Recovering thermodynamics from spectral profiles observed by IRIS (II): improved calculation of the uncertainties based on Monte Carlo experiments

Observations by the Interface Region Imaging Spectrograph (IRIS) in the Mg II h & k spectral lines have provided a new diagnostic window towards the knowledge of the complex physical conditions in the solar chromosphere. Theoretical efforts focused on understanding the behavior of these lines have allowed us to obtain a better and more accurate vision of the chromosphere. These efforts include forward modeling, numerical simulations, and inversions. In this paper, we focus our attention on the uncertainties associated with the thermodynamic model atmosphere obtained after the inversion of the Mg II h & k lines. We have used ~ 50;000 synthetic representative profiles of the IRIS2 database to characterize the most important source of uncertainties in the inversion process, viz.: the inherent noise of the observations, the random initialization of process, and the selection criteria in a high-dimensional space. We have applied a Monte Carlo approach to this problem. Thus, for a given synthetic representative profile, we have created five randomized noise realizations (representative of the most popular exposure times in the IRIS observations), and inverted these profiles five times with different inversion initializations. The resulting 25 inverted profiles, fits to noisy data, and model atmospheres are then used to determine the uncertainty in the model atmosphere, based on the standard deviation and empirical selection criteria for the goodness of fit. With this approach, the new uncertainties of the models available in the IRIS2 database are more reliable at the optical depths where the Mg II h & k lines are sensitive to changes in the thermodynamics.Comment: 13 pages, 8 figures, and 1 tabl