Continuum and line emission of flares on red dwarf stars

Abstract: The emission spectrum has been calculated of a homogeneous pure hydrogen layer, which parameters are typical for a flare on a red dwarf. The ionization and excitation states were determined by the solution of steady-state equations taking into account the continuum and all discrete hydrogen levels. We consider the following elementary processes: electron-impact transitions, spontaneous and induced radiative transitions, and ionization by the bremsstrahlung and recombination radiation of the layer itself. The Biberman--Holstein approximation was used to calculate the scattering of line radiation. Asymptotic formulae for the escape probability are obtained for a symmetric line profile taking into account the Stark and Doppler effects. The approximation for the core of the H$-\alpha$ line by a gaussian curve has been substantiated. The spectral intensity of the continuous spectrum, the intensity of the lines of the Balmer series and the magnitude of the Balmer jump have been calculated. The conditions have been determined for which the Balmer jump and the emission line intensities above the continuum decrease to such low values that the emission spectrum can be assumed to be continuum as well as the conditions at which the emission spectrum becomes close to the blackbody.