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Home All issues Volume 598 (February 2017) A&A, 598 (2017) A30 Full HTML
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A&A
Volume 598, February 2017
Article Number A30
Number of page(s) 15
Section Interstellar and circumstellar matter
DOI https://doi.org/10.1051/0004-6361/201629694
Published online 26 January 2017

© ESO, 2017

1. Introduction

Ammonia (NH3) is frequently used as the standard molecular cloud thermometer (Ho & Townes 1983; Walmsley & Ungerechts 1983; Danby et al. 1988; Mangum et al. 2013b). However, its abundance can vary strongly in different environments (e.g., 10-5 in hot cores; Mauersberger et al. 1987 and 10-8 in dark clouds; Benson & Myers 1983) and is extremely affected by a high UV flux. Species like CH3C2H and CH3CN, also sensitive to kinetic temperature, are not widespread enough (e.g., Güsten et al. 1985; Bally et al. 1987; Nummelin et al. 1998). Therefore, these molecules are of limited use as reliable probes to trace the gas kinetic temperature (Mangum et al. 1993).

Formaldehyde (H2CO) is a ubiquitous molecule in molecular clouds (Downes et al. 1980; Cohen & Few 1981; Bieging et al. 1982; Cohen et al. 1983; Zylka et al. 1992; Mangum et al. 2008, 2013a; Ao et al. 2013; Tang et al. 2013; Ginsburg et al. 2015, 2016). It 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), it is released into the gas phase by shocks or UV heating, and is destroyed by photodissociation. Unlike for NH3, the fractional abundance of H2CO does not vary substantially and is similar even when comparing e.g., the hot core with the compact ridge of the well-studied Orion-KL nebula (Mangum et al. 1990; Mangum & Wootten 1993; Caselli et al. 1993; Johnstone et al. 2003).

Table 1

Source parameters.

Since the relative populations of the Ka ladders of H2CO are governed by collisions, line ratios involving different Ka ladders are good tracers of the kinetic temperature (Mangum et al. 1993; Mühle et al. 2007). Particularly useful are the three transitions of para-H2CO (JKAKC = 303–202, 322–221, and 321–220), which can be measured simultaneously at ~218 GHz with a bandwidth of 1 GHz and whose relative strengths (para-H2CO 322–221/303–202 and 321–220/303–202) provide a sensitive thermometer, possibly the best of the very few that are available for the analysis of dense molecular gas. In the case of optically thin emission, the line ratios are sensitive to gas kinetic temperatures ≲50 K with a small measurement uncertainty (Mangum et al. 1993), which is similar to the kinetic temperature range that the NH3 (2, 2)/(1, 1) ratio is sensitive to (Ho & Townes 1983; Mangum et al. 1992, 2013a).

Measurements of the dense molecular ridge in NGC 2024 with the para-H2CO (303–202 and 322–221) transitions show that the derived kinetic temperatures are warmer (Tkin(H2CO) ~ 45−85 K; Watanabe & Mitchell 2008) than those traced by NH3 (2, 2)/(1, 1) (Tkin(NH3) ~ 27–55 K; Schulz et al. 1991). Using the three transitions of para-H2CO at ~218 GHz to measure the kinetic temperature of the starburst galaxy M82 shows that the derived kinetic temperature (Tkin(H2CO) ~ 200 K; Mühle et al. 2007) is significantly higher than the temperature deduced from the NH3 (1, 1)–(3, 3) lines (Tkin(NH3) ~ 60 K; Weiß et al. 2001) and the dust temperature (Tdust ~ 48 K; Colbert et al. 1999). It is the higher Tkin value from H2CO which is representative for the bulk of the molecular gas in M82 (Mühle et al. 2007). Ao et al. (2013) and Ginsburg et al. (2016) used the same para-H2CO transitions to measure the kinetic temperature of the dense molecular clouds near the Galactic center. They found that these H2CO-derived gas kinetic temperatures (average ~65 K) are uniformly higher than the NH3 (2, 2)/(1, 1) temperatures and the dust temperatures of 14–30 K. Overall, para-H2CO, a molecule which traces the entire dense molecular gas without much bias because of a lack of drastic changes in abundance, appears to be the best long-sought tracer of kinetic temperature of the dense molecular gas at various stages of star formation.

The APEX Telescope Large Area Survey of the GALaxy (ATLASGAL; Schuller et al. 2009), using the Large APEX Bolometer Camera (LABOCA) at 870 μm (Siringo et al. 2009), presents observations in a Galactic longitude range of ±60° and latitude range of ±1.5°. This introduces a global view of star formation at submm wavelengths and identifies a large number of massive clumps forming high-mass stars at various stages in the inner Galaxy (Contreras et al. 2013; Urquhart et al. 2014; Csengeri et al. 2014). In this paper, we aim to measure the kinetic temperature with three transitions of para-H2CO (JKAKC = 303−202, 322–221, and 321–220) toward the massive clumps selected from the ATLASGAL survey. Our main goals are the following: (a) determining to what degree the kinetic temperatures obtained from NH3 and from para-H2CO differ from each other; (b) seeking a correlation between the temperature of the gas and that of the dust; and (c) searching for a correlation between kinetic temperature and line width as is expected in the case of conversion of turbulent energy into heat. In Sects. 2 and 3, we introduce our observations of the para-H2CO triplet and the data reduction, and describe the main results. The comparison of kinetic temperatures derived from para-H2CO, NH3, and dust is discussed in Sect. 4. Our main conclusions are summarized in Sect. 5.

