Understanding the various evolutionary stages of the low-mass star-formation process by SO and SO2

SO and SO₂ are two potential candidates to trace the different evolutionary phases of the low-mass star-formation process. Here, we report observations of SO and SO₂ along with their isotopologues, ³⁴SO and ³⁴SO_2, respectively, in four distinct phases of the low-mass star-formation process (prestellar core, first hydrostatic core, Class 0, and Class I) with an unbiased survey carried out using the Institut de Radioastronomie Millimetrique (IRAM) 30 m telescope. Interestingly, the estimated abundances of SO and SO₂ show an increasing trend from the prestellar phase to the Class 0 stage and then a decrease in the Class I phase. A similar trend is obtained for OCS and H₂S. In contrast, the obtained SO/SO₂ ratio decreases gradually from the prestellar core to the Class I stage. We have used the three-phase Rokko chemical code to explain our observations. The modeled abundances of SO and SO₂ exhibit an increase within the inner region as the cold gas transforms into a hot gas. The modeled abundance ratio of SO to SO₂ exhibits a notably high value in cold gas environments. This ratio decreases to less than 1 within the temperature range of 100–300 K and then increases to approximately 1 beyond 300 K. In the outer region, the simulated ratio consistently exceeds the value of 1. Our work is an observational testbed for modeling the chemistry of SO/SO₂ during low-mass star formation. However, our findings may require more sample sources with higher resolution and a more robust model for validation.

1 Introduction

Sulfur is the 10th most abundant ($\sim 10^{-5}$; García-Rojas et al., 2006; Martín-Hernández et al., 2002) element in the interstellar medium (ISM) and is known to play a significant role in biological systems. Several sulfur-bearing molecules and ions have been observed in the ISM and circumstellar shells (McGuire, 2022, CDMS (https://cdms.astro.uni-koeln.de/classic/molecules)) in the Milky Way, as well as in solar nebula (Fegley Jr, 1999; Pasek et al., 2005; Mandeville, 2010), comets (Biver et al., 1997; Woodney et al., 1997), and other galaxies (Shimonishi et al., 2016; 2018; 2023). The largest sulfur-bearing molecule, ethyl mercaptan, C₂H₅SH, was recently observed in Orion (Kolesniková et al., 2014). The chemistry of interstellar sulfur is still undetermined. Only approximately $0.1\%$ of the measured gas-phase abundance of sulfur-bearing species is found in diffuse clouds compared to dense clouds (Tieftrunk et al., 1994; Charnley, 1997; Wakelam et al., 2004; Jenkins, 2009; Vastel et al., 2018). This reduction in abundance significantly impacts the chemistry of star-forming regions (Jenkins, 2009; Rivière-Marichalar et al., 2019). Since sulfur and oxygen are chalcogens and belong to the same periodic group, their chemical properties are expected to be comparable. The lower electronegativity of sulfur relative to oxygen allows sulfur to absorb a positive charge more easily, while allowing hydrogen bonds to be created. This makes sulfur chemistry more diverse.

SO emission has been found in the disc component of Class 0/I sources and the outflow cavity walls (Sakai et al., 2014; Harsono et al., 2014; Tychoniec et al., 2021), and SO₂ is commonly seen in compact emission toward Class 0 sources and has been suggested to trace accretion shocks at the disk–envelope interface (Oya et al., 2019; Artur et al., 2022). Buckle and Fuller (2003) studied the chemical evolution of SO, SO₂, and H₂S in the low-mass star-formation process. They showed that the chemical evolution of sulfur-bearing species could be a potential indicator of the chemical timescales in the low-mass star-formation process. It has long been proposed that H₂S (Smith, 1991; Charnley, 1997; Navarro-Almaida et al., 2020) and/or Carbonyl Sulfide (OCS) (Hatchell et al., 1998; van der Tak et al., 2003) are major sulfur grain reservoirs, forming SO, SO₂, and other S-bearing molecules in the gas phase (Esplugues et al., 2014; Podio et al., 2014; Holdship et al., 2016). H₂S has not yet been found in the solid phase, although OCS and SO₂ have been detected or tentatively detected in the interstellar ices (Palumbo et al., 1995; Boogert et al., 1997; Rocha et al., 2024). In the cold molecular region, H₂S is the main sulfur reservoir (Smith, 1991; Navarro-Almaida et al., 2020), although it is still debatable in which form sulfur is locked in ice. However, SO/H₂S and SO/SO₂ are suitable molecular clocks for measuring the hot-core evolution (Smith, 1991). Gorai et al. (2017); Laas and Caselli (2019) suggested that various organo-sulfur species are found in the solid phase with lower abundances. Fuente et al. (2023) listed the 20 most abundant sulfur-bearing species, in order of decreasing abundance toward low-, intermediate-, and high-mass star-forming regions that are representative of Taurus, Perseus, and Orion A molecular clouds, respectively. In particular, theoretical work and laboratory experiments show that sulfur allotropes, such as S₈, could be an important reservoir of sulfur (Wakelam et al., 2004; Jiménez-Escobar et al., 2012; Shingledecker et al., 2020; Cazaux et al., 2022). Zhang et al. (2023) compared the distributions of sulfur-bearing molecules (SO, SO₂, ³⁴SO, and CS) and dust polarization of nine sources from the Perseus molecular cloud. This comparative analysis may offer additional diagnostics of physical properties and grain alignment mechanisms in star-forming processes, especially for the shocked regions.

Various sulfur-related molecules, including SO and SO₂ with their ³⁴S isotopologues, were observed at millimeter wavelengths by Herpin et al. (2009) in two mid-infrared quiet and two brighter massive cores with the IRAM 30 m and Caltech Submillimeter Observatory (CSO) telescopes. The study of the differences in abundance ratios between sources shows that the relative abundances of SO and SO₂ increase with time. They found that molecular ratios like SO/SO₂ may be a useful indicator of evolution, depending on the layers probed by the observed molecular transitions. An extensive statistical analysis on detection rates, emitting regions, and molecular column densities of simple sulfur-bearing molecules SO, CS, ³⁴SO, and SO₂, toward a sample of 50 Class 0/I sources in the Perseus star-forming region, was carried out by Artur et al. (2023) in the framework of the Perseus ALMA (Atacama Large Millimeter/submillimeter Array) Chemical Survey (PEACHES; Yang et al., 2021). They demonstrated that the ³²SO/³⁴SO ratio is a useful indicator of the inner high-density envelope and could be used to infer the existence of multiple COMs. Recently, Fontani et al. (2023) analyzed an observation of S-bearing molecules with the IRAM 30 m telescope toward 15 well-known cores classified in the three main evolutionary stages (high-mass starless cores, high-mass protostellar objects, and ultracompact HII regions) of the high-mass star-formation process. The molecular abundances of SO, SO₂, and H₂S exhibit the largest positive correlation with the kinetic temperature, which is thought to be an indicator of evolution.

