ALMA High-resolution Spectral Survey of Thioformaldehyde (H₂CS) Towards Massive Protoclusters

The targeted 11 IRAS sources are a subsample of the ATOMS survey toward 146 massive protoclusters by Liu et al. (2016). The 146 massive protoclusters are very diverse that are suitable for statistics studies for the physical and chemical processes of star formation with different physical conditions. Among them, 30 sources are identified with ”blue profiles” which indicate infall emotions (Chira et al., 2014). Further more, 18 out of the 30 sources are found to be featured by HCN(3-2) and CO(4-3) lines and have virial parameters less than 2 (Yue et al., 2021), suggesting that the 18 sources are experiencing global collapse and undergoing star formation. Finally, 11 massive and luminous sources with collapsing signature were observed with the ALMA.

Table 1 shows key parameters of our sample, such as J2000.0 positions, systemic velocities, distances from the sun and Galactic center, source radius, averaged dust temperatures, bolometric luminosity, and clump mass. Our sources are high-mass star forming regions with bright CS $\rm J=2-1$ emission (T_b $>$ 2 K) indicating dense gas (Bronfman et al., 1996), and bolometric luminosities above 10⁴ L_☉ implying at least a B0.5 type star (Faúndez et al., 2004). The gas mass of all sources exceeds 10³ M_☉. The clump-averaged temperatures range from 23 to 32 K with a median of 28 K.

We observed 11 massive protocluster clumps with ALMA cycle 5 Band-7 from May 18 to May 20, 2018 (UTC) using 43 12-meter antennas in the C43-1 configuration (Project ID: 2017.1.00545.S; PI: Tie Liu). The observations covered four spectral windows (SPWs 31, 29, 27 and 25) with increasing spectral frequency ranges: (i) 342.36-344.24 GHz, (ii) 344.25-346.09 GHz, (iii) 354.27-354.74 GHz, and (iv) 356.60-357.07 GHz. Each window has 1920 channels with a bandwidth of 1875.00 MHz for SPW 31 and SPW 29, and 468.75 MHz for SPW 27 and SPW 25. The integrate on-source time was $\sim$ 3.7 minutes per source. J1650-5044 and J1924-2914 were used as atmosphere, flux and phase calibrators, while J1924-2914 as a bandpass calibrator. We calibrated the visibility data set using CASA software version 5.1.15 with the standard pipeline provided by the ALMA Observatory and imaged it with the TCLEAN task in CASA 5.3.

ALMA Band-7 is ideal for studying interstellar molecules, especially organic and inorganic ones, at high resolution and sensitivity (Jacobsen et al., 2019; Manigand et al., 2021; Lee et al., 2023). We analyzed the spectral lines in two spectral windows (SPW 31 and SPW 29) because of their wide frequency band, which contain a rich molecular line transitions. With a spatial resolution of $\sim$ 0.8–1.2$\arcsec$, and a high sensitivity of $\sim$ 1.2 mJy beam^-1 for continuum and $\sim$ 4.7 mJy per channel for lines, we could easily observe molecular emission lines that could not be found in previous lower resolution observations (Shimonishi et al., 2023).

Molecular lines are powerful tools for revealing the physical state of gas density structures and for exploring various astrochemical processes therein. As mentioned earlier, a total of 145 dense cores have been identified in 11 massive protocluster sources. We extracted the molecular lines from the continuum peak position of each core. Nine transitions of H₂CS are tuned in SPWs 29 and 31 (Maeda et al., 2008; Müller et al., 2019), and their corresponding parameters are summarized in Table A2. The E_u of H₂CS covers a wide range of energy levels from 91 to 419 K, allowing accurately determine the rotation temperature and column density. Therefore, two isolated H₂CS lines with E_u of 90.59 and 143.37 K and two mutually blended H₂CS lines with E_u of 209.09 K were selected for a reliable parameters fitting, as they are separated from other molecular lines and spectrally resolved with higher signal to noise ratios.

By inputting presupposed parameters (the deconvolved size of the continuum core, rotation temperature, source-averaged column density, FWHM, and $\rm V_{off}$), we utilized the XCLASS (Möller et al., 2017) software to obtain the best-fit parameters for rotation temperature, source-averaged H₂CS column density, FWHM, and $\rm V_{off}$ for cores with $\geq$ 3 H₂CS lines. The $\rm V_{off}$ range was approximately determined relative to the systemic velocity $\rm V_{lsr}$ of each source, while the range of the other three parameters was constrained through manual matching. For cores with two velocity components, we set two H₂CS components with different parameters for simultaneous fitting, the final column density is the sum of the two components, and the temperature of the velocity component with higher temperature is used to calculate the column density of H₂. And for the cores with only one $\rm J_{K_{a},K_{c}}=10_{0,10}-9_{0,9}$ line, the temperature was set to the same as that of the natal clump (with an error of 20%), and subsequently the column density parameter was fitted separately.

