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Photochemical origin of SiC₂ in the circumstellar envelope of carbon-rich AGB stars revealed by ALMA

Yanan Feng ^1,2, Xiaohu Li ^1,3,∗,Tom J. Millar ⁴, Ryszard Szczerba ⁵, Ke Wang ⁶, Donghui Quan ^7,1, Shengli Qin ^8,1, Xuan Fang ^9,1,10,11, Juan Tuo ^1,2, Zhenzhen Miao ¹, Rong Ma ^1,2, Fengwei Xu ^6,12, Jingfei Sun ¹, Biwei Jiang ^13,14, Qiang Chang ¹⁵, Jianchao Yang ^1,2, Gao-Lei Hou ¹⁶, Fangfang Li ¹, and Yong Zhang ^17,1,11

Abstract

1

Whether SiC₂ is a parent species, that is formed in the photosphere or as a by-product of high-temperature dust formation, or a daughter species, formed in a chemistry driven by the photodestruction of parent species in the outer envelope, has been debated for a long time. Here, we analyze the ALMA observations of four SiC₂ transitions in the CSEs of three C-rich AGB stars (AI Vol, II Lup, and RAFGL 4211), and found that SiC₂ exhibits an annular, shell-like distribution in these targets, suggesting that SiC₂ can be a daughter species in the CSEs of carbon-rich AGB stars. The results can provide important references for future chemical models.

\helveticabold

2 Keywords:

AGB stars, circumstellar envelope(CSEs), daughter species, mass loss, column density

3 Introduction

Late evolutionary stars with masses between 0.8 and 8 $M\rm_{\odot}$ (Höfner and Olofsson, 2018) experience dramatic mass losses. The stellar wind continues to eject material outward, eventually forming a circumstellar envelope (CSE), often referred to as the molecular space factory. According to different C/O ratios, asymptotic giant branch (AGB) stars are divided into three classes: O-rich AGB stars (oxygen-rich, C/O ${<}$ 1), S-type AGB stars (C/O ${\approx}$ 1), and C-rich AGB stars (carbon-rich, C/O ${>}$ 1). Over 105 molecular species have been detected in the circumstellar envelope of the evolved stars (Decin, 2021). These species, distributed in different areas of the CSEs, can help us to trace shell properties, such as local temperature and gas composition, and help us to understand the chemical synthesis within the objects. A large number of carbon-bearing species are observed to be abundant surrounding the carbon stars, for instance, CO, CS, HC₃N, and C₂H, some of which come from the inner layers of the CSEs, and some are formed in the outer regions (Decin et al., 2008; Li et al., 2016).

The silacyclopropynylidene (SiC₂) was first detected and confirmed in IRC+10216 by Thaddeus et al. (1984) who derived a fairly large column density, 1.5 $\times$ 10¹⁴ cm^-2. Glassgold et al. (1986) suggested that SiC₂ was formed by the reaction of Si⁺ with C₂H₂ or C₂H followed by dissociative recombination with electrons. Glassgold et al. (1991) suggested alternative pathways, initiated by reactions of SiS with C₂H ${}_{2}^{+}$ or C₂H ${}_{3}^{+}$ . All these routes need the presence of UV photons to form cations and radicals, and thus treat SiC₂ as a daughter species.

The spatial distribution of SiC₂ in IRC+10216 was discussed by Takano et al. (1992) and Guelin et al. (1993) who showed that it showed a spherical shell-like structure indicative of a daughter species. Lucas et al. (1995) and Gensheimer et al. (1995) used the Plateau de Bure and Berkeley Illinois Maryland Array (BIMA), respectively, to map SiC₂ emission, showing that it had a shell structure. The first confirmation that SiC₂ was present close to the star came from Cernicharo et al. (2010) who used the Herschel Space Observatory to detect some 55 transitions from energy levels 500-900 K above ground state, implying that SiC₂ was present in the dust-forming zone. Subsequently Fonfría et al. (2014), using the CARMA interferometer, and Prieto et al. (2015) using Atacama Large Millimeter Array (ALMA) detected emission from both the central region and the outer shell.