This paper mainly focuses on the observation of SO and SO₂ in their ground state $(v=0)$ and their isotopologues toward four different stages of the low-mass star formation: prestellar core (PC, L1544), first hydrostatic cores (FHSC, B1-b), Class 0 (IRAS4A), and Class I (SVS13A) phases. Since it is not possible to observe the temporal evolution of a molecular cloud over such an astronomical period, we have used the ASAI (Astronomical Surveys At IRAM; see Section 2 for project description) data, which focus on the study of different evolutionary stages of the low-mass star-formation process. Here, we report the identification of OCS, H₂S, SO, SO₂, ³⁴SO, and ³⁴SO₂ obtained in these four sources. We use rotational diagram analysis to estimate the excitation temperature and column density of these species. Finally, an astrochemical model is used to simulate the abundance of SO and SO₂ for different stages and to compare the simulated abundances with observed values to understand its correlation with different evolutionary stages.

This paper is organized as follows. Section 2 presents the observations and brief information about the targeted sources. Section 3 describes the method used. Results and discussion are presented in Section 4 and Section 5, respectively. Finally, we provide the conclusion in Section 6.

2 Observations and targets

We use publicly available archival data from one of the official repositories of the ASAI data at IRAM. Observations were made with the IRAM 30 m telescope at Pico Veleta (Spain) in the framework of large program ASAI (PIs: Bertrand Lefloch and Raphael Bachiller) data using the broad-band Eight MIxer Receiver (EMIR) connected to the fast Fourier transform spectrometers (FFTSs). These observations cover three frequency bands: 3 mm ($80-116$ GHz), 2 mm ($130-172$ GHz), and 1.3 mm ($200-276$ GHz). The 3-mm observations were performed with a higher spectral resolution of 50 kHz, whereas the 1- and 2-mm observations with a spectral resolution of 200 kHz were used for these observations. The beam size or HPBW (half power beam width) of the IRAM 30 m telescope is determined by the following relation¹: HPBW (arcsec) = 2460/frequency (GHz). The telescope HPBW lies from $\simeq 9^{\prime \prime }$ at 276 GHz to $\simeq 30^{\prime \prime }$ at 80 GHz. For a more detailed description of sensitivity achieved in each observed frequency band and other observation details, see Fuente et al. (2016); Lefloch et al. (2018). This systematic line survey covers the prestellar core, protostar, outflow region, and protoplanetary disk phase to understand the chemical and dynamical evolution of the solar-type protostar. We considered a sample of four template sources, namely, L1544, B1-b, IRAS4A, and SVS13A, covering different stages from the prestellar to the protostellar phase. The sources considered in this study are discussed in the section below.

2.1 L1544

L1544 (${\alpha }_{\mathit{J2000}}$ = 05^h04^m17^s.21, ${\delta }_{\mathit{J2000}}$ = $25°10^{\prime }42^{\prime \prime }.8$) is a dense starless core in the Taurus molecular cloud (TMC). It is in the early stages of star formation before collapsing (Tafalla et al., 1998). It is located at a distance of 140 pc from the Sun (Cernicharo and Guélin, 1987). Before the ALMA high angular resolution band, six continuum emission data of Caselli et al., 2019, 2022, the inner region of the prestellar core (up to a few thousand au scale) remained unexplored. They named the small dense area ($\sim 10^{\prime \prime }\sim$ 1400 AU) “kernel.” Matters accumulate in the core during the prestellar core phase, resulting in a decrease in the temperature and an increase in the central density (Spezzano et al., 2017). As a result, atoms and molecules freeze on the dust and form an icy grain mantle. An extremely low temperature of 7 K (Crapsi et al., 2007) is attained with a core density of 10⁶ cm⁻³ (Caselli et al., 2019). Keto and Caselli (2010) found that a significant dust opacity must be taken into account for modeling to replicate the recorded temperature reduction inside 2000 AU. However, numerous sulfur-related molecules and complex organic molecules (COMs) were detected in the outer layer rather than in the dense inner cores in L1544 (Vastel et al., 2014; López-Sepulcre et al., 2015; Vastel et al., 2018). This is likely due to the non-thermal desorption, causing them to populate the gas phase under such a cold environment.

2.2 B1-b

Barnard 1 (B1) cloud is a moderately active star-forming region. It belongs to the Perseus molecular cloud complex at a distance of 235 pc (Hirota et al., 2008). The Barnard 1 dark cloud is subdivided into several dense cores, namely, B1-a, B1-b, B1-c, and B1-d. The B1-a and B1-c hosting Class 0 sources are associated with high-velocity outflows (Hatchell et al., 2005; 2007). The protostellar core B1-b consists of three remarkable sources, out of which B1-bN and B1-bS (Huang and Hirano, 2013) are two extremely young protostellar objects and are the first hydrostatic core (FHSC) candidates (Larson, 1969, first object to be formed in the collapse of a prestellar core). The spectral energy distribution (SED) modeling from Pezzuto et al. (2012) revealed that the two young protostellar objects are more evolved than prestellar cores but have yet to form Class 0 objects. Particularly, the non-detection of B1-bS at $24\mu$m and detection at $70\mu$m confirms that this source is at the first hydrostatic core stage. Another source, B1-bW, is observed in millimeter and sub-millimeter wavelengths (Gerin et al., 2017; Cox et al., 2018). B1-bN and B1-bS are separated from each other by approximately $18^{\prime \prime }$. The targeted position (${\alpha }_{\mathit{J}2000}$ = 03^h33^m20^s.8, ${\delta }_{\mathit{J}2000}$ = 31°$07^{\prime }34^{\prime \prime }.0$) of B1-b lies in between the two FHSC candidates B1-bN and B1-bS. The two protostellar cores lie inside the HPBW of the 30-m telescope at 3 mm, but they were not resolved at 1 mm with the observations from the same survey (see Figure 1 in Fuente et al., 2016). The overall bolometric luminosity of this system is $0.77L_{\odot }$ (Lefloch et al., 2018) and has a systematic velocity of 6.5 km s⁻¹ (López-Sepulcre et al., 2015). Marcelino et al. (2018) observed that B1-bS shows intense and rich spectra, while B1-bN is mostly free of line emission.

Figure 1

Figure 1. Abundance variation of SO, SO₂, OCS, and H₂S in different evolutionary stages of the low-mass star-formation process. Blue-colored cap-tipped lines represent the uncertainties in the abundance of the observed molecules. A lower limit on H₂S column density is plotted (shown in black-colored up-arrow sign) in the case of L1544, and it is taken from Vastel et al. (2018).

