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Appendix A: Comparison with single dish observations

Fig. A.1 Total intensity of the 12CO and 13CO(J = 3 →  2) transitions. The solid black lines are the spectra observed with the APEX telescope in a single pointing towards the star. The solid red line is the emission detected with ALMA in an area equivalent to the APEX beam. The 13CO ALMA spectrum has a velocity resolution of 3 km s-1, the 12CO ALMA spectrum has a velocity resolution of 0.5 km s-1, and the APEX spectra have a velocity resolution of 1.1 km s-1. The dotted line indicates the 13CO model used to fit the ALMA observations (see text) when observed with APEX resolution. The spectra indicate that the 12CO and 13CO emissions are equally resolved out in the ALMA observations.

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To determine if flux losses due to insufficient uv-coverage of the ALMA observations could affect our conclusions, we compared the interferometric observations with new spectra taken with the APEX telescope. The ¹²CO and ¹³CO(  3 →  2) observations were taken on Jan. 2, 2013 in a single pointing toward the star using the wobbler with a 150′′ throw. The total bandwidth was 2.5 GHz, with 32768 channels, providing an initial resolution of  ~0.1 km s^-1, which was later averaged to  ~1.1 km s^-1.

The resulting spectra are shown in Fig. A.1 together with the ALMA spectra taken over an area corresponding to the APEX beam at the frequency of the CO(  3 →  2) transition (~19′′). From this figure it is immediately obvious that a significant amount of flux is lost in the ALMA observations. We only recover approximately 25% of the total flux, indicating that the circumstellar CO has significant smooth emission over scales larger than  ~15′′. Specifically in the ¹³CO spectrum, most of the emission is lost toward the most red- and blue-shifted peaks, where, as noted above, the caps of the shell make up the largest area. A comparison of the observations with the flux of the model used to fit the ¹³CO data, as shown in Fig. A.1 for a resolution of 19′′ and in Fig. 3 for a resolution of 5′′, shows that most of the

small-scale flux is recovered. Considering that the present-day mass-loss extends out to  <10′′, the lack of ¹³CO in the present-day mass-loss component cannot be due to the flux loss in the interferometric observations. Additionally, the single-dish comparison indicates that the ¹²CO and ¹³CO are similarly resolved out, 25% of the total flux is detected for both transitions, with correspondingly little effect on the observed flux ratios. We thus find that our conclusions based on the ¹²CO and ¹³CO intensity ratios are robust.

Appendix B: Radiative transfer modeling

To more accurately estimate the ¹²CO/¹³CO abundance ratio, we performed radiative transfer calculations for the CO emission using the code described in detail in Schöier & Olofsson (2001). Our model consists of two components; a present-day mass loss and a detached shell. The density, velocity and temperature of the present-day mass loss (with Ṁ = 3 × 10^-7   M_⊙ yr^-1 derived from HCN modeling) are taken to be the same as described in Schöier et al. (2005), as are the stellar parameters. For the shell, we assumed a uniform gas density with a shell width of  ~400 AU and a total mass of 2.5 × 10^-3   M_⊙. These parameters also match the models of M+12, although there it was found that the increased mass-loss during the thermal pulse did not decrease as rapidly as assumed here, as evidenced by the spiral of CO gas connecting the shell with the present-day mass loss. However, we do not include a description of the spiral in our models because no ¹³CO was detected between the shell and the more recent mass loss. We furthermore assumed an average temperature of 50 K for the shell. Because no observations of higher rotational transitions of CO exist that can easily separate the emission originating in the shell from that of the present-day mass loss, the shell temperature is poorly constrained. A somewhat smaller ¹³CO abundance and thus higher ¹²CO/¹³CO ratio (by  ~20%) can reproduce the observed ¹³CO emission at higher temperatures (up to  ~70 K). Finally, we only varied the ¹²CO and ¹³CO abundance ratio in the present-day mass loss.

We do note that the derived ¹²CO/¹³CO ratio for the present-day mass-loss is different from the value of 20 derived from modeling the single-dish CO(J = 2−1) observations (Schöier & Olofsson 2000). However, in that case it was assumed that the ratio in the shell and present-day mass loss was the same, as with the single-dish observations it is impossible to separate the two components. The CO(J = 2−1) model also did not include the at that time unknown spiral component. If we determine the average intensity ratio over the entire envelope of R Scl from the ALMA observations, we find an intensity ratio of 10 ± 3, similar to the value of 12 measured for the CO(J = 2−1) line (Schöier & Olofsson 2000). Furthemore, the new single-dish CO(J = 3−2) APEX observations yield an abundance ratio similar to that found in Schöier & Olofsson (2000), because, as was the case for the CO(J = 2−1) observations, the single-dish data cannot distinguish the detached shell and the present-day mass loss.

	Fig. C.1 Intensity ratio, I12CO/I13CO, (color) and 12CO(J = 3 →  2) flux (contours) for the full velocity channel range. The contour and color levels are as in Fig. 2.
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© ESO, 2013