In a work devoted to single-dish observations of 25 C-rich AGB stars (Massalkhi et al., 2018), SiC₂ and SiC were detected in about half of the sources. They found that the abundance of SiC₂ decreased with increasing envelope density increasing envelope density, indicating that SiC₂ is a parent species in these CSEs. This finding confirms SiC₂ to be a parent species in CSE. De Beck and Olofsson (2020) detected SiC₂ in S-type AGB star W Aql, and they showed that the emission occurs in a ring of radius 1-2^′′.

Most evidence shows that SiC₂ is formed in LTE conditions close to the star, although IRC+10216 has an increase in abundance of SiC₂ at around 10^′′ indicating an additional formation in the outer regions of CSE. To date, no millimeter-wave interferometric array observation of SiC₂ have been published in CSE of C-rich AGB stars other than IRC+10216. In this work, we provide evidence that SiC₂ seems to be a daughter molecule through high-resolution observations of three C-rich AGB stars. We describe the observations in Sect.4. The results are discussed in Sect.5. The conclusions are presented in Sect.6. The spatial distribution and the fractional abundance of SiC₂ in AI Vol together with $5_{0,\,5}-4_{0,\,4}$ transition in RAFGL 4211 are discussed in the main paper, while the rest of the results are presented in the Supplementary Material.

4 Observations

Observations were made using an ALMA 12 m array. The spectral line observations in Band 3 of AI Vol, RAFGL 4211, and II Lup covering four Windows with a bandwidth of 2 GHz were performed on 2015 August 16 (2013.1.00070.S, PI: Nyman, Lars- $\rm\AA$ ke). The data was extracted from ALMA Archive¹¹1https://almascience.nao.ac.jp/aq. For AI Vol, the configuration used for observation is a 12 m main array, baselines: 21 - 783 m. The image cube per spw averages every 2 $\times$ 488 kHz channels. The rms requirement is 3 mJy per 1 arcsec beam, per 0.9 MHz ( $\sim$ 2.7 km s^-1). The synthesized rms is 1.3 mJy/beam, and the synthesized beam is 1.4^′′ $\times$ 0.9^′′. The parameters of the observed transitions are collected in Table 2. The frequency resolution during observation is 1128.9984 kHz, corresponding to the velocity resolution of 2.526 $-$ 3.122 km s^-1. The wide frequency range covers four lines of SiC₂ ( $4_{0,\,4}-3_{0,\,3}$ , $4_{2,\,3}-3_{2,\,2}$ , $4_{2,\,2}-3_{2,\,1}$ , and $5_{0,\,5}-4_{0,\,4}$ ).

AI Vol, RAFGL 4211, and II Lup are all carbon-rich AGB stars with mass loss. A survey conducted by Smith et al. (2015) at the 3 mm band revealed that the three carbon-rich stars possess abundant molecules, and the sensitive detection of molecular spatial distributions relies on more advanced telescopes such as ALMA. In this study, we present the physical parameters taken from the literature and the synthesized beam for the observed sources, which are listed in Table 1.

The imaging process of the calibrated data was performed using CASA 4.3.1²²2https://casa.nrao.edu/ software manually. The “clean” task was employed, and to achieve a balance between spatial resolution and noise gain in the resulting image, the Briggs weighting function was applied along with adjustments to the “robust” parameter of 0.5. The rms was calculated near the center of the field, excluding all emissions within the region. The rms values for all channel maps were obtained using the task “imstat” in CASA software. Each pixel on the image plane corresponded to a size of 0.2 arcseconds. Then we used Python software to map and analyze ALMA product data. To calculate the molecular column density, we employed the shell fitting in the GILDAS software³³3http://www.iram.fr/IRAMFR/GILDAS, along with the splatalogue ⁴⁴4https://splatalogue.online//advanced.php and the CDMS databases⁵⁵5http://www.astro.uni-koeln.de/cdms/catalog (Müller et al., 2005).

