Kinetic temperature of massive star forming molecular clumps measured with formaldehyde. II. The Large Magellanic Cloud

TL;DR

This study measures the gas kinetic temperature in star-forming regions of the LMC using formaldehyde, revealing temperatures comparable to Galactic regions and linking them to star formation activity.

Contribution

First direct measurement of gas kinetic temperature in LMC star-forming regions using formaldehyde, overcoming nitrogen scarcity issues of traditional thermometers.

Findings

Gas temperatures range from 35 to 63 K, averaging 47 K.

Temperatures are consistent with Galactic star-forming regions.

Kinetic temperatures correlate with infrared luminosity and star formation indicators.

Abstract

The Large Magellanic Cloud (LMC), the closest star forming galaxy with low metallicity, provides an ideal laboratory to study star formation in such an environment. The classical dense molecular gas thermometer NH3 is rarely available in a low metallicity environment because of photoionization and a lack of nitrogen atoms. Our goal is to directly measure the gas kinetic temperature with formaldehyde toward six star-forming regions in the LMC. Three rotational transitions of para-H2CO near 218 GHz were observed with the APEX 12m telescope toward six star forming regions in the LMC. Those data are complemented by C18O 2-1 spectra. Using non-LTE modeling with RADEX, we derive the gas kinetic temperature and spatial density, using as constraints the measured para-H2CO 321-220/303-202 and para-H2CO 303-202/C18O 2-1 ratios. Excluding the quiescent cloud N159S, where only one para-H2CO line could be detected, the gas kinetic temperatures derived from the preferred para-H2CO 321-220/303-202 line ratios range from 35 to 63 K with an average of 47 K. Spatial densities of the gas derived from the paraH2CO 303-202/C18O 2-1 line ratios yield 0.4-2.9x10^5 cm^-3 with an average of 1.5x10^5 cm^-3. Temperatures derived from the para-H2CO line ratio are similar to those obtained with the same method from Galactic star forming regions and agree with results derived from CO in the dense regions of the LMC. A comparison of kinetic temperatures derived from para-H2CO with those from the dust also shows good agreement. This suggests that the dust and para-H2CO are well mixed in the studied star forming regions. A correlation between the gas kinetic temperatures derived from para-H2CO and infrared luminosity, represented by the 250um flux, suggests that the kinetic temperatures traced by para-H2CO are correlated with the ongoing massive star formation in the LMC.

Tables

Table 1. Table 1: Source coordinates, integration times, and epochs.

Sources	RA(J2000)	DEC(J2000)	Int. Time	Obs. Date
	h m s	° ′ ″	min
N159W	05:39:35.2	-69:45:37.0	229	July-2008
N113	05:13:17.2	-69:22:23.0	91	September-2008
N44BC	05:22:02.8	-67:57:45.8	68	May-2014
30 Dor	05:38:49.3	-69:04:44.0	64	May-2014
N159S	05:40:02.8	-69:50:32.7	166	May-July-2014
N159E	05:40:04.4	-69:44:34.0	80	July-2014

Table 2. Table 2: Para-H 2 CO and C 18 O spectral parameters a .

Sources	Molecule	Transition	$\int$$T$mbd$v$	$V_{\mathrm{lsr}}$	FWHMb	$T$mb	rms
			K km s-1	km s-1	km s-1	K	mK
30 Dor	H2CO	303 – 202	0.401 (0.026)	250.92 (0.21)	6.12 (0.47)	0.061	6.8
	H2CO	322 – 221	0.114 (0.023)	251.61 (0.70)	6.48 (1.19)	0.017	6.5
	H2CO	321 – 220	0.109 (0.021)	251.01 (0.41)	4.29 (1.00)	0.023	6.4
	C18O	2 – 1	0.190 (0.026)	251.25 (0.48)	7.09 (1.34)	0.025	5.6
N113	H2CO	303 – 202	0.930 (0.029)	234.25 (0.07)	4.86 (0.17)	0.181	7.0
	H2CO	322 – 221	0.217 (0.035)	234.40 (0.58)	7.05 (1.20)	0.029	6.9
	H2CO	321 – 220	0.213 (0.025)	234.36 (0.33)	5.69 (0.68)	0.035	7.3
N44BC	H2CO	303 – 202	0.775 (0.026)	283.86 (0.11)	6.37 (0.23)	0.114	6.5
	H2CO	322 – 221	0.155 (0.019)	283.97 (0.45)	6.98(0.88)	0.021	5.2
	H2CO	321 – 220	0.152 (0.021)	283.45 (0.47)	6.50 (0.90)	0.022	5.1
	C18O	2 – 1	0.558 (0.022)	283.78 (0.12)	6.08 (0.28)	0.086	6.2
N159W	H2CO	303 – 202	0.788 (0.019)	236.78 (0.07)	5.82 (0.17)	0.127	6.2
	H2CO	322 – 221	0.101 (0.017)	237.00 (0.30)	3.65 (0.70)	0.026	6.4
	H2CO	321 – 220	0.105 (0.017)	236.98 (0.53)	5.94 (1.00)	0.017	5.2
N159E	H2CO	303 – 202	0.555 (0.017)	234.53 (0.09)	5.84 (0.21)	0.090	4.9
	H2CO	322 – 221	0.112 (0.018)	234.45 (0.47)	6.46 (1.37)	0.016	4.3
	H2CO	321 – 220	0.073 (0.016)	232.94 (0.59)	5.36 (1.53)	0.013	3.9
	C18O	2 – 1	0.231 (0.019)	234.85 (0.23)	6.17 (0.66)	0.035	4.8
N159S	H2CO	303 – 202	0.056 (0.010)	235.87 (0.45)	4.45 (0.80)	0.012	3.9
	H2CO	322 – 221	0.005	…	…	…	4.9
	H2CO	321 – 220	0.005	…	…	…	3.4
	C18O	2 – 1	0.161 (0.006)	236.35 (0.07)	3.27 (0.19)	0.047	3.4
			0.047 (0.006)	232.39 (0.30)	3.40 (0.52)	0.013	3.4

Table 3. Table 3: Integrated intensity ratios, column densities, spatial densities, and temperatures.

