our H i and H2 kinetic temperature assumption by calculating the range in the [C ii] intensities associated with the different ISM phases resulting from assuming $T^{\rm H^{0}}_{\rm kin}=40$ K and $T^{\rm H^{0}}_{\rm kin}=100$ K in the LMC and $T^{\rm H^{0}}_{\rm kin}=55$ K and $T^{\rm H^{0}}_{\rm kin}=100$ K in the SMC. We used $T^{\rm H^{0}}_{\rm kin}=55$ K as a lower kinetic temperature limit in the SMC, as this is the lowest temperature where we could find solutions of the thermal pressure in the SMC (see Section 4.3). The derived uncertainties are shown as error bars in Figure 5.

Note that the assumed temperature of the CO--dark H2 gas is lower than the H2 rotational temperature in lines--of--sight compiled by Welty2012 in the LMC and SMC. These H2 temperatures range from 40 to 120 K, with average values of 85 K in both the LMC and SMC. This range corresponds, for our assumption of $T^{\rm H_{2}}_{\rm kin}=0.7T^{\rm H^{0}}_{\rm kin}$, to a range in H0 kinetic temperature between 57 and 170 K. However, the LOSs studied by Welty2012 have total hydrogen column densities that are much lower compared to the values derived in our survey (see Figure LABEL:fig:welty), and therefore are diffuse and likely warmer LOSs.

Another source of uncertainty originates from beam filling effects produced by the different angular resolution of our observations. The angular resolution of the data used in our [C ii] decomposition varies from 12″ for [C ii] to 60″ for H i. As described in Appendix LABEL:sec:beam-dilut-corr, we derived correction factors using the 160 $\mu$m map for [C ii] and H i, and the 24 $\mu$m continuum maps for the SHASSA observations. We estimate that the contribution from the different ISM phases to the observed [C ii] emission would change typically by 10%, 14%, 17%, and 16% for PDRs, CO--dark H2 gas, H i gas, and ionized gas in the LMC, respectively, and by 6%, 4%, 15%, and 8% for PDRs, CO--dark H2 gas, H i gas, and ionized gas in the SMC, respectively. In Figure LABEL:fig:contribution_dil, we present the fraction of [C ii] originating from different ISM phases as a function of the observed [C ii] intensity in the case when the intensities are corrected by beam dilution effects. We choose not to include the variation in the intensities due to beam filling factors in Figure 5 due to the uncertainty in whether the 24 $\mu$m and 160 $\mu$m emission represents the spatial distribution of the [C ii] associated with ionized and neutral gas, respectively.

4. Physical parameters

4.1. Determination of Visual Extinction

We used the Herschel HERITAGE (Meixner2013) dust continuum maps of the LMC and SMC to determine the dust column density, in terms of the visual extinction $A_{\rm V}$, in our sample. We assume that the dust spectral energy distribution (SED) in the LMC and SMC can be described by the emission predicted from an optically thin modified black body at an equilibrium temperature $T_{\rm dust}$. The dust opacity at 160 $\mu$m is given by

[TABLE]

where $I_{\rm 160\mu m}$ is the dust continuum intensity at 160 $\mu$m and $B_{\nu}(T_{\rm dust},{\rm 160\mu m})$ is the intensity of a black body with a temperature $T_{\rm dust}$ at 160 $\mu$m. We determined the opacity at 160 $\mu$m using the HERITAGE 160 $\mu$m map together with the dust temperatures fitted by Gordon2014 for a single temperature blackbody modified by a broken power-law emissivity, their preferred dust emission model. Both the 160 $\mu$m and dust temperature maps have a common resolution of 40″. The average ($\pm$ standard deviation) dust temperature is 22.8$\pm$4.1 K in the LMC and 23.1$\pm$2.5 K in the SMC.

