Kinetics of hydrogen in chromospheres of red dwarfs

A method is suggested and solution is conducted of the stationary equations for an 8-level hydrogen atom with an approximate account for lines radiative transfer in an optically thick layer. Ionization and excitation of hydrogen atoms are caused by electron collisions; the influence of photospheric radiation was neglected. The medium stays motionless, and the photon escape from the layer is connected with gradual diffusion in frequency during multiple scatterings. Mean over the layer probabilities of photon escape are introduced into the stationary equations. They are determined for a finite-thickness layer with an uniform distribution of primary photon sources and with an absorption coefficient accounting for Stark and Doppler effects. As an example of application of the calculations, an interpretation is presented of the data on the Balmer decrement in the maximum of the stellar flare of YZ CMi on March 4, 1985. It is shown that the transition from a steep Balmer decrement to a mildly sloping one is due to a decrease of the photon escape probability in the higher members of Balmer series, i.e. the lines later than Hγ