HINTS OF A ROTATING SPIRAL STRUCTURE IN THE INNERMOST REGIONS AROUND IRC +10216

Interferometers are known to filter out the flux that cannot be observed in the shortest baselines, and which correspond to extended emission. Due to this, and considering the shortest baselines we had in these interferometric maps, we estimate that emission extending more than 13''–14'' was filtered out.

To estimate the amount of flux filtered out by the interferometer, we have compared the brightness integrated in the channel maps with the profiles obtained by the single-dish IRAM 30 m telescope. No corrections were made regarding the primary beam of both observatories since in most cases the emission was found to be relatively compact with respect to those and because the comparison was only intended to estimate if a large fraction of the emission was or was not filtered out. In Figure 1, this comparison is presented: single-dish profiles in red and those obtained with the ALMA interferometer in black.

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To conclude, Figure 1 shows that significant flux losses are only found for the channel maps of Al-bearing molecule emission. In particular, the effect is most noticeable for the most abundant isotopologues of AlF and AlCl.

The emission maps from the NaCl transitions are presented in Figures 2–4. As mentioned above the emission from the NaCl J = 20–19 is severely contaminated by vibrationally excited H¹³CN transitions. We expect this vibrationally excited emission to be restricted to the innermost regions of the molecular envelope of IRC +10216 and to be relatively narrow (Cernicharo et al. 2013). Therefore, while the emission from the inner regions might be polluted, the extended emission is most probably only a consequence of the NaCl J = 20–19 brightness distribution. In that sense, we can estimate the extent of the NaCl J = 20–19 emission. The extent of the emission in the central channels ranges between 25 and 34 in diameter, which corresponds to a radius of 2.4 10¹⁵ cm (=60 R_*) and 3.3 10¹⁵ cm (=83 R_*), respectively.

The molecular emission map of NaCl J = 21–20 is presented in Figure 2. The extent of NaCl J = 21–20 emission reaches a maximum radius of ∼3'' from the star in a southwest clump. The bulk of the emission is restricted to a radius of 16. A central relative minimum is clearly visible in the central maps of this transition, surrounded by two maxima. The size of this minimum is ∼05, which corresponds to a radius of 4.9 × 10¹⁴ cm (=12 R_*). It is important to note that this minimum is similar to the size of the HPBW, i.e., it is spatially resolved. In addition, we can exclude this minimum to be result of a self-absorption of the NaCl emission by the cold gas closer to us, as it is visible from positive to negative velocities (v_sys = −26.5 km s⁻¹).

A detailed look at the maps reveals that the velocity field of the region where the two maxima and the minimum are located can be associated with a narrow feature in the line profile (see Figure 5). This feature is centered at the v_LSR = −26.5 km s⁻¹ and has an FWHM of ∼6 km s⁻¹. This contrasts with the expected expansion velocity of ∼11 km s⁻¹ (Agúndez et al. 2012) for gas lying within this region. At first glance, the structure observed is most likely explained by a torus almost edge-on, with a P.A. of ∼766. However, this P.A. is not compatible with the ∼120° P.A. of the dust lane observed by Tuthill et al. (2000) or Jeffers et al. (2014). We will show below that this disagreement in the P.A. is only apparent. A rotation of the structure responsible for the emission peaks in the central channels around the star, plus an almost face-on angle of this structure reconciles the P.A. angle observed in the ALMA interferometric maps with that observed in IR emission. In Section 3.5 we explore the brightness distributions that could result in the structures observed. Since the interferometric maps observed here observed show not only the structure but also the kinematics, the structures directly in the maps need to be carefully interpreted. In Section 4.1 we present a simple kinematic model of the structures found to be most suitable to reproduce the maps observed in Section 3.5. This allows us to constrain kinematics of the observed structures.

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The position–velocity diagram obtained along the two maxima observed in the NaCl J = 2–1 map (Figure 6) shows that this structure is, as already mentioned, narrow in velocity, which shows that the structure responsible for these two maxima is practically static with respect to the rest of the gas. Also, the P–V diagram shows that while a maximum is slightly shifted toward positive velocities with respect to the systemic velocity, the other is shifted to negative velocities. This fact suggests that the two-peak structure is rotating. In Section 4.1 we present a simple kinematic model that supports this scenario.

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The intensity of the NaCl v = 1 transitions is relatively low. Both transitions have similar intensities (see Figure 1). However, the UV coverage of the J = 20–19, v = 1 transition is much better than for the J = 21–20, v = 1 transition, which results in more reliable maps. The emission maps from the NaCl v = 1 excited state J = 20–19 are presented in Figure 3.

