Bayesian analysis of the solar corona.

Abstract

In spite of the instrumental improvements to acquire data and the new techniques developed to analysed them, the solar corona is one of the regions of the Sun with more unresolved questions. New methods to compare between observations and theoretical or numerical models are necessary to reveal the main physical conditions and processes of this atmospheric layer.

This thesis entails a step further those methods development through the elaboration of new tools based on Bayesian statistics. Contrary to others type of statistics, the Bayesian approach permits to include in our analyses observations, prior information before taking data, as well as all kind of uncertainties. Hence, Bayesian analyses about the solar corona allow the inference of physical parameters, the comparison between models by computing their associated plausibility, and further predict new observations.

The thesis is performed within the coronal seismology context, in which observations and magnetohydrodynamical models are confronted. In particular, we have centred on the study of transversal waves supported by two coronal structures: coronal loops and prominence threads.

Regarding coronal loops, we have first inferred the most probable values of the magnetic field strength and how it depends with the internal density. Moreover, we have inferred the density contrast between the surrounding corona and the loop densities, as well as other structural parameters. We have further computed the plausibility of resonant absorption, phase mixing, and wave leakage mechanisms in explaining the observed damping of transverse waves. Our results indicate that none of these mechanisms explains all the observations. The evidence depends on the particular values of the measured wave period and damping time, and also on their uncertainties. Finally, we have considered resonant absorption of propagating waves to compare the evidence by assuming an exponential decay and a Gaussian one. In principle, none of these profiles seem to be more adequate than the another in explaining the data.

Concerning to prominence threads, we have first obtained the most probable values of the magnetic field strength. Secondly, we have considered the ratio between the fundamental mode period and that of the first overtone in transverse waves, to infer the density contrast, as well as the length of the threads. When we have compared models of period ratios under the short and long thread approximations, the results indicate that period ratios around unity are better explained by the long thread approximation, while the rest of period ratio values are more likely for the short thread approximation. Next, we have assumed a model that includes a mass flow contribution, in order to infer the total length of flux tubes containing threads. Furthermore, we have selected resonant absorption in the Alfvén continuum, resonant absorption in the slow continuum, and Cowling's diffusion as damping mechanisms. We have inferred their corresponding parameters and we have performed a plausibility comparison between them. Clearly, resonant absorption in the Alfvén continuum is the most plausible mechanism in explaining the damping process for threads. Lastly, we have considered resonant absorption in the Alfvén continuum of propagating waves to compare evidences of an exponential decay and a Gaussian one. Differently to coronal loops, the evidence for each profile depends on particular observed values of damping lengths and wavelengths.

To finish, we have posed some future work that derives from this thesis within coronal studies.