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Temporal Evolution of Mhd Waves in Solar Coronal Arcades

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Temporal Evolution of Mhd Waves in Solar Coronal Arcades DOCTORAL THESIS 2019 TEMPORAL EVOLUTION OF MHD WAVES IN SOLAR CORONAL ARCADES Samuel Rial Lesaga palabra DOCTORAL THESIS 2019 Doctoral Programe of Physics TEMPORAL EVOLUTION OF MHD WAVES IN SOLAR CORONAL ARCADES. Samuel Rial Lesaga Thesis supervisor: I~nigoArregui Uribe-Echevarria Thesis supervisor: Ram´onOliver Herrero Thesis Tutor: Alicia Sintes Olives Doctor by the university of the Balearic islands Supervisor letter Supervisor letter v Supervisor letter Supervisor letter Dr. I˜nigo Arregui Uribe-Echebarria of the Instituto de Astrof´ısica de Canarias. DECLARE: That the thesis entitled “Temporal evolution of magnetohydrodynamic waves in solar coronal arcades”, presented by Samuel Rial Lesaga to obtain the PhD degree, has been completed under my supervision. For all intents and purposes, I hereby sign this document. Signature Firmado por ARREGUI URIBE- ECHEVARRIA IÑIGO - 15392542E el día 20/05/2019 con un certificado emitido por AC FNMT Usuarios Dr. I˜nigo Arregui Uribe-Echebarria La Laguna, 17 May 2019 vi Acknowledgments En primer lugar me gustar´ıaagradecer al Dr. Ramon Oliver la amistad, la con- fianza y el apoyo incondicional que me siempre me ha ofrecido. El siempre ha sabido animarme y motivarme en los m´ultiplesmomentos dif´ıcilesque ha tenido esta tesis y estoy plenamente convencido de que si no hubiera sido por ´elesta tesis no existir´ıa. Gracias Al Dr. I~nigoArregui por su paciencia y su confianza en mi trabajo y en mi. Gracias motivarme cuando no lo estaba y por hacerme ver que este esfuerzo merece la pena. Al Dr. Jos´eLuis Ballester y a todo el grupo de personas que forman o han formado parte el grupo de f´ısicasolar de la Universitat de les Illes Balears y con los que he compartido alg´uncongreso, desayuno o cena. Un buen ambiente de trabajo siempre es una gran ayuda a la hora de realizar cualquier trabajo y en este caso ha sido genial. A mis padres, Rub´eny Clarisa, porque siempre me han apoyado durante este pro- ceso que parec´ıano tener fin, por la formaci´ony valores que me han dado y por muchas otras cosas que es imposible enumerar aqu´ı. A mi pareja Diana por apoyarme y estar siempre a mi lado sin importarle el camino que elija por muy extra~noque este sea. Finalmente agradezco al Ministerio de Educaci´ony Ciencia la concesi´onde la beca asociada al proyecto BES-2007-16670 gracias a la cual este trabajo ha sido posible. vii List of publications The format of this thesis is compendium of articles. In the following list appear the published articles from which the present thesis is made. • Rial, S., Arregui, I., Oliver, R. and Terradas, J.: 2019, Determining nor- mal mode features from numerical simulations using CEOF analysis: I. Test case using transverse oscillations of a magnetic slab, ApJ 876(1), 86, doi: 10.3847/1538-4357/ab1417 • Rial, S., Arregui, I., Terradas, J., Oliver, R. and Ballester, J. L.: 2010, Three- dimensional Propagation of Magnetohydrodynamic Waves in Solar Coronal Arcades, ApJ 713, 651661, doi:10.1088/0004-637X/713/1/651. • Rial, S., Arregui, I., Terradas, J., Oliver, R. and Ballester, J. L.: 2013, Wave Leakage and Resonant Absorption in a Loop Embedded in a Coronal Arcade, ApJ 763, 16, doi:10.1088/0004-637X/763/1/16. ix Aim of the thesis The aim of this thesis is to go a step further in the theoretical modeling of coro- nal loops. Following that direction, our main goal is to be able to theoretically reproduce part of the observed complexity that these structures display when a sudden release of energy occurs in the solar corona. Since not too much time ago, the theoretical models of these features have been rather simple. In order to have simple solutions, these models use big approximations, such as, straight instead of curved structures, one-dimensional/two-dimensional structures, etc. In order to go beyond that simple models, our aim is to increase the complexity of the theoretical models by adding what we think can be some key ingredients just like the curvature or three-dimensionality. In this work we will adopt the approach of increase the complexity of the model step by step to create a solid base of knowledge that helps us understand the underlying physics. Therefore we will begin with a well known two-dimensional problem and then we will allow perturbations propagate in the third direction as a first step towards three-dimensionality. These are known as 2:5 dimensional models. Afterwards, we will add more ingredients such as a sharp model of coronal loop, different density profiles, curvature, etc. The study of coronal loop oscillations can be done from several points of view but in this thesis we will focus in two of them. The first one is to solve the time- dependent MHD equations by means of a temporal code. In the first two papers Rial et al.