Resolving the extended stellar atmospheres of asymptotic giant branch stars at (sub)millimetre wavelengths

Context. The initial conditions for mass loss during the asymptotic giant branch (AGB) phase are set in their extended atmospheres, where, among others, convection and pulsation driven shocks determine the physical conditions. Aims. High resolution observations of AGB stars at (sub)millimetre wavelengths can now directly determine the morphology, activity, density, and temperature close to the stellar photosphere. Methods. We used Atacama Large Millimeter/submillimeter Array (ALMA) high angular resolution observations to resolve the extended atmospheres of four of the nearest AGB stars: W Hya, Mira A, R Dor, and R Leo. We interpreted the observations using a parameterised atmosphere model. Results. We resolve all four AGB stars and determine the brightness temperature structure between 1 and 2 stellar radii. For W Hya and R Dor we confirm the existence of hotspots with brightness temperatures >3000 to 10 000 K. All four stars show deviations from spherical symmetry. We find variations on a timescale of days to weeks, and for R Leo we directly measure an outward motion of the millimetre wavelength surface with a velocity of at least 10.6 +/- 1.4 km s(-1). For all objects but W Hya we find that the temperature-radius and size-frequency relations require the existence of a (likely inhomogeneous) layer of enhanced opacity. Conclusions. The ALMA observations provide a unique probe of the structure of the extended AGB atmosphere. We find highly variable structures of hotspots and likely convective cells. In the future, these observations can be directly compared to multi-dimensional chromosphere and atmosphere models that determine the temperature, density, velocity, and ionisation structure between the stellar photosphere and the dust formation region. However, our results show that for the best interpretation, both very accurate flux calibration and near-simultaneous observations are essential