2. Selection of targets, observations, and data reduction

We have selected 30 massive clumps of the Galactic disk at various stages of high-mass star formation and with strong NH3 emission from the ATLASGAL survey (see Table 1). At Effelsberg, the NH3(J,K) = (1, 1), (2, 2), and (3, 3) lines have been measured by Wienen et al. (2012) who determined kinetic temperatures, based on the NH3 (2, 2)/(1, 1) ratio, ranging from 11 to 61 K. The sample of high-mass star forming clouds at various evolutionary stages contains infrared dark clouds (IRDCs), clouds hosting extended green objects (EGOs) that are thought to trace outflows and are generally thought to be in an early stage of massive star formation (Cyganowski et al. 2008, 2011; Chen et al. 2013a,b), and clouds associated with HII regions based on the SIMBAD Astronomical Database1.

Table 2

CH3OH (422–312) spectral parameters.

Sources observed are listed in Table 1. Our observations were carried out in 2015 April, July, and October with the 15 m James Clerk Maxwell Telescope telescope (JCMT) on Mauna Kea. The beam size is ~23″ and the main-beam efficiency is ηmb = Ta∗/Tmb\hbox{$T_a^*/T_{\rm mb}$}≃ 0.7 at 218 GHz2. The para-H2CO JKAKC = 303–202, 322–221, and 321–220 transitions have rest frequencies of 218.222, 218.475, and 218.760 GHz, respectively, which are measured simultaneously by employing the ACSIS digital autocorrelation spectrometer with the special backend configuration RxA−H2CO−250 × 3 allowing for three windows, each with a bandwidth of 250 MHz3. This provides a velocity resolution of 0.084 km s-1 for para-H2CO (303−202 and 322−221) and 0.042 km s-1 for para-H2CO (321–220); CH3OH (422–312) at 218.440 GHz is also observed together with para-H2CO (322–221).

Data reduction for spectral lines was performed using Starlink4 and GILDAS5. To enhance signal-to-noise ratios (S/N) in individual channels, we smoothed contiguous channels to a velocity resolution ~0.33 km s-1.

3. Results

Of the 30 massive clumps observed (see Table 1), 25 are detected in the para-H2CO (303–202) line. Among the 25 para-H2CO (303–202) detections, 10 also show the para-H2CO (322–221) and (321–220) lines, while 18 also exhibit emission from the CH3OH (422–312) line (218.440 GHz), which is well separated from the para-H2CO (322–221) transition in all cases. The para-H2CO and the CH3OH line spectra are presented in Figs. A.1 and A.2. Line parameters are listed in Tables B.1 and 2, where integrated intensity (∫Tmbdv), local standard of rest velocity (Vlsr), line width (FWHM), and peak antenna brightness temperature (Tmb) were obtained from Gaussian fits. Five sources show no H2CO and CH3OH, namely G10.99-0.08, G13.28-0.3, G30.24+0.57, G31.70-0.49, and G34.37-0.66. G30.24+0.57 has a low H2 column density of 2.2 × 1022 cm-2 (Wienen et al. 2012). G10.99-0.08, G13.28-0.3, G31.70-0.49, and G34.37-0.66 are associated with infrared dark clouds, which have a low kinetic temperature in the range of 10.5–13.5 K. This suggests that para-H2CO and CH3OH are excited with difficulty in these low-density and/or low-temperature regions. Nevertheless, high detection rates of H2CO (~83%) and CH3OH (~60%) indicate that the two molecular species are commonly formed in the massive clumps of our sample.

thumbnail Fig. 1

Example of RADEX Non-LTE modeling of the N(H2CO)–n(H2) relation for a kinetic temperature of 40 K. The source is G5.89-0.39. Contours enclose regions of low reduced χ2red\hbox{$^2_{\rm red}$} based on 303–202 and 322−221 para-H2CO brightness temperatures. Contours are χ2red=3\hbox{$^2_{\rm red} = 3$}, 2, and 1.

3.1. H2CO column density

To determine the para-H2CO column densities and gas kinetic temperatures, we use the RADEX non-LTE model (van der Tak et al. 2007) offline code6 with collision rates from Wiesenfeld & Faure (2013). The RADEX code needs five input parameters: background temperature, kinetic temperature, H2 density, para-H2CO column density, and line width. For the background temperature, we adopt 2.73 K. Model grids for the para-H2CO lines encompass 40 densities (n(H2) = 103–108 cm-3), 40 para-H2CO column densities (N(para-H2CO) = 1012–1016 cm-2), and 40 temperatures ranging from 10 to 110 K. For the line width, we use the observed line width value.

thumbnail Fig. 2

Column densities of N(para-NH3) and N(para-H2CO) (derived at density 105 cm-3) (a), b)), fractional abundance of N(para-NH3)/N(H2) and N(para-H2CO)/N(H2) (c), d)), and N(para-NH3)/N(para-H2CO) (e), f)) vs. column density N(H2) and kinetic temperature Tkin(NH3).

Table 3

Para-H2CO column densities and kinetic temperature.