We also calculated the optimal outcomes using two algorithm namely Genetic algorithm (GA) and Levenberg-Marquardt algorithm (LM) and determined the errors of temperatures and column densities using the Markov chain Monte Carlo algorithm (MCMC). All fitted H₂CS parameters are summarized in columns (5) to (8) of Table 2.

Here we define line-rich cores as those with abundant molecular spectral lines (at least 50 lines) and potential CH₃OCHO detection (Kurtz et al., 2000; Ceccarelli, 2004; Jørgensen et al., 2020). Warm cores have H₂CS detection but no CH₃OCHO detection. Cold cores have only one or no H₂CS line. Among the 145 cores, 28 cores are considered line-rich with at least 50 lines detected in SPWs 29 and 31 (Liu et al., 2023). Additionally, 25 less-line-rich cores (warm cores) and 92 cores with several molecular lines (cold cores) are also found. We used the XCLASS (Möller et al., 2017) software for H₂CS line identification. Among the 145 cores, 72 have H₂CS line emission. Multiple H₂CS lines can be detected in all line-rich and warm cores, and 19 out of 92 cold cores only have single H₂CS line transition. The reason whether a core has H₂CS transition detected may be attributed to the relationship between the continuum peak flux (F_P) and mass of the core (M_core). Figure 2 illustrates 145 cores that the peak flux of 84.7% (61 out of 72) cores containing H₂CS meets Log F_P $>$ 0.3 Log M_core + 1.2 and the peak flux of 84.9% (62 out of 73) cores without H₂CS has Log F_P $<$ 0.3 Log M_core + 1.2.

Figure 3 shows typical H₂CS lines in I16076 for ”line-rich core”, ”warm core”, and ”cold core”. These three types of cores show different number and emission intensity of molecular lines. The fitting results of the other cores are shown in Figure A2.

Figure 4 shows the 870 $\mu$m continuum maps of the 11 protocluster clumps, overlaid with contours of the H₂CS $\rm J_{K_{a},K_{c}}=10_{0,10}-9_{0,9}$ Moment 0 (integrated intensity) maps. For the continuum maps, we zoom in on the central regions of the protoclusters to see the intensities of H₂CS emissions in detail. The moment 0 maps demonstrate that H₂CS is widely distributed throughout the clumps.

Among our targeted 11 sources, I14382 and I17204 are 2 sources with a few molecular emission lines and only contain warm cores and cold cores, and H₂CS is distributed within very small areas around warm cores. For the two sources I14498 and I15596, the emissions of H₂CS molecule are mainly around the compact regions of the line-rich cores. And for the remaining 7 sources, the spatial distribution of H₂CS emission is similar with the dust emission. The observations revealed that the emission of H₂CS is originated from extended regions surrounding both compact line-rich cores and warm cores and also can cover plenty of regions of the cold cores.

Temperature is an indicator of the interstellar chemical complexity and star formation process (Sánchez-Monge et al., 2017; Gorai et al., 2020; Liu et al., 2020a; Peng et al., 2022). It affects the mass estimation of dense gas. It also provides the main thermal pressure source within molecular gas (Rosen et al., 2020; Rosen, 2022), which counteracts gravity in the early stages of star formation. Thus, accurate temperature measurements enable an appropriate understanding of star formation mechanism. H₂CS can provide such an useful tracer of gas temperature.

Table 3 lists the number of these three-type cores. The H₂CS temperature ranges from 23 to 121 K for all cores. The range is 68 to 121 K for line-rich cores and 40 to 88 K for warm cores. The temperatures for cold cores range from 23 to 32 K, which are equal to the clump temperatures. Compared to the temperatures of CH₃OCHO of line-rich cores, H₂CS shows no significant temperature differences within uncertainties, because the molecule is thermalized in line-rich core regions. Therefore, we choose the higher gas temperature of H₂CS and CH₃OCHO as $\rm T_{d}$. In addition, H₂CS is more widely distributed than CH₃OCHO in protoclusters and can applicably determine the temperature of cold cores, warm cores and line-rich cores, indicating that H₂CS is a more efficient temperature tracer as it can trace more extended regions than CH₃OCHO.

Based on Table 2 and Figure 5, several significant characteristics can be found among line-rich, warm, and cold cores by comparing $\rm N_{H_{2}}$ and $\rm N_{H_{2}CS}$ parameters. For line-rich cores, $\rm N_{H_{2}CS}$ ranges from $3.8\times 10^{14}$ to $3.6\times 10^{16}$ $\rm cm^{-2}$, with a mean of $8.0\times 10^{15}$ $\rm cm^{-2}$. For warm and cold cores, $\rm N_{H_{2}CS}$ ranges from $2.1\times 10^{13}$ to $1.9\times 10^{15}$ $\rm cm^{-2}$ and $5.6\times 10^{13}$ to $4.5\times 10^{14}$ $\rm cm^{-2}$, with means of $4.0\times 10^{14}$ and $1.5\times 10^{14}$ $\rm cm^{-2}$, respectively. The line-rich cores have higher $\rm N_{H_{2}CS}$ values than the other two types of cores. The warm cores have a wider range of $\rm N_{H_{2}CS}$ than the cold ones, but the values overlap, despite the mean $\rm N_{H_{2}CS}$ of warm cores being much higher (about twice) than that of cold cores.

