A new way to measure the departure from thermodynamic equilibrium in stellar atmospheres

A new way to measure the departure from thermodynamic equilibrium is proposed based on the departure factor which evaluates the deviation from a Boltzmann level distribution, used by Short and Hauschildt (2005) and others. The way is based on an explicit relationship describing the departure factor as a function of line to continuum source, dynamic temperature and line photon frequency, under three assumptions that the scattering can be neglected, the background continuum can be treated as a Planck function, and finally the complete redistribution can be true. It has the advantage that the departure can be very conveniently evaluated from the spectral analysis with only the radiative transfer involved. Some physical insights are recovered for some extreme cases. Some example calculations of the departure are presented for the quiet Sun, faint solar flare and strong solar flare for the generally used solar chromospheric lines: Hα, Hβ, CaII H, K and triplet. It is revealed that in the case of solar flares, the departure is less than thermodynamic equilibrium along the larger depth range than in the quiet sun due to chromospheric condensation. It becomes hard to distinguish the departures for the different lines of the same atom or ion. It is expected that this investigation can be constructive for studying stellar atmospheres in cases where the three assumptions are close to reality. (research papers)