						$N$(H2)
Sources	321-220		H2CO 303-202	$N$(C18O)	$N$(para-H2CO)	C18O	CO	$n$(H2)	$T_{\mathrm{kin}}$	$T_{\mathrm{LTE}}$	$T_{\mathrm{dust}}$c
	303-202		C18O 2-1	$\times {10}^{14}$ cm-2	$\times {10}^{12}$ cm-2	$\times {10}^{22}$ cm-2		$\times {10}^5$ cm-3	K	K	K
30 Dor	0.27$\pm$0.05		2.12$\pm$0.32	1.0	1.0	0.7	0.6	1.45${}_{-0.42}{}^{}{}_{}{}^{+0.69}$	63.0${}_{-13.9}{}^{}{}_{}{}^{+18.2}$	70.4	70–75
N113a	0.23$\pm$0.03		1.22$\pm$0.12	2.7	2.7	2.0	1.0	0.89${}_{-0.15}{}^{}{}_{}{}^{+0.18}$	53.6${}_{-6.1}{}^{}{}_{}{}^{+6.7}$	54.1	30–51
N44BC	0.20$\pm$0.03		1.39$\pm$0.07	3.0	3.0	2.1	1.3	1.13${}_{-0.16}{}^{}{}_{}{}^{+0.18}$	47.3${}_{-5.4}{}^{}{}_{}{}^{+6.0}$	45.9	35–45
N159Wb	0.13$\pm$0.02		1.01$\pm$0.08	3.7	3.7	2.7	1.8	1.00${}_{-0.14}{}^{}{}_{}{}^{+0.20}$	35.3${}_{-3.8}{}^{}{}_{}{}^{+3.7}$	32.0	30–40
N159E	0.13$\pm$0.03		2.39$\pm$0.21	1.2	1.2	0.9	0.8	2.92${}_{-0.71}{}^{}{}_{}{}^{+1.15}$	37.2${}_{-5.7}{}^{}{}_{}{}^{+5.9}$	46.4	30–40
N159S	0.085		0.35$\pm$0.07	0.9	0.9	0.6	1.4	$>$0.43	26.9	25.1	20–30

Equations

$$N({\mathrm{C}}^{18}\mathrm{O})=5.3\times 10^{14}\int T_{\mathrm{mb}}({\mathrm{C}}^{18}\mathrm{O},J=2-1)\mathrm{d}v,$$

$$T_{\mathrm{kin}}=\frac{47.1}{ln(0.556\frac{I(3_{03}-2_{02})}{I(3_{22}-2_{21})})},$$

Full text

*Aims. *The classical dense molecular gas thermometer NH3 is rarely available in a low metallicity environment because of photoionization and a lack of nitrogen atoms. Our goal is to directly measure the gas kinetic temperature with formaldehyde toward six star-forming regions in the LMC.

Methods. Three rotational transitions (J$${}_{\rm K_{A}K_{C}} = 303-202, 322-221, and 321-220) of para-H2CO near 218 GHz were observed with the Atacama Pathfinder EXperiment (APEX) 12 m telescope toward six star forming regions in the LMC. Those data are complemented by C18O 2-1 spectra.

Results. Using non-LTE modeling with RADEX, we derive the gas kinetic temperature and spatial density, using as constraints the measured para-H2CO 321-220/303-202 and para-H2CO 303-202/C18O 2-1 ratios. Excluding the quiescent cloud N159S, where only one para-H2CO line could be detected, the gas kinetic temperatures derived from the preferred para-H2CO 321-220/303-202 line ratios range from 35 to 63 K with an average of 47 $\pm$ 5 K (errors are unweighted standard deviations of the mean). Spatial densities of the gas derived from the para-H2CO 303-202/C18O 2-1 line ratios yield 0.4 – 2.9 $\times$ 105 cm*-3* with an average of 1.5 $\pm$ 0.4 $\times$ 105 cm*-3*. Temperatures derived from the para-H2CO line ratio are similar to those obtained with the same method from Galactic star forming regions and agree with results derived from CO in the dense regions ($n$(H2) $>$ 103 cm*-3*) of the LMC. A comparison of kinetic temperatures derived from para-H2CO with those from the dust also shows good agreement. This suggests that the dust and para-H2CO are well mixed in the studied star forming regions. A comparison of kinetic temperatures derived from para-H2CO 321-220/303-202 and NH3(2,2)/(1,1) shows, however, a drastic difference. In the star forming region N159W, the gas temperature derived from the NH3(2,2)/(1,1) line ratio is $\sim$16 K (Ott et al., 2010), which is only half the temperature derived from para-H2CO and the dust. Furthermore, ammonia shows a very low abundance in a 30*′′* beam. Apparently, ammonia only survives in the most shielded pockets of dense gas not yet irradiated by UV photons, while formaldehyde, less affected by photodissociation, is more widespread and is also sampling regions more exposed to the radiation of young massive stars. A correlation between the gas kinetic temperatures derived from para-H2CO and infrared luminosity, represented by the 250 $\mu$m flux, suggests that the kinetic temperatures traced by para-H2CO are correlated with the ongoing massive star formation in the LMC.

1 Introduction

The Large Magellanic Cloud (LMC), at a distance of $\sim$50 kpc (Pietrzyński et al., 2013), is the nearest low metallicity (Rolleston, 2002) star-forming galaxy to the Milky Way. The relatively face-on view offered by the LMC provides an ideal perspective to study star formation, particularly massive star formation associated with its numerous stellar clusters. In the LMC, the FUV field is stronger than in the Milky Way (Westerlund, 1990). It is thus well suited to study the properties of the interstellar medium, the evolution of molecular clouds, and star formation in an active low metallicity galaxy, also providing a link to galaxies at high redshift.

