Eclipsing time variations from 3D magnetohydrodynamical simulations

Magnetic fields are ubiquitous in the Universe. In particular, the magnetic activity of the Sun has been observed for centuries and studied for more than a century. Nowadays we know that most stars are magnetized. Yet, the mechanism by which magnetic fields are sustained is not well understood. Dynamo theory, which describes how magnetic fields are amplified and sustained, has mostly been used to explain solar phenomena with moderate success. A field where dynamo theory has hitherto not been exploited is in binary stars. Most of our knowledge of stellar structure and evolution come from carefully inferring stellar parameters from binaries. Measures of magnetic fields in stars are much more difficult to obtain, therefore limiting our knowledge thereof. A possibility to overcome this is encountered in close binaries via gravitational quadrupole variations which arise from density fluctuations of magnetic origin. This is observed as periodic eclipsing time variations in some close binaries. Two mechanisms stand out as potential explanations, namely the Applegate and Lanza mechanisms. This thesis expands previous analytical works by solving the magnetohydrodynamic equations in a convective shell, representing a Sun-like star. It is found that the density fluctuations are too small to explain the observations with the original Applegate mechanism. However, when the magnetic field has a strong non-axisymmetric component, the Lanza mechanism can predict the observations to an order-of-magnitude approximation. The simplicity of the Lanza mechanism allows to overcome the problems of the Applegate mechanism and may offer a new way of studying stellar magnetic fields by measurements of eclipsing time variations in close binaries.