We ran RADEX to obtain beam averaged para-H2CO column densities and calculated the behavior of the χ2red\hbox{$^2_{\rm red}$} value of the observed 303–202 and 322–221 (or 321–220) para-H2CO line brightness temperatures (see Fig. 1). The value of χ2red\hbox{$^2_{\rm red}$} is defined as χred2=Σi(TR(obs)i−TR(mod)i)2σTR(obs)i2,\begin{equation} \chi^2_{\rm red} = \Sigma_{\rm i} \frac{(T_{\rm R(obs)_i}-T_{\rm R(mod)_i})^2}{\sigma_{T_{\rm R(obs)_i}}^2}, \end{equation}(1)where TR(obs)i and TR(mod)i represent the observed main beam brightness temperatures (Tmb) and RADEX non-LTE modeled brightness temperatures, and σ2TR(obs)i\hbox{$_{T_{\rm R(obs)_i}}^2$} represents the uncertainty in TR(obs)i including the rms noise in the spectra and the absolute temperature calibration uncertainty. One degree of freedom is used to the fit χ2red\hbox{$^2_{\rm red}$} value. The reduced χ2red\hbox{$^2_{\rm red}$} value depends of course on Tkin, but also to a lesser degree on H2 density and para-H2CO column density. To provide a feeling of the related uncertainties, we take as an example source G5.89-0.39 (see Fig. 1), which is a typical case. This figure shows that χ2red\hbox{$^2_{\rm red}$} depends on the H2 density and para-H2CO column density at low densities (n(H2) < 106 cm-3), while the kinetic temperature is kept constant at ~40 K (which is close to the actual temperature, see below). For higher densities, χ2red\hbox{$^2_{\rm red}$} decreases only slowly with H2 density. The entire plot provides a lower limit to the column density at N(H2CO) ~ 1014 cm-2.

The H2 density of the ATLASGAL clumps is ~105 cm-3 (Beuther et al. 2002; Motte et al. 2003; Wienen et al. 2012). As can be seen in Fig. 1, our characteristic source G5.89-0.39 also shows the lowest χ2red\hbox{$^2_{\rm red}$} values near this density, so we adopt an H2 volume density of n(H2) = 105 cm-3. The results are listed in Table 3. Including all sources, the N(para-H2CO) range is 0.4−47 × 1013 cm-2 with an average of 6.5 × 1013 cm-2, which agrees with the results from other star forming regions and from protostellar cores (Mangum et al. 1993; Hurt et al. 1996; Watanabe & Mitchell 2008). At densities n(H2) = 105 cm-3, the fractional abundance N(para-H2CO)/N(H2) becomes 0.4−5.4 × 10-10, where N(H2) is derived from the 870 μm continuum emission (Wienen et al. 2012).

The column densities of para-NH3 derived from the (1, 1) and (2, 2) lines (Wienen et al. 2012), those of para-H2CO (derived at density 105 cm-3), and the fractional abundances of N(para-H2CO)/N(H2), N(para-NH3)/N(H2), and N(para-NH3)/N(para-H2CO) with corresponding H2 column density and kinetic temperature Tkin(NH3) are shown in Fig. 2. The para-NH3 column densities range from 1015 to 1016 cm-2 and show no correlation with the H2 column density and gas kinetic temperature in the massive clumps (see Figs. 2a,b). Variations in the fractional abundance of N(para-NH3)/N(H2) amount to nearly two orders of magnitude (2.6 × 10-8–1.5 × 10-6). The N(para-NH3)/N(H2) ratio decreases with increasing H2 column density and kinetic temperature (see Figs. 2c,d). The para-H2CO column density increases proportionally with the H2 column density and gas kinetic temperature (see Figs. 2a,b). The fractional abundance of N(para-H2CO)/N(H2) remains stable with increasing H2 column density and kinetic temperature (see Figs. 2c,d). Nevertheless, the scatter amounts to 0.4–5.4, i.e., by more than a factor of 10. The relative abundances N(para-NH3)/N(para-H2CO) range from 4.9 × 100 to 7.4 × 102 and decrease with H2 column density and kinetic temperature (see Figs. 2e,f). The stable fractional para-H2CO abundances as a function of N(H2) and Tkin (see Figs. 2c,d) indicates that H2CO is a more reliable tracer of the H2 column density than NH3.

thumbnail Fig. 3

Example of RADEX non-LTE modeling of the para-H2CO kinetic temperature for G5.89-0.39. Para-H2CO 303–202 (red solid and dotted lines represent observed values and uncertainties), 322–221 and 321–220 (a) and b), blue solid and dotted lines) line brightness temperatures and para-H2CO 322–221/303–202 and 321–220/303–202 ratios (black solid and dotted lines). The gray region is characterized by χ2red\hbox{$^2_{\rm red}$} (<1.5) with density n(H2) and kinetic temperature Tkin for a para-H2CO column density 4.7 × 1014 cm-2.