The extent of the NaCl v = 1 J = 20–19 transition might seem relatively large (∼1'') for a v = 1 rotational transition line. However, our observations showed that other vibrationally excited transitions such as, for instance, H¹³CN (0, 1^1f, 0) J = 3–2, which has an excitation energy of 1038.7 K, also presents an extent of ∼1''. Therefore, we could expect NaCl v = 1, J = 20–19 with an excitation energy of 649.9 K to be at least as extended as the H¹³CN v₂ = 1 rotational transition lines.

The emission from Na³⁷Cl J = 21–20 is remarkably similar to that of the most abundant isotopologue. The radial extent of the emission for this transition is ∼27. In particular the central relative minimum is also observed in this transition. Since the NaCl J = 21–20 and Na³⁷Cl J = 21–20 transition map have been observed within different setups (setup 3 and setup 4, respectively) we can claim that the structures observed cannot be related to instrumental effects.

Compared with other emission maps, such as H¹³CN J = 3–2 or ²⁹SiO J = 6–5 (Velilla Prieto et al. 2015; J. Cernicharo et al. 2016, in preparation), the NaCl emission is relatively compact. Despite this, several of the structures observed in Figure 2 are compatible with the spiral structure already reported by Cernicharo et al. (2015). In particular, a detailed comparison of the NaCl J = 21–20 emission with that of the two isotopomers H¹³CN J = 3–2 and HC¹⁵N J = 3–2 presented by J. Cernicharo et al. (2016, in preparation) showed that the spatial distribution of all these emission lines is very similar (see Figure 7). The blob observed in the NaCl J = 21–20 map at Δδ = −2 and Δα = −2 from the star is located at a spiral arm observed in H¹³CN J = 3–2. Also, it is important to note that the peak emission of H¹³CN J = 3–2 is located in the central minimum observed in the NaCl J = 21–20 map.

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We have obtained interferometric maps for the KCl and K³⁷Cl J = 35–34 as well as for KCl J = 34–33 and K³⁷Cl J = 36–35. These maps are presented in Figures 8–10, except for KCl J = 35–34 which presents severe contamination from other lines (see below).

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In the case of KCl J = 34–33, the minimum in the central region of the central channels is not clearly seen due to the lower intensity of the emission, but the elongation observed seems to correspond to the two maxima observed in the central channel maps of the NaCl J = 21–20 emission. The same features can be observed in the isotopologue K³⁷Cl J = 36–35 and J = 35–34. The extent of the KCl J = 34–33 emission is ∼25.

While KCl J = 34–33 is free from overlap with other lines, KCl J = 35–34 presents an overlap with several lines (see Section 3). However, in contrast to to the case of NaCl J = 21–20, the overlapping lines are not as close to the rest frequency of KCl J = 35–34. Therefore, as shown in Figure 11, some central channels are free of contamination from other lines. In particular, the channels between velocities −23.3 km s⁻¹ and −25.8 km s⁻¹ present only the emission from KCl J = 35–34. These contamination-free channels show also an elongation and a central minimum as that observed in NaCl. The KCl J = 35–34 emission map shows an extent of ∼2''.

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As for NaCl, the emission from the central elongated region can be directly associated with a narrow feature in the line profile.

As we have mentioned in Section 2.1, the extended emission from the AlCl lines is not fully recovered. In the case of AlCl J = 18–17, since it is severely contaminated by other transition lines, which are expected to come from both the innermost regions (HCN vibrationally excited) and from regions located at 15'' (C₂H, see Guélin et al. 1997), we cannot determine if the emission from this AlCl transition itself is filtered out or the structure of this emission in the innermost regions.

On the contrary, the molecular lines J = 18–17 and J = 19–18 of Al³⁷Cl present no overlap with other lines and the effect of the flux filtering is relatively small. The emission from these transitions shows a roughly spherical distribution (Figures 12 and 13).

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The inspection of the innermost regions traced by the Al³⁷Cl J = 18–17 and J = 19–18 maps reveals that the emission peaks at the continuum intensity peak. No central minimum is observed in any of the AlCl transitions.

