Monte Carlo Markov chain DEM reconstruction of isothermal plasmas

Abstract

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 Δ log T 0.05. Also, the DEM curves obtained using lines calculated with an isothermal plasma and with a Gaussian distribution with FWHM of log T 0.05 are very similar. Two near-isothermal components can be resolved if their temperature separation is Δ 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.

Investigating the Reliability of Coronal Emission Measure Distribution Diagnostics Using Three-Dimensional Radiative Magnetohydrodynamic Simulations

“…We note that for the side view cases, high in the corona, the uncertainties of these EMDs on the coarser temperature grid even appear overestimated, since the χ 2 0 (EMD) drops to very low values. This is consistent with the findings of Landi et al (2012) who explored the ability of the MCMC methods to diagnose isothermal EMD. Landi et al (2012) find indeed that for isothermal plasma a bin width of Δ log T ∼ 0.05 is sufficient to diagnose the temperature distribution from spectral data.…”

“…Several methods have been developed to reconstruct EMDs from a set of observed intensities in lines, or passbands in the case of imaging observations (see, e.g., review by Phillips et al 2008, and the discussion and references in Hannah & Kontar 2012). Here we test the Monte Carlo Markov chain (hereafter MCMC) forward modeling method (Kashyap & Drake 1998), which is widely used and considered to provide robust results (see, e.g., Landi et al 2012;Hannah & Kontar 2012; see also http://www.lmsal.com/∼boerner/demtest/ for a recent comparative analysis of results from different methods, applied to AIA). With respect to several other methods, the MCMC method has the advantages of not imposing a pre-determined functional form for the solution, and, most importantly, of estimating the uncertainties associated with the resulting EMD (see, e.g., Kashyap & Drake 1998;Testa et al 2011 for additional details).…”

The evolution of the emission measure distribution in the core of an active region

“…It tends to underestimate the peak of the DEM at 3 MK, while the emission measure above 3 MK is overestimated. If a finer grid is chosen, the DEM peak tends to agree with the spline method, but the DEM in the 1-3 MK range shows large deviations (for a discussion on the MCMC_DEM grid size see Landi et al 2012;Testa et al 2012). The XRT_DEM method Nb.…”

Inference of Heating Properties From “Hot” Non-Flaring Plasmas in Active Region Cores. Ii. Nanoflare Trains

“…Warren et al (2012) find 7b10, with uncertainties of ±2.5-3, for 15 AR cores, although Del Zanna & Mason (2014), using observations from the Solar Maximum Mission, claim larger values for b. It must be noted though that reconstructing EM(T) from spectroscropic and narrow-band observations is nontrivial, with different inversion methods often giving significantly different results (Landi et al 2012;Guennou et al 2013). …”