Theory of gyroresonance and free-free emissions from non-Maxwellian quasi-steady-state electron distributions

Currently there is a concern about ability of the classical thermal (Maxwellian) distribution to describe quasi-steady-state plasma in solar atmosphere including active regions. In particular, other distributions have been proposed to better fit observations, for example, kappa- and $n$-distributions. If present, these distributions will generate radio emissions with different observable properties compared with the classical gyroresonance (GR) or free-free emission, which implies a way of remote detecting these non-Maxwellian distributions in the radio observations. Here we present analytically derived GR and free-free emissivities and absorption coefficients for the kappa- and $n$-distributions and discuss their properties, which are in fact remarkably different from each other and from the classical Maxwellian plasma. In particular, the radio brightness temperature from a gyrolayer increases with the optical depth $\tau$ for kappa-distribution, but decreases with $\tau$ for $n$-distribution. This property has a remarkable consequence allowing a straightforward observational test: the gyroresonance radio emission from the non-Maxwellian distributions is supposed to be noticeably polarized even in the optically thick case, where the emission would have strictly zero polarization in the case of Maxwellian plasma. This offers a way of remote probing the plasma distribution in astrophysical sources including solar active regions as a vivid example.