The emission of AlF J = 8–7 is presented in Figure 14. As shown in Figure 1, this molecular transition is clearly affected by flux filtering. The central channels of this transition present only the compact emission which has not been filtered. Therefore, we cannot estimate the extent of this emission. Only at extreme velocities is the flux completely recovered. The emission at these extreme velocities is relatively extended compared with that at central velocities. This can be explained as an AlF J = 8–7 brightness distribution that peaks at the star and that is, on the large scale, diffuse and somehow homogeneous. This diffuse emission would be filtered out in the central velocity channels where it is more extended and would only be recovered in at the extreme velocities. The brightness distribution per channel observed in the AlF map is very similar to those observed in Al³⁷Cl maps. Therefore, we might expect a similar molecular distribution for both Al-bearing molecules.

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After a detailed inspection of the brightness distribution of the metal-bearing transitions observed, we can separate the structures observed into two groups: the Al-bearing species shows an emission peak close to the star, while the KCl and NaCl emission maps reveal a central minimum surrounded by two peaks.

This may be interpreted at first glance as a toruslike structure rich in salts (KCl, NaCl) and poor in AlCl and AlF, while the abundance close to the star is by contrast poor in salts and rich in Al-bearing molecules.

A deep analysis of the central relative minimum shows that the two maxima located at both sides of the minimum are directly related to a particularly narrow feature (FWHM ∼ 6 km s⁻¹) centered at the systemic velocity (Figure 5). In Section 4 we present a further analysis of the characteristics for the possible structures responsible for the observed features.

In any case, it is surprising that the toruslike structure is visible only in NaCl and KCl emission lines, while it is not seen in the Al-bearing species. It might be the case that the two maxima correspond to a larger structure, which might be suppressed due to the image deconvolution. Also, as already mentioned, recent studies have suggested the presence of a spiral structure in the ejecta around IRC +10216 (see Cernicharo et al. 2015; Velilla Prieto et al. 2015; J. Cernicharo et al. 2016, in preparation).

To explore the possibility that such a spiral is responsible for the structures observed in the NaCl and KCl maps, we have modeled a brightness distribution that consists of a Fermat spiral distribution, which is parameterized by the equation r²(θ) = a² θ, convolved with a Gaussian function.

We used the GILDAS ALMA simulator to transform this brightness distribution into visibilities corresponding to the cycle 0 extended configuration and we generated the corresponding dirty and cleaned maps. The image restoration procedure was exactly the same as used for the ALMA on-source data. Also the integration time on-source was the same as in the observation and the UV plane coverage so obtained was similar.

In addition to this simulation, to explore other possible scenarios, we have modeled three other brightness distributions. The first brightness distribution corresponds to a toruslike structure, which for the central velocities, corresponds to two maxima plus a weak Gaussian distribution that corresponds to the rest of the emission observed in the NaCl and KCl emission maps. The brightness peak at the torus is 10 times that of the Gaussian distribution. The second distribution corresponds to a spherical shell with the size of the toruslike structure. This structure might be clumpy and appear in the maps as two maxima, similar to a torus. The third brightness distribution is a spherical shell with the addition of a Gaussian distribution.

It is important to note that the torus structure introduced for the simulations corresponds only to the central velocity channel. In this sense, for an expanding (and/or rotating) torus, the central channel will present exactly the same structure—apart from a relative rotation—except for the case in which the plane of the torus is exactly face-on. In the rest of the cases, the velocity components corresponding to the systemic velocity will appear as two maxima, varying only the P.A. of the imaginary line connecting both density peaks.

The simulations that best resemble the structures observed are those resulting from a spiral and from a Gaussian plus a torus brightness distribution (see Figures 15 and 16).

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It has been shown that if the interferometric clean beam is remarkably elongated, i.e., if the source presents a low elevation with respect to the interferometer, a spherical shell could appear in the restored maps as two emission peaks separated by a central minimum (see HCN J = 1–0 emission map by Quintana-Lacaci et al. 2008).

A spherical shell for the decl. of IRC +10216, which results in a relatively elongated beam, could only resemble a toruslike structure if the signal to noise of the map is remarkably low. The spherical structure is visible from low fluxes to 70% of the emission peak. Therefore, the rms noise of the map should be ∼0.2 times the peak flux of the observation. In our case, this ratio is 0.022, i.e., 10 times lower, therefore any circular structure should be visible. In the case where we add a spherical Gaussian distribution, we have similar problems. While the circular structure might be less evident, we cannot reproduce the elongation observed in the ALMA KCl and NaCl maps.

