Stellar Models with Magnetism and Rotation: Mixing Length Theories and Convection Simulations

Abstract

Some low-mass stars appear to have larger radii than predicted by standard 1D structure models; prior work has suggested that inefficient convective heat transport, due to rotation and/or magnetism, may ultimately be responsible. In this thesis, we explore this possibility using a combination of 1D stellar models, 2D and 3D simulations, and analytical theory. First, we examine this issue using 1D stellar models constructed using the Modules for Experiments in Stellar Astrophysics (MESA) code. We begin by considering standard models that do not explicitly include rotational/magnetic effects, with convective inhibition modelled by decreasing a depth-independent mixing length theory (MLT) parameter αMLT. We provide formulae linking changes in αMLT to changes in the interior specific entropy, and hence to the stellar radius. Next, we modify the MLT formulation in MESA to mimic explicitly the influence of rotation and magnetism, using formulations suggested by Stevenson (1979) and MacDonald and Mullan (2014) respectively. We find rapid rotation in these models has a negligible impact on stellar structure, primarily because a star’s adiabat, and hence its radius, is predominantly affected by layers near the surface; convection is rapid and largely uninfluenced by rotation there. Magnetic fields, if they influenced convective transport in the manner described by MacDonald and Mullan (2014), could lead to more noticeable radius inflation. Finally, we show that these non-standard effects on stellar structure can be fabricated using a depth-dependent αMLT: a non-magnetic, non-rotating model can be produced that is virtually indistinguishable from one that explicitly parameterises rotation and/or magnetism using the two formulations above. We provide formulae linking the radially-variable αMLT to these putative MLT reformulations.

We make further comparisons between MLT and simulations of convection, to establish how heat transport and stellar structure are influenced by rotation and magnetism, by looking at the entropy content of 2D local and 3D global convective calculations. Using 2D “box in a star” simulations, created using the convection code Dedalus, we investigate changes in bulk properties of the specific entropy for increasingly stratified domains. We observe regions stable against convection near the bottom boundary, resulting in the specific entropy in the bulk of the domain exceeding the bottom boundary value: this could be a result of physical effects, such as increased amounts of viscous dissipation for more supercritical, highly stratified cases, but may also be influenced by the artificial boundary conditions imposed by these local simulations. We then turn to 3D global simulations, created using the convection code Rayleigh, and investigate these same properties as a function of rotation rate. We find the average of the shell-averaged specific entropy gradient in the middle third of the domain to scale with rotation rate in a similar fashion to the scaling law derived via MLT arguments in Barker et al. (2014), i.e., |⟨ds/dr⟩| ∝ Ω^4/5.