A numerical model of a solar flare based on electron beam heating of the chromosphere

There are two parts to this paper. In the first we calculate the hydrodynamic response of the solar atmosphere to the injection of an intense beam of electrons in a numerical simulation of a solar flare. In the second we predict the spectroscopic consequences of the hydrodynamic behaviour calculated in the first part. The hydrodynamics is predicted by solving the equations of conservation of mass, momentum, and energy. The latter is expressed as two temperature equations; one for the electrons and the other for the neutral atoms and positive ions of hydrogen. The equations are solved in one dimension and the geometric form is of a semi-circular loop having its ends in the photosphere. The results show how the loop is filled at supersonic speed with plasma at temperatures characteristic of flares. At the same time a compression wave is predicted to propagate down towards the photosphere. After the heating pulse stops, the plasma that has risen into the loop, starts to decay and return to the condition it was in before the pulse started. In predicting the spectrum that would be emitted by such a plasma calcium was chosen for illustration. The first and main part of this calculation was setting up and solving the time-dependent equations of ionization/recombination. In order to provide a standard for comparison the same ionization and recombination rate coefficients are used to predict the steady-state distribution of populations of ionization stages. This is then compared with the distribution found from the time-dependent solution and shows that there is a negligibly small time lag predicted by the time-dependent result. However the more significant comparisons to make are between the temperatures of the peak abundances of the various ions under the assumptions of steady-state and time-dependent ionization. For the particular circumstances chosen here the temperature differences are predicted to be in the neighbourhood of 10% or less and in view of the overall accuracy of the atomic data are not significant. It would appear therefore that the much simpler assumption of steady-state ionization balance leads to results of acceptable accuracy for the particular case considered.