# Wave coupling in the solar atmosphere from sub-photosphere to the corona

- Irantzu Calvo Santamaria

- Elena Khomenko Director
- Manuel Collados Vera Director

Defence university: Universidad de La Laguna

Year of defence: 2015

Type: Thesis

## Abstract

The solar atmosphere has been studied for decades by means of observations, theory and numerical simulations. However, due to its complexity, it is difficult to fully understand all the phenomena taking place in the atmosphere. Starting from the photosphere up to the corona, the solar atmosphere is strongly stratified and the magnetic fields filling it are highly complex. Moreover, the coupling between different layers in still an open question, among others. It is well known that waves experience several phenomena as they propagate from the photosphere upwards into the corona. The fast and slow magneto-acoustic waves propagating in the photosphere reach the equipartition layer where the plasma ß=1. This means that the gas pressure and magnetic pressure are balanced, and the waves pass from a plasma where the gas pressure dominates to a magnetically dominated region. Therefore, the properties of the waves change at that region. The phenomenon taking place there is the fast to slow, or vice versa, mode conversion, in which there is a transfer of energy between magnetic and acoustic waves. Another important obstacle is the transition region, where the temperature increases from some thousands to millions of Kelvin in few hundred kilometres. This represents a huge discontinuity for waves, and thus, part of them are reflected downwards. In addition, due to the density decrease in that thin layer, the Alfvén velocity increases significantly, resulting on a refraction of magnetic waves in this layer. Thus, crossing the transition region is a big deal for fast magnetic waves, and therefore it is hard to understand the high temperatures in the corona as due to fast waves, given that the energy they carry is supposed to return to lower layers. That could be explained by means of the energy carried by Alfvén waves. Part of these pure magnetic waves are found to be produced by the mode conversion of fast magnetic waves. This mode conversion is even more complex as it takes place where magnetic fast waves refract. Hence, the fast to Alfvén mode conversion can happen in a wide range of heights in the upper atmosphere. Apart from the transition region and the equipartition layer, waves can find more obstacles, such as the location of the acoustic cut-off frequency and null points, among others. The study of these phenomena can give us information about the atmospheric and magnetic properties. Most of the works done by means of MHD waves are focused on individual layers. Some of them take into account two of them (photosphere and chromosphere), but there are few works that aim to study the solar atmosphere as a whole. Numerically, this is rather difficult since simulations require covering changes in pressure and density by many orders of magnitude in the numerical domain simultaneously. The aim of this thesis is to understand how the different atmospheric layers are dynamically and magnetically coupled by mean of MHD waves. Also important is the estimation of the amount of energy excited below the photosphere reaches the corona, and whether this energy is of magnetic or acoustic nature. To that end, we focus our study on the wave propagation from layers below the photosphere up to the corona. The complexity, of either the structure of the atmosphere and the magnetic field configurations, makes it unfeasible to analytically solve the MHD equations. In order to solve them in complex situations, we make use of numerical simulations. We use the MANCHA code that fully solves the non-linear equations of the MHD. The stratification of our model is obtained by coupling different semi-empirical models, from -5 Mm up to the higher chromosphere. The corona is treated as an isothermal gas with a temperature of one million Kelvin. We choose two- and three- dimensional complex magnetic fields, which resemble network and internetwork regions, and contain a wide range of magnetic field inclinations. We start with a study of the wave behaviour in the linear regime. Even though the numerical code solves the non-linear equations, we make the amplitude of the perturbations sufficiently small to avoid the development of non-linearities. In this part we study the wave propagation driven by three different perturbations: vertical and horizontal periodic drivers, and an instantaneous pressure pulse. The wave behaviour is different in the three cases considered, but, in all numerical runs, we find that the energy reaches the corona more preferably along the field lines and it is of acoustic nature. The two-dimensional magnetic field configuration chosen contains a null point. The presence of the null point changes the behaviour of the waves as they propagate close to it. The null point seems to absorb waves and emit them in all directions. This property, together with the refraction of magnetic waves in the transition region, makes most of the magnetic energy stay below the transition region. We also obtain a spatial frequency distribution that is in agreement with the results obtained from observations. After studying the differences in the wave behaviour by different linear drivers, we carry out a two dimensional non-linear numerical simulation using the same atmospheric stratification and magnetic field configuration as that used in the linear case. We perturb the atmosphere with a pressure pulse. The comparison of the wave propagation in linear and non-linear regimes allows us to distinguish more clearly the non-linearities developed by waves and how they change the whole picture of the wave behaviour. The wave propagation pattern is clearly different, being the most remarkable difference the development of shock waves in the non-linear regime. Particularly interesting is the interaction between hydrodynamic shock waves and the null point, that results in uncommon and interesting phenomena. In order to study the Alfvén waves behaviour, a three-dimensional numerical simulation is also performed. The magnetic field topology chosen in this case has no symmetry and this further complicates the analysis. We propose a new way of decoupling slow and fast magneto-acoustic and Alfvén waves, which gives encouraging results. We also calculate the mean acoustic and energy transport into the corona, where Alfvén waves are detected. The last part of the thesis presents an observational analysis of wave propagation. We analyse multi-layer multi-wavelength data obtained with the IBIS spectropolarimeter installed at the Dunn Solar Telescope (DST). The aim of this analysis is to study the wave propagation from the photosphere to the chromosphere, and the dependence of the observed wave properties with the viewing angle. We analyse the photospheric FeI 6173 Å and the chromospheric CaII 8542 Å lines, at two different regions, one located at the disk center (¿=0.99) and the other one located at ¿=0.73. We obtain interesting results when comparing the power spectra of the two different active regions, where we see oscillations of different frequency that could be the result of the different perspective or viewing angle. We also study the relation between the frequency distribution and the magnetic field inclination, where we obtain that higher frequency oscillations are found in more vertical magnetic fields.