It is important to understand the reasons that would prevent Al-bearing molecular transitions from presenting the two maxima observed in KCl and NaCl.  The dipole moments of NaCl (9.0012 D) and KCl (10.27 D) are significantly higher than those of AlCl (1.00 D) and AlF (1.53 D).  Because of this, both Al-bearing species are more easily thermalized than the salts. NaCl and KCl would be mainly thermalized in the densest regions, while AlCl and AlF emission lines would be thermalized both in dense and diffuse regions of the inner regions around IRC +10216. Therefore, we would expect to detect the emission from NaCl and KCl arising from dense regions, while Al-bearing molecules could be detected both in the arms of a spiral and in the inter-arm regions. This could be translated, in the simulations we performed, as the addition of an "inter-arm" brightness distribution in the first case of the spiral structure and in the second case as a lower brightness ratio between the torus and the Gaussian distribution.

In the case of the spiral, we add a Gaussian distribution that fills the inter-arm gaps of the spiral structure, as expected for the Al-bearing transition, with a brightness ratio between the spiral and the Gaussian of 4. The result of the simulation is that the spiral structure would disappear in the resulting map of such a brightness distribution for Al-bearing species (see Figure 17).

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In the case of the torus plus the Gaussian distribution, we created a brightness distribution like that of Figure 16 but with a brightness peak ratio of 2 (Figure 18). The simulation shows that also in this case, the torus would not be visible for Al-bearing species.

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These two simulations show that while in the Al-bearing transition maps we do not see the spiral or the torus structure, we cannot claim that these features are not present.

In summary, these simulations suggest that the most probable scenario is that the structures observed in NaCl and KCl emission maps are resulting from a spiral distribution of the molecular gas, which is in fact compatible with the spiral-like structure already observed in CO (Cernicharo et al. 2015) and recently in other species such as H¹³CN (J. Cernicharo et al. 2016, in preparation).

Although from NaCl and KCl it could not be possible to discard a torus structure, the lack of similar structures in HCN, SiC_2, and other high dipole and abundant molecules favor the spiral structure seen in HCN.

4.0.1. Model Fitting

For our model we considered up to J = 100 and v = 5. We divided the spherical envelope into 100 concentric shells and solved the excitation conditions of NaCl in each shell assuming a large velocity gradient approximation, which assumes that each shell of the envelope is radiatively isolated. Therefore, we can solve the statistical equilibrium equation in each shell.

For both the spiral and the torus scenarios we have only varied the NaCl abundance profile, while we have kept unaltered the H₂ density profile presented by Cernicharo et al. (2013).

In the case of the spiral structure, the best fit for the azimuthally averaged emission of NaCl J = 21–20 and v = 1, J = 20–19 maps is presented in Figure 20. The abundance profile obtained is presented in Figure 21. This abundance profile is that presented by Agúndez et al. (2012), multiplied by 1.2, except for two regions, one located between 10¹⁵ cm and 2.6 × 10¹⁵ cm which has to be multiplied by 1.5 and a region with negligible abundance of NaCl located between 2.5 × 10¹⁵ cm and 3.4 × 10¹⁵ cm. The intermediate empty region is most probably related to the spiral structure itself and traces the inter-arm region.

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We estimate the mass of the spiral to be 1.6 × 10³² gr (=0.08 $\;{M}_{\odot }$) and the NaCl mass in the spiral to be 1.0 × 10²² gr (=1.7 × 10⁻⁶M_Earth).

In addition, we have used the averaged density to fit the single-dish emission profiles from the NaCl transitions J = 7–6 to J = 27–26 presented by Agúndez et al. (2012; Figure 22). Most of these lines are relatively well fitted, showing that the model obtained from the NaCl J = 21–20 ALMA interferometric maps also is able to reproduce the single-dish NaCl line profiles from low-energy to high-energy transitions. The NaCl J = 20–19 line shows a poor fit, but this is a result of the aforementioned blending of this line with the H¹³CN J = 3–2 v = (0, 1^1f, 0) transition.

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In the case of the torus, the fitting of the two cuts is presented in Figure 23. We have found that the torus should have a minimum and maximum radius of 4 × 10¹⁴ cm and 1.1 × 10¹⁵ cm, respectively, which corresponds to ∼27 AU and ∼73 AU. We found the fractional abundance of NaCl in the torus to follow an r³ law (Figure 24).