We also derive averaged column densities and fractional abundances of para-NH3 and para-H2CO in the subsamples consisting of HII regions, EGOs, and IRDCs. For NH3, the average column densities N(para-NH3) are 1.84 (±1.00) × 1015, 2.32 (±0.45) × 1015, and 3.55 (±2.00) × 1015 cm-2, with the errors representing the standard deviations of the mean. The fractional abundances N(para-NH3)/N(H2) are 0.74 (±0.25) × 10-7, 0.74 (±0.37) × 10-7, and 2.06 (±0.67) × 10-7 in HII regions, EGOs, and IRDCs, respectively. For H2CO, the average column densities N(para-H2CO) are 1.16 (±1.35) × 1014, 1.04 (±0.93) × 1014, and 2.81 (±2.00) × 1013 cm-2. Fractional abundances N(para-H2CO)/N(H2) are 3.32 (±1.36) × 10-10, 2.53 (±1.21) × 10-10, and 1.23 (±0.66) × 10-10 in HIIs, EGOs, and IRDCs. Average variations of fractional abundances of N(para-H2CO)/N(H2) in different stages of star formation amount to nearly a factor of 3, which is similar to the amount of change seen in the fractional abundance N(para-NH3)/N(H2). Therefore, we confirm that H2CO can be widely used as a probe to trace the dense gas without drastic changes in abundance during various stages of star formation.

3.2. Kinetic temperature

The para-H2CO (303–202) line is the strongest of the three 218 GHz para-H2CO transitions. In order to avoid small uncertain values in the denominator, we used the para-H2CO 322−221/303−202 and 321−220/303–202 ratios to derive the kinetic temperature. The two ratios trace the kinetic temperature with an uncertainty of ≲25% below 50 K (Mangum et al. 1993). An example is presented to show how the parameters are constrained by the reduced χ2red\hbox{$^2_{\rm red}$} value, line brightness, and line ratio distribution of para-H2CO in the Tkin-n(H2) parameter space in Fig. 3. We used the column density derived at 105 cm-3 to constrain the kinetic temperature.

Our results are listed in Table 3. The para-H2CO 322−221/303–202 line ratio is sensitive to the gas density at spatial densities n(H2) < 105 cm-3 (see Fig. 3), so it seems that this line ratio is not quite as good as 321–220/303–202 as a thermometer to trace kinetic temperature in the low-density regions of a molecular cloud. At high density n(H2) ≳ 105 cm-3, the two ratios (322−221/303–202 and 321–220/303–202) show a similar behavior to kinetic temperature and spatial density. The comparison of kinetic temperatures derived from both para-H2CO 322−221/303−202 and 321–220/303–202 ratios suggests that the two ratios trace similar temperatures at a density of 105 cm-3 (see Table 3). The para-H2CO 322–221 and 321–220 transitions, have similar energy above the ground state, Eu ≃ 68 K, similar line brightness (see Table B.1), and are often detected at the same time (e.g., Bergman et al. 2011; Wang et al. 2012; Lindberg & Jørgensen 2012; Ao et al. 2013; Immer et al. 2014; Treviño-Morales et al. 2014; Ginsburg et al. 2016); therefore, para-H2CO 322–221/303–202 and 321–220/303–202 ratios are both good thermometers to determine kinetic temperature in dense regions (n(H2) ≳ 105 cm-3). However, at lower densities, the 321−220/303–202 ratio should be preferred.

The para-H2CO line intensity ratios 322–221/303−202 and 321–220/303–202 can provide a measurement of the kinetic temperature of the gas in local thermodynamic equilibrium (LTE). The kinetic temperature can be calculated from para-H2CO transitions assuming that the lines are optically thin, and originate from a high-density region (Mangum et al. 1993) Tkin=47.1ln(0.556I(303−202)I(322−221)),\begin{equation} T_{\rm kin} = \frac{47.1}{\ln(0.556\frac{I(3_{03}-2_{02})}{I(3_{22}-2_{21})})}, \end{equation}(2)where I(303–202)/I(322–221) is the para-H2CO integrated intensity ratio. The results of the kinetic temperature calculations from the para-H2CO 303–202/322–221 integrated intensity ratio are listed in Table 3. The kinetic temperatures derived from this method have an uncertainty of ≲30% (Mangum et al. 1993). Considering this uncertainty, the temperatures derived from LTE and the RADEX non-LTE model are consistent (see Table 3).

thumbnail Fig. 4

Comparison of integrated intensities of para-H2CO (303–202), CH3OH (422–312), NH3 (1, 1), and 870 μm continuum flux densities. Dashed lines are the results from linear fits. Solid lines correspond to Y = X. Gauss fitted peak temperatures and line widths of NH3 (1, 1) are from Wienen et al. (2012). Assuming Gaussian profiles, we plot integrated intensities calculated with ∫T(v)dv=π/4ln2\hbox{$T(v){\rm d}v = \sqrt{\pi/4 \ln 2}$}·Tpk·ΔVFWHM.

4. Discussion

4.1. Comparison of H2CO, CH3OH, NH3, and 870 μm emission

We compare the integrated intensities of para-H2CO (303–202), CH3OH (422–312), and NH3 (1, 1) with 870 μm emission in Fig. 4. It shows that the molecules follow the 870 μm intensity distribution. The integrated intensities of para-H2CO (303–202), CH3OH (422–312), and NH3 (1, 1) are also compared in Fig. 4. There is a good correlation between para-H2CO (303–202) and CH3OH integrated intensities (correlation coefficient R2 ~ 0.7). Line widths of para-H2CO (303–202) and CH3OH also tend to be similar (see Tables B.1 and 2). This suggests that the two molecules may trace similar regions and/or are chemically linked in their parent massive clumps.