The physical properties of the molecular gas in the LMC, in particular the kinetic temperature, are not well constrained. The easily thermalized and optically thick rotational CO transitions are good temperature tracers of the cold and dense gas in local clouds. Generally, however, they often suffer from a lack of information on the beam filling factor in extragalactic clouds. Multi-level observations of suitable molecules deliver the most reliable temperature determinations. The metastable lines of ammonia (NH3) are frequently used as the standard molecular cloud thermometer in molecular clouds within our Galaxy and also in external galaxies (Ho & Townes, 1983; Walmsley & Ungerechts, 1983; Danby et al., 1988; Henkel et al., 2000, 2008; Weiß et al., 2001; Mauersberger et al., 2003; Ao et al., 2011; Lebrón et al., 2011; Ott et al., 2011; Wienen et al., 2012; Mangum et al., 2013a). However, the ammonia abundance can vary strongly in different molecular environments (e.g., 10*-5* in dense, molecular $``$hot cores$"$ around newly formed massive stars, Mauersberger et al. 1987; 10*-8* in dark clouds, Benson & Myers 1983; Chira et al. 2013; 10*-10* in a massive star forming cloud of the LMC, Ott et al. 2010) and is extremely affected by a high UV flux. Thus, in a low metallicity environment with high UV flux and a lack of shielding dust grains, ammonia is of limited use as a reliable probe to trace the gas kinetic temperature. To make this problem even more severe, the LMC is also a galaxy with particulary low nitrogen abundance ($\sim$10% solar, Wang et al. 2009; Ott et al. 2010).

Formaldehyde (H2CO) is a ubiquitous molecule in the Galactic interstellar medium (ISM) of our and external galaxies (Downes et al., 1980; Cohen & Few, 1981; Bieging et al., 1982; Cohen et al., 1983; Baan et al., 1986, 1990, 1993; Henkel et al., 1991; Zylka et al., 1992; Hüttemeister et al., 1997; Heikkilä et al., 1999; Wang et al., 2004, 2009; Mangum et al., 2008; Zhang et al., 2012; Mangum et al., 2013b; Ao et al., 2013; Tang et al., 2013; Ginsburg et al., 2015, 2016; Guo et al., 2016). H2CO is thought to be formed on the surface of dust grains by successive hydrogenation of CO (Watanabe & Kouchi, 2002; Woon, 2002; Hidaka et al., 2004): CO $\rightarrow$ HCO $\rightarrow$ H2CO. Variations of the fractional abundance of H2CO do not exceed one order of magnitude. For example, the fractional abundance of H2CO is similar across various sub regions of the well-studied Orion-KL nebula, i.e., the $``$hot core$"$ and the $``$compact ridge$"$ (Mangum et al., 1990, 1993; Caselli et al., 1993; Johnstone et al., 2003).

Para-H2CO has a rich variety of millimeter and submillimeter transitions. Line ratios of para-H2CO involving different $K_{\rm a}$ ladders are good tracers of the kinetic temperature, such as para-H2CO $J$KaKc = 322-221/303-202, 423-322/404-303, and 523-422/505-404, since the relative populations of the $K_{\rm a}$ ladders of para-H2CO are predominantly governed by collisions (Mangum & Wootten, 1993; Mühle et al., 2007). Among these para-H2CO lines, the above three transitions with rest frequencies of 218.222, 218.475, and 218.760 GHz, respectively, are particularly useful for use a thermometer, because they are strong enough for extragalactic observations and because they can be measured simultaneously within a bandwidth of 1 GHz. Temperature determined from these ratios are free from uncertainties related to pointing accuracy, calibration or different beam sizes. Since the line emission is optically thin and the levels are located up to 68 K above the ground state, the line ratios are sensitive to gas kinetic temperatures up to 50 K with relatively small uncertainties (Mangum & Wootten, 1993; Ao et al., 2013). Para-H2CO 3–2 line ratios have been used to measure the molecular gas kinetic temperatures in our Galactic center (Qin et al., 2008; Ao et al., 2013; Johnston et al., 2014; Ginsburg et al., 2016; Immer et al., 2016), star formation regions (Mangum & Wootten, 1993; Mitchell et al., 2001; Watanabe & Mitchell, 2008; Tang et al., 2016), as well as in external galaxies (e.g., Mühle et al. 2007).

Multitransition observations of molecular clouds in the LMC (Johansson et al., 1998; Heikkilä et al., 1999; Israel et al., 2003; Kim et al., 2004; Bolatto et al., 2005; Pineda et al., 2008; Mizuno et al., 2010; Minamidani et al., 2008, 2011; Fujii et al., 2014; Paron et al., 2016) suggest that the molecular gas traced by CO may be warmer and/or denser than in our Galaxy. NH3(1,1) and (2,2) lines have been surveyed toward seven star-forming regions in the LMC by Ott et al. (2010) using the Australia Telescope Compact Array (ATCA). Emission is only detected in the massive star-forming region N159W. This represents so far the only detection of NH3 in the Magellanic Clouds. The gas kinetic temperature derived from NH3 (2,2)/(1,1) is cold ($\sim$16 K), which is two times lower than the derived dust temperature 30 – 40 K (Heikkilä et al., 1999; Bolatto et al., 2000; Gordon et al., 2014). Ott et al. (2010) also found a low fractional NH3 abundance of $\sim$4 $\times$ 10*-10*, which is lower by 1.5 – 5 orders of magnitude than those observed in Galactic star-forming regions. Previous observations of formaldehyde have been made in the LMC (e.g., Whiteoak & Gardner 1976; Johansson et al. 1994; Heikkilä et al. 1999; Wang et al. 2009) and H2CO has been detected in many dense clumps. These observations show that the fractional abundance of para-H2CO ranges from 1 to 6 $\times$ 10*-10*, which agrees with the values found in our Galactic molecular clouds (e.g., Güsten & Henkel 1983; Zylka et al. 1992; Johnstone et al. 2003; Ao et al. 2013; Tang et al. 2016).

For this paper, we have carried out deep observations of the six star forming regions 30 Dor, N44BC, N113, N159E, N159S, and N159W in the LMC. Targeting three transitions of para-H2CO (J$${}_{K_{A}K_{C}} = 303-202, 322-221, and 321-220) as well as C18O 2-1 we simultaneously determine kinetic temperatures and spatial densities at high precision. In Sections 2 and 3, we introduce our observations of the para-H2CO triplet and the data reduction, and describe the main results. These are then discussed in Section 4. Our main conclusions are summarized in Section 5.