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The azimuthally averaged emission has been fitted using an average of the two density profiles obtained, i.e., that of the torus and of the spherical emission. We have found an appropriate fit for the azimuthally average emission assuming that 65% of the emitting mass comes from the torus-free abundance profile and 35% from the torus NaCl abundance profile. The result of azimuthally averaging a torus would result in a spherical hollow shell. Therefore, as this scenario consists of a spherical shell plus a torus, the azimuth average of these two structures can be regarded as a spherical torus-free shell plus a hollow shell, a result of the torus. In that sense, we can estimate the mass of this simulated spherical shell as:

$$\begin{eqnarray}&&{M}_{\mathrm{shell}}={M}_{\mathrm{noTorus}}+{M}_{\mathrm{Torus}}=4\pi {\displaystyle \int }_{0}^{{r}_{\infty }}{r}^{2}\;n(r)\;{dr}\end{eqnarray} \tag{ 1 }$$

where $n(r)=0.65\;{n}_{\mathrm{noTorus}}(r)+0.35\;{n}_{\mathrm{Torus}}(r)$. Therefore, we can estimate the total mass of the torus as:

$$\begin{eqnarray}&&{M}_{\mathrm{Torus}}=4\pi \;\times \;0.35\times {\displaystyle \int }_{{r}_{\mathrm{in}}}^{{r}_{\mathrm{out}}}{r}^{2}\;{n}_{\mathrm{Torus}}(r)\;{dr}\end{eqnarray} \tag{ 2 }$$

The mass of the torus obtained is 2.1 × 10²⁹ gr (=1.1 × 10⁻⁴$\;{M}_{\odot }$), and the total mass of NaCl in the torus is 8.7 × 10¹⁹ gr (=1.5 × 10⁻⁸ M_Earth).

In both cases, we found significant departures in the quality of the fits for mass variations larger than 20%.

In order to understand the kinematic characteristics of the structures, the spiral or the torus, observed in the NaCl and KCl emission maps, we have developed a simple model of expanding and rotating spiral and torus structures. The aim of this model is to understand the kinematics and spatial distribution expected for different structures.

We adopted as the P.A. of the spiral and the torus that of the dust lane observed by Jeffers et al. (2014) and Tuthill et al. (2000) (P.A. = 120°). In order to generate a kinematic model that qualitatively reproduces the observations we have to find the value of three parameters: the expansion velocity (v_exp), the rotation velocity (v_rot), and the inclination with respect to the plane of the sky (i). For a fixed parameter, any of the three aforementioned, the other two are intercorrelated, i.e., for a fixed inclination, only one combination of v_rot and v_exp fits the observations. The expansion velocity at the regions where we have found the inner radius to lie is relatively well constrained to be between ∼11 km s⁻¹ (Fonfría et al. 2008) and ∼12.5 km s⁻¹ (Decin et al. 2010). The difference in the inclination and the rotation velocity is negligible when assuming the former or the latter expansion velocity.

We do not have any information on the possible tilt of the orbital plane of the spiral or the torus with respect to the plane of the sky. CO maps from Cernicharo et al. (2015) suggest that the inclination of the spiral is close to face-on. In any case, the inclination with respect to the plane of the sky together with the rotation has a direct effect on the P.A. of the structures observed in the maps. In particular, except for the edge-on case, a rotation in the spiral/torus would result in a P.A. rotation of the plane of the spiral/torus in the observed velocity maps.

We simulated the density maps at each velocity for a Fermat spiral or for a torus with a radial density profile and inner and outer radius such as those obtained in the previous section. These density maps were convolved with the beam of the NaCl J = 21–20 line and compared with these emission maps in order to obtain the best possible fit to the observations.

Since we expect our estimate of the expansion velocity of the spiral/torus and the P.A. of the dark lane observed in IR emission is well constrained, we could use our kinematic model to constrain the inclination of the orbital plane with respect to the plane of the sky. We compared the kinematic model with the observations varying the inclination angle between 90° and 0°. We found the best fit for i ∼ 15 ± 10°.

Note that since we present density maps, we do not take into account any excitation effects or possible self-absorptions. The aim of the model is to understand the kinematics of the spiral and of the torus, but not to completely reproduce the observations.

The parameters for which we found the best fit are presented in Table 4. The comparison between the models (contours) and the NaCl J = 21–20 emission map (colors) is presented in Figure 25. The rotation of the spiral/torus is in fact the reason why the NaCl maps present an elongation with a P.A. of ∼766 while the real P.A. of this feature is coincident with the dust lane observed by Tuthill et al. (2000), i.e., ∼120°.

