Resolving the stellar activity of the Mira AB binary with ALMA

Aims. We present the size, shape, and flux densities at millimeter continuum wavelengths, based on ALMA science verification observations in Band 3 (similar to 94.6 GHz) and Band 6 (similar to 228.7 GHz), from the binary Mira A (o Ceti) and Mira B. Methods. The Mira AB system was observed with ALMA at a spatial resolution down to similar to 25 mas. The extended atmosphere of Mira A and the wind around Mira B sources were resolved, and we derived the sizes of Mira A and of the ionized region around Mira B. The spectral indices within Band 3 (between 89-100 GHz) and between Bands 3 and 6 were also derived. Results. The spectral index of Mira A is found to change from 1.71 +/- 0.05 within Band 3 to 1.54 +/- 0.04 between Bands 3 and 6. The spectral index of Mira B is 1.3 +/- 0.2 in Band 3, in good agreement with measurements at longer wavelengths; however, it rises to 1.72 +/- 0.11 between the bands. For the first time, the extended atmosphere of a star is resolved at these frequencies, and for Mira A the diameter is similar to 3.8 x 3.2 AU in Band 3 (with brightness temperature T-b similar to 5300 K) and similar to 4.0 x 3.6 AU in Band 6 (T-b similar to 2500 K). Additionally, a bright hotspot similar to 0.4 AU, with T-b similar to 10 000 K, is found on the stellar disk of Mira A. The size of the ionized region around the accretion disk of Mira B is found to be similar to 2.4 AU. Conclusions. The emission around Mira B is consistent with emission from a partially ionized wind of gravitationally bound material from Mira A close to the accretion disk of Mira B. The Mira A atmosphere does not fully match predictions with brightness temperatures in Band 3 significantly higher than expected, potentially owing to shock heating. The hotspot is very likely due to magnetic activity and could be related to the previously observed X-ray flare of Mira A.