H2CO and CH3OH are thought to be formed by successive hydrogenation of CO on grain surfaces: CO → HCO → H2CO → CH3O → CH3OH (Watanabe & Kouchi 2002; Woon 2002; Hidaka et al. 2004). Previous observations of para-H2CO and CH3OH in the Orion Bar photon-dominated region (PDR) have suggested that para-H2CO traces the interclump material. CH3OH is found mainly in the clumps, so that the two species trace different environments (Leurini et al. 2006, 2010). Our result differs from what is found for the Orion Bar, but is consistent with the majority of results where the two species are similarly distributed as in e.g., W3, CrA, L1157, W33, and NGC 2264 (Wang et al. 2012; Lindberg & Jørgensen 2012; Gómez-Ruiz et al. 2013; Immer et al. 2014; Cunningham et al. 2016). The likely reason is the different molecular environment. CH3OH is more easily photodissociated than H2CO in the PDRs.

For the integrated intensities of I(para-H2CO)–I(NH3) and I(CH3OH)–I(NH3), correlation coefficients (R2) are 0.4 and 0.3, respectively, so they are only weakly correlated. Nearly all line widths of para-H2CO (303–202) and CH3OH are greater than those of NH3 (1, 1) (see Tables B.1 and 2, and Tables 1 and 2 in Wienen et al. 2012). The weak correlation can be explained if para-H2CO and CH3OH trace a higher density gas than NH3 (1, 1).

4.2. Comparison of kinetic temperatures derived from H2CO and NH3

For our massive clump samples with kinetic temperatures derived by para-H2CO (321–220/303–202) and NH3 (2, 2)/(1, 1), the kinetic temperature ranges for para-H2CO from 30 to 61 K (average 46 ± 9 K), and for NH3 from 21 to 48 K (average 32 ± 8 K), respectively. The comparison of kinetic temperature derived from the para-H2CO (321–220/303–202) and the NH3 (2, 2)/(1, 1) line ratios is shown in Fig. 5. The kinetic temperatures derived from para-H2CO and NH3 agree in five sources, namely in G5.89-0.39, G5.90-0.44, G28.86+0.07, G31.40-0.26, and G35.19-0.74. Higher kinetic temperatures (difference >10 K) traced by para-H2CO as compared to NH3 are found in G12.91-0.26, G14.20-0.19, G14.33-0.64, G30.70-0.07, and G35.03+0.35. It seems that para-H2CO traces a slightly higher temperature than NH3 (2, 2)/(1, 1) in the massive clumps. The probable reason is that para-H2CO may trace hotter and denser regions, while the NH3 (2, 2)/(1, 1) line ratio traces cooler and more diffuse gas (Ginsburg et al. 2016). The different beam sizes for para-H2CO (JCMT beam ~23′′) and NH3 (Effelsberg beam ~40′′) data also have to be considered. The source sizes (FWHM) derived from para-H2CO range from 20′′ to 31′′ (Csengeri et al. 2014), which match the JCMT beam but are smaller than the Effelsberg beam. The smaller JCMT beam size compared to Effelsberg might imply that the para-H2CO data focus more on the inner active cloud cores than the NH3 data do. Therefore, the determination of kinetic temperature differences may be influenced, to a certain degree, by beam size.

For an evaluation of whether beam size or other parameters play the dominant role in revealing differences between Tkin(para-H2CO) and Tkin(NH3 (2, 2)/(1, 1)), we have to check observational results in a systematic way. The NH3 (1, 1) and (2, 2) transitions are sensitive to cold (10–40 K; Ho & Townes 1983; Mangum et al. 1992, 2013a) and dense (≳104 cm-3; Rohlfs & Wilson 2004) gas. Previous para-H2CO (322–221/303–202) and NH3 (2, 2)/(1, 1) observations toward protostars, bipolar flows, submillimeter clumps, far infrared sources, active star formation sources, the Galactic center, Large Magellanic Clouds, and starburst galaxies show significantly different gas kinetic temperatures. Previous observed results with different telescopes are listed in Table 4. For L1527, L1551, N159W, and W3IRS4, the kinetic temperature difference still is <30 K. Larger differences (>45 K) are found in NGC 2071 and NGC 2024FIR5. The most significant difference is in the starburst galaxy M82 (Tkin(NH3) deduced from (1, 1)–(3, 3), Weiß et al. 2001). Toward NGC 2071 and M82, the NH3 beam was the larger one, but in the case of NGC 2024FIR5 we find the opposite. We also find the opposite in the case of N159W, Tkin(NH3) < Tkin(para-H2CO) in spite of a smaller ammonia beam. Therefore, the beam size difference between our JCMT para-H2CO and the Effelsberg NH3 data is likely not a dominant factor.

As shown in Fig. 5, it seems that the differences between Tkin(para-H2CO) and Tkin(NH3 (2, 2)/(1, 1) vary with evolutionary stage of the respective massive star formation region. The derived kinetic temperatures from para-H2CO are distinctly higher than those from NH3 (2, 2)/(1, 1) in the clumps associated with EGOs (difference >14 K; G12.91-0.26, G14.20-0.19, G14.33-0.64, and G35.03+0.35). Similar temperature differences have been found in L1527, L1551, NGC 2024FIR5, NGC 2071, and W3IRS4, which are well-known outflow objects. The derived kinetic temperatures from NH3 (2, 2)/(1, 1) may reflect an average temperature of cooler and more diffuse gas. The outflow/shock could heat the dense gas traced by H2CO. Therefore, in these cases, para-H2CO probes higher temperature gas which appears to be related to gas excited by star formation activities (e.g., outflows, shocks). The kinetic temperatures derived from para-H2CO and NH3 (2, 2)/(1, 1) are in agreement in the sources associated with HII regions (difference <14 K; G5.89-0.39, G5.90-0.44, G28.86+0.07, and G31.40-0.26). This indicates that temperature gradients potentially probed by para-H2CO and NH3 (2, 2)/(1, 1) in different parts of the clouds are small. To conclude, para-H2CO is a good thermometer, like NH3, to trace the gas kinetic temperature (Tkin(gas) ≳30 K) in the molecular environment surrounding HII regions. Large differences in kinetic temperatures between Tkin(para-H2CO) and Tkin(NH3 (2, 2)/(1, 1) may indicate clouds in different evolutionary stages of massive star formation.