Lee2015 presented maps of the visual extinction in the LMC and SMC derived from dust continuum emission. They converted the 160 $\mu$m opacity to $A_{\rm V}$ using, $A_{\rm V}=2200\tau_{\rm 160\mu m}$, which is the average of different methods to relate these quantities based on data in the Milky Way. (We refer the reader to their paper for more details on how this conversion factor is determined.) The different methods described in Lee2015 show a scatter from the adopted conversion factor between $A_{\rm V}$ and $\tau_{\rm 160\mu m}$ of about 40%, and we adopt this value as the uncertainty in our determination of $A_{\rm V}$.

We compared the values of $A_{\rm V}$ derived here with those presented by Lee2015 who derived the 160 $\mu$m opacity using the HERITAGE 160 $\mu$m map and dust temperatures determined by fitting a single temperature blackbody with an assumed $\beta=1.5$ wavelength dependence of the dust opacity. We find that our $A_{\rm V}$ values are in reasonable agreement with those derived by Lee2015, with differences typically within the assumed 40% uncertainty.

4.2. Dust-to-Gas ratio

The dust--to--gas ratio (DGR) is a fundamental parameter relating the quantities of gas and dust in the ISM of galaxies and the variation of the DGR as a function of environment reflects the evolution of galaxies (Dwek1998). In the following, we test our determination of gas column densities and visual extinctions in our sample by checking whether these two quantities are related by the DGRs that are typically found in the LMC and SMC. We initially test diffuse LOSs in our sample, but we will extend this comparison to our entire sample in Section LABEL:sec:h-h_2-transition to test our determination of H2 column densities.

The ratio of the total hydrogen column density, $N({\rm H})=N({\rm H^{+}})+N({\rm H^{0}})+2N({\rm H_{2})}$, to color excess, $E$(B-V), in the ISM of the Milky Way is $N({\rm H})$/$E$(B-V)=$5.8\times 10^{51}$ cm*-2* mag*-1* (Bohlin1978). Assuming a ratio of the total to selective extinction of $R_{\rm V}$=3.1, results in a relationship between the hydrogen column density and visual extinction of $N$(H)/$A_{\rm V}$=1.88$\times 10^{21}$ cm*-2* ${\rm mag}^{-1}$ in the Milky Way. In the LMC, $N({\rm H})$/$E$(B-V) is observed to be $2\times 10^{22}$ cm*-2* mag*-1* (Koornneef1982; Fitzpatrick1985), while in the SMC, $N({\rm H})$/$E$(B-V) ranges between $2.6\times 10^{22}$ cm*-2* mag*-1* (Martin1989) and $8.7\times 10^{22}$ cm*-2* mag*-1* (Fitzpatrick1985b). We adopt an intermediate value for the SMC of $6.6\times 10^{22}$ cm*-2* mag*-1*. Assuming $R_{\rm V}$=3.4 in the LMC and $R_{\rm V}$=2.7 in the SMC (Gordon2003), results in $N({\rm H})/A_{\rm V}$=$5.56\times 10^{21}$ cm*-2* mag*-1* for the LMC and $2.43\times 10^{22}$ cm*-2* mag*-1* for the SMC. Note that the value of $R_{\rm V}$ assumed here corresponds to that in diffuse regions, and it might be larger in denser regions (Weingartner2001; Whittet2001). Considering that a given line of sight might intersect both dense and diffuse regions, Whittet2001 estimated in the Milky Way an effective $R_{\rm V}$ along the line--of--sight that increases up to $\sim$4.0 for $A_{\rm V}\simeq$10 mag. Thus, the $N({\rm H})/A_{\rm V}$ ratio can be lower by up to $\sim$30% in denser LOSs.