2 Observations and data reduction

Our observations were carried out in 2008 and 2014 (summarized in Table 1) with the Atacama Pathfinder EXperiment (APEX) 12 m telescope located on Chajnantor (Chile) using the APEX-1 (SHeFI) receiver. The beam size is $\sim$30*′′* ($\sim$7 pc at 50 kpc distance) at 218 GHz. The main beam efficiency and the forward efficiency were 0.75 and 0.97, respectively. N113 and N159W were observed in 2008 with an old Fast Fourier Transform Spectrometer (FFTS), which consists of two units with a bandwidth of 1 GHz each and a velocity resolution of 0.1675 km s*-1*. The frequency is centered at 218.480 GHz. Our data includes all three of the 218 GHz para-H2CO lines. 30 Dor, N159E, N159S, and N44BC were observed in 2014. Here we used the new eXtended bandwidth Fast Fourier Transform Spectrometer (XFFTS) backend with two spectral windows of 2.5 GHz bandwidth and a velocity resolution of 0.1047 km s*-1*. The central frequency is set at 218.550 GHz. These data do not only include the three para-H2CO lines but also the 219.560 GHz C18O (2-1) transition.

Toward each of the six star forming regions in the LMC Wong et al. (2011) took a single pointing, high sensitivity ($\sim$5 mK rms, $T_{\rm mb}$ scale, beam size $\sim$30*′′) spectrum centered on its CO emission peak which will be used to estimate $N$(H2) in Section 4.1. Ancillary C18*O 2-1 data have been published by Heikkilä et al. (1998) and Wang et al. (2009). In addition, ammonia (NH3) data from the LMC (Ott et al., 2010) and Herschel infrared data will also play an important role.

Data reduction for spectral lines was performed using CLASS from the GILDAS package111http://www.iram.fr/IRAMFR/GILDAS. To enhance signal to noise ratios (S/N) in individual channels, we smoothed contiguous channels to a velocity resolution of $\sim$1.0 km s*-1*. Sources observed are listed in Table 1.

3 Results

The three para-H2CO lines are detected in all sources except N159S. There, only the strongest para-H2CO line, the 303-202 transition, is detected. C18O (2-1), measured in 30 Dor, N159E, N159S, and N44BC, is detected in all sources. The para-H2CO and C18O line spectra are presented in Figure 1. Line parameters are listed in Table 2, where velocity-integrated intensity, \int$$Tmbd$v$, local standard of rest velocity, $V_{\rm lsr}$, full width to half maximum line width, FWHM, peak main beam brightness temperature, $T$mb, and rms noise, were obtained from Gaussian fits.

3.1 Kinetic temperature and spatial density

To determine gas kinetic temperatures and spatial densities, we use the RADEX non-LTE model (van der Tak et al., 2007) offline code333http://var.sron.nl/radex/radex.php with H2CO collision rates from Wiesenfeld & Faure (2013) and C18O collision rates from Yang et al. (2010). The RADEX code needs five input parameters: background temperature, kinetic temperature, H2 density, column density, and line width. For the background temperature, we adopt 2.73 K. Model grids for the para-H2CO and C18O lines encompass 30 densities ($n$(H2) = 103 – 107 cm*-3*) and 30 temperatures ranging from 10 to 110 K. For the line width, we use the observed line width value (Table 2). The total beam averaged column density of C18O can be obtained from the $J$ = 2–1 integrated intensity following Batrla & Wilson (2003).

[TABLE]

where $\int T_{\rm mb}({\rm C^{18}O},J=2-1){\rm d}v$ is the C18O (2-1) integrated intensity. The results are listed in Table 4. In the LMC, the gas is well mixed so that isotope ratios are pretty much the same throughout the galaxy (Johansson et al., 1994; Chin et al., 1997; Heikkilä et al., 1998, 1999; Wang et al., 2009). In the local ISM, the 16O/18O ratio is approximately 500 (Wilson & Rood, 1994). We have, however, to keep in mind that fractional abundances in the LMC differ from those in the local ISM. In the LMC, 18O is underabundant with respect to 16O by about a factor of $\sim$4 (16O/18O $\sim$2000 in the LMC, Chin 1999; Wang et al. 2009), while 18O is underabundant by a factor of $\sim$2.4 with respect to 17O (locally, 18O/17O $\sim$4.1, Zhang et al. 2007; Wouterloot et al. 2008; in the LMC $\sim$1.7, Heikkilä et al. 1998; Wang et al. 2009). Therefore, $N$(H2)/$N$(C18O) ratios should be higher by a factor of $\sim$3 in the LMC with respect to the local ISM. This correlation will be used to derive H2 column densities. The results for the H2 column density are listed in Table 4. Assuming a CO to H2 conversion factor of $X_{CO}$ $\sim$ 4 $\times$ 1020 cm*-2* (K km s*-1*)-1 for the LMC (Pineda et al., 2009; Wang et al., 2009), we can also derive a column density of $N$(H2) from the CO(1-0) integrated intensity moment map reported by Wong et al. (2011). The results of $N$(H2) are listed in Table 4. The H2 column densities derived from C18O and CO are consistent with in the estimated uncertainty by a factor of two.

Previous observational results on transitions of C18O (1-0, 2-1) and para-H2CO (202-101, 303-202, 322-221 and 321-220) using the 15 m Swedish-ESO Submillimetre Telescope (SEST) show that the column density ratio of $N$(C18O)/$N$(para-H2CO) is $\sim$ 100 in dense clumps of the LMC (Heikkilä et al., 1998, 1999; Wang et al., 2009). Assuming that the $N$(C18O)/$N$(para-H2CO) ratio is the same in our sample, we estimate the column density of para-H2CO from the $N$(C18O) column density. The results are listed in Table 4.

