Description

Neutron stars are extremely dense objects that form after supernova explosions in massive stars. They rotate very fast, spinning up to about a thousand times a second. Most of our understanding about neutron stars comes by observing radiation that is created by the combined effect of their magnetic field and rapid rotation.

This project will explore the structure of the magnetic field in the interior and magnetosphere of a neutron star. We will explore equilibrium solutions and conditions under which these solutions evolve with time. The simplest models resemble the magnetic field outside a rapidly rotating magnet in vacuum, while things can become very complicated if the currents that flow in the magnetosphere or the evolution of the field inside the star are taken into account. This is because of relativistic and non-linear effects that become important once we start considering more realistic approximations.

The twisted magnetic field outside a strongly magnetised neutron star.

We will start by reviewing the equations that govern the magnetic field in neutron stars understanding the standard solutions. Then, there exist many possibilities for students to specialise, using input from current research. Numerically inclined students may explore computational solutions with magnetic fields whose structure is more complicated than the dipole that is usually assumed. Students more interested in theory may consider developing analytical approximate solutions looking for oscillations and instabilities of the magnetic field. These could be related to observed phenomena of bursts and flares that are sometime seen in strongly magnetised neutron stars.

Prerequisites

Analysis in Many Variables II (or Mathematical Methods in Physics) is essential. Special Relativity & Electromagnetism II would be useful. Mathematical Modelling II would be useful if you are interested in numerical solutions.

Resources

We will start with chapter 13 of Stellar magnetism by Leon Mestel, Oxford University Press, 2003.

We will review the paper on The electromagnetic fields of an idealized star in rigid rotation in vacuo by A. Deutsch.