All stars, and many planets, carry energy by convection in some parts of their interiors. The heat transport associated with this convection, which must be calculated in order to construct a consistent stellar or planetary structure model, is influenced by rotation or magnetism. But a quantitative understanding of the effects these have on the convection, and so ultimately on stellar/planetary evolution, is still lacking. A central problem is that the convective dynamics occur on timescales that are much shorter than the evolutionary ones. Hence, numerical simulations that can adequately resolve the convective flows cannot be evolved over evolutionary timescales in order to investigate long-term effects on stellar structure.
In recent work, we have circumvented this problem by using a hierarchy of approaches, ranging from 3D simulations to 1D models. With the aid of DiRAC resources, we conducted a large survey of 3D simulations in localised, Cartesian domains tilted at some angle with respect to the rotation vector (described in Currie, Barker, Lithwick, Browning 2020, MNRAS, 493, 5233).
These box simulations served as idealised representations of a small part of a rotating star or planet, situated at various latitudes. We used these to analyse the rich variety of phenomena that occur as the rotation rate and latitude are changed, and to compute how the temperature gradient established by the convection varies with these parameters. Broadly, rotation makes the heat transport less efficient, leading to steeper temperature gradients. We compared the results of these calculations to expectations from semi-analytical theory: in particular, we showed that a new multi-mode “rotating mixing length” theory (based on earlier work by Stevenson 1979) provides a reasonably good description of the dynamics at most latitudes and rotation rates. This semi-analytical model could be incorporated into 1D stellar evolution codes. Separately, we have carried out 1D stellar evolutionary models (with the open-source code MESA), informed by our 3D simulations, to begin studying what effects the stabilising influence of rotation (or magnetism) has on stellar structure (e.g., Ireland & Browning 2018). These results have, for example, provided constraints on the mechanisms responsible for the apparent “inflation” of some low-mass stars, which seem to be systematically larger than standard (non-rotating, non-magnetic) models predict.
