Markov‐Chain Monte Carlo Reconstruction of Emission Measure Distributions: Application to Solar Extreme‐Ultraviolet Spectra

Abstract

We have developed a new method for the reconstruction of differential emission measure distributions based on a Metropolis Markov-chain Monte Carlo (MCMC[M]) method. This technique allows us to (1) relax nonphysical smoothness constraints generally imposed on DEMs, (2) determine confidence bounds on the computed values, and (3) include extra information in the form of upper limits. Using the MCMC[M] algorithm, we reanalyze extreme ultraviolet spectral line fluxes obtained from Solar Extreme Ultraviolet Rocket Telescope and Spectrograph observations by Brosius et al. to obtain differential emission measure (DEM) distributions for active and quiet regions on the Sun. Both active- and quiet-region DEMs show a probable minimum near log T ≈ 5.6; the quiet-region DEM drops off beyond log T = 6.4, while the active-region DEM does not show evidence of a significant downturn even at log T = 7. The most striking aspect of our results is that the latter also shows several sharp peaks (of width ~0.1 dex), notably at log T = 6 and 6.3, and a broad feature, beyond log T = 6.5. We also explore the limitations on DEM reconstruction imposed by imperfect atomic data, choice of spectral lines, uncertainties in abundances, and other systematic errors. Within these limitations, we discuss the derived emission measure distribution and comment on its implications to coronal structure. We conclude that calculation of uncertainties on the DEM are crucial in the interpretation of structure seen in reconstructions. Further, a careful selection of the spectral lines used to infer the DEM is needed in order to avoid artificially generating structure in the DEM.