thumbnail Fig. 5

Comparison of kinetic temperatures derived from para-H2CO 321–220/303–202 (black squares) and NH3 (2, 2)/(1, 1) (red points) ratios. Para-H2CO and NH3 kinetic temperatures of L1551, L1527, NGC 2071, NGC 2024FIR5, and W3IRS4 are selected from Takano (1986), Mangum et al. (1993), Moriarty-Schieven et al. (1995), Jijina et al. (1999), and Watanabe & Mitchell (2008).

Table 4

Previous results of observed para-H2CO and NH3 temperatures.

The kinetic temperatures based on para-H2CO data disagree with the values obtained from NH3 (1, 1) and (2, 2), but agree with the properties of the high-excitation component traced by CO in the starburst galaxy M82 (Mühle et al. 2007). Ao et al. (2013) found that the para-H2CO kinetic temperatures are consistent with the temperatures derived from high-J NH3 (Mauersberger et al. 1986) in the Galactic CMZ. Higher excited NH3 lines commonly lead to higher kinetic temperatures. Therefore, if higher NH3 levels (e.g., NH3 (2, 2)/(4, 4); Mangum et al. 2013a; Gong et al. 2015) are also involved in measuring the kinetic temperatures, the values derived from para-H2CO and NH3 might become consistent in these sources where we have found a discrepancy. Thus detailed comparisons of Tkin values deduced from para-H2CO and high-J NH3 transitions would be meaningful.

4.3. Comparison of kinetic temperatures derived from the gas and the dust

The observed gas and dust temperatures do not agree in the Galactic CMZ (Güsten et al. 1981; Ao et al. 2013; Ott et al. 2014; Ginsburg et al. 2016; Immer et al. 2016). However, the temperatures derived from dust and gas are often in agreement in the active dense clumps of Galactic disk clouds (Dunham et al. 2010; Giannetti et al. 2013; Battersby et al. 2014). The dust temperatures are obtained from SED fitting to Herschel HiGal data at 70, 160, 250, 350, and 500 μm and ATLASGAL data at 870 μm for our samples, following the method described in König et al. (submitted). The results are listed in Table 1. The derived kinetic temperature range is 11–54 K (average 26 ± 8 K). A comparison of gas kinetic temperature derived from para-H2CO (321–220/303–202) and NH3 (2, 2)/(1, 1) against HiGal dust temperatures is shown in Fig. 6. For the temperatures derived from para-H2CO, most sources (G12.91-0.26, G14.20-0.19, G14.33-0.64, G28.86+0.07, G31.40-0.26, and G35.03+0.35) show a higher temperature (difference >9 K) than the HiGal dust temperature. The difference is due to the dust that may trace an average temperature covering a rather wide range of densities and is not as influenced by outflowing gas as para-H2CO. The gas temperatures determined from NH3 (2, 2)/(1, 1) agree with the HiGal dust temperatures considering the uncertainties, which agrees with previous results found in the active dense clumps of Galactic disk clouds (Dunham et al. 2010; Giannetti et al. 2013; Battersby et al. 2014).

4.4. Non-thermal motion and turbulence

We computed thermal linewidth (σT), non-thermal velocity dispersion (σNT), thermal sound speed (as), and the ratio of thermal to non-thermal pressure (Rp) (Lada 2003). The σT, σNT, as, and Rp are given by

σ T = k T kin m x , σ NT = Δ V 2 8 ln 2 − σ T 2 , a s = k T kin μ m H , R p = a s 2 σ NT 2 , \begin{eqnarray} &&\sigma_{\rm T} = \sqrt{\frac{kT_{\rm kin}}{m_x}},\\ &&\sigma_{\rm NT} = \sqrt{\frac{\Delta V^2}{8\ln2}-\sigma_{\rm T}^2},\\ &&a_{\rm s} = \sqrt{\frac{kT_{\rm kin}}{\mu m_{\rm H}}},\\ &&R_{\rm p} = \frac{a_{\rm s}^2}{\sigma_{\rm NT}^2}, \end{eqnarray}

where k is the Boltzmann constant, Tkin is the kinetic temperature of the gas, mx is the mass of the relevant molecule, ΔV is the measured FWHM linewidth of either the para-H2CO 303–202 or the NH3 (1, 1) transitions, μ = 2.37 is the mean molecular weight for molecular clouds, and mH is the mass of the hydrogen atom. The derived values of σT, σNT, as, and Rp are listed in Table 5.

thumbnail Fig. 6

Comparison of gas kinetic temperatures derived from para-H2CO 321–220/303–202 (black squares) and NH3 (2, 2)/(1, 1) (red points) ratios against the HiGal dust temperatures. The straight line indicates locations of equal temperatures. Two sources (G5.97-1.36 and G17.10+1.02) with particularly large Tkin(NH3) errors are not shown here.