2.3 IRAS4A

NGC1333-IRAS4A (or simply IRAS4A, ${\alpha }_{\mathit{J}2000}$ = 03^h29^m10^s.42, ${\delta }_{\mathit{J}2000}$ = 31°$13^{\prime }32^{\prime \prime }.2$) is a protobinary system located in the NGC1333 star-forming region of the Perseus molecular cloud at a distance of 299 $\pm$ 15 pc (Zucker et al., 2018) having a systematic velocity of 7.2 km s⁻¹ (Taquet et al., 2015). Interferometric measurements revealed that this binary system comprises two Class 0 objects: IRAS4A1 and IRAS4A2 separated by $1.8^{\prime \prime }$ (Looney et al., 2000; López-Sepulcre et al., 2017; Tobin et al., 2018). The overall bolometric luminosity and its total envelope mass are estimated to be $9.1L_{\odot }$ and $5.6M_{\odot }$, respectively (Kristensen et al., 2012; Karska et al., 2013; Tobin et al., 2016). A spectacular large-scale (a few arcminutes) bipolar molecular outflow is associated with the IRAS4A system (Blake et al., 1995; Choi, 2005; Yıldız et al., 2012; Santangelo et al., 2014). IRAS4A1 is likely chemically rich, but dust optical depth does not allow us to observe the richness, as demonstrated by De Simone et al. (2020), but in IRAS4A2, numerous emissions from COMs have been identified (Bottinelli et al., 2004; 2007; Taquet et al., 2015; Santangelo et al., 2015; López-Sepulcre et al., 2017).

2.4 SVS13A

SVS13A is a Class I protostar belonging to the SVS13 cluster, located in the NGC1333 star-forming region in Perseus. The Global Astrometric Interferometer for Astrophysics, Gaia, has precisely determined its distance to be 299$\pm$14 pc (Zucker et al., 2018). The continuum observations of the SVS13 system at 82 GHz were performed in the framework of the Large Program Seeds of Life in Space (SOLIS) using the IRAM-Northern Extended Millimeter Array (NOEMA) interferometer by Bianchi et al. (2019). They showed that this SVS13 system is mainly composed of three sources. The Class I protostar, SVS13A (${\alpha }_{\mathit{J}2000}$ = 03^h29^m03^s.73, ${\delta }_{\mathit{J}2000}$ = 31°$16^{\prime }03^{\prime \prime }.8$) is the brightest source in the millimeter range. SVS13B is a younger Class 0 source located $\sim 15^{\prime \prime }$ southeast (SE) concerning SVS13A, and there is another source, namely, SVS13C, which is located at a distance $\sim 20^{\prime \prime }$ to SVS13A. It is also revealed from the observation that the source SVS13A is also composed of two binary systems, VLA4A and VLA4B, with a separation of $\sim 0.3^{\prime \prime }$ to each other (Anglada et al., 2000; Tobin et al., 2016; 2018), and a third object VLA3 is located close $(\sim 4^{\prime \prime })$ to the SVS13A source. From Lefloch et al. (1998), it is known that a large-scale molecular envelope surrounds these three objects. SVS13A has a luminosity $(L_{\mathit{bol}})$ of $\sim 32.5L_{\odot }$ (Tobin et al., 2016) with a systematic velocity of 8.6 km s⁻¹ (Chen et al., 2009), and it is driving an extended molecular outflow (Lefloch et al., 1998; Codella et al., 1999; Dionatos et al., 2020) as well as younger flows moving toward SE directions (Lefèvre et al., 2017). It hosts rich chemistry, including emission from several interstellar complex organic molecules (López-Sepulcre et al., 2015; De Simone et al., 2017; Bianchi et al., 2019; Belloche et al., 2020; Codella et al., 2021; Yang et al., 2021; Diaz-Rodriguez et al., 2022; Hsieh et al., 2024).

We found that our calculated column densities for SO and ³⁴SO fall within the margin of error of the values reported in Vastel et al. (2018) and Fuente et al. (2016). However, instead of directly using those values, we prefer to reanalyze the data as we disclosed discrepancies between the data used in those papers and the data available in the public domain. For instance, in the case of L1544, Vastel et al. (2018) reported three transitions of SO, but we found only two transitions because the 109.2522 GHz transition falls outside the publicly available data range ($80-106$ GHz) [https://www.iram.fr/ILPA/LP007]. Similarly, in the case of B1-b, one transition of SO₂ at 116.98045 GHz, included in the analysis by Fuente et al. (2016), falls outside the archival dataset available at [https://www.iram.fr/ILPA/LP007], which covers the following ranges: $80.5-112.3$ GHz, $129.9-172.7$ GHz, and $200.5-276$ GHz. On the other hand, increasing the sample size would enhance the robustness of the findings. However, the necessary transitions we obtained in L1544, B1-b, IRAS4A, and SVS13A were not identified in TMC-1 and L1527 to progress further. For instance, in TMC-1, only one transition of SO was detected, with no transitions observed for ³⁴SO, SO₂, H₂S, OCS, and ³⁴SO₂ in the archival data. Similarly, in L1527, SO and SO₂ lines were detected, but no transitions of other relevant species (³⁴SO, ³⁴SO₂, H₂S, and OCS) were found. Consequently, we cannot ascertain the variations in SO, SO₂, OCS, and H₂S abundances in TMC-1 and L1527. Hence, we excluded them from our analysis and focused only on L1544, B1-b, IRAS4A, and SVS13A.

3 Methodology

3.1 Line identification

The line identification of all observed molecular species presented in this paper was carried out with the help of CASSIS (Caux et al., 2011)² software (developed by IRAP-UPS/CNRS). Assuming no beam dilution, the observed line intensities (in the unit of antenna temperature, $T_A^{*}$) were transformed into the main-beam temperature $(T_{mb})$ by using the relation, $T_{mb}$ = $T_A^{*}\times F_{\mathit{eff}}$/$B_{\mathit{eff}}$, where F_eff and $B_{\mathit{eff}}$ are the forward and beam efficiencies, respectively. The center frequency of a line of a given species (atom, molecule, or ion) in the laboratory is compared to the measured frequency of that species to identify a spectral line. The Cologne Database for Molecular Spectroscopy (CDMS³; Müller et al., 2005), which is relevant for molecular astrophysics in the regime of radio to the far-infrared, is used here to know the spectroscopic details of a molecule. In this study, we check the line blending and consider only those transitions with an intensity greater than or equal to 3$\sigma$, where $\sigma$ is the RMS (root mean square) noise. Finally, we use the local thermodynamical equilibrium (LTE) modeling to confirm or reject the identification by creating synthetic spectra and comparing them with the observed profile.