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Table 4.  IRC +10216's Spiral/Torus Kinematic Model Parameters

Parameter	Value
Rin	02
Routa	056
i	15°
P.A.	120°
Vexp	11 km s−1
Vrot	8 km s−1

Note.

^aOuter radius for the torus case.

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As we have mentioned, this model is a just first approximation. In order to accurately derive the properties of the innermost structures observed a 2D radiative transfer code is essential.

As we have shown, the inner structures observed in the NaCl and KCl maps might correspond to the innermost regions of the spiral observed in CO by Cernicharo et al. (2015).

Jeffers et al. (2014) suggested that the origin of the dust lane observed is the interaction with a binary. These authors also suggested that the orbital plane of the binary is nearly edge-on. However, Cernicharo et al. (2015) and J. Cernicharo et al. (2016, in preparation) presented models that showed that the spiral structure observed in CO can only be a consequence of an interaction with a binary with the orbital plane close to face-on and having episodic mass-loss ejections. Our kinematic model also suggests that the orbital plane of the spiral is close to face-on. In particular, the structure observed might just be the inner regions of the spiral structure observed in CO by Cernicharo et al. (2015).

In case the structure responsible for the features observed is a spiral, its origin would be the partner star itself. The NaCl mass derived assuming this scenario is 1.0 × 10²² gr (=1.7 × 10⁻⁶ M_Earth), which is ∼0.2 times the mass of NaCl found in the Earth's oceans.

The absence of the features in the Al-bearing interferometric maps might be related to the different dipole moment of the salts and the Al-bearing species observed. This would result in the NaCl and KCl brightness distributions being much more sensitive to density than those of AlCl and AlF. Our simulations have shown that the presence of diffuse emission would prevent the detection of the two maxima from being observed in the Al-bearing molecules.

IRC +10216 has been extensively imaged at different wavelengths and with very different spatial resolutions. All of these observations can be combined to build a complete view of the circumstellar environment of IRC+10216 IRC +10216.

We can divide the structures observed in IRC +10216 mainly into four different groups: the spiral/concentric shells, an outflow, a dark lane and a large-scale bow shock recently observed by Sahai & Chronopoulos (2010) in UV emission. This bow shock was found at 21' and was suggested to be the result of the interaction of the IRC +10216 molecular gas with the ISM. This has been later confirmed by Matthews et al. (2015), who have detected a H i shell coincident with the UV emission observed by Sahai & Chronopoulos (2010). This H i emission presents both a density enhancement at the edge of the H i shell and a slight velocity decrease with respect to the inner molecular gas. These two effects are explained by the interaction of the H i shell with the ISM.

The concentric shells were first observed in dust scattered light (Mauron & Huggins 2000). They found irregularly spaced shells reaching a radius of ∼50''. These shells also have been observed in CO emission extending up to ∼180'' from the star (see, e.g., Fong et al. 2003; Cernicharo et al. 2015). Both Mauron & Huggins (2000) and Cernicharo et al. (2015) argued that the formation of these shells was compatible with a spiral structure which suggested the presence of a binary system. Our analysis of the kinematics of the inner structure suggest that the orbital plane is tilted with respect to the plane of the sky by 15 ± 10°.

In the sub-arcsecond scale, an elongation with a P.A. of ∼20° has been observed at 2 μm (Weigelt et al. 1998) with an extent of ∼300 mas, also in the V-band by Mauron & Huggins (2000), and in molecular emission by, e.g., Fonfría et al. (2014) and Velilla Prieto et al. (2015). This elongation has been suggested to be related to a bipolar outflow (Fonfría et al. 2014; Tuthill et al. 2000).

Also, the 2 μm observations obtained by Weigelt et al. (1998) revealed a dark lane almost orthogonal to the bipolarity observed. This dark lane was also inferred by Tuthill et al. (2000) and later on confirmed by Jeffers et al. (2014), who obtained polarized light images of IRC +10216. In addition, we have found that this dust lane is compatible with the presence of a rotating spiral or torus.

All these observations suggest that IRC +10216 has been ejecting mass episodically, and the resulting ejecta have been clearly influenced by the presence of a partner star orbiting in a plane close to the plane of the sky. In the innermost regions, observations suggest the presence of a NaCl-rich structure, rotating in the same plane as the orbital plane of the binary system. Orthogonal to this plane, there is an outflow observed in molecular emission and visible light. This structure observed in NaCl might be the inner regions of the spiral observed at larger scales, which is visible in NaCl and KCl emission thanks to the high dipole moment compared with AlF and AlCl.