The para-H2CO (303-202) line is the strongest of the three 218 GHz para-H2CO transitions observed by us. In order to avoid small uncertain values in the denominator, the para-H2CO 322-221/303-202 and 321-220/303-202 ratios are most suitable to derive the kinetic temperature. The para-H2CO 322-221 and 321-220 transitions have similar energy above the ground state, $E_{u}$ $\simeq$ 68 K, similar line brightness, and are often detected at the same time (e.g., Mühle et al. 2007; Bergman et al. 2011; Wang et al. 2012; Lindberg & Jørgensen 2012; Ao et al. 2013; Immer et al. 2014, 2016; Treviño-Morales et al. 2014; Ginsburg et al. 2016; Tang et al. 2016); therefore, para-H2CO 322-221/303-202 and 321-220/303-202 ratios are both good thermometers to determine the gas temperature. The kinetic temperature is traced by these two ratios with an uncertainty of $\lesssim$ 25% below 50 K (Mangum & Wootten, 1993). While at $n$(H2) $\gtrsim$ 105 cm*-3* both ratios are similarly suitable, the para-H2CO 322-221/303-202 line ratio is affected by gas density at $n$(H2) $<$ 105 cm*-3* (Tang et al., 2016). For our sample, spatial density measurements probed by molecular tracers like CS, SO, CO, CI, H2CO, HCO+, and HCN (Heikkilä et al., 1998, 1999; Kim et al., 2004; Wang et al., 2009) show a range of 0.3 – 10 $\times$ 105 cm*-3*. Therefore, in this work we use the para-H2CO 321-220/303-202 integrated intensity ratio to derive the kinetic temperature (Ginsburg et al., 2016; Immer et al., 2016).

In our Galaxy, spatial densities, $n$(H2), derived from para-H2CO (303-202) are higher than from C18O (2-1). However, in the LMC, with lower density regions often being photoionized, this may be different. Therefore, here the para-H2CO 303-202/C18O 2-1 integrated intensity ratio is used to constrain the spatial density assuming the two tracers have a similar spatial extent and sample the same region. For both lines we find similar line parameters (e.g., $V_{\rm lsr}$, FWHM, see Table 2) in our sample, so our assumption is reasonable. igure 2 shows how the parameters are constrained by the line ratio distribution of para-H2CO 321-220/303-202 and para-H2CO 303-202/C18O 2-1 in the $T_{\rm kin}$-$n$(H2) parameter space. The determined results are listed in Table 4. The spatial density of our sample derived from the para-H2CO 303-202/C18O 2-1 ratio shows a relatively narrow range of 0.4 – 2.9 $\times$ 105 cm*-3* with an average of 1.5 $\pm$ 0.4 $\times$ 105 cm*-3* (see Figure 2 and Table 4; errors given here and elsewhere are unweighted standard deviations of the mean), which is consistent with the results for the same dense clumps found from observations of e.g., SO, HCO+, c-C3H2, CH3OH, and H2CO (Heikkilä et al., 1999; Wang et al., 2009).

As already mentioned, our three para-H2CO (3-2) transitions are sensitive to gas at density $\sim$105 cm*-3* (Immer et al., 2016). To highlight how much the derived kinetic temperature depends on the derived density based on the admittedly uncertain assumption that para-H2CO 303-202 and C18O 2-1 trace the same gas, we have plotted in Figure 3 the relation between kinetic temperature and the para-H2CO 321-220/303-202 ratio at spatial density $n$(H2) = 105 cm*-3* with column density of $N$(para-H2CO) = 2.1 $\times$ 1012 cm*-2* and line width of 6 km s*-1* (these are rough average values for our sample) using RADEX. Comparing this with the actually obtained values for individual sources derived from our para-H2CO 321-220/303-202 and para-H2CO 303-202/C18O 2-1 ratios, the plot demonstrates that the temperatures derived in the two different ways are in a good agreement.

Local thermodynamic equilibrium (LTE) is a good approximation for the H2CO level populations under optically thin high-density conditions (Mangum & Wootten, 1993; Watanabe & Mitchell, 2008). Although LTE and RADEX non-LTE models use different approximations and assumptions, it is useful to check how the temperatures derived by the two methods compare. The para-H2CO line intensity ratios 322-221/303-202 and 321-220/303-202 can be used to measure the LTE kinetic temperature because (see Section 1) the $K_{\rm a}$ = 0 and 2 ladders of para-H2CO are mainly connected by collisions. The LTE kinetic temperature can be calculated assuming that the lines are optically thin, and originate from a high-density region (Mangum & Wootten, 1993).

[TABLE]

where $I$(303-202)/$I$(322-221) is the para-H2CO integrated intensity ratio. The LTE kinetic temperatures are listed in Table 4. The uncertainty is $\lesssim$ 30% for this method of temperature measurement (Mangum & Wootten, 1993). Considering this uncertainty, the temperatures derived from LTE and the RADEX non-LTE model are consistent with each other.

3.2 Individual sources

Below, results from the six sources covered by this study are individually discussed.

3.2.1 30 Dor

Our three para-H2CO and C18O 2-1 transitions have already been observed toward 30 Dor by Heikkilä et al. (1999) with the SEST (beam size $\sim$23*′′), but only para-H2CO 303*-202 was detected. With our higher sensitivity we detect all four lines and confirm their para-H2CO results. The kinetic temperature derived from para-H2CO (321-220/303-202) is $\sim$63 K, which is the highest value determined in our sample. 30 Dor, hosting a cluster of O3 stars that rivals super star clusters, is the most spectacular star forming region in the Local Group (Walborn & Blades, 1997; Massey & Hunter, 1998), which makes such a high $T_{\rm kin}$ value comprehensible. The spatial density derived from the para-H2CO 303-202/C18O 2-1 ratio is $\sim$1.5 $\times$ 105 cm*-3* at this temperature, which agrees with results derived from other species (e.g., CS, SO, HCO+, Heikkilä et al. 1999).