3.2 Rotation diagram analysis

We applied the rotational diagram method whenever we detected multiple transitions of the same species in the same source. The analysis of rotational diagrams holds significant importance in demonstrating the essential characteristics of molecular clouds and their individual components. This method proves most effective when the source completely occupies the beam and the emitted radiation is optically thin. In LTE, all transitions are thermalized according to the Boltzmann distribution. Within the context of LTE, an optically thin transition results in an antenna temperature that is directly proportional to the column density of the observed transition’s upper level.

The column density at the upper level for optically thin lines (Sutton et al., 1995; Goldsmith and Langer, 1999) can be written as

$\frac{N_u^{\mathit{thin}}}{g_u}=\frac{3k_B\int T_{mb}dV}{8{\pi }^3\nu S{\mu }^2},(1)$

where $g_u$ is the degeneracy of the upper state; $\int T_{mb}dV$ is the integrated intensity of the line, which was calculated from observations by doing the Gaussian fitting; $k_B$ is the Boltzmann constant; $\nu$ is the frequencies at which the different transition occurs; $S$ is the line strength, which is the square of the matrix elements for the direction cosines between molecular-fixed components of the dipole moment and the electric field (Yamamoto, 2017); and $\mu$ is the permanent electric dipole moment of a molecule. The total column density $N_{\mathit{total}}$ is given as follows:

$\frac{N_u^{\mathit{thin}}}{g_u}=\frac{N_{\mathit{total}}}{Q\left(T_{\mathit{rot}}\right)}{e}^{-E_u/k{T}_{\mathit{rot}}},(2)$

where Q$(T_{\mathit{rot}})$ is the partition function at the rotational temperature $T_{\mathit{rot}}$ and $E_u$ is the energy of the upper state. We have the final following relation after taking the log in both sides of Equation 2:

$\log \left(\frac{N_u^{\mathit{thin}}}{g_u}\right)=-\left(\frac{\log e}{T_{\mathit{rot}}}\right)\left(\frac{E_u}{k_B}\right)+\log \left(\frac{N_{\mathit{total}}}{Q\left(T_{\mathit{rot}}\right)}\right).(3)$

After using the Equation 1, from Equation 3, the column density and rotational temperature can be determined by plotting many transitions log$(N_u^{\mathit{thin}}/g_u)$ against $E_u/k_B$ and fitting data points with a straight line. The slope and the intercept of this straight line correspond to $T_{\mathit{rot}}$ and $N_{\mathit{total}}$, respectively. All the spectroscopic parameters required in the above analysis are taken from the CDMS database. For the partition function, we interpolate the data given in the databases and estimate the appropriate $Q(T_{\mathit{rot}})$ at the derived rotational temperature. We were able to create a rotational diagram for at least one species in each source. Hence, whenever a rotational diagram was not possible, we applied the LTE model to generate synthetic spectra using the temperature derived for the particular source with the rotational diagram approach. We found good agreement between the observed and modeled spectra, considering the obtained column density and temperature along with their uncertainties, which were obtained from the rotational diagram.

4 Results

The line parameters of ³⁴SO and ³⁴SO₂ transitions are measured by fitting a single Gaussian profile to the observed profile by the method discussed in Section 3.1. In contrast, no Gaussian fitting is done on SO and SO₂ molecules as their transitions could be optically thick $(\tau >1)$. The detected transitions of ³⁴SO and ³⁴SO₂ and their line parameters are noted in Table 1, and we mention the transitions of SO and SO₂ for different sources in Table 2. The fitted spectra of ³⁴SO and ³⁴SO₂ are shown in Figures 2–6.

Table 1

Table 1. Observed transitions of ³⁴SO,³⁴SO₂, OCS, and H₂S toward the selected sources L1544, B1-b, IRAS4A, and SVS13A for which line parameters are calculated.

Table 2

Table 2. Observed other transitions of SO and SO₂ toward these selected sources L1544, B1-b, IRAS4A, and SVS13A.

Figure 2

Figure 2. Observed transitions of ³⁴SO and ³⁴SO₂ toward L1544 and B1-b. The top two figures are for L1544, and the rest are for B1-b. The black-colored histogram represents the observed spectra, while the Gaussian-fitted spectra are shown with blue-colored lines. The upper state energy $E_{up}$ (in the unit of K) corresponding to each of the transitions is mentioned in each panel.

Figure 3

Figure 3. Observed transitions of ³⁴SO and ³⁴SO₂ toward IRAS4A. The black-colored lines represent the observed spectra, while the Gaussian-fitted spectra are shown with blue-colored lines. The upper state energy $E_{up}$ (in the unit of K) corresponding to each of the transitions is mentioned in each panel. The ³⁴SO (6₅–5₄) transition is blending with ethanol.

Figure 4

Figure 4. Observed transitions of ³⁴SO toward SVS13A. The black-colored lines represent the observed spectra, while the Gaussian-fitted spectra are shown with blue-colored lines. The upper state energy $E_{up}$ (in the unit of K) corresponding to each of the transitions is mentioned in each panel.

Figure 5

Figure 5. Observed transitions of OCS toward L1544 and H₂S toward B1-b, IRAS4A, and SVS13A. The black-colored lines represent the observed spectra, while the Gaussian-fitted spectra are shown in blue-colored lines. The upper state energy $E_{up}$ (in the unit of K) corresponding to each of the transitions is mentioned in each panel.

Figure 6

Figure 6. Observed transitions of OCS toward B1-b, IRAS4A, and SVS13A. The black-colored lines represent the observed spectra, while the Gaussian-fitted spectra are shown with blue-colored lines. The upper state energy $E_{up}$ (in the unit of K) corresponding to each of the transitions is mentioned in each panel.

We anticipated that at a reasonable temperature of the studied sources, the critical number density of the transitions for ³⁴SO and ³⁴SO₂ was comparatively lower than that of the sources. This indicates that collisions occur frequently enough to maintain the populations close to their LTE values. Thus, we assume that all the transitions of ³⁴SO and ³⁴SO₂ are optically thin and are in LTE conditions. We use the rotation diagram method discussed in Section 3.2 to analyze cloud properties from molecular line emission by plotting the column density per statistical weight of a number of molecular energy levels as a function of their energy above the ground state.

