THERMAL X-RAY SPECTRAL TOOLS. I. PARAMETERIZING IMPULSIVE X-RAY HEATING WITH A CUMULATIVE INITIAL TEMPERATURE (CIT) DISTRIBUTION

Abstract

In collisional ionization equilibrium, the X-ray spectrum from a plasma depends on the differential emission measure (DEM), distributed over temperature. Due to the well-known ill conditioning problem, no precisely resolved DEM can be inverted directly from the spectrum, so often only a gross parameterization of the DEM is used to approximate the data, in hopes that the parameterization can provide useful model-independent constraints on the heating process. However, ill conditioning also introduces ambiguity into the various different parameterizations that could approximate the data, which may spoil the perceived advantages of model independence. Thus, this paper instead suggests a single parameterization for both the heating mechanism and the X-ray sources, based on a model of impulsive heating followed by radiative cooling. This approach is similar to a flow approach but allows injection at multiple initial temperatures and applies even when the steady state is a distribution of different 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 parameterization for X-ray spectra that is especially streamlined for higher density plasmas with efficient radiative cooling and minimal thermal conduction and mixing. The method also provides some internal consistency checks on the validity of its assumptions. A heuristic general version is then applied over a wide range of astrophysical applications to schematically explore potential alternative models for these phenomena.