3.2.2 N113

All three 218 GHz para-H2CO lines as well as C18O 2-1 transition have been observed by Wang et al. (2009) and Heikkilä et al. (1998) with the SEST. Para-H2CO 303-202 and C18O 2-1 were detected. We detect the three transitions of para-H2CO for the first time. The kinetic temperature derived from para-H2CO (321-220/303-202) is $\sim$54 K. N113 is the LMC star forming region with the most luminous 22 GHz H2O maser (Whiteoak & Gardner, 1986; Lazendic et al., 2002; Oliveira et al., 2006), not quite as spectacular as 30 Dor, but hosts a few bright HII regions whose stellar energy feedback is likely to have elevated its temperature, thus leading to the second highest $T_{\rm kin}$ value. The spatial density derived from para-H2CO 303-202/C18O 2-1 (ratio data from Wang et al. (2009) and Heikkilä et al. (1998), assuming that the para-H2CO 303-202/C18O 2-1 ratio at the SEST beam size, $\sim$23*′′, is similar to that in the APEX beam size, $\sim$30′′, see Section 3.2.4) is $\sim$8.9 $\times$ 104 cm-3* at temperature $\sim$54 K, which agrees with results from other molecules (e.g., CS, HCO+, HCN, Wang et al. 2009).

3.2.3 N44BC

C18O 2-1 has been detected in N44BC by Heikkilä et al. (1998) with the SEST. We detect the three 218 GHz para-H2CO transitions and the C18O line. Our observations confirm their C18O 2-1 result. The kinetic temperature derived by para-H2CO (321-220/303-202) is $\sim$47 K. Such a high temperature likely results from the stellar energy feedback from the adjacent super bubble on the molecular cloud, which also shows bright mid-IR emission (Chen et al., 2009). The spatial density derived from the para-H2CO 303-202/C18O 2-1 ratio is $\sim$1.1 $\times$ 105 cm*-3* at this temperature, which agrees with results from other molecules (e.g., CO, CI, Heikkilä et al. 1998; Kim et al. 2004).

3.2.4 N159W

The three para-H2CO 218 GHz transitions as well as C18O 2-1 have been detected in N159W by Heikkilä et al. (1998, 1999) with the SEST. Our observations confirm their para-H2CO results. The kinetic temperature derived by para-H2CO (321-220/303-202) is $\sim$35 K. The spatial density derived from the para-H2CO 303-202/C18O 2-1 ratio (data from Heikkilä et al. 1998, 1999) is $\sim$1.0 $\times$ 105 cm*-3* at this temperature, which agrees with results measured by other species (e.g., CS, SO, Heikkilä et al. 1999). To quantify potential differences in temperature and density derived from APEX and SEST data, we determined the temperature and the density with the same method using the SEST para-H2CO and C18O data from Heikkilä et al. (1998, 1999). The derived temperature and density are 30.3${}^{+5.7}_{-5.4}$ K and 1.14${}^{+0.35}_{-0.23}$ $\times$ 105 cm*-3*, respectively. This indicates nearly the same spatial density and a few Kelvin difference for the kinetic temperature. This temperature difference is similar to its 1$\sigma$ uncertainty ($\sim$6 K). Therefore, the temperature gradient and density gradient is small when moving from a beam size of 7.3 pc (APEX) to 5.6 pc (SEST).

3.2.5 N159E

The three para-H2CO 218 GHz transitions as well as C18O 2-1 are detected. To our knowledge, it is the first detection of para-H2CO in the N159E region. The source shows similar properties as N159W. The kinetic temperature derived from para-H2CO (321-220/303-202) is $\sim$37 K. The spatial density derived from the para-H2CO 303-202/C18O 2-1 ratio is $\sim$2.9 $\times$ 105 cm*-3* at this temperature.

3.2.6 N159S

Two velocity components are detected by C18O, at 232.4 and 236.4 km s*-1*. Para-H2CO 303-202 is detected at a velocity of 235.9 km s*-1* (see Table 2). However, the para-H2CO 322-221 and 321-220 lines are not detected. The dust temperature ranges from 20 to 30 K (Gordon et al., 2014). N159S appears to be a cold cloud (Heikkilä et al., 1999), and has been shown to host no massive star formation at present and during the last 10 Myr (Chen et al., 2010). The upper limit to the kinetic temperature derived from para-H2CO (321-220/303-202) based on our observational 3$\sigma$ limit for the 321-220 line is $\sim$27 K. The spatial density derived from the para-H2CO 303-202/C18O 2-1 ratio is $>$4.3 $\times$ 104 cm*-3*, which is consistent with results measured by other species (e.g., CS, SO, Heikkilä et al. 1999).

4 Discussion

4.1 Comparison of temperatures derived from H2CO, CO,

NH3, and the dust

The kinetic temperatures of molecular clumps in the LMC have been calculated by multi-transition data of CO (Johansson et al., 1998; Heikkilä et al., 1999; Israel et al., 2003; Kim et al., 2004; Bolatto et al., 2005; Pineda et al., 2008; Mizuno et al., 2010; Minamidani et al., 2008, 2011; Fujii et al., 2014; Paron et al., 2016). These observations show that the higher temperatures ($T_{\rm kin}$ $\gtrsim$ 100 K) occur in cloud regions that are of lower density ($\lesssim$103 cm*-3*) and that the gas is colder ($T_{\rm kin}$ = 10 – 80 K) in regions of higher density (104 – 105 cm*-3*). As already mentioned in Section 3.1, the spatial density range of our sample derived from the para-H2CO 303-202/C18O 2-1 ratio with respect to the Galaxy is 0.4 – 2.9 $\times$ 105 cm*-3* with an average of 1.5 $\pm$ 0.4 $\times$ 105 cm*-3*. Excluding the quiescent cloud N159S, where only one para-H2CO line could be detected, the gas kinetic temperatures derived from para-H2CO (321-220/303-202), range from 35 to 63 K with an average of 47 $\pm$ 5 K. Temperatures and densities derived from CO are for 30 Dor $T_{\rm kin}$ $\sim$ 40 – 80 K and $n$(H2) $\sim$ 3$\times$103 – 3$\times$105 cm*-3* (Johansson et al., 1998; Heikkilä et al., 1999; Minamidani et al., 2008), N159W $T_{\rm kin}$ $\sim$ 16 – $>$30 K and $n$(H2) $\sim$ 3$\times$103 – 8$\times$105 cm*-3* (Johansson et al., 1998; Heikkilä et al., 1999; Bolatto et al., 2005; Minamidani et al., 2008), N159E $T_{\rm kin}$ $>$ 40 K and $n$(H2) $\sim$ 1$\times$103 – 3$\times$105 cm*-3* (Minamidani et al., 2008), and N159S $T_{\rm kin}$ $\sim$ 10 – 60 K and $n$(H2) $\sim$ 1$\times$103 – 1$\times$105 cm*-3* (Heikkilä et al., 1999; Minamidani et al., 2008). Temperatures derived from para-H2CO are consistent with but much more precise than the results derived from CO in the dense regions ($>$103 cm*-3*).