We tested our estimate of the visual extinction by comparing $A_{\rm V}$ with $N({\rm H}^{+})$+$N({\rm H^{0}})$ in LOSs where [C ii] was not detected. These lines--of--sight (5 in the LMC and 7 in the SMC) likely have little or no H2 and/or have densities and temperatures that are insufficient for producing [C ii] emission that will be detectable in the sensitivity limits of our survey. They are therefore well suited for our comparison between visual extinctions and the H*+*+H0 column densities as they are likely to have a negligible or no contribution from dust associated with H2 to the observed $A_{\rm V}$. The H+ column densities for these LOSs were determined in Section 3.1 and on average represent 5% and 1.4% of the $N({\rm H}^{+})$+$N({\rm H^{0}})$ column densities in the LMC and SMC, respectively. The $A_{\rm V}$ and $N({\rm H^{+}})$ data points used here were derived from dust continuum and H$\alpha$ maps that were smoothed to the 60″ resolution of the H i data. In Figure 7, we show $N({\rm H}^{+})$+$N({\rm H^{0}})$ as a function of $A_{\rm V}$ for LOSs in our sample where the [C ii] was not detected. We also include in the plot straight lines that represent the predicted H++H0 column density for a given value of $A_{\rm V}$ using the dust--to--gas ratios for the LMC, SMC, and Milky Way discussed above. Given the uncertainties in the determination of $A_{\rm V}$, we consider that our derived values of $A_{\rm V}$ are consistent with the observed H i column densities and the independently measured gas--to--dust ratios in the LMC and SMC.

4.3. Thermal Pressures of the diffuse ISM in the Magellanic Clouds

The thermal pressure of the diffuse ISM is an important parameter which, despite being a small fraction of the total ISM pressure (Boulares1990), plays a fundamental role in the phase transition from warm and diffuse to cold and dense atomic gas (Pikelner1968; Field1969; Wolfire1995; Wolfire2003; Jenkins2011). Thus, studying the diffuse ISM thermal pressure is important for our understanding of molecular cloud formation and the regulation of star formation in galaxies (Mckee1989; Blitz2006; Ostriker2010).

In the Magellanic clouds the thermal pressure of the gas is expected to be larger than the solar neighborhood because of larger FUV fields and lower dust abundances, affecting the thermal balance (Wolfire et al. 2017 in preparation; Sandstrom2010; Welty2016). Bolatto2011 compared the relationship between gas surface density and star formation rate in the SMC and found that a thermal pressure $p_{\rm th}/k_{\rm B}=3\times 10^{4}$ K cm*-3* is required to find agreement between observations and the theoretical predictions from Ostriker2010.

An estimate of the thermal pressure of the diffuse ISM is also a requirement for the determination of the column density of the CO--dark H2 gas using [C ii] observations (Pineda2013). In the following we derive the thermal pressures of the diffuse ISM of the LMC and SMC by using LOSs where we detect H i and [C ii] but where no CO and/or [C i] is detected. These LOSs (14 in the LMC and 6 in the SMC) are likely diffuse and the [C ii] emission arises from both cold atomic and CO--dark H2 gas.

As discussed in Section 3, the observed [C ii] intensity is the sum of the emission associated with the ionized, atomic, and molecular gas components. For each LOS used here, we subtracted the [C ii] emission associated with ionized gas derived in Section 3.1. The remaining [C ii] intensity is thus described by six parameters (see Equation 2): the kinetic temperature ($T^{\rm H^{0}}_{\rm kin}$ and $T^{\rm H_{2}}_{\rm kin}$), volume density ($n_{\rm H^{0}}$ and $n_{\rm H_{2}}$), and C*+* column densities ($N({\rm C}^{+})_{\rm H^{0}}$ and $N({\rm C^{+}})_{\rm H_{2}})$ of gas associated with the H0 and H2 layers.

The total column density of C+ along the line of sight is the sum of the column of C+ associated with the different collisional partners,

[TABLE]

We used the H i 21 cm observations to determine the column density of atomic hydrogen that is associated in velocity with the observed [C ii] emission in Section 3.2 and the H+ column density associated with ionized gas in Section 3.1. The H0 and H+ column densities are in turn converted to a C+ column density by multiplying the carbon fractional abundances of the LMC and SMC discussed in Section 3.

