Si-BEARING MOLECULES TOWARD IRC+10216: ALMA UNVEILS THE MOLECULAR ENVELOPE OF CWLeo

In Figures 1 and 2, we show maps of the emission of the lines SiC₂ ${{J}_{{{K}_{a}},{{K}_{c}}}}$=11$_{6,6}$– 10$_{6,5}$, ²⁹SiO J = 6 − 5, and ²⁹SiS J = 15 − 14 in their ground vibrational state at different offset velocities with respect to the systemic velocity of the source.

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SiC₂ (Figure 1) displays a central component elongated in the NE–SW direction with a size of ∼4–5'' along the nebular axis and ∼3–4'' in the perpendicular direction. The elongation is also observed in the ²⁹SiO emission (see below) and in the SiO and SiC₂ maps by Fonfría et al. (2014), where the authors invoke a possible bipolar outflow to explain it. At the systemic velocity of the source and at +6 km s⁻¹ offset, a ringlike, clumpy, and weak component is seen ∼10–11'' from the central star. The angular distance between the position of the star and the ring structure, considering a distance of ∼130 pc to the star from us (Groenewegen et al. 2012), corresponds to a linear distance of ∼2 × 10¹⁶ cm. This ringlike component is consistent with the peak abundance of SiC₂ in the outer envelope of IRC+10216 reported in Lucas et al. (1995) and the chemical model of Cernicharo et al. (2010). Although, this ringlike structure is probably filtered in our data given the shortest baselines used. Between the central and the ringlike structure, emission of SiC₂ is either very low or absent (Lucas et al. 1995). Finally, the redshifted emission (+12 km s⁻¹) displays a quasi-circular distribution with a diameter of ∼5–6''. These brightness distributions could be interpreted as the SiC₂ is formed in regions close to the star, then it condenses onto the dust grains, and eventually it reappears at the outer shells of the CSE, perhaps as a hollow shell, as the consequence of the interaction between the UV Galactic radiation field and the CSE (Lucas et al. 1995; Fonfría et al. 2014).

For ²⁹SiO (Figures 1 and 2), the bulk of the emission arises from a compact central component with a size of 2''. This line also displays an extended and clumpy distribution, elongated in the NE–SW and with a size of ∼6–7''. At velocities close to the terminal expansion velocity, ∼14.5 km s⁻¹(Cernicharo et al. 2000), the brightness distribution is elongated in the NE–SW direction with a size of ∼3–4''. The blueshifted emission at −13 km s⁻¹ displays a decrease just in front of the star, which can be interpreted as self-absorption and probably absorption of the continuum emission mostly coming from the star. There is no conclusive explanation for the elongation; nevertheless, some authors pointed out that it could evidence the presence of a bipolar outflow in the CSE (Fonfría et al. 2014). The possible presence of a binary companion to CWLeo could also play a decisive role in this scenario (Guelin et al. 1993; Cernicharo et al. 2015).

The observed brightness distributions of the vibrationally excited SiS lines are expected to be compact and centered on the star since the involved levels are excited at the high temperatures prevailing close to the star. The SiS J = 15 − 14 v = 0 line, which displays maser emission (Fonfría Expósito et al. 2006), shows a circular brightness distribution with a diameter of ∼2'' at the systemic velocity of the source. For the SiS J = 15 − 14 v $\geqslant$ 1 lines, the observed distributions are not spatially resolved. Figure 1 shows the emission of the ²⁹SiS J = 15 − 14 v = 0 line, which displays a brightness distribution of a compact source surrounding the central star with a diameter of ∼2''. A large-scale artificial modulation can be seen below the 25σ level. Since it is related to the visibilities at short baselines, we do not expect it to modify the shape and flux of the compact central component of the brightness distribution. Also, the quality of the SiS and ²⁹SiS maps is affected owing to the low uv coverage and non-neglible contribution of the sidelobes for setups 3–5 (see Table 1). The lines that lie in the range covered by setup 6 are those of high vibrationally excited states (e.g., SiS J = 15 − 14 v $\geqslant$ 10; ²⁹SiS J = 15 − 14 v $\geqslant$ 6), which are tentative and spatially unresolved.