Except for N159E, all our sources have been surveyed in NH3 (1,1) and (2,2) by Ott et al. (2010). These lines are only detected in the massive star-forming region N159W. We compare fractional abundances of $N$(para-NH3)/$N$(H2) and $N$(para-H2CO)/$N$(H2) to column density $N$(H2) obtained from 12CO(1-0) in Figure 4. These show that formaldehyde has a stable fractional abundance ranging from 0.6 to 5.7 $\times$ 10*-10* cm*-2* with an average of 2.7 $\pm$ 1.8 $\times$ 10*-10* cm*-2* in molecular clouds of the LMC with $N$(H2) column densities ranging from 0.4 to 2 $\times$ 1022 cm*-2*. Ammonia only survives in a high column density environment with $N$(H2) $\sim$ 2 $\times$ 1022 cm*-2*. The fractional abundance of ammonia is $\sim$ 10*-10* – 10*-9* in N159W and M82, which is similar to that of formaldehyde in the LMC. As already mentioned, the kinetic temperature derived from the NH3 (2,2)/(1,1) line ratio in N159W is $\sim$16 K (Ott et al., 2010), which is two times lower than that derived from para-H2CO. Previous para-H2CO (322-221/303-202) and NH3 (2,2)/(1,1) observations toward the starburst galaxy M82 also show significantly different gas kinetic temperatures (Weiß et al., 2001; Mühle et al., 2007). M82, a satellite galaxy like the LMC, shows a similar environment, involving low metallicity combined with a high UV flux. This only leaves NH3 surviving in the most shielded pockets of molecular gas, resulting in a low fractional abundance (see Figure 4) and a low kinetic temperature. Furthermore, this abundance is demonstrating in an exemplary way that H2CO is less affected by photodissociation, sampling a more extended region. Therefore, para-H2CO traces in these instances a higher temperature than NH3 (2,2)/(1,1). We conclude that para-H2CO line ratios are a superior thermometer to trace dense gas temperatures in low metallicity galaxies with strong UV radiation. Nevertheless, more detailed spatially resolved comparisons of H2CO with NH3 temperatures would be very interesting because it could provide more information on temperature gradients and the location of different kinetic temperature layers.

The temperatures derived from dust and gas are often in agreement in the active and dense clumps of Galactic disk clouds (Dunham et al., 2010; Giannetti et al., 2013; Battersby et al., 2014). However, observed gas and dust temperatures do not agree with each other in the Galactic Central Molecular Zone (CMZ) and external galaxies (Güsten et al., 1981; Ao et al., 2013; Mangum et al., 2013a; Ott et al., 2014; Ginsburg et al., 2016; Immer et al., 2016). Dust temperatures in the LMC have been obtained by Gordon et al. (2014) using Herschel 100 to 500 $\mu$m dust continuum emission data. They range approximately from 13 to 73 K. For our sample, the dust temperatures range from 30 to 75 K (Werner et al., 1978; Heikkilä et al., 1999; Bolatto et al., 2000; Wang et al., 2009; Seale et al., 2014; Gordon et al., 2014) while the para-H2CO derived temperature ranges from 35 to 63 K. The temperatures derived from para-H2CO ratios and dust emission are therefore in good agreement (see Table 4). This indicates that the dust and H2CO kinetic temperatures are equivalent in the star forming regions of the LMC. Assuming that H2CO traces the bulk of the dense molecular gas and that ammonia shows very low abundances, this can be generalized in the sense that dense gas and dust temperatures are generally equivalent.

4.2 Star-forming regions in the Galaxy, the LMC, and other galaxies

The gas temperatures of ATLASGAL (APEX Telescope Large Area Survey of the GALaxy) massive star forming clumps have been measured by para-H2CO (303-202, 322-221, and 321-220) line ratios (Tang et al., 2016). The thus derived gas kinetic temperatures at density n(H2) = 105 cm*-3* with size of 0.3 – 0.7 pc range from 30 to 61 K with an average of 46 $\pm$ 9 K, which agrees remarkably well with the results in the LMC with a beam size of $\sim$7 pc. Large area mapping measurements of kinetic temperatures in the Galactic CMZ with the same transitions of para-H2CO (Ao et al., 2013; Ginsburg et al., 2016) suggest that the mean gas temperature is $\sim$48 K at $n$(H2) = 105 cm*-3* or $\sim$65 K at $n$(H2) = 104 cm*-3* in the whole $\sim$300 pc surveyed region. It shows a higher $T_{\rm kin}$ value than our observed results. The spatial densities derived from the para-H2CO 303-202/C18O 2-1 ratio in our sample agree with the observed results in the Galactic clumps (Beuther et al., 2002; Motte et al., 2003; Wienen et al., 2012, 2015), HII regions (Henkel et al., 1983; Ginsburg et al., 2011), and giant molecular clouds (GMCs) (Wadiak et al., 1988; Ginsburg et al., 2015; Immer et al., 2016). This agreement indicates that the physical conditions of the star forming regions should be similar in both the LMC and our Galactic disk.