The data are indeed very well approximated by a straight line (see Figure 7), which confirms that the assumptions of LTE and optical depth $(\tau )$ $\ll 1$ are valid in the case of these two species. The rotation diagrams of ³⁴SO and ³⁴SO₂ are shown in Figure 7. The derived temperatures and column densities are summarized in Table 3. The SO and SO₂ lines are often optically thick in star-forming regions. We have calculated the column density/abundance of SO and SO₂ for different sources. We check the ratio of ³²S/³⁴S in all sources by calculating ³²SO/³⁴SO and ³²SO₂/³⁴SO₂. It is approximately 8 for L1544 and varies from 6.4 to 7.4 for B1-b and for IRAS4A; this value lies between 5.6 and 11. We observed that it is very small compared to the local ISM value ($\sim$22.5; Lodders, 2003, $24\pm 4$; Yan et al., 2023), and given that no known fractionation reaction is available for sulfur, we have speculated that it might be due to the effect of the optical depth issue. Therefore, we derive the column density values of SO and SO₂ from their isotopologues by considering the ³²S/³⁴S ratio $\sim 22.5$. Table 3 refers to the obtained values of the column densities of these molecules.

Figure 7

Figure 7. Rotational diagram for ³⁴SO, ³⁴SO₂, OCS, and H₂S molecules in all sources, wherever it is possible to perform.

Table 3

Table 3. Derived rotational temperatures, column densities, and abundances (with respect to H₂) of SO,³⁴SO, SO₂, and³⁴SO₂ in different stages of the low-mass star-formation process.

4.1 L1544

We identify two transitions of SO and one transition each of ³⁴SO, SO₂, and ³⁴SO₂ in this source. In addition to these two transitions of SO at 86.0939 and 99.2998 GHz, Vastel et al. (2018) found another transition at 109.2522 GHz, but this transition is not available in the archival data (available between $80and106$ GHz). They obtained a rotational temperature of 7.9 K and column density of $(7.2\pm 3.2)\times 10^{12}$ cm⁻² from rotational diagram analysis for SO. They varied the excitation temperature for ³⁴SO within 5–6 K and reported a column density of $(1.3-1.6)\times 10^{12}$ cm⁻². Our derived column density reported in Table 3 is within the error bar of Vastel et al. (2018).

We are unable to determine the rotational temperature and column density from the rotation diagram analysis since we do not observe multiple transitions of ³⁴SO, ³⁴SO₂, and OCS in this source. The column densities of ³⁴SO, ³⁴SO₂, and OCS are derived by solving Equation 2 under the assumption of LTE and optically thin condition. We calculate the column density of OCS by taking the average for those two transitions mentioned in Table 1 and it is similar to that derived by Vastel et al. (2018) $\sim 4.1\times 10^{12}$ cm⁻²) from rotational diagram analysis. Figure 5 shows the Gaussian fitted spectra of these two transitions. In this study, we assume that the observed molecular species emit from the same region and a rotational temperature of $\sim$8 K (as Vastel et al., 2018 obtained for SO molecule). We observe similar spatial velocity and full width at half maxima (FWHM) of these molecules, which support our assumptions. No transition of H₂S is found in this source. Therefore, we use the 168.76276 GHz (lies outside in our used archival dataset) transition from Vastel et al. (2018) to observe the variation in this species throughout the evolutionary stages. Although Vastel et al. (2018) estimated a lower limit for the H₂S column density of $1.6\times 10^{12}$ cm⁻², based on a simple LTE modeling using an excitation temperature of 10 K. The derived column densities and abundances in this source are noted in Table 3.

4.2 B1-b

In this source, we observe 15, 10, 18, and 4 transitions of SO, ³⁴SO, SO₂, and ³⁴SO₂, respectively. Loison et al. (2019) analyzed 3 mm data from existing surveys with the IRAM 30 m telescope with five dense cores (including B1-b) to verify their modeled results. In this source, they observed four optically thick transitions of SO at 86.0939, 99.2998, 100.0295, and 109.2521 GHz. Including these four transitions of SO, nine other transitions were considered by Fuente et al. (2016) as optically thin. We report two additional transitions of SO at 172.1814 and 251.8257 GHz in addition to observed transitions by Fuente et al. (2016). Loison et al. (2019) used three transitions of ³⁴SO at 84.4106, 97.7154, and 106.7433 GHz to perform the rotational diagram analysis. They obtained a rotational temperature of $6.5\pm 0.7$ K. Except for the transitions at 246.6633 and 253.2070 GHz (weak in our observation), here we identify the same transitions for ³⁴SO reported by Fuente et al. (2016). We did not consider them in our analysis as they have low intensity ($20-25$ mK) as compared to the other observed lines ($52-220$ mK). A rotational temperature of $\sim 8$ K and column density of $\sim 1.1\times 10^{13}$ cm⁻² are obtained for ³⁴SO in our case. However, if we include these two weak transitions of ³⁴SO in the rotational diagram analysis, we observe a minor deviation from our present values of column density and excitation temperature.

In the case of SO₂, we observe the same transitions as reported by Fuente et al. (2016), except the transition at 116.9804 GHz, which is not available in the archival data (available between $80.5and112.3$, $129.9and172.7$, and $200.5and276$ GHz). A column density of $\sim 2.0\times 10^{12}$ cm⁻² for ³⁴SO₂ is derived from rotational diagram analysis in our work, while Fuente et al. (2016) derived a value of $1.1\times 10$¹² cm⁻² by taking into account the same transitions as us. We identify a total of six transitions of OCS in this source, and by performing RD analysis, we derive an excitation temperature of 14.5 K and a column density of $\sim 2\times 10^{13}$ cm⁻² for this species. The observed transitions of OCS are shown in Figure 6. In the case of H₂S, we observe two transitions at 168.76276 and 216.71044 GHz, but we estimate the column density based on the former transition (see Figure 5) because the 216.71044 GHz transition depicts an absorption-like profile.

4.3 IRAS4A

A total of 17 transitions of SO (out of which 15 are unblended and two are blended at 129.1389 GHz with HOCH₂CN and 258.2558 GHz with c-C₃H₂) with upper state energies between $9and57$ K are observed. We observe a total of 30 transitions of SO₂ in this source, out of which the transitions at 132.7448 and 254.2805 GHz are blended with CH₃COCH₃ and H₂COH⁺, respectively. In the case of ³⁴SO, we observe 13 transitions. Among them, the transitions at 246.6634 GHz may be blended slightly with C₂H₅OH. The rotational diagram analysis yields a rotational temperature of $\sim 10$ K and a column density of $\sim 1.0\times 10^{13}$ cm⁻² excluding this transition. Four transitions of ³⁴SO₂ are observed in this source. The transition at 229.8576 GHz is found to be blended with C₂H₃CN and CH₂DOH. The rotational diagram analysis is performed excluding this transition and yields a rotational temperature of $\sim 39$ K and column density of $\sim (3.5\pm 0.5)\times 10^{12}$ cm⁻². Here, we observe a total of 14 transitions of OCS having an energy range of 12–148 K. We obtain an excitation temperature of 48 K and a column density of $\sim 4.2\times 10^{13}$ cm⁻² for this molecule. The observed OCS transitions are shown in Figure 6. We observe two transitions of H₂S at 168.76276 and 216.71044 GHz in this source. We use Equation 2 to calculate the column density of this species based only on the 216.71044 GHz transition (see Figure 5), as the other transition has an absorption-like profile.

