The precise mechanisms that provide the non-radiative energy for heating the chromosphere and the corona of the Sun and those of other stars constitute an active field of research. By studying stellar chromospheres one aims at identifying the relevant physical processes. Defining the permittable extent of the parameter space can also serve as a template for the Sun-as-a-star. Earlier observations with Herschel and APEX have revealed the temperature minimum of alpha Cen, but these were unable to spatially resolve the binary into individual components. With the data reported here, we aim at remedying this shortcoming. Furthermore, these earlier data were limited to the wavelength region between 100 and 870mu. In the present context, we intend to extend the spectral mapping to longer wavelengths, where the contrast between stellar photospheric and chromospheric emission becomes increasingly evident. ALMA is particularly suited to point sources, such as unresolved stars. ALMA provides the means to achieve our objectives with both its high sensitivity of the collecting area for the detection of weak signals and the high spatial resolving power of its adaptable interferometer for imaging close multiple stars. This is the first detection of main-sequence stars at a wavelength of 3mm. Furthermore, the individual components of the binary alpha CenAB are clearly detected and spatially well resolved at all ALMA wavelengths. The high S/N of these data permit accurate determination of their relative flux ratios. The previously obtained flux ratio of 0.44, which was based on measurements in the optical and at 70mu, is consistent with the present ALMA results, albeit with a large error bar. Given the distinct difference in their cyclic activity, the similarity of their submm SEDs appears surprising.
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