  The precise mechanisms that provide the non-radiative energy for heating the
chromosphere and the corona of the Sun and other stars are at the focus of
intense contemporary research. Observations at submm/mm wavelengths are
particularly useful to obtain information about the run of the temperature in
the upper atmosphere of Sun-like stars. We used ALMA to study the chromospheric
emission of the aCen binary system in all six available frequency bands during
Cycle2 in 2014/15. Since ALMA is an interferometer, the multi-telescope array
is particularly suited for the observation of point sources. With its large
collecting area, the sensitivity is high enough to allow the observation of
nearby main-sequence stars at submm/mm wavelengths for the first time. The
comparison of the observed spectral energy distributions with theoretical model
computations provides the chromospheric structure in terms of temperature and
density above the stellar photosphere and the quantitative understanding of the
primary emission processes. Both stars were detected and resolved at all ALMA
frequencies. For both aCenA and B, the existence and location of the
temperature minima, firstly detected from space with Herschel, are well
reproduced by the theoretical models of this paper. For aCenB, the temperature
minimum is deeper than for A and occurs at a lower height in the atmosphere,
but for both stars, Tmin/Teff is consistently lower than what is derived from
optical and UV data. The submm/mm emission of the aCen stars is indeed very
well reproduced by modified chromospheric models of the Quiet Sun. This most
likely means that the non-radiative heating mechanisms of the upper atmosphere
that are at work in the Sun are operating also in other solar-type stars.