Taquet et al. (2020) performed interferometric data analysis of IRAS4A within the framework of the SOLIS program (Ceccarelli et al., 2017). They compared interferometry results with single-dish results (ASAI) at EMIR and smoothed over the wide-band receiver (WIDEX) resolution for different sulfur-bearing species. They discussed the various line features (narrow, broad, and moderately broad), including possible physical reasons for their origin (also see Ospina-Zamudio et al., 2018).

4.4 SVS13A

We observed four transitions of SO (among them, the transition at 129.1389 GHz is blended with HOCH₂CN and the 258.2558 GHz transition is blended with c-C₃H₂), five unblended transitions of its isotopologue ³⁴SO, 27 transitions of SO₂ (out which six transitions are blended with different molecules), and only one clean transition of ³⁴SO₂ is observed in this source. Table 1 lists the detected transitions and the line parameters. We observe all ³⁴SO transitions in the 1-mm band having upper state energy $34-56$ K and peak velocity close to the systematic velocity of the source ($8.1-8.7$ km.s⁻¹). We identify a few inverse P Cygni profiles of SO and SO₂ in this source, which are not discussed here. We use Equation 2 to derive the column density of ³⁴SO₂ and H₂S (based on 216.71044 GHz transition; see Figure 10) by assuming an excitation temperature of 80 K (Bianchi et al., 2019). The rotational diagram of the OCS molecule in this source shows that the data points are scattered over the fitted line, i.e., the data points are not well-fitted over the line, and hence, we get a higher value of excitation temperature of approximately 200 K for this molecule. Figure 6 shows the observed spectra of OCS in this source.

Codella et al. (2021) used 3-mm and 1-mm data of NGC1333 SVS13A obtained with the IRAM-NOEMA interferometer in the framework of the SOLIS Large Program. They presented the spatial distribution on the $\le$ 300 au scale of the line emission of SO, ³⁴SO, and some other S-bearing species. Furthermore, they compared their results with the ASAI data of SO, SO₂, and H₂CS and concluded that the contribution of the SO emission from the extended region is considerable, whereas SO₂ and H₂CS are less affected by the emission filtering.

5 Discussion

5.1 Observed abundance of SO and SO₂ and their ratio

Figure 1 illustrates the abundance variation of SO and SO₂, derived from the ³⁴S isotopologues by assuming the ³²S/³⁴S elemental ratio of 22.5 (Lodders, 2003) in four distinct phases of the low-mass star-formation process. We observe the abundance of all species initially low in the prestellar phase (L1544), then increases at the first hydrostatic core stage (B1-b), and reaches a maximum value at the Class 0 hot corino stage (IRAS4A). It decreased slightly in the further evolved Class I stage (i.e., SVS13A). We assume the excitation temperature of 8 K (for ³⁴SO and ³⁴SO₂) for L1544 and 80 K (for ³⁴SO₂) for SVS13A to calculate the abundance of these species. The abundances of SO and SO₂ show a similar trend when the excitation temperature is changed from 6 to 10 K for L1544 and from 60 to 100 K for SVS13A. Figure 1 depicts a similar trend for the other two major sulfur-bearing species: OCS and H₂S.

Figure 8 shows the obtained SO/SO₂ ratio for the four sources. The ratio decreases gradually from the prestellar core phase to the Class 0 phase. In the case of SVS13A, we obtain a large uncertainty in this ratio, so it is challenging to distinguish between the Class 0 and Class I source based on the SO/SO₂ ratio obtained from this observation. However, it is worth pointing out that we obtain an SO/SO₂ ratio $>$ 1 for all the stages from this observation.

Figure 8

Figure 8. SO/SO₂ ratio in different evolutionary stages of the low-mass star-formation process.

5.2 Comparison with the other study

Very recently, Bhat et al. (2023) used similar sources to understand the evolutionary sequence of the low-mass star-formation process with complex organic molecules. They also found a similar trend with the COMs as it is obtained for SO and SO₂ here. A similar type of work is reported by Buckle and Fuller (2003), where they surveyed sulfur-bearing species (H₂S, SO, and SO₂) for 10 Class 0 and nine Class I sources with the 12 m telescope on Kitt Peak at National Radio Astronomy Observatory (NRAO). They reported a slight decrease in the abundance in the Class I source compared to the Class 0 source. They obtained the mean fractional abundances toward the core approximately $\sim 3.1\times 10^{-9}$ and $\sim 7.1\times 10^{-10}$ for SO, $\sim 4.1\times 10^{-10}$ and $\sim 3.0\times 10^{-10}$ for SO₂ in Class 0 and Class I source, respectively. A similar variation in the abundance of SO and SO₂ in Class 0 and Class I sources is also reported in their work. Another work on single-dish line observations of the envelopes around a sample of 18 low-mass prestellar and protostellar objects was carried out by Jørgensen et al. (2004) and reported an average abundance of $\sim$ $1.5\times 10$⁻⁹, $2.0\times 10$^−9, and $2.3\times 10$⁻⁹ for SO in prestellar, Class 0, and Class I stage. They also found a similar variation over the prestellar phase to Class I stage.