The Cycle 0 observations with ALMA allowed us to detect several J = 15 − 14 lines of high vibrationally excited states of SiS isotopologues, in particular, up to v = 7 for the main isotopologue (see Figure 3). The SiS J = 15 − 14 v = 8 and v = 10 lines are probably blended with unidentified lines, so we consider them to be tentative. Additionally, the SiS J = 15 − 14 v = 9 line is considered tentatively detected because even though its FWHM measured seems to follow the trend shown in Figure 3, its measured integrated intensity is underestimated considering the population diagram of Figure 3. All these lines display a compact unresolved emission peaking at the central star. The FWHM of the lines measured from the spectra at the stellar position decreases with increasing upper level energy (see Figure 3). We verified this behavior for SiS, ²⁹SiS, ³⁰SiS, Si³³S, and Si³⁴S. In the dust formation region, the gas displays a velocity gradient as a function of the radial distance to the star, i.e., the closer to the star the lower the expansion velocity (Agúndez et al. 2012 and references therein). Hence, those lines involving higher vibrational states, which are excited in inner and warmer regions, are narrower. Thermal broadening for the SiS lines excited in the dust formation region is ∼1 km s⁻¹, and thus this mechanism could only account partially for the FWHM variation of the lines.

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We analyzed the excitation conditions of SiS with the rotational diagram technique (Goldsmith & Langer 1999) using the spectra at the stellar position (see Figure 3). We considered two different linear trends for the observational data: one for the transitions with E$_{{\rm up}}\;\lesssim \;$ 2500 K (i.e., v = 0, 1, and 2) and a different trend for the rest (i.e., v = 3–7). The v $\geqslant$ 8 lines are excluded from the fit. The values derived from the v = 0 to v = 2 fit are uncertain owing to the maser nature of the SiS J = 15 − 14 v = 0 line and also to possible optically thick emission. Both data series show a linear behavior consistent with a single vibrational (excitation) temperature for each of the fits. The vibrational temperature derived from the fit involving the transitions in high-energy vibrational states is higher than the temperature derived for the low vibrational levels. Therefore, the emission produced by SiS transitions in high-energy vibrational states can only arise from regions close to the photosphere. This result is similar to the one obtained by Cernicharo et al. (2011) for HCN.

We used a large velocity gradient (LVG) code to model the SiS emission (Cernicharo 2012). Further details about the spectroscopic data used in the calculations are given in Section 3.2.1. The SiS collisional data were taken from Toboła et al. (2008) and extrapolated to high rovibrational levels. We adopted a distance to the star of ∼130 pc, an effective temperature of ∼2330 K, and a stellar radius of ∼4 × 10¹³ cm as input for our model (Cernicharo et al. 2000; Monnier et al. 2000; Groenewegen et al. 2012). We used two different models: (i) the model of Agúndez et al. (2012), which was used to reproduce the molecular abundances in the inner layers of IRC+10216, which we call the "2012 model," and (ii) this work, which is a modification of model (i). We modified the H₂ density, decreasing it by a factor ∼2, as described in Cernicharo et al. (2013; this was used to reproduce the dust nucleation zone, 1–10 ${{R}_{\star }}$, of IRC+10216). Additionally, the SiS abundance in the dust nucleation zone needs to be balanced with a similar increase (factor of ∼2) to avoid an underestimation of the SiS emission. From these models (see Figure 3), we obtain a good agreement with the vibrational temperature derived from the vibrational diagram and moderate discrepancies with the total column density within a factor of ∼2. These discrepancies in the column density may be explained by the dilution due to the size of the emitting region compared to the half power beam width of the synthetic beam, which would increase the optical depth of the lines. The size of the emitting region should decrease with the vibrational state owing to the energies needed to excite those lines. With our models, we found moderate to high optical depths τ(v = 1) ∼ 10 to τ(v = 4) ∼ 0.8 for abundance profile (i) and τ(v = 1) ∼ 47 to τ(v = 8) ∼ 1.0 for abundance profile (ii).

