HYDRO2GEN: Non-thermal hydrogen Balmer and Paschen emission in solar flares generated by electron beams

Aims. Sharp rises of hard X-ray (HXR) emission accompanied by H↵ line profiles with strong red-shifts up to 4 Å from the central wavelength, often observed at the onset of flares with the Specola Solare Ticinese Telescope (STT) and the Swedish Solar Telescope (SST), are not fully explained by existing radiative models. Moreover, observations of white light (WL) and Balmer continuum emission with the Interface Region Imaging Spectrograph (IRIS) reveal strong co-temporal enhancements and are often nearly cospatial with HXR emission. These effects indicate a fast effective source of excitation and ionisation of hydrogen atoms in flaring atmospheres associated with HXR emission. In this paper we investigate electron beams as the agents accounting for the observed hydrogen line and continuum emission. Methods. Flaring atmospheres are considered to be produced by a 1D hydrodynamic response to the injection of an electron beam defining their kinetic temperatures, densities, and macro velocities. We simulated a radiative response in these atmospheres using a fully non-local thermodynamic equilibrium (NLTE) approach for a 5-level plus continuum hydrogen atom model, considering its excitation and ionisation by spontaneous, external, and internal diffusive radiation and by inelastic collisions with thermal and beam electrons. Simultaneous steady-state and integral radiative transfer equations in all optically thick transitions (Lyman and Balmer series) were solved iteratively for all the transitions to define their source functions with the relative accuracy of 105. The solutions of the radiative transfer equations were found using the L2 approximation. Resulting intensities of hydrogen line and continuum emission were also calculated for Balmer and Paschen series. Results. We find that inelastic collisions with beam electrons strongly increase excitation and ionisation of hydrogen atoms from the chromosphere to photosphere. This leads to an increase in Lyman continuum radiation, which has high optical thickness, and after the beam is off it governs hydrogen ionisation and leads to the long lasting order of magnitude enhancement of emission in Balmer and Paschen continua. The ratio of Balmer-to-other-continuum head intensities are found to be correlated with the initial flux of the beam. The height distribution of contribution functions for Paschen continuum emission indicate a close correlation with the observations of heights of WL and HXR emission reported for limb flares. This process also leads to a strong increase of wing emission (Stark’s wings) in Balmer and Paschen lines, which is superimposed on large red-shifted enhancements of H↵-H line emission resulting from a downward motion by hydrodynamic shocks. The simulated line profiles are shown to fit the observations for various flaring events closely