The Temperature and Emission Measure Distribution in the Quiet and Active Solar Corona: A Bayesian Approach

The reconstruction of the differential emission measure (DEM) from observations of spectral line intensities provides information on the temperature distribution of the emission measure in the region observed. The inversion process is known to be highly unstable, and it has been necessary to provide additional constraints, such as requiring that the DEM should be smooth. However, this is a nonphysical constraint. The goal of this analysis is to make an empirical determination of the ability of a set of emission-line intensities to constrain the reconstruction. Here, a simple model is used, by means of a Markov Chain Monte Carlo process, to arrive at solutions that reproduce the observed intensities in a region of the quiet Sun and a solar active region. These solutions are compared by means of the reduced chi-squared. The conclusion from this analysis is that the observations are only capable of constraining a model consisting of four temperature-emission measure pairs plus a determination of the standard deviation of the model from the observed line intensities. A more complex model with five temperature-emission measure pairs does not improve the fit and leads to parameters that are irrelevant. A more general conclusion is that the information content of a set of observed emission lines is limited with respect to the determination of the emission measure distribution.