COOLING OF SOLAR-FLARE PLASMAS .1. THEORETICAL CONSIDERATIONS

Theoretical models of the cooling of flare plasma are reexamined. By a ssuming that the cooling occurs in two separate phases where conductio n and radiation, respectively, dominate, a simple analytic formula for the cooling time of a flare plasma is derived. Unlike earlier order-o f-magnitude scalings, this result accounts for the effect of the evolu tion of the loop plasma parameters on the cooling time. When the condu ctive cooling leads to an ''evaporation'' of chromospheric material, t he cooling time scales as L(5/6)/p(1/6), where the coronal radiative l oss 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 tempe rature). When the conductive cooling is static, the cooling time scale s as L(3/4)/n(1/4). I, deriving these results, use was made of an impo rtant scaling law (T proportional to n(2)) during the radiative coolin g phase that was first noted in one-dimensional hydrodynamic numerical simulations (Serio et al. 1991; Jakimiec et al. 1992). Our own simula tions show that this result is restricted to approximately the radiati ve loss function of Rosner, Tucker, and Vaiana (1978). For different r adiative loss functions, other scalings result, with T and n scaling a lmost linearly when the radiative loss falls off as T-2. It is shown t hat these scaling laws are part of a class of analytic solutions devel oped by Antiochos (1980b).