In the present work, the Jacobi coordinate system was used. The center of the coordinates is placed in the NaCl center of mass (c.m.), and the vector R connects the NaCl c.m. with the He atom. The rotation of the NaCl molecule is defined by the θ angle. The calculations were performed for eight NaCl bond lengths r = [4.0, 4.2, 4.35, 4.46125, 4.65, 4.85, 5.0, 5.1] a₀, where a₀ is the Bohr radius, which allows us to take into account vibrational motion of NaCl molecule up to v = 4.

The intermolecular coordinates θ and R were varied from 0° to 180° by step of 10° and from 2.75 to 40 a₀ accordingly. In order to better represent the repulsive part of the PES, we have interpolated the ab initio calculations on a fine grid of θ angles for each r distance in order to use more angles in the fitting procedure.

All electronic-structure calculations were performed using the MOLPRO program (Werner et al. 2010). The ab initio calculations were carried out using the coupled cluster approach with perturbative treatment of triple excitations (CCSD(T)) (Hampel et al. 1992) with a correlation-consistent weighted core-valence quadruple zeta (aug-cc-pwCVQZ) basis set (Prascher et al. 2011) which accounts for the core–core and core–electron correlation effects. Bond functions were placed midway between the He atom and the NaCl c.m. to permit a better description of correlation effects. In the calculations of the interaction energies, the basis set superposition error was corrected using the counterpoise scheme (Boys & Bernardi 1970).

The PES V(R, θ, r) was fitted to the analytical form:

$$\begin{eqnarray}&&V(R,\theta ,r)=\displaystyle \sum _{n=1}^{N}\displaystyle \sum _{l=0}^{M}{B}_{l,n}(R){(r-{r}_{e})}^{n-1}{P}_{l0}(\mathrm{cos}(\theta )),\end{eqnarray} \tag{ 3 }$$

where r_e was taken to be 4.46125 a₀. B_l,n(R) are the expansion coefficients and their radial dependence is represented as cubic splines. The basis functions P_l0(cos(θ)) are the Legendre polynomials. In our fit, N = 8 and M = 20.

A.2.1. Rotational Excitation of NaCl by He

The three-dimensional (3D) PES was then used for quantum scattering calculations. In the calculations, we neglect the hyperfine splitting of the NaCl rotational levels (j) due to Na and Cl non zero nuclear spins. Hyperfine resolved rate coefficients can be obtained from the present data using recouping techniques as described in Faure & Lique (2012).

First, we performed pure rotational excitation calculations using the 3D PES with the NaCl bond length fixed at ground state vibrationally averaged value (r₀ = 4.4696 a₀, Caris et al. 2002). Because the exact close-coupling (CC) approach of Arthurs & Dalgarno (1960) is very computationally intensive for molecules with small rotational constants, we used the coupled-states approximation (CS) (McGuire & Kouri 1974) for the determination of cross sections between rotational levels $[\sigma (j\to {j}^{\prime })].$

The validity of the CS approach compared to a full CC approach has been tested for selected energies. It is found that the CS approach can lead to inaccuracies of 20–30% for low-energy cross sections (<50 cm⁻¹), but agreement improves between CC and CS cross sections when the energy is greater than 50 cm⁻¹, and we expect that the CS rate coefficients will be accurate as soon as we considered temperatures above 20–30 K.

The standard time-independent coupled scattering equations were solved using the MOLSCAT code (Hutson & Green 1994). The calculations were carried out using the propagator of Manolopoulos (1986) with integration range from 2.75 to 40 a₀. The reduced mass of the complex was set to μ = 3.764 a.m.u. In order to converge the inelastic cross sections between the first 81 rotational levels of NaCl, the rotational basis set was extended, at high collisional energy, up to j = 100. The rotational spectroscopic constants were taken from Caris et al. (2002).