Using the three transitions of para-H2CO at $\sim$218 GHz to measure the kinetic temperature of the starburst galaxy M82 shows that the derived kinetic temperature ($T_{\rm kin}$(H2CO) $\sim$ 200 K; Mühle et al. 2007) is significantly higher than in the LMC. Kinetic temperatures of starburst galaxies measured with multi-inversion transitions of NH3 show a range from 24 to $\gtrsim$ 250 K (Henkel et al., 2000, 2008; Mauersberger et al., 2003; Ao et al., 2011; Lebrón et al., 2011; Mangum et al., 2013a). The temperatures derived from para-H2CO line ratios in the LMC overlap with the values found for a sample at lower temperature (e.g., M83, NGC6946). This is likely due to the inclusion of higher excited ammonia lines, which, however, should be difficult to detect in the LMC because there particularly warm regions irradiated by enhanced UV radiation should be almost devoid of NH3. The spatial densities in starburst galaxies derived from ortho-H2CO (211-212/110-111) line ratios (Mangum et al., 2008, 2013b) show a similar range (104.5–105.5 cm*-3*) to that derived from para-H2CO 303-202/C18O 2-1 ratios in the LMC. This indicates that star formation in the LMC and external galaxies may arise from dense molecular gas ($>$104 cm*-3*), but gas heating rates may be quite different.

4.3 Correlation of gas temperature with star formation

In star forming galaxies, a lack of correlation between the gas kinetic temperatures traced by NH3 and star formation rate indicated by infrared luminosity was found by Mangum et al. (2013a). To investigate how the kinetic temperatures traced by para-H2CO correlate with star formation in the LMC, we compared the gas kinetic temperature to the Herschel 250 $\mu$m dust emission which indicates the infrared luminosity (Seale et al., 2014). We averaged the Herschel 250 $\mu$m data over a 30*′′* beam corresponding to our para-H2CO data. A comparison between gas kinetic temperatures derived from para-H2CO and the Herschel 250 $\mu$m flux is shown in Figure 5. It reveals a correlation of gas temperature and 250 $\mu$m flux for the five sources with all 218 GHz para-H2CO lines detected (slope = 0.97 $\pm$ 0.49, correlation coefficient $R$ $\sim$ 0.75). According to the relation between the infrared luminosity and 250 $\mu$m flux $L_{\rm FIR}$ $\propto$ $F_{\rm S250}^{1.2}$ in the LMC (Seale et al., 2014), the infrared luminosity and the gas temperature derived from para-H2CO are related by a power-law of the form $L_{\rm FIR}$ $\propto$ $T_{\rm kin}^{1.2\pm 0.59}$ where the power-law index is lower than that of the Stefan-Boltzmann law ($L$ $\propto$ $T_{\rm kin}^{4}$). This suggests that this picture is an oversimplification, and that star formation occurs in extended regions leading to the formation of stellar clusters with multiple FIR sources (e.g., Chen et al. 2009, 2010). Assuming that the 250 $\mu$m flux is mostly coming from clusters of FIR sources distributed across the regions from where the H2CO emission is arising, this can be generalized in the sense that the gas heating mechanism must be related to the formation of young massive stars. To find out whether the bulk of the H2CO emission is originating from within individual clusters of FIR sources, in between adjacent such FIR clusters, or both, higher resolution H2CO observations would be mandatory.

We need more data points in the LMC to understand the relationship between $T_{\rm kin}$ and star formation and to then apply this relationship to more distant galaxies with ALMA. Para-H2CO 321-220/303-202 and para-H2CO 303-202/C18O 2-1 line ratios provide a direct estimate of the gas kinetic temperatures and spatial densities for molecular gas on a scale of $\sim$7 pc in the star forming regions of the LMC. It would be meaningful to use these line ratios to measure the physical properties of the dense molecular gas at smaller linear scales with ALMA and to start systematic investigations in more distant star-forming galaxies.

5 Summary

We have measured the kinetic temperature and spatial density with para-H2CO (J$${}_{K_{A}K_{C}} = 303-202, 322-221, and 321-220) line ratios and the C18O 2-1 line in massive star-forming regions of the LMC. Kinetic temperatures derived from the above mentioned formaldehyde 218 GHz line triplet are compared with those obtained from the dust and, in one case, also from ammonia using the 12-m APEX telescope. The main results are the following:

Using the RADEX non-LTE program, we derive gas kinetic temperatures and spatial densities modeling the measured para-H2CO 321-220/303-202 and para-H2CO 303-202/C18O 2-1 line ratios. 2. 2.

The gas kinetic temperatures derived from para-H2CO (321-220/303-202) line ratios of the star forming regions in the LMC are warm, ranging from 35 to 63 K with an average of 47 $\pm$ 5 K, which is similar to that obtained from Galactic disk massive star forming clumps. 3. 3.

The spatial density derived from the para-H2CO 303-202/C18O 2-1 ratio shows a range of 0.4 – 2.9 $\times$ 105 cm*-3* with an average of 1.5 $\pm$ 0.4 $\times$ 105 cm*-3*. It agrees with results measured by ortho-H2CO (211-212/110-111) line ratios in Galactic regions of massive star formation. 4. 4.

Temperatures derived from the para-H2CO line ratios agree with those derived from CO in dense regions ($n$(H2) $>$ 103 cm*-3*). The gas temperature derived from the NH3 (2,2)/(1,1) line ratio is $\sim$16 K in N159W (Ott et al., 2010), which is two times lower than the temperature derived from the para-H2CO line ratio and the dust. Ammonia only survives in the most shielded pockets of molecular gas in the LMC*′*s low metallicity environment affected by a high UV flux. Formaldehyde is less affected by photodissociation and traces a more extended region. 5. 5.

A comparison of the gas kinetic temperature derived from para-H2CO and the temperature obtained from dust emission shows good agreement. It indicates that the bulk of the dense gas and dust are in approximate thermal equilibrium in the dense star formation regions of the LMC. 6. 6.

A correlation between the gas kinetic temperatures derived from para-H2CO and infrared luminosity indicated by the 250 $\mu$m flux suggests that our kinetic temperatures traced by para-H2CO are closely associated with extended star formation in the LMC.

Acknowledgements.

We thank the staff of the APEX telescope for their assistance in observations. The authors are also thankful for the helpful comments of the anonymous referee. This work was funded by The National Natural Science Foundation of China under grant 11433008 and The Program of the Light in China*′*s Western Region (LCRW) under grant Nos.XBBS201424 and The National Natural Science Foundation of China under grant 11373062. C.H acknowledges support by a visiting professorship for senior international scientists of the Chinese Academy of Sciences (2013T2J0057). This research has used NASA’s Astrophysical Data System (ADS).