5 Result

5.1 Spatial distribution of SiC₂

We obtained four transitions of SiC₂ in each source, except for the $4_{2,\,2}-3_{2,\,1}$ transition, which was not observed in II Lup. Based on the $S\mu^{2}$ from Table 4, the $4_{2,\,2}-3_{2,\,1}$ transition of SiC₂ in the 3 mm wavelength range ranked third in terms of signal intensity. However, we did not detect any signal. Our data were obtained from the ALMA Archive, and from the data information, we found that the other three transitions of SiC₂ and the data from the two additional sources had map sizes of 800 $\times$ 800 or 640 $\times$ 640 pixels. In contrast, the data without signal detection only covered a map size of 300 $\times$ 300 pixels. We speculate that there may have been some unknown special circumstances during the observations that led to the absence of signal.

AI Vol does not have the strongest spectral line signal, but the signal-to-noise ratio of spatial brightness distribution is higher than that of the other two stars. Cernicharo et al. (2015) have reported the observations and model results of a C-rich AGB star, IRC+10216. They suggest that a companion star may explain the spiral structure of its CSE. Lykou et al. (2018) reported spiral structures of several parent molecules in II Lup, suggesting that the companion star is the main forming mechanism of mass loss. The results show that the spectral line signal of AI Vol is stronger than RAFGL 4211 (in Figures 6 and A9). In order to get reliable results, we concentrate on analyzing the distribution around the center star of AI Vol (in Sect. 5.1.1). The rotational diagrams method was used to calculate fractional abundance, and the detailed analysis is presented in Sect. 5.2.

5.1.1 AI Vol

Figures 1 and 2 shows SiC₂ ( $4_{0,\,4}-3_{0,\,3}$ and $4_{2,\,2}-3_{2,\,1}$ ) radial velocity channel map toward C-rich AGB star AI Vol (The other transitions are shown in Figures (A1 and A2)). Around the local standard of rest velocity $V\rm_{LSR}$ of AI Vol (-39 km s^-1), SiC₂ shows a ring distribution around the center star with a diameter of $\thicksim$ 4-6^′′ ( $\thicksim$ 2840.95 $-$ 4258.08 au), and the signal strength reaches 20.4 and 13.7 $\sigma$ for $4_{0,\,4}-3_{0,\,3}$ and $4_{2,\,2}-3_{2,\,1}$ transitions. Based on the images presented by Decin et al. (2015), it is evident that the parent molecules, such as SiO, exhibit a concentrated distribution within a compact structure surrounding the central star. In contrast, our observation reveals a characteristic pattern specific to the daughter molecules, distributed in hollow rings around the star (Agúndez et al., 2015, 2017). The brightness distributions of Figures 1 and 2 under different velocity components are all coming from the transitions ( $4_{0,\,4}-3_{0,\,3}$ and $4_{2,\,2}-3_{2,\,1}$ ), without spatial extension caused by the fine structure.

Brightness distribution of the $4_{0,\,4}-3_{0,\,3}$ transition of SiC₂ and the 2 - 1 transition of SiO around $V\rm_{LSR}$ channels (from - 32.3 to - 46.5 km s^-1) is shown in Figure 3. We can see that the maximum emission of SiC₂ occurs at the radius $\sim$ 3^′′, with a hole in the distance from the star $\sim$ 2^′′. The studies conducted by Takano et al. (1992) and (Agúndez et al., 2015) showcase the spatial distribution of the daughter species centered around $V\rm_{LSR}$ . SiO is present as the parent species in three types of AGB stars (Cherchneff, 2006; Ramstedt et al., 2009). The SiC₂ and SiO shown in Figure 3 represent the spatial distribution characteristics of the daughter species and parent species, respectively, exhibiting distinct hollow and compact structures.