Using the above methodology, we obtained the energy variation of the excitation cross sections between the first 81 rotational states of NaCl. Rotationally resolved coefficients were obtained by averaging the appropriate cross sections over a Boltzmann distribution of velocities at a given kinetic temperature T:

$$\begin{eqnarray}{k}_{j\to {j}^{\prime }} & = & {\left(\displaystyle \frac{8{\beta }^{3}}{\pi \mu }\right)}^{1/2}{\displaystyle \int }_{0}^{\infty }\sigma (j\to {j}^{\prime })({E}_{k})\\ & & \times {E}_{k}\mathrm{exp}(-\beta {E}_{k}){{dE}}_{k}\end{eqnarray} \tag{ 4 }$$

where $\beta ={({k}_{{\rm{B}}}T)}^{-1}$ and k_B is the Boltzmann constant. The total energy E is related to the kinetic energy according to $E={E}_{k}+{\epsilon }_{j,}$ where _j is the energy of the initial rotational level. The calculations were carried out up to total energy (E) of 10000 cm⁻¹ which allowed us to get, after averaging, the rate coefficients for temperatures ranging from 5 to 1500 K.

A.2.2. Ro-vibrational Excitation of NaCl by He

Then, we have performed ro-vibrational excitation calculations using the 3D PES. The Vibrational Close-Coupling rotational Infinite Order Sudden (VCC-IOS) method (Parker & Pack 1978) was employed to obtain the inelastic cross sections for the ro-vibrational excitation of NaCl by He.

In the VCC-IOS approximation the matrix elements of the potential between vibrational states of the NaCl molecule are required for each R and θ are expressed as:

$$\begin{eqnarray}&&{V}_{v,{v}^{\prime }}(R,\theta )=\langle v(r)| V(r,R,\theta )| {v}^{\prime }(r)\rangle \end{eqnarray} \tag{ 5 }$$

The NaCl vibrational wave functions $| v(r)\rangle$ were obtained by the DVR method of Colbert & Miller (1992) from a NaCl potential calculated at the same level of accuracy as the NaCl–He PES (without the inclusion of midbond functions). The vibrational wave functions were taken with j = 0.

Within the VCC-IOS approach, the rotational levels are treated as being degenerate. Hence, the problem reduces to the computation of vibrationally (in)elastic S-matrix elements calculated with a close-coupling approach at fixed values of the θ Jacobi angles for a given L-value (L is a relative angular momentum quantum number). This fixed-angle S-matrix elements must then be multiplied by the appropriate spherical harmonics and integrated over θ to give the fundamental IOS cross sections ${\sigma }^{\mathrm{IOS}}(v,0\to {v}^{\prime },L)$(E) out of the v, j = 0 level.

The de-excitation ro-vibrational cross sections are expressed in a reduced form in terms of the ${\sigma }^{\mathrm{IOS}}(v,0\to {v}^{\prime },L)$ cross sections of Parker & Pack (1978):

$$\begin{eqnarray}{\sigma }^{\mathrm{IOS}}(v,j\to {v}^{\prime },{j}^{\prime }) & = & \displaystyle \sum _{L}(2{j}^{\prime }+1){\left(\begin{array}{ccc}{j}^{\prime } & j & L\\ 0 & 0 & 0\end{array}\right)}^{2}\\ & & \times {\sigma }^{\mathrm{IOS}}(v,0\to {v}^{\prime },L)\end{eqnarray} \tag{ 6 }$$

where the large parentheses denote the "3-j" symbols; v, j and v', j' are, respectively, the initial and final vibrational and rotational states.

The time-independent scattering equations were solved using the MOLSCAT code of Hutson & Green (1994) in order to obtain the fundamental ${\sigma }^{\mathrm{IOS}}(v,0\to {v}^{\prime },L)$ cross sections. Similar parameters to those used in the calculations for the pure rotational excitation were used. In order to converge the cross sections for v = 0–3, the v = 4 vibrational level was also included. The summation in Equation (6) was performed for L from 0–201. The vibrational spectroscopic constants were taken from Brumer & Karplus (1973).

Using the above methodology, we obtained the energy variation of the (de-)excitation cross sections ($\sigma (v,j\to {v}^{\prime },{j}^{\prime })$) between the ro-vibrational states of NaCl with v ≤ 3 and j ≤ 80. Corresponding rate coefficients were obtained by averaging the appropriate cross sections over a Boltzmann distribution as for the pure rotational excitation. Cross section calculations up to a total energy (E) of 10,000 cm⁻¹ allowed us to get after averaging the rate coefficients for temperatures ranging from 100 to 1500 K.

As NaCl is a heavy molecule with a small rotational constant, the IOS approach, although it neglects the energy structure of the rotational levels and is expected to be poor at low energies, seems to be appropriate for the temperature range considered in this work. The fact that the CS and the VCC-IOS rate coefficients agree well for the v = 0 state confirms the hypothesis.