Monte Carlo Markov chain DEM reconstruction of isothermal plasmas

Context. Recent studies carried out with SOHO and Hinode high-resolution spectrometers have shown that the plasma in the off-disk solar corona is close to isothermal. If confirmed, these findings may have significant consequences for theoretical models of coronal heating. However, these studies have been carried out with diagnostic techniques whose ability to reconstruct the plasma distribution with temperature has not been thoroughly tested. Aims. In this paper, we carry out tests on the Monte Carlo Markov chain (MCMC) technique with the aim of determining: 1) its ability to retrieve isothermal plasmas from a set of spectral line intensities, with and without random noise; 2) to what extent can it discriminate between an isothermal solution and a narrow multithermal distribution; and 3) how well it can detect multiple isothermal components along the line of sight. We also test the effects of 4) atomic data uncertainties on the results, and 5) the number of ions whose lines are available for the DEM reconstruction. Methods. We first use the CHIANTI database to calculate synthetic spectra from different thermal distributions: single isothermal plasmas, multithermal plasmas made of multiple isothermal components, and multithermal plasmas with a Gaussian DEM distribution with variable width. We then apply the MCMC technique on each of these synthetic spectra, so that the ability of the MCMC technique at reconstructing the original thermal distribution can be evaluated. Next, we add a random noise to the synthetic spectra, and repeat the exercise, in order to determine the effects of random errors on the results. We also we repeat the exercise using a different set of atomic data from those used to calculate synthetic line intensities, to understand the robustness of the results against atomic physics uncertainties. The size of the temperature bin of the MCMC reconstruction is varied in all cases, in order to determine the optimal width. Results. We find that the MCMC technique is unable to retrieve isothermal plasmas to better than Delta log T similar or equal to 0.05. Also, the DEM curves obtained using lines calculated with an isothermal plasma and with a Gaussian distribution with FWHM of log T similar or equal to 0.05 are very similar. Two near-isothermal components can be resolved if their temperature separation is. log T = 0.2 or larger. Thus, DEM diagnostics has an intrinsic resolving power of log T = 0.05. Atomic data uncertainties may significantly affect both temperature and peak DEM values, but do not alter our conclusions. The availability of small sets of lines also does not worsen the performance of the MCMC technique, provided these lines are formed in a wide temperature range. Conclusions. Our analysis shows the present limitations in our ability to identify the presence of strictly isothermal plasmas in stellar and solar coronal spectra.