The solar corona has a temperature of order 1 MK, which is almost 200 times the temperature of the underlying surface. This fact has puzzled solar physicists for more than six decades. As of today, most solar physicists agree that the mechanism that heats the corona is connected to the dynamics of the magnetic fields in the photosphere. The question is: how does the coronal heating depend on the photospheric magnetic fields? That is the problem which this thesis focuses on.
Before investigating the problem, an introduction to the Sun is given, reviewing everything from the basics of a general star to the structure of the entire Sun, going through each layer, with focus on the atmosphere. Finally, the corona is brought into discussion, which leads us to the coronal heating problem. Two plausible heating mechanisms are discussed, both related to the generation of current sheets: 1) the stressing of a magnetic field which collapses into tiny current sheets (width of order 10 m) which eventually burst out as a nanoflare, a mechanism introduced by Parker (1988), and 2) a hierarchy of current sheets, analyzed by Galsgaard & Nordlund (1996), which also includes large-scale current sheets (width of several megameters) not related to nanoflares. Both mechanisms are actively referred to in the later chapters of this thesis.
To analyze the problem, the numerical code Bifrost is applied to solve the MHD equations on three-dimensional cutouts of the quiet-Sun (QS) atmosphere. Five theoretical models with different magnetic field configurations are evolved over time intervals of 30-80 min of solar time, and the resulting coronal temperatures and amounts of Joule heating (ohmic heating) in each model are analyzed, compared to each other and compared to the corresponding results of a standard model evolved by Hansteen et al. (2010).
The results confirms that both the tiny current sheets related to nanoflares and the hierarchy of largescale current sheets are plausible mechanisms for coronal heating. It is plausible that the magnetic field structure in the QS photosphere is in the form of a “salt-pepper” pattern with poles of upwardand downward-oriented fields. The simulations indicate that the coronal heating increases with the typical separation distance between magnetic poles in the photosphere, at least when this separation distance is shorter than 6-7 Mm (which is approximately the numerical upper limit for typical separation distances in the models evolved in this thesis). This is probably because an increased mean separation distance between magnetic poles allows a more complex hierarchy of current sheets to evolve. It is also confirmed that an atmosphere of homogeneous vertical magnetic fields does not produce the high temperatures observed in the corona above unipolar regions such as plage.