Recently, Fontani et al. (2023) analyzed data from the IRAM 30 m telescope, focusing on 15 cores categorized into three primary evolutionary stages of the high-mass star-formation process: high-mass starless cores (HMSC), high-mass protostellar objects (HMPO), and ultracompact H II (UCHII) regions. Their findings indicated an increase in the abundance of SO and SO₂ with the evolutionary stages. Additionally, they observed a positive correlation of SO and SO₂ with the gas kinetic temperature (T_k), dust temperature (T_dust), luminosity (L), and luminosity-to-mass ratio (L/M). Similar trends were obtained for the evolutionary stages of the low-mass star-forming regions with our analysis. However, they did not find a tangible trend for the SO/SO₂ ratio with the evolutionary stages. Initially, they observed an increasing trend for SO/SO₂ during the transition from cold HMSC to warm HMSC. For HMPO and UCHII, a comparative decrease was noted compared to the HMSC stages. However, they did find that the SO/SO₂ ratio consistently exceeded 1. Furthermore, Herpin et al. (2009) observed two mid-infrared quiet and two brighter massive cores. They determined that for cold outer regions (approximately 60 K), the SO/SO₂ ratio increases with the evolutionary stages. However, a definitive trend for the inner region could not be established based on their observations, whereas Wakelam et al. (2011) proposed that this ratio decreases with time in massive cores. Based on the low-energy transitions obtained in our study, we observed a declining trend for the SO/SO₂ ratio with the evolutionary stages of the low-mass star-forming region, which is just the opposite of that obtained by Herpin et al. (2009) and partially hinted from Fontani et al. (2023) for the high-mass star-forming region. The observed opposite trend between high-mass and low-mass cases arises due to several factors, such as density, temperature, envelope mass, and luminosity spatial resolutions. We need a large sample for both high-mass and low-mass cases with similar angular resolutions and sensitivity observations for statistical analysis. The column density ratio between SO₂ and SO is reported by Artur et al. (2023) as a function of bolometric temperature $(T_{\mathit{bol}})$ and bolometric luminosity $(L_{\mathit{bol}})$ of the PEACHES sample sources. They found no clear trend for SO/SO₂ as a function of $T_{\mathit{bol}}$. This ratio shows a tentative increasing trend for $L_{\mathit{bol}}$ between 1 and $10L_{\odot }$ and for $L_{\mathit{bol}}$ higher than $10L_{\odot }$, a tentative decreasing trend is seen for the SO/SO₂ ratio, which may be due to the photo-dissociation of SO₂ and enhancement of SO in those very luminous sources. However, in this work, a tentative trend in SO/SO₂ variation throughout various evolutionary phases of low-mass stars has been observed, providing systematic data for the first time for a small sample sources. Despite that, detailed investigations with a larger sample size are needed to confirm it. Nevertheless, analyzing a larger sample is beyond the scope of this work and will be addressed in future papers.

5.3 Chemical modeling

We use the three-phase (phase I $\to$ gas, phase II $\to$ icy grain surface, and phase III $\to$ homogeneous bulk ice mantle) Rokko code (Furuya et al., 2015; 2017) for the chemical modeling. A multilayer would form if more species are deposited than the available binding sites. Several monolayers of ice would build up during the evolution of grain. In the two-phase model, all the adsorbed materials are considered as the surface and are chemically reactive but indistinguishable. In the three-phase model, a distinction is made by considering the mantle and surface. All layers beneath the surface layers are considered the mantle, which is chemically unreactive. The surface layer is considered to be chemically active. In this work, we consider only the uppermost four monolayers as active ice layers; all the layers, including these active ice layers, are considered the bulk ice mantle. The gas and ice phase networks are adopted from Garrod (2013). We consider thermal desorption, photo-desorption, chemical desorption, and stochastic heating by cosmic rays (CRs). The chemical desorption of H₂S is important for the gas-phase abundances of S-bearing molecules. The chemical desorption probability of H₂S was determined to be 4% based on laboratory experiments (Oba et al., 2019; Furuya et al., 2022). The initial elemental abundances were used from Garrod (2013), which is originally based on the initial low metal elemental abundance set by Graedel et al. (1982), with the exception of He, C⁺, N, and O values, which were obtained from their diffuse cloud model.

In an ideal scenario, it would be savvy to analyze how a molecular cloud evolves as it moves from the prestellar core stage to the Class I stage. However, for simplicity, we will limit our model to the Class 0 stage. Here, we track the time evolution of both the inner portion and envelope of a cloud. Three stages are considered (see Figure 9): collapsing stage ($t_{\mathit{coll}}=1\times 10^6$ years), warm-up stage ($t_w=2.85\times 10^5$ years), and post-warm-up stage ($t_{pw}=1\times 10^5$ years). During the collapsing stage, the cloud is allowed to collapse from a minimum density (${\rho }_{\mathit{min}}=3\times 10^3$ cm⁻³) to a maximum density (${\rho }_{\mathit{max}}=10^7$ cm⁻³ for the inner portion and ${\rho }_{\mathit{max}}=10^5$ cm⁻³ for the envelop). The visual extinction can increase from a minimum value of 2 mag to ${A_V}_{\mathit{max}}$ mag during this stage, as described by Garrod and Pauly (2011). The dust temperature is calculated based on the visual extinction parameter by the relation used in Garrod and Pauly (2011). The parameters we are considering illustrate a range of dust temperatures from 8 K to 16 K and a range of visual extinction from 2 mag to 446 mag during the collapsing stage of the inner region. For the envelop region, the dust temperature and visual extinction parameters are 8 K–16 K and 2 to 20 magnitudes, respectively. In the inner region of the warm-up stage, the temperature would increase to 400 K (50 K for the outer region) in $t_w=2.85\times 10^5$ years. In the warm-up stage, a good coupling between the gas and dust temperature is considered when the dust temperature increases beyond 10 K. During the warm-up stage, the density and visual extinction are kept constant at ${\rho }_{\mathit{max}}$ and ${A_V}_{\mathit{max}}$, respectively, but the temperature is allowed to increase up to a temperature $T_{\mathit{max}}$ in $t_w$ years. In the post-warm-up stage, density, temperature, and visual extinction are constant at ${\rho }_{\mathit{max}}$, $T_{\mathit{max}}$, and ${\mathrm{A}}_{{\mathrm{V}}_{\max }}$, respectively.

Figure 9

Figure 9. Time evolution of the physical parameters (density, temperature, and $A_V$) considered for the inner (HC) and envelop (ENV) regions is shown with dashed and solid curves, respectively.

Figures 10, 11 refer to the time evolution of SO and SO₂ and their ratio, respectively. The observed abundances shown in Figure 1 depict a sequential increasing trend from the prestellar core phase/first hydrostatic collapse phase (cold gas) to the Class 0 phase (warm gas). Our modeled abundances shown in Figure 10 show a similar trend. The horizontal lines mark the observed abundances. For the cold region (collapsing phase), the observed abundances of SO and SO₂ are taken from the abundances reported in Table 3 for L1544 and B1-b. For the warmer region (warm-up and post-warm-up stages), the abundances noted for the IRAS4A and SVS13A are highlighted. In the cold phase, the abundances of SO and SO₂ in the inner region (HC) match well with the observation at a time of $10^5$ years, whereas for the outer region (ENV), it is $5\times 10^5$ years. In the warm-up stage, the abundances overproduce SO and SO₂ for a temperature beyond 100 K. Conversely, the outer region underproduces the abundance. Our analysis reveals that in the inner section, particularly during the late warm-up and post-warm-up stages ($>100$ K), a significant amount of sulfur is present in the form of SO and SO₂. It is important to note that we initially assume an elemental sulfur abundance relative to H of $8\times 10^{-8}$ in our model, and our peak abundances (beyond the collapsing stage) of SO and SO₂ relative to H are $2.7\times 10^{-8}$ and $5.7\times 10^{-8}$, respectively. This is not the case for the outer region.