The northeast part of the shell emission has relatively stronger spectral signals. The SiC₂ ( $4_{0,\,4}-3_{0,\,3}$ ) transition for AI Vol is stronger than the other transitions, and the hollow shell structure can be seen more clearly. The SiC₂ at different velocity components showed an elongated cavity extending from the inner region to a location with a southern radius of $\sim$ 2^′′. This structure may be caused by the companion star, but the AI Vol has no spiral structure typical of the companion star (Cernicharo et al., 2015). The gas expands at a lower velocity near the star, and lower-excited state transitions farther from the star are more spatially distributed than higher-excited state transitions in the same source. This is seen in Figure 4 where the zeroth-order moment map of the of the $(5_{0,\,5}-4_{0,\,4})$ transition has a smaller extent than that of the $(4_{0,\,4}-3_{0,\,3})$ transition.

The difference between Figure 3 and Figure 4 lies in their representation of the data. In Figure 3, we present channel maps which provide images of vertical slices through the expanding envelope while Figure 4 shows the line intensity integrated over all velocities. From Figure 3, we can see the clear feature of SiC₂ as a daughter molecule. Figure 4 offers a broader perspective by showcasing the distribution of all signals. More over, it reveals that the gas intensity spatial distribution of AI Vol for different transitions varies in size. Compared to transitions with low rotational quantum numbers, transitions with high rotational quantum numbers are distributed closer to the star.

The inner region of the AGB stars is at $\lesssim$ 20 $R_{\ast}$ (3.89 $\times$ 10¹⁴ cm), and the intermediate area of the CSE of AI Vol is at $\lesssim$ 70 $R_{\ast}$ (1.36 $\times$ 10¹⁵ cm) (Decin et al., 2008). So the radius of the SiC₂ molecules in the AI Vol coincides with the region of the daughter species in the model (Li et al., 2016).

5.1.2 RAFGL 4211 and II Lup

Figure 5 and Figures (A3, A4, A5) show the channel maps of the four transitions of SiC₂ for RAFGL 4211. The synthesized beam of observation is 1.00 $\times$ 1.00 ^′′, with position angles (PA) 0^∘. The signal strengths range from 5 $\sigma$ to 8 $\sigma$ . Brightness distribution radius is $\sim$ 5^′′ around $V\rm_{LSR}$ = - 3.0 km s^-1 velocity (distance from star center to peak intensity). A hollow shell structure exists within the radius $\sim$ 3^′′ of the star. The SiC₂ spatial distribution range of RAFGL 4211 is found to be $\sim$ 6.36 $\times$ 10¹⁶ - 8.90 $\times$ 10¹⁶ cm. In addition to focusing on the brightest component, we see some clump distributions in the outer regions.

Figures (A6, A7, A8) show the channel map of the three transitions of II Lup. The emission $4_{2,\,2}-3_{2,\,1}$ has no obvious signal and linewidth (the third panel at the bottom of Figure A9). The synthesized beam of observation is 0.75 $\times$ 0.45 ^′′. The signal strengths range from 6 $\sigma$ to 11 $\sigma$ . Figure A8 shows that $5_{0,\,5}-4_{0,\,4}$ emission has the form of a ring around the central position. The brightness distribution radius of the II Lup near $V\rm_{LSR}$ = 15.5 km s^-1 velocity is $\sim$ 10^′′. The SiC₂ spatial distribution range of II Lup is found to be $\sim$ 3.74 $\times$ 10¹⁶ - 7.48 $\times$ 10¹⁶ cm. As with RAFGL 4211, some clumps can be seen at $\sim$ 16^′′. This clump may be part of a spiral structure caused by a companion star.

5.1.3 Summary of morphology

The SiC₂ channel map (Figure 2 and 5) of AI Vol and RAFGL 4211 shows distinct daughter species characteristics. The SiC₂ radius greater than 20 $R_{\ast}$ distribution in the three C-rich AGB stars is consistent with the distribution of daughter species in O-rich AGB stars (Li et al., 2014). The distribution in hollow rings of the three sources indicates that SiC₂ is formed in the star’s outer layer through chemical reactions. This is the same as the ring distribution of SiC₂ in IRC+10216 (Takano et al., 1992). Gensheimer et al. (1995) reported that the inner and outer radii of SiC₂ of IRC+10216 are mainly distributed in the range of $\sim$ 2 $\times$ 10¹⁶ - 6 $\times$ 10¹⁶ cm. In the analyzed observations of three sources, the SiC₂ spatial distribution range is about 2.12 $\times$ 10¹⁶ - 8.90 $\times$ 10¹⁶ cm. To sum up, combining the ring brightness distribution of SiC₂ obtained in this work, we confirm that SiC₂ is the daughter molecule in the CSEs of C-rich AGB stars.

