COOLING OF SOLAR-FLARE PLASMAS .1. THEORETICAL CONSIDERATIONS

Theoretical models of the cooling of flare plasma are reexamined. By assuming that the cooling occurs in two separate phases where conduction and radiation, respectively, dominate, a simple analytic formula for the cooling time of a flare plasma is derived. Unlike earlier order-of-magnitude scalings, this result accounts for the effect of the evolution of the loop plasma parameters on the cooling time. When the conductive cooling leads to an ''evaporation'' of chromospheric material, the cooling time scales as L(5/6)/p(1/6), where the coronal radiative loss function is assumed to vary as T--1/2 and quantities are evaluated at the start of the decay phase (defined as the time of maximum temperature). When the conductive cooling is static, the cooling time scales as L(3/4)/n(1/4). I, deriving these results, use was made of an important scaling law (T proportional to n(2)) during the radiative cooling phase that was first noted in one-dimensional hydrodynamic numerical simulations (Serio et al. 1991; Jakimiec et al. 1992). Our own simulations show that this result is restricted to approximately the radiative loss function of Rosner, Tucker, and Vaiana (1978). For different radiative loss functions, other scalings result, with T and n scaling almost linearly when the radiative loss falls off as T-2. It is shown that these scaling laws are part of a class of analytic solutions developed by Antiochos (1980b).