A useful approximation to the cooling coefficient of trace elements

Radiative cooling is an important ingredient in hydrodynamical models invol ving evolution of high-temperature plasmas. Unfortunately, calculating an a ccurate cooling coefficient generally requires the solution of over 100 dif ferential equations to follow the ionization. We discuss here a simple two- parameter approximation for the cooling coefficient due to elements heavier than H and He, for the temperature range T = 10(4)-10(8) K. Tests of the m ethod show that it successfully tracks the ionization level in severe dynam ical environments and accurately approximates the nonequilibrium cooling co efficient of the trace elements, usually to within 10% in all cases for whi ch cooling is actually important. The error is large only when the temperat ure is dropping so rapidly due to expansion that radiative cooling is negli gible, but even in this situation, the ionization level is followed suffici ently accurately. The current approximation is fully implemented in publicl y available FORTRAN code. A second paper will discuss general approaches to approximation methods of this type, other realizations that could be even more accurate, and the potential for extension to calculations of nonequili brium spectra.