3.2.1. SiS Potential Energy Function and Vibrational Dipole Moment

The potential energy function used to describe the internuclear motions of the SiS isotopologues is a Born–Oppenheimer (BO) potential properly extended to accommodate Born–Oppenheimer breakdown (BOB) corrections. The effective potential has the form (Campbell et al. 1993; Ram et al. 1997; Dulick et al. 1998; Coxon & Hajigeorgiou 2000)

$$\begin{eqnarray}\begin{array}{ccccccccccccccc} {{V}^{{\rm eff}}}(r) & = & {{V}^{{\rm BO}}}(r)+\frac{{{V}_{A}}(r)}{{{M}_{A}}}+\frac{{{V}_{B}}(r)}{{{M}_{B}}} \\ {} & {} & -\frac{{{\hbar }^{2}}}{2\mu }[1+q(r)]\frac{J(J+1)}{{{r}^{2}}}, \\ \end{array}\end{eqnarray} \tag{ 1 }$$

where M_A and M_B are the silicon and sulfur atomic masses and μ is the reduced mass. The BO potential is given by

$$\begin{eqnarray}&&{{V}^{{\rm BO}}}(r)={{D}_{e}}{{\left[ \frac{1-{{e}^{-\beta (r)}}}{1-{{e}^{-\beta (\infty )}}} \right]}^{2}},\end{eqnarray} \tag{ 2 }$$

where

$$\begin{eqnarray}&&\beta (r)=z\mathop{\sum }\limits_{i=0}^{4}{{\beta }_{i}}{{z}^{i}},\end{eqnarray} \tag{ 3 }$$

$$\begin{eqnarray}&&\beta (\infty )=\mathop{\sum }\limits_{i=0}^{4}{{\beta }_{i}},\end{eqnarray} \tag{ 4 }$$

and

$$\begin{eqnarray}&&z=\frac{r-{{r}_{e}}}{r+{{r}_{e}}},\end{eqnarray} \tag{ 5 }$$

and the BOB potential and centrifugal correction terms are represented by the power expansions

$$\begin{eqnarray}&&{{V}_{A}}(r)=\mathop{\sum }\limits_{i=1}u_{i}^{A}{{z}^{i}},\end{eqnarray} \tag{ 6 }$$

$$\begin{eqnarray}&&{{V}_{B}}(r)=\mathop{\sum }\limits_{i=1}u_{i}^{B}{{z}^{i}},\end{eqnarray} \tag{ 7 }$$

$$\begin{eqnarray}&&q(r)=M_{A}^{-1}\mathop{\sum }\limits_{i=1}q_{i}^{A}{{z}^{i}}+M_{B}^{-1}\mathop{\sum }\limits_{i=1}q_{i}^{B}{{z}^{i}}.\end{eqnarray} \tag{ 8 }$$

The potential parameters were obtained by nonlinear least squares fitting to the observed infrared and microwave line positions of the SiS isotopologues up to v = 12. The final data set included a total of 2863 lines, 414 rotational transitions (Tiemann et al. 1972; Sanz et al. 2003; Müller et al. 2007), and 2449 rovibrational transitions (Birk & Jones 1972; Frum et al. 1990). Mass-independent Dunham coefficients, U_ij, have been derived by Müller et al. (2007). The fit to the potential energy function was performed using the Levenberg–Marquardt algorithm (Levenberg 1944; Marquardt 1963) to minimize the ${{\chi }^{2}}$ function, with the line positions weighted by the square of the experimental uncertainties. The rovibrational energy levels of the isotopologues needed to calculate the line positions were computed by solving the radial Schrödinger equation using the variational method of Harris et al. (1965) along with harmonic-type basis functions. The potential parameters obtained in the fit are given in the comments of Table 2. The final ${{\chi }^{2}}$ value was 1.767. The unweighted standard deviations for the rotational and vibrational–rotational line positions were 0.0229 MHz and 0.000657 cm⁻¹, respectively.

