Flows, Instabilities, and Magnetism In Stars and Planets

Abstract

Flows, instabilities, and magnetism play significant roles in the internal and atmospheric dynamics of objects ranging from the smallest exoplanets to the largest stars. These phenomena are governed by the equations of magnetohydrodynamics (MHD), which link the flows and magnetic fields, and from which the operational parameters and growth rates of instabilities can be recovered. Here we present an overview of interesting phenomena (such as the internal dynamics of stellar and planetary objects, as well as instabilities which might operate within these environs), as well as computational techniques by which these phenomena might both be understood and analysed (through both ‘simplifications’ of the MHD equations and different numerical/computational approaches). We first present an investigation into the Heat-Flux-Driven Buoyancy Instability (HBI) within stellar and planetary atmospheres, considering both the parameter space it might operate within as well as its non-linear effects during said operation. We find that whilst the HBI may be able to play a role in Solar, stellar and planetary atmospheres, it is likely to be quite limited in scope, only operating within small regions. However, its dramatic consequences for heat transport in the non-linearly evolved state, and the prospects that it may operate outside the narrow regimes that our analytical analysis suggested, suggest that it may merit further study. This is followed with a discussion of a method by which the surface flows of exoplanets might be measured: The Rossiter-Mclaughlin Effect at Secondary Eclipse (RMse). We formulate the effect, showing that the formalism is identical to the traditional Rossiter-Mclaughlin effect, albeit in a different frame (a planet transiting a star becomes a star transiting a planet), and consider its observational implications: the effect should be observable for the brightest planet hosting stars using upcoming 40m-class telescopes (i.e.E-ELT). We finish with a series of 3D anelastic simulations of fully convective stars, designed to investigate how the internal flows are affected by varying stellar parameters, as well as a possible link between residual entropy and differential rotation contours, and a method by which this link can be used (via the thermal wind equation - TWE) to extrapolate the internal rotation. We find a clear transition between ‘solar-like’ and ‘anti-solar’ internal dynamics, characterised in the meridional circulation, differential rotation, residual entropy, and angular momentum flux profiles. Furthermore we find that, whilst the alignment between residual entropy and differential rotation contours is somewhat varied, the resultant extrapolation, via the TWE, produces a generally good fit to the differential rotation contours, suggesting a general robustness to the theory.