Application of statistical analysis techniques to solar and stellar phenomena

Abstract

Currently, solar observers are investigating spectroscopic images of the Sun's outermost atmosphere (the corona), which are challenging long-held views on the density and temperature structure of this environment. The corona is "filled" with magnetic strands but determining their precise nature is not straightforward.
One way of revealing the nature of the coronal heating mechanism is by comparing simple theoretical one dimensional hydrostatic loop models with observations of the temperature and/or density structure along these features. The most wellknown method for dealing with comparisons like that is the x2 approach. In this research we consider the restrictions imposed by this approach and present an alternative way for making model comparisons using Bayesian statistics. In order to quantify our beliefs we use Bayes factors and information criteria such as AIC and BIC. Three simulated data-sets are analysed in order to validate the procedure and assess the effects of varying error bar size. Another three datasets
(Ugarte-Urra ci at., 2005; Priest ci at., 2000; Young ci al., 2007) are analysed using the method described above. For the Ugarte-Urra ci at. and Young ci al. data-sets, we conclude apex dominant heating is the likely heating candidate, whereas the Priest ci al. data-set implies basal heating. Note that these new results (regarding the Ugarte-Urra ci at. and Priest ci at. data-sets) are different from those obtained using the chi-squared statistic.
The second research project involves extensive model comparison against solar flare plasma observed cooling curves. After a solar flare erupts, flare-loops form which cool over thousands of seconds. How the plasma cools over time is investigated. In this case, we test the adequacy of the zero-dimensional EBTEL (Enthalpy-Based Thermal Evolution of Loops) model as introduced by Klimchuk, Patsourakos, and Cargill (2008). An interesting approach here is to define the form of the non-thermal heating input to the system and compare it with the thermal heating input. For the data-set under investigation (Raftery et al., 2009) a Full-Gaussian energy profile is proposed. Also, from the data it is not possible to distinguish which of the thermal or non-thermal heat flux is more dominant, so both can be equally considered for temperature, density and pressure evolution of the system.
Finally, the last part of this research is dedicated to recurrent nova outbursts. RS Ophiuehi is a nova produced by a white dwarf star and a red giant. In this case the white dwarf will steadily acerete gases on its surface from the red giant's outer atmosphere. About every twenty years, enough material will be accreted on the white dwarf's surface in order to produce an eruption. Over the past one hundred years at least five such outbursts have been observed. As another application of Bayesian model comparison techniques, curve fitting models are tested against light curves of RS Ophiuchi outbursts in order to decide upon the one that best describes the data. Furthermore, the magnitude of the star is analysed using wavclet analysis techniques. Ways of deriving the Cone of Influence are presented. An outcome of this analysis is that we can quantitatively confirm that an outburst occurred around November 26, 1945, which was not recorded due to the observational seasonal gaps. This was originally proposed by Oppenheimer and Mattei (1993) but was never accepted as a confirmed outburst.
Also, this method reveals a pre-outburst signal in the light curve. For this, the way in which the wavelet analysis can be beneficial for future outburst predictions is presented.