5.2 Abundance

We use the rotational diagrams method to estimate the abundance of SiC₂ and the spectral line profiles of the four transitions are shown in Figure 6. Using the parameters in Table 2, the molecular excitation temperature and column density are calculated under the assumption of LTE, and the equation is as follows (Zhang et al., 2009; Wang et al., 2014, e.g.),

\ln(\frac{3kW}{8\pi^{3}{\nu}S\mu^{2}})=\ln(\frac{N}{Q})-\frac{E\rm_{u}}{kT\rm_{ex}},

(1)

Here, $N$ is the total column density of the molecule, $Q$ partition function, $E\rm_{u}$ upper-level energy, $T\rm_{ex}$ is the excitation temperature, $k$ the Boltzmann constant, $\rm\upsilon(Hz)$ the rest frequency, $W$ ( $\int T\rm_{R}d\upsilon$ ) spectral line integral intensity, $S\mu^{2}$ the product of the line strength and the square of the electric dipole moment. The values of $S\mu^{2}$ and $E\rm_{u}/k$ are taken from the splatalogue databases⁶⁶6https://splatalogue.online//advanced.php. As the upper energy levels are close in temperature, the errors on the derived quantities are rather large.

In order to determine the relative abundance of SiC₂ to H₂, it is necessary to evaluate the average H₂ column density within the radius occupied by SiC₂. This can be achieved by employing the following equation (Gong et al., 2015),

N_{\rm H_{2}}=\frac{\dot{M}R/V\rm_{exp}}{\pi R^{2}m\rm_{H_{2}}}=\frac{\dot{M}}{\pi RV\rm_{exp}\mu m\rm_{H}}.

(2)

For AI Vol, $\dot{M}$ = 4.9 $\times$ $10^{-6}$ $M\rm_{\odot}$ $\rm yr^{-1}$ (Danilovich et al., 2018), R is the radius of the peak of the highest brightness point in Figure 4, which is 3^′′; $V\rm_{exp}$ the expansion velocity of 12 km s^-1 (Nyman and Olofsson, 1995), $m\rm_{H}$ the mass of hydrogen, $\mu$ the mean molecular weight of 2.8 of Gong et al. (2015). The derived column density of $\rm H_{2}$ is 5.52 $\times$ $10^{20}$ $\rm cm^{-2}$ . In the rotational analysis using Equation 1, we added error propagating and obtained the error of excitation temperature ( $\delta$ $T\rm_{ex}$ ) and column density ( $\delta$ $N$ ), with the integral intensity of 1 $\sigma$ -error. The formulas for $\delta$ $T\rm_{ex}$ and $\delta$ $N$ are as follows,

\delta T_{ex}=\frac{1}{m^{2}_{R}}\delta m_{R},

(3)

and

\delta N=\sqrt{\delta^{2}_{N,Q}+\delta^{2}_{N_{C_{R}}}}.

(4)

The slope, $m\rm_{R}$ , and intercept, $C$ _R. $\delta$ $N$ is the uncertainty contribution from the rotation partition function and the intercept of the rotational diagram.

In the practical calculations, firstly, the excited temperature and column density of SiC₂ are fitted by using the rotation diagram method that described in equation 1, and plotted in Figure 7; secondly, the fractional abundance of SiC₂ is calculated by $f$ = $N/N_{\rm H_{2}}$ . In AI Vol, we obtained $f$ (SiC₂) = 1.55 $\times$ $10^{-8}$ , which is an order of magnitude lower than the SiC₂ abundance in IRC+10216, which is around $10^{-7}$ (Agúndez et al., 2012; Velilla-Prieto et al., 2018; Cernicharo et al., 2010; Fonfría et al., 2014). Table 3 presents the fractional abundances, column densities, and excitation temperatures of SiC₂ for all three stars. We found that the fractional abundance of SiC₂ increases with the increasing wind density in the three observed C-rich AGB stars.

