Aims: We investigate the X-ray, UV, and also the radio continuum arising from plasmas with a non-Maxwellian distribution of electron energies. The two investigated types of distributions are the κ- and n-distributions.
Methods: We derived analytical expressions for the non-Maxwellian bremsstrahlung and free-bound continuum spectra. The spectra were calculated using available cross-sections. Then we compared the bremsstrahlung spectra arising from the different bremsstrahlung cross-sections that are routinely used in solar physics.
Results: The behavior of the bremsstrahlung spectra for the non-Maxwellian distributions is highly dependent on the assumed type of the distribution. At flare temperatures and hard X-ray energies, the bremsstrahlung is greatly increased for κ-distributions and exhibits a strong high-energy tail. With decreasing κ, the maximum of the bremsstrahlung spectrum decreases and moves to higher wavelengths. In contrast, the maximum of the spectra for n-distributions increases with increasing n, and the spectrum then falls off very steeply with decreasing wavelength. In the millimeter radio range, the non-Maxwellian bremsstrahlung spectra are almost parallel to the thermal bremsstrahlung. Therefore, the non-Maxwellian distributions cannot be detected by off-limb observations made by the ALMA instrument. The free-bound continua are also highly dependent on the assumed type of the distribution. For n-distributions, the ionization edges disappear and a smooth continuum spectrum is formed for n ≧ 5. Opposite behavior occurs for κ-distributions where the ionization edges are in general significantly enhanced, with details depending on κ and T through the ionization equilibrium. We investigated how the non-Maxwellian κ-distributions can be determined from the observations of the continuum and conclude that one can sample the low-energy part of the distribution from the continuum.