We address the inversion problem of deriving the differential emission measure (DEM) distribution D(T) = nenHdV/d log T from the spectrum of an optically thin plasma. In the past we have applied the iterative Withbroe-Sylwester technique and the Polynomial technique to the analysis of EXOSAT spectra of cool stars, but recently we have applied the inversion technique discussed by Craig & Brown (1986) and Press et al. (1992) in the analysis of EUVE spectra of cool stars. The inversion problem-a Fredholm equation of the first kind-is ill-posed and solutions tend to show large, unphysical oscillations. We therefore apply a second-order regularization, i.e., we select the specific DEM for which the second derivative is as smooth as is statistically allowed by the data. We demonstrate the importance of fitting lines and continuum simultaneously, discuss the effect on the DEM of continuum emission at temperatures where no line diagnostics are available, and address possible ways to check various model assumptions such as abundances and photon destruction induced by resonant scattering.
Spectroscopy and Differential Emission Measure Diagnostics of a Coronal Dimming Associated with a Fast Halo CME
