SOLAR-FLARE MODEL ATMOSPHERES

Solar flare model atmospheres computed under the assumption of energetic equilibrium in the chromosphere are presented. The models use a static, one-dimensional plane-parallel geometry and are designed within a physically self-consistent coronal loop. Assumed flare heating mechanisms include collisions from a flux of nonthermal electrons and X-ray heating of the chromosphere by the corona. The heating by energetic electrons accounts explicitly for variations of the ionized fraction with depth in the atmosphere. X-ray heating of the chromosphere by the corona incorporates a flare loop geometry by approximating distant portions of the loop with a series of point sources, while treating the loop leg closest to the chromospheric footpoint in the plane-parallel approximation. Coronal flare heating leads to increased heat conduction, chromospheric evaporation and subsequent changes in coronal pressure; these effects are included self-consistently in the models. Cooling in the chromosphere is computed in detail for the important optically thick H I, Ca II and Mg II transitions using the non-LTE prescription in the program MULTI. Hydrogen ionization rates from X-ray photoionization and collisional ionization by nonthermal electrons are included explicitly in the rate equations. The models are computed in the ''impulsive'' and ''equilibrium'' limits, and in a set of intermediate ''evolving'' states. The impulsive atmospheres have the density distribution frozen in the pre-flare configuration, while the equilibrium models assume the entire atmosphere is in hydrostatic and energetic equilibrium. The evolving atmospheres represent intermediate stages where hydrostatic equilibrium has been established in the chromosphere and corona, but the corona is not yet in energetic equilibrium with the flare heating source. Thus, for example, chromospheric evaporation is still in the process of occurring. We have computed the chromospheric radiation that results from a range of coronal heating rates, with particular emphasis on the widely observed diagnostic Halpha. Our principal results are the following: 1. Only in models with low coronal pressure (i.e., in models where very little evaporation has occurred) does the nonthermal electron flux provide significant heating in the chromosphere. 2. After evaporation has occurred and the coronal pressure is high, the dominant source of chromospheric heating is the X-ray irradiation from the hot corona. However, this reprocessed heat source never exceeds approximately 6% of the original flare energy flux deposited in the corona by the beam. 3. In order to obtain the broad, intense Halpha profiles that are actually observed in flares, there must be either (a) a condition of low coronal pressure in the overlying loop; or (b) heating at the top of the chromosphere from a source other than the beam and its products (X-rays, heat conduction). The reason is that only with a low-pressure corona is there enough chromospheric heating from the beam to raise enough column mass to temperatures of approximately 10(4) K necessary to produce copious Halpha. 4. The depth of the Halpha central reversal was correlated with the incident coronal beam flux F-20 in our models in the sense that models with large beam flux have profiles with smaller central reversal. 5. Losses from ions other than those we treat in detail play a very important, and in many cases dominant, role in the cooling of the chromosphere. Further models should include the radiation backwarming effects of these losses. 6. The power-law dependence of the ratio F(Halpha)/F-20 on the beam flux F-20, which has been empirically determined, was reproduced in some of our models. However, we find that a more physically meaningful parameter during the evolution of a single loop is the pressure, P, since the chromospheric heating after evaporation has occurred depends primarily on the coronal pressure (or alternatively the conductive flux or coronal column depth) and not on the beam flux. Our conclusion is that the Halpha fluxes and profiles actually observed in flares can only be produced under conditions of a low-pressure corona with strong beam heating. Therefore we suggest that Halpha in flares is produced primarily at the footpoints of newly heated loops where significant evaporation has not yet occurred. As a single loop evolves in time, no matter how strong the heating rate may become, the Halpha flux will diminish as the corona becomes denser and hence more effective at stopping the beam. This prediction leads to several observable consequences regarding the spatial and temporal signatures of the X-ray and Halpha radiation during flares.