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In collisional ionization equilibrium (CIE), the X-ray spectrum from a plasmadepends on the distribution of emission measure over temperature (DEM). Due tothe well-known ill conditioning problem, no precisely resolved DEM can beinverted directly from the spectrum, so often only a gross parametrization ofthe DEM is used to approximate the data, in hopes that the parametrization canprovide useful model-independent constraints on the heating process. However,ill conditioning also introduces ambiguity into the various differentparametrizations that could approximate the data, which may spoil the perceivedadvantages of model independence. Thus, this paper instead suggests a singleparametrization for both the heating mechanism and the X-ray sources, based ona model of impulsive heating followed by complete cooling. This approach issimilar to a ``cooling flow'' approach, but allows injection at multipleinitial temperatures, and applies even when the steady state is distribution ofdifferent shock strengths, as for a standing shock with a range of obliquities,or for embedded stochastic shocks that are only steady in a statistical sense.This produces an alternative parametrization for X-ray spectra that isespecially streamlined for higher density plasmas with efficient radiativecooling, and provides internal consistency checks on the assumption ofimpulsive heating followed by complete cooling. The result is no longer modelindependent, but the results are more directly interpretable in terms of usefulphysical constraints on the impulsive heating distribution.

Parametrizing Impulsive X-ray Heating with a Cumulative Initial-Temperature Distribution