# Angular momentum transport and magnetism in stars and planets [Browning 2021]

## Angular momentum transport and magnetism in stars and planets

**Supervisor**: Professor Matthew Browning

In general, I am happy to supervise a variety of potential projects that deal with the fluid dynamics of stellar or planetary interiors in one way or another. Most projects with me would involve some large-scale numerical simulation and analytical theory, which we would aim to compare to relevant observations.

When motions occur inside a star or planet, they can transport both heat and angular momentum. Because these motions — whether convective, wave-like, or some mix of the two — are ubiquitous, so is angular momentum transport. As a consequence, different parts of planetary and stellar interiors often rotate at different rates, with profound consequences for the mixing of material, the generation of stellar and planetary magnetism, and the end-states of stellar evolution. The spin rates of massive stellar cores, for example, may influence the nature of the compact remnant that occurs after core collapse, and strongly affect the natal spin rates of black holes, now being probed by gravitational wave astronomy.

Recent observations have revealed that our current theoretical understanding of the angular momentum transport — and hence of differential rotation — has some major shortcomings. For example, asteroseismic measurements of the rotation rates of stars have demonstrated that evolved stellar cores rotate much slower than simple theoretical models of the transport would predict. Major puzzles have come from observations of objects in our own Solar System, too: for example, the Juno mission has recently revealed that Jupiter's observed banded zonal flows persist only throughout the outermost few percent of the planet, with a transition to nearly solid-body rotation below this. This has been widely interpreted as arising from magnetic field feedbacks on the flow, with the observed transition to solid-body rotation occurring at roughly the depth where the conductivity becomes high enough for the field to couple to the motion. This is in sharp contrast to the Sun, where conductivity is high throughout and yet a substantial shear is maintained. The different outcomes likely reflect the different regimes of flow speed and rotation rate in the two objects -- but a consistent theory of angular momentum transport in magnetised convection zones that can explain both outcomes in any detail has not yet been forthcoming.

In this project, you will use a combination of 3D numerical simulations, analytical theory, and 1D modeling to study the angular momentum transport achieved by flows in stellar and planetary interiors. Along the way, you will study the magnetic fields that are generated by the flows (and which in turn also affect the momentum transport). Your precise role will depend to some extent on your own background and interests. Between us (i.e., you, me, and various collaborators), we will aim to conduct a set of 3D simulations in both local (Cartesian) and global (spherical) geometries, and compare the resulting transport to that envisioned in recently-developed semi-analytical theories. This will involve using massively parallel computers based here in Exeter, and elsewhere. We will use the simulations to test and calibrate the semi-analytical prescriptions, and ultimately attempt to incorporate these into a 1D evolutionary model of structure and evolution. We may also, more speculatively, explore the possibility that the heat and angular momentum transport, and field generation, can be solved for self-consistently, in parallel with the evolutionary calculation, essentially by solving a highly simplified set of fluid equations for a finite number of spatial modes.

This project would be most suitable for someone with an interest in astrophysical fluid dynamics, as applied to stars or planets. It will require some level of proficiency with computation, so at least a modest amount of programming experience (and a basic familiarity with Unix-based environments) would be helpful. Some prior familiarity with fluid dynamics/MHD would be great, but is not essential.

**Background reading** (and about my work generally):

An example of some observational/theoretical motivation for this project:

— Fuller, Piro, and Jermyn (2019), “Slowing the spins of stellar cores,” MNRAS 485, 3661

General background on stellar fluid dynamics, magnetism, etc:

—Brun & Browning (2017), “Magnetism, dynamo action, and the solar-stellar connection,” Living Reviews in Solar Physics, 14, 4

An example paper about local-scale calculations:

— Currie, Barker, Lithwick, Browning (2020), “Convection with misaligned gravity and rotation: simulations and rotating mixing length theory,” MNRAS 493, 5233

An example of global-scale calculations:

— Duarte, Wicht, Browning, Gastine (2016), “Helicity inversion in spherical convection as a means for equatorward dynamo wave propagation,” MNRAS 456, 1708

An example of 1D modeling informed by theory/simulations:

— Ireland & Browning (2018), “The radius and entropy of a magnetized, rotating, fully convective star: analysis with depth-dependent mixing length theories,” ApJ 856, 132