To derive the column density of C+ associated with H2, we need an estimate of the total hydrogen column density along the line of sight. The visual extinction along the line--of--sight is the sum of that from dust associated with molecular hydrogen, with CNM and WNM atomic gas, and with ionized gas, so that

[TABLE]

We estimated $A^{\rm HI,CNM}_{\rm V}$ and $A^{\rm HI,WNM}_{\rm V}$ by converting the integrated intensities of H i associated (CNM) and not associated (WNM) to the observed [C ii] emission and applying the dust--to--gas ratios discussed in Section 4.2. The same dust--to--gas ratio was applied to the H+ column densities to estimate visual extinction associated with ionized gas. The visual extinction associated with H2 is then estimated by subtracting that associated with H0 and H+ to the observed value. We then converted $A_{\rm V}^{{\rm H}_{2}}$ to a H2 column density using a dust--to--gas ratio, and to $N({\rm C}^{+})_{\rm H_{2}}$ using a fractional abundance of carbon.

With an estimate of $N({\rm C}^{+})_{\rm H^{0}}$ and $N({\rm C}^{+})_{\rm H_{2}}$, the remaining parameters are the kinetic temperatures and volume densities of the molecular and cold atomic gas. We assumed that for the diffuse lines--of--sight where only H i and [C ii] are detected there is thermal pressure equilibrium in the interface between the cold H i and the CO--dark H2 layers,

[TABLE]

Assuming a kinetic temperature for the H i layer of 70 K and for the CO--dark H2 layer of 49 K (see discussion in Section 3.4), we searched for a thermal pressure that can reproduce the observed [C ii] intensity. Figure 8 shows histograms of the thermal pressures derived in the LMC and SMC. The average ($\pm$ standard deviation) thermal pressure is $p_{\rm th}/k_{\rm B}=10^{4.5\pm 0.3}$ K cm*-3* in the LMC and $p_{\rm th}/k_{\rm B}=10^{5.0\pm 0.2}$ K cm*-3* in the SMC. We note that components that are associated with the 30 Doradus nebula in the LMC tend to higher thermal pressures compared to those in other regions of the LMC. Without the LOSs associated with 30 Doradus, we find an average thermal pressure in the LMC of $p_{\rm th}/k_{\rm B}=10^{4.2\pm 0.1}$ K cm*-3* while LOSs associated with 30 Doradus have $p_{\rm th}/k_{\rm B}=10^{4.9\pm 0.2}$ K cm*-3*. These LOSs appear to be influenced by the feedback effects of the R136 super star cluster (Pellegrini2011). The average value for the SMC is in reasonable agreement with that suggested by Bolatto2011.

We tested the sensitivity of the derived thermal pressures to the assumed kinetic temperature of the gas. For low temperatures, the thermal pressure solutions become uncertain, as higher volume densities are needed to reproduce the observed emission, and collisional deexcitation become important, reducing the dependence of the [C ii] intensity on volume density (Goldsmith2012). In the LMC the thermal pressure increases by a factor of 1.2 between 100K and 70K and by a factor of 6 between 100 K and 40 K. In the SMC, we could not find reliable solutions for temperatures lower than 55 K. Between 100 K and 70 K, the thermal pressure increases by a factor of 1.5 and between 100 K and 55 K, by a factor of 3.5.

We also studied the effects of beam dilution in our determination of thermal pressures in the LMC and SMC. For that purpose, we smoothed the dust continuum data used to calculate $A_{\rm V}$, and the H$\alpha$ data used to estimate the contribution from ionized gas to the [C ii] emission, to the 60″ resolution of the H i data used to calculate $N({\rm H^{0}})$. We additionally corrected the observed [C ii] emission with the beam dilution factor we estimated in Appendix LABEL:sec:beam-dilut-corr to correspond to emission at 60″ resolution. We used this data to recalculate the thermal pressures in our sub--sample. We find that applying a beam dilution factor to the data used in our calculation results in thermal pressures that are reduced by factors of $\sim$1.4 in both the LMC and SMC.

We note that the statistical significance of our determination of the thermal pressure in the LMC and SMC is limited by the small number of LOSs we were able to use. Using the technique presented here in future large scale maps of the Magellanic Clouds in [C ii] will dramatically improve the significance of this result, and will allow us to compare the distribution of thermal pressures in the LMC and SMC with that in the Milky Way (Jenkins2011).

4.4. Kinetic temperatures and H2 Column and Volume

Densities