The temperature structure of chromospheric flares heated by non-thermal electrons

Heating of the deep chromosphere by a vertically descending beam of non-thermal electrons with power-law energy spectrum, in flares, is analysed. In lower regions of the flare, radiative losses can balance the energy input and the flare structure is described in terms of instantaneous quasi-steady temperature/depth profiles. Motion of the optical flare material is at constant pressure and is constrained to be purely vertical by a vertical magnetic field. The ionisation of hydrogen is determined by the same non-LTE processes as in the quiet chromosphere. Temperature profiles are obtained for a wide range of electron beam intensities and spectral indices and are discussed in terms of optical flare observations. Due to the steepness of the electron spectra, typical densities in the optical flare vary only over a narrow range, despite the diversity of beam intensities, in agreement with observation.Above a certain region, the flare material cannot attain a radiatively steady state against the electron input but evaluation of the level at which this occurs leads to an estimate of the mass of material involved in the high temperature flare plasma in this model. Results, which are again insensitive to the electron beam parameters, are found to be in satisfactory agreement with observations of the mass of flare ejecta and of soft X-ray flare emission measures.