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Appendix A: Properties of the two main continuum components

In Table A.1 we list the properties of the two main continuum components, C and VY.

Appendix B: Comparison with other (sub-)mm observations

There have been many previous (sub-)millimeter continuum flux density measurements of VY CMa. In Fig. B.1, we present both the single-dish observations, using the compilations of Knapp et al. (1993) and Ladjal et al. (2010), and the interferometric measurements from this paper and from SMA observations (Shinnaga et al. 2004; Muller et al. 2007; Kamiński et al. 2013). It is immediately apparent that the interferometric observations systematically underestimate the total flux density and can be attributed to flux density that is resolved out by missing short baselines, as well as by having low surface brightness. The MRS at higher frequencies is smaller so more flux density is resolved out, resulting in a larger discrepancy between the single-dish and interferometric measurements. The spectral index determined from the single-dish observations is α = 2.5 ± 0.2 and is consistent with our findings in Sect. 3.2 for the optically thin dust. We note that the single-dish data points in Fig. B.1 will also contain flux density from molecular emission lines. Kamiński et al. (2013) find that this accounts for about 25% of their measured flux density between 279 and 355 GHz. This level will vary at the different frequencies and will mainly result in an added upward scatter but should not affect the overall spectral index. Assuming the true spectral index of the interferometric observations to be the same as that of the single-dish observations and assuming there are no significant changes in dust properties on the different scales, we can conclude that the ALMA observations lose ~65% of the emission at 321 GHz and ~72% of the emission at 658 GHz. Considering the MRS and sensitivity of the ALMA observations, most of the submillimeter dust continuum flux density is thus located in a smooth low surface brightness distribution stretching beyond ~4″, which is consistent with the dust distribution seen over ~8″ with the HST (e.g., Smith et al. 2001).

Fig. B.1 Compilation of the single dish bolometer and interferometric mm/sub-mm continuum observations of VY CMa. The gray filled circles are single-dish flux density measurements, while the blue filled diamonds and the red filled squares are interferometric measurements. The solid line indicates the spectral index fit to the single-dish observations, with α = 2.5 ± 0.2, while the dotted line is a linear fit to the interferometric observations.

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Appendix C: Stellar flux density contribution

The stellar flux density contribution S_⋆, needs to be considered when calculating the dust mass from the VY component at these ALMA frequencies. Previous studies have estimated this contribution by calculating the flux density of an optically thick blackbody of radius R_⋆ and temperature T_eff. Estimating the contribution from this method yields S_⋆ = 26.5 mJy at 321 GHz and S_⋆ = 111 mJy at 658 GHz, where we have assumed a stellar radius of R_⋆ = 1420 R_⊙ (6.84 AU or 5.7 mas) and an effective temperature T_eff = 3490 K (Wittkowski et al. 2012). However, RSGs have weakly ionized extended atmospheres, which will become opaque at (sub-)mm frequencies. To estimate this contribution at these ALMA frequencies, we scaled the Harper et al. (2001) semi-empirical model for the M2 Iab RSG Betelgeuse (without the silicate dust) to the angular diameter of VY CMa. The main source of opacity in this model is the H⁻ and H free-free opacity from electrons produced by photoionized metals. We then assumed the same ionization fraction and scaled the particle densities so that good agreement was obtained with the Very Large Array centimetre observations of VY CMa from Lipscy et al. (2005). The stellar contribution from this weakly ionized atmosphere is 36 mJy at 321 GHz and 124 mJy at 658 GHz.

© ESO, 2014