Comparisons of velocity dispersion, thermal sound speed, and kinetic temperature are shown in Fig. 7 and Table 5. The derived non-thermal velocity dispersions of para-H2CO and NH3 are higher than the thermal linewidths. This indicates that the line broadening of para-H2CO and NH3 is dominated by non-thermal motions in these massive clumps. Para-H2CO traces higher non-thermal motions (average σNT = 2.1 ± 0.6 km s-1) than those traced by NH3 (for our selected sample, the average becomes σNT = 1.1 ± 0.4 km s-1; for all NH3 samples observed by Wienen et al. 2012, the average becomes σNT = 0.9 ± 0.4 km s-1). Para-H2CO linewidths appear to be affected strongly by non-thermal motions.

The average values of the Mach number (given as M = σNT/as) for para-H2CO and NH3 are 6.2 ± 1.5 and 3.4 ± 1.1, which indicates that the velocity distributions within these massive clumps are significantly influenced by supersonic non-thermal components (e.g., turbulent motions, infall, outflow, rotation, shocks, and/or magnetic fields; Urquhart et al. 2015). The mean value of the Mach number derived from NH3 agrees with the result (~3.2) of the Bolocam Galactic Plane Survey (BGPS) sources (Dunham et al. 2011). The determined ratio of thermal to non-thermal pressure, Rp (see Eq. (6)), ranges from 0.01 to 0.05 and the average becomes 0.03 ± 0.01 for para-H2CO. For NH3, we find values between 0.02 and 0.37 and the average becomes 0.11 ± 0.08 (all NH3 samples observed by Wienen et al. 2012, yield 0.01–0.47 and the average becomes 0.10 ± 0.06). The low Rp values indicate that non-thermal pressure is dominant in these massive clumps.

thumbnail Fig. 7

Non-thermal velocity dispersion (σNT) vs. gas kinetic temperature for para-H2CO (black squares) and NH3 (red points). For the black squares, the gas kinetic temperatures were derived from para-H2CO 321–220/303–202 line ratios. For the red points, they were obtained from the NH3 (2, 2)/(1, 1) line ratios. The black line is the corresponding thermal sound speed. Two sources (G5.97-1.36 and G17.10+1.02) with particularly large Tkin(NH3) errors are not shown here.

It is expected that the correlation between kinetic temperature and line width is due to a conversion of turbulent energy into heat (Güsten et al. 1985; Molinari et al. 1996; Ginsburg et al. 2016; Immer et al. 2016). Recent para-H2CO observations of the CMZ have shown that the warm dense gas is most likely heated by turbulence (Ao et al. 2013; Ginsburg et al. 2016; Immer et al. 2016). Clumps formed in turbulent molecular clouds are significantly affected by the temperature of the cloud material (Bethell et al. 2004). We examine whether there is a relationship between turbulence and temperature in our massive clumps. We adopt the non-thermal velocity dispersion of NH3 and para-H2CO as proxy for the turbulence, and the kinetic temperatures of NH3 (2, 2)/(1, 1) and para-H2CO (321–220/303–202) as the gas kinetic temperature. Figure 7 shows that the non-thermal velocity dispersion of NH3 and para-H2CO are significantly positively correlated with the gas kinetic temperature. This implies that those massive clumps are turbulent and the gas may be heated by turbulent heating.

Table 5

Thermal and non-thermal parameters.

5. Summary

We have measured the kinetic temperature with para-H2CO (JKAKC = 303–202, 322–221, and 321–220) and compare the kinetic temperature derived from this formaldehyde 218 GHz line triplet with those obtained from ammonia for 30 massive star forming clumps using the 15 m JCMT. The main results are the following:

  • 1.

    The integrated intensity distributions of para-H2CO, CH3OH, and NH3 agree well with the 870 μm intensity distributions. The integrated intensities and linewidths of H2CO and CH3OH are also consistent in our clumps. They may trace similar regions and/or be chemically linked, while the correlation with NH3 is less pronounced.

  • 2.

    Using the RADEX non-LTE model, we derive gas kinetic temperatures by modeling the measured para-H2CO 322−221/303–202 and 321–220/303–202 line ratios. We find that the two ratios are good thermometers to trace kinetic temperatures in dense regions (n(H2) ≳ 105 cm-3) of the massive clumps, while for lower densities the 321–220/303–202 line ratio should be preferred.

  • 3.

    The gas kinetic temperature of the massive clumps measured by NH3 (2, 2)/(1, 1) line ratios (Wienen et al. 2012) ranges from 11 to 61 K (average 27 ± 12 K). The derived dust temperature range from Herschel HiGal data is 11–54 K with an average of 26 ± 8 K. The gas kinetic temperature derived from para-H2CO (321–220/303–202) line ratios of the massive clumps ranges from 30 to 61 K with an average of 46 ± 9 K, which is higher than that measured by the NH3 (2, 2)/(1, 1) transitions and the dust emission.

  • 4.

    A comparison of kinetic temperatures derived from para-H2CO, NH3 (2, 2)/(1, 1), and the dust emission indicates that in many cases para-H2CO traces a similar kinetic temperature to the NH3 (2, 2)/(1, 1) transitions and the dust associated with the HII regions. Distinctly higher temperatures are probed by para-H2CO in the clumps associated with outflows/shocks.