Figure 10

Figure 10. Time evolution of SO and SO₂ in the inner (HC) and outer (ENV) regions is represented by the dashed and solid curves, respectively. Various evolutionary stages (CS$\to$ collapsing stage, WS$\to$ warm-up stage, and PWS$\to$ post-warm-up stage) are annotated on the graphs. The red and green shaded regions represent the observed abundances of SO and SO₂ in the cold (L1544 and B1-b) and the warm region (IRAS4A and SVS13A), respectively.

Figure 11

Figure 11. Time evolution of the SO/SO₂ ratio in the inner (HC) and outer (ENV) regions. Various evolutionary stages are annotated as given in Figure 1. The horizontal shaded region represents the observed abundances from Table 3 for the cold region (L1544 and B1b) and warm region (IRAS4A and SVS13A).

In Figure 11demonstrates a decreasing trend from, the time evolution of SO/SO₂ is depicted. The observed abundance ratio between SO and SO₂ (see Figure 8) demonstrates a decreasing trend from cold gas to hot gas. This decreasing trend is similarly reflected in the modeled ratio depicted in Figure 11. Over time, density increases in the collapse stage, resulting in a steady declining trend of this ratio up to approximately $10^5$ years for the inner region (HC) and approximately $5\times 10^5$ years for the outer region (ENV). During the collapsing phase in the inner region (HC), the ratio of $SO/S{O}_2$ is significantly greater than 1. Between 100 and 300 K, the ratio is less than 1, but it is approximately 1 for temperatures exceeding 300 K, with a moderate warm-up time of $2.85\times 10^5$. In the outer region (ENV), SO/SO₂ remains consistently greater than 1 throughout the period. Our observations, as presented in Figure 8, also revealed a $SO/S{O}_2$ ratio greater than 1 for all stages, indicating the proximity of the observed region to the envelop region examined in this study.

Drozdovskaya et al. (2018) carried out the large unbiased Protostellar Interferometric Line Survey (PILS) of IRAS 16293-2422 with ALMA in the $329-363$ GHz frequency range (Band 7) with a spectral resolution of 0.2 km s^-1 and a beam size of $0.5^{\prime \prime }$ (or $60-74$ au in diameter, assuming a distance of $120-147$ pc) to search for S-bearing molecules. They detected the SO₂ molecule in the $v=0$ state based on 13 clean, non-blended lines at a column density of $1.5\times 10^{15}$ cm⁻², whereas they measured an upper limit of SO species in the same state with a value of $5.0\times 10^{14}$ cm⁻². They compared the SO/SO₂ ratio $(\sim 0.33)$ data with the 67P/C-G Comet and found that these two objects are in close agreement. Our model shows an SO/SO₂ ratio $\gg 1$ during the cold phase. In the late warm-up phase, it is $<1$ ($100-300$ K for the inner region). However, for temperatures exceeding 300 K, we observe it at approximately 1. This is possible because the data analyzed here obtained a rotational temperature for SO and SO₂ at 10 K and 44 K, respectively, for class 0 stage, suggesting the emission from different materials. In addition, our modeling suggests an SO/SO₂ ratio $<1$ at a much warmer region when compared to this observation.

6 Conclusion

We systematically investigated two primary sulfur-bearing species and their corresponding isotopologues by employing systematic data from the IRAM 30 m and astrochemical simulations. The major conclusions of this work are summarized as follows.

$•$ In this study, we reported the detection of SO, SO₂, ³⁴SO, ³⁴SO₂, OCS, and H₂S in four distinct phases of the low-mass star-formation process. Our analysis encompassed comprehensive line parameters for these molecules. Since SO and SO₂ are expected to be optically thick, we estimate their column density based on their isotopologues containing ³⁴S. The rotational diagram method or a simple LTE fitting was performed to determine their excitation temperature and column density. The abundances of SO, SO₂, OCS, and H₂S species exhibit an increase until the class 0 phase, followed by a decline in the class I stage.

$•$ Our assessment extends to comparing the abundance of SO, SO₂, and their abundance ratio and outcomes derived from our models. This comparison, in turn, has facilitated the estimation of the temporal span of their abundances and the ratio of each phase. Observed SO and SO₂ abundances increase from cold to a hot gas, whereas the SO/SO₂ ratio decreases.

$•$ Our model depicts that most sulfur is locked as SO and SO₂ when temperatures surpass 100 K. A notable contrast in the SO/SO₂ ratio between the inner and outer regions was obtained from our model. Within the inner region, the SO/SO₂ ratio is markedly higher than 1 at early times ($8-16$ K), declining to below 1 at intermediate times ($100-300$ K), and remaining at approximately 1 at later times (beyond 300 K). Our observations, depicted in Table 3; Figure 11, reveal a declining trend of the SO/SO₂ ratio across the evolutionary stages. Yet it remains greater than 1 at all stages. Given that our observations primarily capture low excitation transitions, they are focused on the intermediate region bridging the modeled inner and outer zones.

We note that additional observations of sample sources at various phases are required to obtain a trustworthy picture of the chemical evolution throughout the solar-type star-formation process. This entails not just a significantly higher quantity of sources but also higher spatial and angular resolution to enable meaningful comparison across various evolutionary stages.

Data availability statement

Publicly available datasets were analyzed in this study. This data can be found here: We analyzed the ASAI data available in https://www.iram.fr/ILPA/LP007/. The CASSIS 503 software (https://cassis.irap.omp.eu/) was used for line analysis and for line identification.

Author contributions

RG: writing–original draft and writing–review and editing. AD: writing–original draft and writing–review and editing. PG: writing–original draft and writing–review and editing. SM: writing–original draft and writing–review and editing. KF: writing–original draft and writing–review and editing. KT: writing–original draft and writing–review and editing. TS: writing–original draft and writing–review and editing.

Funding

The author(s) declare that no financial support was received for the research, authorship, and/or publication of this article.

Acknowledgments

RG acknowledges the support from the Swami Vivekananda Merit-cum-Means Scholarship provided by the Government of West Bengal. AD is grateful for the assistance from the Centre for Astrochemical Studies (CAS) division at Max Planck Institute for Extraterrestrial Physics, Germany.

Conflict of interest

The authors declare that the research was conducted without any commercial or financial relationships that could potentially create a conflict of interest.

The author(s) declared that they were an editorial board member of Frontiers, at the time of submission. This had no impact on the peer review process and the final decision.

Publisher’s note

All claims expressed in this article are solely those of the authors and do not necessarily represent those of their affiliated organizations, or those of the publisher, the editors, and the reviewers. Any product that may be evaluated in this article, or claim that may be made by its manufacturer, is not guaranteed or endorsed by the publisher.

Footnotes

¹https://publicwiki.iram.es/Iram30mEfficiencies

²https://cassis.irap.omp.eu/

³http://cdms.astro.uni-koeln.de/classic/

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