In the previous astrochemical models of C-rich CSEs of AGB stars, SiC₂ is always treated as a parent species with an initial abundance of $\thicksim$ $10^{-5}$ (Li et al., 2014; Massalkhi et al., 2018; Van de Sande and Millar, 2022). However, this study clearly shows that this species is a daughter species and therefore the chemistry of SiC₂ in the chemical models needs to be reinvestigated.

5.3 SiC₂ chemistry

Previous studies of the silicon chemistry in the CSEs of AGB stars mainly arise from those models constructed for the carbon-rich AGB star IRC+10216. The detailed discussion on the chemistry of the triangular molecule SiC₂ in the inner CSE can be found in Willacy and Cherchneff (1998), in the outer CSE in Takano et al. (1992), Gensheimer et al. (1995), and MacKay and Charnley (1999), where SiC₂ is found to be mainly formed via ion-neutral reactions and destructed to SiC due to photodissociation induced by the photons from the interstellar medium. Cernicharo et al. (2010) introduced three key reactions to the formation of SiC₂ (i.e., Si reacts with C₂H₂, Si reacts with C₂H, and Si⁺ reacts with C₂H), and then can successfully explain the enhanced abundance of SiC₂ from observations. The chemistry of those cyclic molecules is complex. The study of c-SiC₃ by Yang et al. (2019) suggested that the carbon-silicon molecules in the CSE may not only come from complex ion-molecule reactions or photodissociation of high-molecular-weight carbon-silicon molecules but also from bimolecular neutral-neutral reactions, and leading to the formation of naked carbon-silicon molecules via photochemical dehydrogenation. Since SiC₂ is likely the gas-phase precursor in forming SiC dust in carbon stars (Massalkhi et al., 2018), the interaction between gas and dust, in addition to the non-spherical and clumpy structures of the envelopes of the stars, will need to be considered in the future chemical models.

6 Conclusion

To explore whether SiC₂ is a parent or a daughter species, we have analyzed the ALMA observations of SiC₂ ( $4_{0,\,4}-3_{0,\,3}$ , $4_{2,\,3}-3_{2,\,2}$ , $4_{2,\,2}-3_{2,\,1}$ , and $5_{0,\,5}-4_{0,\,4}$ ) for the three carbon stars, and compared them with the SiC₂ results in the C-rich AGB star IRC +10216. The abundance of SiC₂ in the three selected stars is calculated by the rotational diagrams method. Our analysis revealed that the SiC₂ molecules in the CSEs of the carbon stars exhibited a hollow shell structure, with a distinct brightness distribution at different velocities, therefore we conclude that SiC₂ exists as a daughter molecule in the CSEs of these sources. Our results are in contrast to some previous reports which concluded that SiC₂ is a parent molecule in the envelopes of carbon stars. More sensitive observations may, of course, detect SiC₂ emission at low levels in the inner CSE. Our findings provide new insights into the chemical processes occurring in the CSEs of evolved stars and contribute to our understanding of the chemical evolution of ISM. Further detailed understanding of SiC₂ formation requires studying and comparing more C-rich AGB stars by combining the results of the single-dish and high-resolution interferometric observations.

Conflict of Interest Statement

The authors declare that the research was conducted in the absence of any commercial or financial relationships that could be construed as a potential conflict of interest.

Author Contributions

YF conducted the project, processed the ALMA archive data, and wrote the draft. XL initiated the project, guided the work, and revised the manuscript. TM was involved in interpreting the results and reviewing and revising the manuscripts. RS provided continuous manuscript revision. KW provided insights and feedback during the analysis process of the results. FX helped with the data analysis. DQ, SQ, XF, BJ, QC, GH, FL, and YZ provided comments and suggestions on the manuscript. JT, ZM, RM, JS, and JY were involved in analyzing the results and provided suggestions for the manuscript. All authors discussed and contributed to the final version of the manuscript.

