Modelling the corona of stars more active than the Sun using 3D MHD simulations
by Juxhin Zhuleku
Date of Examination:2021-02-19
Date of issue:2021-06-10
Advisor:Prof. Dr. Hardi Peter
Referee:Prof. Dr. Hardi Peter
Referee:Prof. Dr. Andreas Tilgner
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Description:Ph.D. thesis
Abstract
English
Cool stars like our Sun are surrounded by coronae with temperatures up to several million Kelvin. After decades of research, there has been no definite explanation as to why the coronae of stars are several orders of magnitude hotter than their surfaces. Because of the high temperature, the solar and stellar coronae exhibit high X-ray emission. Coronae of stars more active than the Sun can generally appear to have even 1000 times stronger X-ray emission than the solar corona. The coronal X-ray activity of the Sun and other stars is governed by the surface magnetic field. The relationship between the coronal X-ray luminosity $L_{\rm{X}}$ and the surface magnetic flux $\Phi$ of the Sun and other stars has been shown to follow a power-law relation, $L_{\rm{X}}\propto \Phi^m$, by numerous observational studies. Depending on the study, $1\leq m <3$. Until now there is no clear explanation of why there is a power-law dependence between $L_{\rm{X}}$ and $\Phi$ and also why $m$ is found to differ from one study to another. In this thesis, we aim to explain this power-law relationship quantitatively through a simple analytical model and through 3D magnetohydrodynamic (MHD) models of the solar and stellar coronae. Our analytical model is based on a combination of the Rosner, Tucker \& Vaiana (RTV) scaling laws \citep{Rosner}, coronal heating mechanisms, for example nano flares, and the temperature response for different instruments. This results in a simple analytical power-law expression, that can explain the power-law relation between the X-ray luminosity $L_{\rm{X}}$ and the surface magnetic flux $\Phi$. The power-law index $m$ is found to be in the range from 0.8 to 1.6 which is in agreement with the range of $m$ reported by observational studies. Furthermore, we also find that the sensitivity of each individual instrument at a specific temperature range can have a significant influence on the power-law index $m$. This has been overlooked for all observational studies. To further investigate the $L_{\rm{X}}\propto \Phi^m$ relationship in a more complex environment, we use 3D MHD numerical models to simulate the part of the corona above an active region. We use the solar coronal model developed by \cite{Bingthesis}, that has successfully reproduced some of the key aspects of coronal structures. A hot and dynamic corona with temperatures of 1 MK and more is self-consistently created. We investigate how the coronal X-ray emission changes with the magnetic field strength and the size of the underlying active region. Firstly, we increase the strength of the vertical surface magnetic field by a constant factor while keeping the size of the active region constant. With this approach, we reach values of the surface magnetic field up to 20 kG. This value of the magnetic field is extremely high for the Sun but it is speculated to be common in more active stars. The coronal temperature and density obtained by our model are in good agreement with the RTV scaling laws. Furthermore, the coronal X-ray luminosity $L_{\rm{X}}$ synthesized from our model increases with the surface magnetic flux $\Phi$, which is consistent with other studies. We find this relation to be a power-law $L_{\rm {X}}\propto \Phi^m$ with the power-law index $m=3.4$. Secondly, we increase the overall surface magnetic flux by increasing the size of the active region while keeping the strength of the surface magnetic field constant. We see an increase in the coronal temperature, although the increase is not as strong as in the first approach. The synthetic X-ray emission increases with the surface magnetic flux, in agreement with the previous approach. In this case, however, the index $m\simeq2.2$ is found to be less steep than for the first approach. Overall, our results provide new insight into the $L_{\rm{X}}\propto \Phi^m$ relationship. The sensitivity of each instrument at a specific temperature range can explain the difference of $m$ found in observations. In addition, our analytical model and numerical experiments can provide an explanation of why the dependence of the X-ray luminosity $L_{\rm{X}}$ and the surface magnetic flux is a power-law.
Keywords: Sun: corona-stars: coronae- X-ray:stars- magnetohydrodynamics (MHD)- methods: numerical