(2010) and Rial et al.(2013) we use this approach. The second approach consists in solve the normal modes of the system. The standard method to do so can be in general a difficult task because an specially designed numerical code is needed. For that reason another goal of this thesis is to develop a technique that allow us to find an alternative way to find the normal modes of any system. In Rial et al.(2019) we explain how this technique works as well as its advantages and disadvantages. xi Abstract of the thesis 0.1 Abstract In this thesis we will study vertical oscillations in a potential arcade under the approximation of a zero-β plasma, when different density profiles are considered. On one hand we will focus on the time-dependent problem to analyze the other side of the magnetohydrodynamic oscillations coin which traditionally is given by the normal mode analysis. We are going to study the propagation, energy transformation and damping of the impulsively generated waves as well as its relevant spatial and temporal scales in order to complete the picture. In order to study the wave damping, we examine two physical mechanisms that may be involved in the fast attenuation of the observed vertical coronal loop oscillations, namely wave leakage through wave tunneling and resonant absorption. In this wok whenever is possible, the time-dependent results are going to be compared with known normal mode properties to gain knowledge of how both sides are related as well as to test them. On the other hand, we also will investigate the use of a new technique of obtaining the system normal modes when the standard normal mode analysis is difficult to be carried out. We will apply it to a straight coronal loop model and we will obtain them with the desired degree of accuracy thanks to several criteria based on the convergence of the method. 0.2 Resumen En esta tesis estudiaremos las oscilaciones verticales de una arcada potencial en la aproximaci´on β ∼ 0 de un plasma, cuando diferentes perfiles de densidad son considerados. Por un lado nos vamos a centrar en la evoluci´ontemporal de este problema para as´ıanalizar la otra cara de la moneda de las oscilaciones magnetohidrodin´amicas, la cual tradicionalmente se ha estudiado mediante el an´alisisde modos normales. Vamos a estudiar la propagaci´on,la conversi´onenerg´eticay la atenuaci´onde ondas generadas mediante un impulso inicial, as´ıcomo las escalas espaciales y temporales generadas, para de esta manera obtener una imagen lo m´ascompleta posible. Para el estudio de la atenuaci´on, vamos a examinar dos mecanismos f´ısicosque podr´ıan estar involucrados en la r´apida atenuaci´onde la oscilaciones verticales observadas en bucles coronales, que son la emisi´onde energ´ıamediante \wave tunneling" y absorci´onresonante. En este trabajo, siempre que sea posible, se van a comparar los resultados de las simulaciones temporales con las propiedades conocidas que han de poseer los modos normales. Esto nos va a servir como un m´etodo de comprobaci´on de nuestros resultados adem´asde ayudarnos a entender como ambas visiones est´an relacionadas entre si. xiii 0.3. RESUM Abstract of the thesis Por otro lado lado vamos a investigar el uso de una nueva t´ecnicapara obtener los modos normales de un sistema cuando el m´etodo est´andardes dif´ıcilde llevar a cabo. Este m´etodo lo vamos aplicar a un modelo de bucle coronal recto y vamos a obtener los modos normales del sistema con el grado de precisi´onque deseemos mediante el uso de un criterio de convergencia. 0.3 Resum En aquesta tesi estudiarem les oscil·lacions verticals d'una arcada potencial en l'aproximaci´o β ∼ 0 d'un plasma quan diferents perfils de densitat s´onconsiderats. Per un costat ens centrarem en l'evoluci´otemporal d'aquest problema per tal d'analitzar l'altra cara de la moneda de les oscil·lacions magnetohidrodin`amiques, la qual tradicionalment s'ha estudiat mitjan¸cant l’an`aliside modes normals. Es- tudiarem la propagaci´o,la conversi´oenerg`eticai l'atenuaci´ode les ones generades mitjan¸cant un pols inicial, aix´ıcom les escales espacials i temporals generades, per tal de ser capa¸cosd'obtenir una imatge el m´escompleta possible. Per a l'estudi de l'atenuaci´o,examinarem dos mecanismes f´ısicsque podrien estar involucrats en la r`apida atenuaci´ode les oscil·lacions verticals observades en els bucles coronals, que s´onl’emissi´od'energia mitjan¸cant \Wave tunneling" i l’absorci´oressonant. En aquest treball, sempre que sigui possible, compararem els resultats de les nostres simulacions temporals amb les propietats conegudes que han de tenir els modes normals.
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