Funding

X. Li acknowledges support from the Xinjiang Tianchi project (2019). TJM is grateful to the Leverhulme Trust for the award of an Emeritus Fellowshiop. This work was also funded by the National Science Foundation of China (12173023), the China Manned Space Project (CMS-CSST-2021-A09), the National Science Foundation of China (11973013), and the National Key Research and Development Program of China (22022YFA1603102). National Natural Science Foundation of China (92261101) and the Innovation Capability Support Program of Shaanxi Province (2023-CX-TD-49). National Natural Science Foundation of China (11973075). X. Fang, S. Qin, and Y. Zhang thank the Xinjiang Uygur Autonomous Region of China for support from the Tianchi Talent Program.

Acknowledgments

We appreciate the invaluable suggestions of the two anonymous reviewers on this work, which has been significantly improved the quality of this paper. This paper makes use of the following ALMA data: ADS/JAO.ALMA 2013.1.00070.S. ALMA is a partnership of ESO (representing its member states), NSF (USA), and NINS (Japan), together with NRC (Canada), MOST and ASIAA (Taiwan), and KASI (Republic of Korea), in cooperation with the Republic of Chile. The Joint ALMA Observatory is operated by ESO, AUI/NRAO, and NAOJ. We are very grateful to Professor Lars- $\rm\AA$ ke Nyman (the PI of the ALMA project that provided the data for this work) for his valuable comments and suggestions. This research has made use of astropy⁷⁷7www.astropy.org, a community-developed core Python package for astronomy, astropy, and matplotlib.

Data Availability Statement

The datasets analyzed for this study can be found in the ALMA Science Archive ⁸⁸8https://almascience.nrao.edu.

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Figure captions

Table 1: Source and observational parameters.

Name	IRAS	Mass loss rate	Distance	$V\rm_{LSR}$	$V\rm_{exp}$	$\theta\rm_{beam}$
		( $M\rm_{\odot}$ $\rm yr^{-1}$ )	(pc)	(km s^-1)	(km s^-1)	(^′′)
AI Vol	IRAS 07454-7112	$4.9(-6)^{(2)}$	$710^{(2)}$	$-39.0^{(2)}$	$12.0^{(2)}$	1.51 $\times$ 0.99⁽¹⁾
RAFGL 4211	IRAS 15082-4808	$1.0(-5)^{(3)}$	$850^{(4)}$	$-3.0^{(5)}$	$19.5^{(3)}$	1.00 $\times$ 1.00⁽¹⁾
II Lup	IRAS 15194-5115	$1.7(-5)^{(2)}$	$500^{(2)}$	$-15.5^{(2)}$	$21.5^{(2)}$	0.75 $\times$ 0.45⁽¹⁾

Note. $a(b)=a\times 10^{b}$ . Mass loss, distance, local standard of rest ( $V\rm_{LSR}$ ) and expansion ( $V\rm_{exp}$ ) velocities from the literature, and synthesized beam, $\rm\theta_{beam}$ . References: ⁽¹⁾ This work. ⁽²⁾Danilovich et al. (2018). ⁽³⁾Woods et al. (2003). ⁽⁴⁾Groenewegen et al. (2002). ⁽⁵⁾Smith et al. (2015).

Table 2: Spectral line parameters of different transitions in SiC₂ obtained via shell fitting using GILDAS.