  • 5.

    Kinetic temperatures obtained by para-H2CO trace turbulence to a higher degree than NH3 (2, 2)/(1, 1) in the massive clumps. The non-thermal velocity dispersions of para-H2CO and, to a lesser degree, NH3 are positively correlated with the gas kinetic temperature. The massive clumps are significantly influenced by supersonic non-thermal motions.

Acknowledgments

We thank the staff of the JCMT telescope for their assistance in observations. The authors are grateful for the helpful comments of the referee. We thank Jens Kauffmann and Yan Gong for valuable comments. 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, and partly supported by the National Basic Research Program of China (973 program, 2012CB821802). 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).

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Appendix A: Spectra of para-H2CO and CH3OH

thumbnail Fig. A.1

Spectra of para-H2CO. Black: para-H2CO 303–202, Red: para-H2CO 322–221, and Blue: para-H2CO 321–220.

thumbnail Fig. A.2

CH3OH (422–312) spectra.

Appendix B: Additional table

Table B.1

Para-H2CO spectral parameters.

All Tables

Table 1

Source parameters.

In the text
Table 2

CH3OH (422–312) spectral parameters.

In the text
Table 3

Para-H2CO column densities and kinetic temperature.

In the text
Table 4

Previous results of observed para-H2CO and NH3 temperatures.

In the text
Table 5

Thermal and non-thermal parameters.

In the text
Table B.1

Para-H2CO spectral parameters.

In the text

All Figures

thumbnail Fig. 1

Example of RADEX Non-LTE modeling of the N(H2CO)–n(H2) relation for a kinetic temperature of 40 K. The source is G5.89-0.39. Contours enclose regions of low reduced χ2red\hbox{$^2_{\rm red}$} based on 303–202 and 322−221 para-H2CO brightness temperatures. Contours are χ2red=3\hbox{$^2_{\rm red} = 3$}, 2, and 1.
In the text
thumbnail Fig. 2

Column densities of N(para-NH3) and N(para-H2CO) (derived at density 105 cm-3) (a), b)), fractional abundance of N(para-NH3)/N(H2) and N(para-H2CO)/N(H2) (c), d)), and N(para-NH3)/N(para-H2CO) (e), f)) vs. column density N(H2) and kinetic temperature Tkin(NH3).
In the text
thumbnail Fig. 3

Example of RADEX non-LTE modeling of the para-H2CO kinetic temperature for G5.89-0.39. Para-H2CO 303–202 (red solid and dotted lines represent observed values and uncertainties), 322–221 and 321–220 (a) and b), blue solid and dotted lines) line brightness temperatures and para-H2CO 322–221/303–202 and 321–220/303–202 ratios (black solid and dotted lines). The gray region is characterized by χ2red\hbox{$^2_{\rm red}$} (<1.5) with density n(H2) and kinetic temperature Tkin for a para-H2CO column density 4.7 × 1014 cm-2.
In the text
thumbnail Fig. 4

Comparison of integrated intensities of para-H2CO (303–202), CH3OH (422–312), NH3 (1, 1), and 870 μm continuum flux densities. Dashed lines are the results from linear fits. Solid lines correspond to Y = X. Gauss fitted peak temperatures and line widths of NH3 (1, 1) are from Wienen et al. (2012). Assuming Gaussian profiles, we plot integrated intensities calculated with ∫T(v)dv=π/4ln2\hbox{$T(v){\rm d}v = \sqrt{\pi/4 \ln 2}$}·Tpk·ΔVFWHM.
In the text
thumbnail Fig. 5

Comparison of kinetic temperatures derived from para-H2CO 321–220/303–202 (black squares) and NH3 (2, 2)/(1, 1) (red points) ratios. Para-H2CO and NH3 kinetic temperatures of L1551, L1527, NGC 2071, NGC 2024FIR5, and W3IRS4 are selected from Takano (1986), Mangum et al. (1993), Moriarty-Schieven et al. (1995), Jijina et al. (1999), and Watanabe & Mitchell (2008).
In the text
thumbnail Fig. 6

Comparison of gas kinetic temperatures derived from para-H2CO 321–220/303–202 (black squares) and NH3 (2, 2)/(1, 1) (red points) ratios against the HiGal dust temperatures. The straight line indicates locations of equal temperatures. Two sources (G5.97-1.36 and G17.10+1.02) with particularly large Tkin(NH3) errors are not shown here.
In the text
thumbnail Fig. 7

Non-thermal velocity dispersion (σNT) vs. gas kinetic temperature for para-H2CO (black squares) and NH3 (red points). For the black squares, the gas kinetic temperatures were derived from para-H2CO 321–220/303–202 line ratios. For the red points, they were obtained from the NH3 (2, 2)/(1, 1) line ratios. The black line is the corresponding thermal sound speed. Two sources (G5.97-1.36 and G17.10+1.02) with particularly large Tkin(NH3) errors are not shown here.
In the text
thumbnail Fig. A.1

Spectra of para-H2CO. Black: para-H2CO 303–202, Red: para-H2CO 322–221, and Blue: para-H2CO 321–220.
In the text
thumbnail Fig. A.2

CH3OH (422–312) spectra.
In the text

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