The abundance of H₂CS versus H₂ ($\rm f_{H_{2}CS}$) is calculated via $\rm N_{H_{2}CS}$/$\rm N_{H_{2}}$. Apparently, $\rm f_{H_{2}CS}$ varies similarly to $\rm N_{H_{2}CS}$. Numerous studies have analyzed $\rm N_{H_{2}CS}$ and $\rm f_{H_{2}CS}$ in diverse massive star formation regions. Table A3 lists the results of previous studies on H₂CS in line-rich cores of massive star formation regions. We combine these 7 line-rich cores with our 28 line-rich core samples, resulting in 35 line-rich core samples. Among the line-rich cores, Mon R 2 IRS 3 A (Fuente et al., 2021) and Sgr B2 (Möller et al., 2021) have lower $\rm N_{H_{2}CS}$ than the line-rich cores studied here. Except for these 2 line-rich cores, the other 33 have similar $\rm N_{H_{2}CS}$ ranges from $4.5\times 10^{14}$ to $3.6\times 10^{16}$ $\rm cm^{-2}$. These results indicate that $\rm N_{H_{2}CS}$ varies greatly among different line-rich cores within and outside the Galaxy.

Similarly, due to physical differences, $\rm N_{H_{2}}$ can vary greatly among different interstellar environments, leading to variation in $\rm f_{H_{2}CS}$. It is worth noting that I16351 core7 has a very high $\rm f_{H_{2}CS}$ of $1.6\times 10^{-7}$. The reason for this large value is its high $\rm N_{H_{2}CS}$ and low $\rm N_{H_{2}}$. Except for this line-rich core, the abundance values of the other 34 are within the same range, from $1.7\times 10^{-10}$ to $5.1\times 10^{-8}$.

Through the results collated in Table 2, we can clearly find that temperature has a significant effect on the value of H₂CS abundance. Considering two variables X and Y, the formula for Pearson’s correlation coefficient r can be expressed as:

where $\rm\bar{X}$ and $\rm\bar{Y}$ are the mean values of X and Y. The value of Pearson’s correlation coefficient for temperature and $\rm f_{H_{2}CS}$ is 0.71. The value of $\rm f_{H_{2}CS}$ relies on temperature, and the corresponding trend line shown in left panel of Figure 5 is fitted as,

with uncertainties of 9.4% and 1.3% for slope and intercept. We find the abundance tends to increase with increasing temperature. H₂CS molecule is thought to be trapped on icy dust grains and principally form on dust grain surface at low temperatures (Jørgensen et al., 2020), and is generally desorbed from the grain surface into gas-phase as the temperature increases (Vidal & Wakelam, 2018; Vidal et al., 2019). The chemical property of H₂CS in the hot regions is to a high degree inherited from the surrounding cold dust regions (el Akel et al., 2022). Therefore $\rm f_{H_{2}CS}$ would be a good tracer of gas temperature.

Since $\rm N_{H_{2}CS}$ and $\rm f_{H_{2}CS}$ show the same trend in all types of cores, it would be pertinent to discuss the relationship of $\rm N_{H_{2}CS}$ and $\rm f_{H_{2}CS}$. The value of Pearson’s correlation coefficient for $\rm N_{H_{2}CS}$ and $\rm f_{H_{2}CS}$ is 0.88, indicating a high correlation between H₂CS and H₂.

The correlation between $\rm N_{H_{2}CS}$ and $\rm f_{H_{2}CS}$ is shown in right panel of Figure 5. We can see that $\rm N_{H_{2}CS}$ is sensitive to changes in $\rm f_{H_{2}CS}$. Thus, the trend line of $\rm N_{H_{2}CS}$ and $\rm f_{H_{2}CS}$ can be expressed using the following equation,

with uncertainties of 5.3% and 3.1% for slope and intercepts. The red dots represent line-rich cores that have abundant organic molecules and high temperatures, column densities, and abundances of H₂CS. The line-rich cores have higher $\rm N_{H_{2}CS}$ and $\rm f_{H_{2}CS}$ than warm cores and cold cores. Additionally, warm cores are largely scattered above the line, while cold cores are below the line. This indicates that warm cores have higher $\rm f_{H_{2}CS}$ than cold cores at same $\rm N_{H_{2}CS}$.

This trend suggests that different regions have varying chemical characteristics and that the H₂CS abundances are enhanced from cold cores, warm cores to line-rich cores. Additionally, this proportional relationship can provide insights into the distribution and formation of H₂CS in interstellar space. Further observations and studies are still needed to better understand the physical and chemical properties of H₂CS in space.