		AI Vol				RAFGL 4211				II Lup
Transition	Frequency	rms	$\int T\rm_{R}d\upsilon$	$T\rm_{peak}$	$S/N$	rms	$\int T\rm_{R}d\upsilon$	$T\rm_{peak}$	$S/N$	rms	$\int T\rm_{R}d\upsilon$	$T\rm_{peak}$	$S/N$
	(GHz)	(mK)	(K km s^-1)	(K)		(mK)	(K km s^-1)	(K)		(mK)	(K km s^-1)	(K)
$J_{Ka,\,Kc}$ = $4_{0,\,4}-3_{0,\,3}$	93.06363900	6.70	1.26 ( $\pm$ 0.21)	0.14	20.45	16.40	1.48 ( $\pm$ 0.52)	0.14	8.60	21.49	9.51 ( $\pm$ 0.75)	0.54	25.11
$J_{Ka,\,Kc}$ = $4_{2,\,3}-3_{2,\,2}$	94.24539300	2.73	0.29 ( $\pm$ 0.09)	0.03	10.99	10.70	0.53 ( $\pm$ 0.34)	0.06	5.51	25.13	6.82 ( $\pm$ 0.88)	0.37	14.82
$J_{Ka,\,Kc}$ = $4_{2,\,2}-3_{2,\,1}$	95.57938100	2.55	0.32 ( $\pm$ 0.08)	0.04	13.73	16.30	0.91 ( $\pm$ 0.52)	0.10	6.13	47.30	$-$	$-$	$-$
$J_{Ka,\,Kc}$ = $5_{0,\,5}-4_{0,\,4}$	115.38238880	6.64	0.48 ( $\pm$ 0.21)	0.04	5.27	40.60	4.45 ( $\pm$ 1.30)	0.33	8.08	72.80	17.20 ( $\pm$ 2.55)	0.80	11.03

Note. The uncertainties are indicated in parentheses. The S/N is calculated by $T\rm_{peak}$ /rms.

Table 3: The deduced excitation temperature (

T\rm_{ex}

), column density (

N

), fractional abundance (

f

) of SiC₂ relative to H₂ in the target sources by the rotational diagram method, along with the previous observational results.

	This work			Other observations
Source	$T\rm_{ex}$	$N$ $\times$ 10¹³	$f$ $\times$ 10^-8	$T\rm_{ex}$	$N$ $\times$ 10¹³	$f$ $\times$ 10^-7	$\dot{M}$ $/$ $V$ _exp $\times$ 10^-7
	(K)	(cm^-2)		(K)	(cm^-2)		( $M\rm_{\odot}$ $\rm yr^{-1}$ km^-1 s)
AI Vol	6.66 ( $\pm$ 1.33)	0.90 ( $\pm$ 0.49)	1.64	14.00 ( $\pm$ 16.00)^(b)	0.40 ( $\pm$ 0.50)^(b)	2.30^(a)	4.08^(c)
RAFGL 4211	17.25 ( $\pm$ 13.07)	1.60 ( $\pm$ 2.10)	4.62	35.00 ( $\pm$ 51.00)^(b)	4.00 ( $\pm$ 3.00)^(b)	4.90^(a)	5.13^(c)
II Lup	4.12	43.22	47.46	19.00 ( $\pm$ 11.00)^(b)	4.00 ( $\pm$ 2.00)^(b)	12.00^(a)	7.91 ${}^{(a,\,c)}$

Note. $\dot{M}$ $/$ $V\rm_{exp}$ : the CSEs wind density. The uncertainties are listed in parentheses, which are obtained by considering the 1 $\sigma$ signal via the error propagation. The fitting of II Lup was performed using only two data points, which resulted in a lower precision and the absence of error estimation. References: ^(a) Woods et al. (2003);^(b) Smith et al. (2015);^(c) Danilovich et al. (2018).

Table 4: Upper energy,

E

_u, and

S\mu^{2}

of molecular SiC₂ in the observed transitions, extracted from the “Splatalogue” database.

Transition	$E$ _u	$S\mu^{2}$
	(K)	(Debye²)
$J_{Ka,\,Kc}$ = $4_{0,\,4}-3_{0,\,3}$	11.23	22.82
$J_{Ka,\,Kc}$ = $4_{2,\,3}-3_{2,\,2}$	19.12	17.18
$J_{Ka,\,Kc}$ = $4_{2,\,2}-3_{2,\,1}$	19.22	17.18
$J_{Ka,\,Kc}$ = $5_{0,\,5}-4_{0,\,4}$	16.77	28.46