A comparative study of resistivity models for simulations of magnetic reconnection in the solar atmosphere

Magnetic reconnection is a fundamental mechanism in astrophysics. A common challenge in mimicking this process numerically in particular for the Sun is that the solar electrical resistivity is small compared to the diffusive effects caused by the discrete nature of codes. We aim to study different anomalous resistivity models and their respective effects on simulations related to magnetic reconnection in the Sun. We used the Bifrost code to perform a 2D numerical reconnection experiment in the corona that is driven by converging opposite polarities at the solar surface. This experiment was run with three different commonly used resistivity models: 1) the hyper-diffusion model originally implemented in Bifrost, 2) a resistivity proportional to the current density, and 3) a resistivity proportional to the square of the electron drift velocity. The study was complemented with a 1D experiment of a Harris current sheet with the same resistivity models. The 2D experiment shows that the three resistivity models are capable of producing results in satisfactory agreement with each other in terms of the current sheet length, inflow velocity, and Poynting influx. Even though Petschek-like reconnection occurred with the current density-proportional resistivity while the other two cases mainly followed plasmoid-mediated reconnection, the large-scale evolution of thermodynamical quantities such as temperature and density are quite similar between the three cases. For the 1D experiment, some recalibration of the diffusion parameters is needed to obtain comparable results. Specifically the hyper-diffusion and the drift velocity-dependent resistivity model needed only minor adjustments, while the current density-proportional model needed a rescaling of several orders of magnitude.Comment: 15 pages, 8 figures, 1 movi

On how the heating of the Solar Corona depends on the complexity of the magnetic field in the Solar Photosphere

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