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The radio continuum spectrum of Mira A and Mira B up to submillimeter wavelengths

We present new measurements of the flux densities at submillimeter wavelengths based on ALMA band 7 (338 GHz) and band 9 (679 GHz) observations to better constrain the origin of the continuum emission of the Mira AB binary system and to check its orbit. We have measured the Mira A and Mira B continuum in ALMA band 7, with a resolution of ~0"31, and for the first time in ALMA band 9, with a resolution of ~0"18. We resolved the binary system at both bands, and derived the continuum spectral index of the stars and their relative position. We also analyzed ALMA SciVer data obtained in bands 6 and 3. Measurements at centimeter wavelengths obtained by other authors have been included in our study of the spectral energy distribution of the Mira components. The Mira A continuum emission has a spectral index of 1.98+-0.04 extending from submillimeter down to centimeter wavelengths. The spectral index of the Mira B continuum emission is 1.93+-0.06 at wavelengths ranging from submillimeter to ~3.1 mm, and a shallower spectral index of 1.22+-0.09 at longer wavelengths. The Mira A continuum emission up to submillimeter wavelengths is consistent with that of a radio photosphere surrounding the evolved star for which models predict a spectral index close to 2. The Mira B continuum emission cannot be described with a single ionized component. An extremely compact and dense region around the star can produce the nearly thermal continuum measured in the 0.4-3.1 mm wavelength range, and an inhomogeneous, less dense, and slightly larger ionized envelope could be responsible for the emission at longer wavelengths. Our results illustrate the potential of ALMA for high precision astrometry of binary systems. We have found a significant discrepancy of ~14 milliarcsec between the ALMA measurements and the predicted orbit positions.