On the Origin of Optical Radiation during the Impulsive Phase of Flares on dMe Stars. I. Discussion of Gas Dynamic Models

In connection with a published critique, the author justifies the use of a motionless homogeneous plane layer of pure hydrogen plasma that is near local thermodynamic equilibrium (LTE) for analyzing the characteristics of the radiation from a chromospheric condensation of thickness ∆ z =10 km in a gas dynamic model of stellar flares. It is shown that the shock-wave model of flares proposed by Belova and Bychkov, as opposed to the model of Kostyuk and Pikel’ner, has irremovable internal defects owing to exclusion of the interaction between a thermal wave (temperature jump) and a non-stationary radiative shock. In particular, this model (a) does not make it possible to increase the geometric thickness of a chromospheric condensation owing to divergence of the fronts of the thermal and shock waves during impulsive heating, (b) cannot provide heating of the chromospheres of red dwarfs over significant distances, and (c) predicts Hα line profiles in conflict with observational data. It is argued that: (a) the shock-wave model of Belova and Bychkov represents a development of the kinematic model of solar flares (Nakagawa et al.) and its application to dMe stars, specifically, a study of the radiative response of the chromosphere of a red dwarf to impulsive heating in the simplest gas dynamic statement of the problem (a thermal wave is excluded; a stationary approach is used); (b) in terms of the Kostyuk and Pikel’ner model, the regions behind the stationary shock fronts do not correspond to a chromospheric condensation with time-varying thickness but to zones in which the plasma relaxes to a state of thermal equilibrium. It is emphasized that separation of the Kostyuk and Pikel’ner model into “thermal” and “shock-wave” components is fundamentally impossible.