Table 2.  Calculated Vibrational Dipole Moment Matrix Elements (D) for ²⁸Si³²S

v'/v''	0	1	2	3	4	5	6	7	8	9	10	11	12
0	1.7420	...	...	...	...	...	...	...	...	...	...	...	...
1	−0.1348	1.7658	...	...	...	...	...	...	...	...	...	...	...
2	−0.6333 × 10−2	−0.1907	1.7896	...	...	...	...	...	...	...	...	...	...
3	0.4068 × 10−3	0.1101 × 10−1	0.2336	1.8135	...	...	...	...	...	...	...	...	...
4	−0.3379 × 10−4	−0.8184 × 10−3	−0.1564 × 10−1	0.2697	1.8375	...	...	...	...	...	...	...	...
5	−0.3359 × 10−5	−0.7613 × 10−4	−0.1302 × 10−2	0.2027 × 10−1	−0.3016	1.8615	...	...	...	...	...	...	...
6	0.3804 × 10−6	−0.8306 × 10−5	0.1329 × 10−3	−0.1852 × 10−2	−0.2493 × 10−1	0.3304	1.8857	...	...	...	...	...	...
7	0.4752 × 10−7	0.1018 × 10−5	0.1569 × 10−4	−0.2046 × 10−3	0.2465 × 10−2	0.2961 × 10−1	−0.3568	1.9100	...	...	...	...	...
8	−0.6394 × 10−8	−0.1363 × 10−6	−0.2061 × 10−5	0.2587 × 10−4	−0.2916 × 10−3	−0.3137 × 10−2	0.3433 × 10−1	0.3814	1.9343	...	...	...	...
9	−0.9087 × 10−9	−0.1952 × 10−7	−0.2934 × 10−6	0.3612 × 10−5	−0.3918 × 10−4	−0.3943 × 10−3	0.3866 × 10−2	0.3909 × 10−1	−0.4045	1.9587	...	...	...
10	0.1339 × 10−9	0.2936 × 10−8	0.4441 × 10−7	−0.5435 × 10−6	0.5779 × 10−5	0.5594 × 10−4	−0.5130 × 10−3	−0.4649 × 10−2	0.4388 × 10−1	0.4262	1.9833	...	...
11	0.2005 × 10−10	0.4562 × 10−9	0.7033 × 10−8	−0.8654 × 10−7	0.9143 × 10−6	0.8674 × 10−5	−0.7649 × 10−4	−0.6482 × 10−3	0.5485 × 10−2	0.4871 × 10−1	−0.4469	2.0079	...
12	−0.2954 × 10−11	−0.7182 × 10−10	−0.1147 × 10−8	0.1437 × 10−7	−0.1525 × 10−6	−0.1437 × 10−5	0.1241 × 10−4	0.1011 × 10−3	−0.8003 × 10−3	−0.6373 × 10−2	0.5358 × 10−1	0.4667	2.0326

Note. Internuclear potential energy parameters for the SiS molecule: D_e = 51993.7274 cm⁻¹, r_e = 1.929260274 Å, ${{\beta }_{0}}$ = 5.9671641, ${{\beta }_{1}}$ = 5.8793706, ${{\beta }_{2}}$ = 9.3200373, ${{\beta }_{3}}$ = 18.402479, ${{\beta }_{4}}$ = 18.451287, u$_{1}^{{\rm Si}}$ = −749.1309 cm⁻¹ amu, u$_{2}^{{\rm Si}}$ = 6844.274 cm⁻¹ amu, u$_{1}^{{\rm S}}$ = −1003.321 cm⁻¹ amu, u$_{2}^{{\rm S}}$ = 7128.960 cm⁻¹ amu.

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The dipole moment function used for SiS was determined semiempirically by Piñeiro et al. (1987), and the dipole moment matrix elements were computed up to v = 4. In Table 2, we provide them up to v = 12. The agreement between our calculations and those of Piñeiro et al. (1987) for v ≤ 4 is excellent.

SiC was detected in IRC+10216 by Cernicharo et al. (1989) with line profiles indicating that the molecule was produced in an external shell, probably as a product of the photodissociation of SiC₂. Our observations did not cover any frequency range where SiC lines could arise; however, lines of ²⁹SiC and SiC v = 1 lie in this range, but they were not detected. For a temperature in the photosphere of 2300 K, a significant number of SiC molecules could be in the v = 1 state (E$_{{\rm up}}\;\sim \;$ 1400 K) and higher vibrational levels. We derived an upper limit to the SiC column density of 4.4 × 10¹⁴ cm⁻² from the ²⁹SiC upper limit, where we used an isotopic ²⁸Si/²⁹Si ratio of 20 (Cernicharo et al. 1989, 1991). Hence, SiC₂ is the main carrier of SiC bonds in the gas phase in the dust formation zone of IRC+10216.