The magneto-rotational instability: from accretion disks to stars and planets?

Image: measurements of solar “torsional oscillations,” showing that these begin near the surface.  [Vasil et al. 2024, Nature, https://www.nature.com/articles/s41586-024-07315-1] As background, try the accompanying “News & Views” article by Ellen Zweibel: https://www.nature.com/articles/d41586-024-01357-1

Supervisor: Professor Matthew Browning

Note: I am interested in fluid dynamics in stars and planets generally, and open to working on a wide array of topics with interested students; if there is something you really want to do, by all means contact me (m.k.m.browning@exeter.ac.uk) to discuss it.  But here’s an example project:

The magneto-rotational instability (MRI) is a powerful instability that occurs when a magnetic field threads through a region which has angular velocity decreasing (with increasing distance from the axis of rotation).  In the context of accretion disks around compact objects, it has been studied for decades, and is now generally thought to be one of the principal drivers of turbulence in such disks — and this turbulence, ultimately, is what allows them to accrete. 

Very recently, it has been suggested by Vasil et al. 2024 (Nature) that the Sun’s magnetic field is also partly shaped by the MRI.  In this case, the instability would be acting in what is called the “near surface shear layer,” in the outer portions of the Sun’s convection zone.  This is a dramatic departure from the conventional wisdom, which holds that the magnetic field is generated much deeper in the interior.  If it holds, it would have deep implications for how we understand — and ultimately predict — Solar magnetic activity, which can have major impacts here on Earth.  Vasil et al. show that some aspects of MRI-driven field evolution match the Sun’s observed magnetic activity remarkably well.

In this project, you will conduct the first examination of the consequences of this idea for other stars and planets (and also check whether this idea can really work in the Sun!).  Because this is such a new topic, there are many ways the project could go.  At minimum, I would like us to understand what the “MRI-driven dynamo” would predict for magnetism in stars of different masses and rotation rates.  We have strong observational constraints on these stars’ magnetic activity (for example, on the relation between stellar rotation rate and activity cycle period), so we will determine whether these match the MRI-dynamo predictions.  We will use both analytical methods and numerical simulations with the open-source software package Dedalus.   Separately, we will also investigate (using numerical simulations and analytical theory) how the MRI “modes” interact with the (generally much faster) convective motions that also occur in the Sun.  Naively, you might expect that the fastest instability (in this case convection) would “win,” leaving not much trace of the MRI behaviour — so we might test this idea by varying simulation parameters to alter the growth rates of the MRI and convective instabilities (possibly alongside other effects, like baroclinic instability).   Finally, we will also explore whether similar MRI-driven dynamos might operate in the interiors of gas giant planets, and if so what the resulting magnetism might look like. 

This project would be most suitable for students who are comfortable with mathematics, and who have an interest in astrophysical fluid dynamics (ideally, stars and planets in particular). Some programming experience (with Python) would also be helpful. My advice would be  to read the papers below and see if you find them interesting (and/or terrifying!) to decide if this project is for you.