Now, imagine how a bubble is inflated by the AGN, detaches and rises upwards through the surrounding intracluster medium. There is a buoyant upwards force on the bubble equal to the weight of displaced external medium minus the bubble's own weight, and a detached bubble will reach a terminal velocity where this force is balanced by aerodynamic drag. While the bubble is being inflated, if its volume is increasing at a constant rate then bubble's radius will increase in time as t^(1/3), so that the 'expansion velocity' goes at t^(-2/3), i.e. the expansion slows down. Once the expansion velocity drops below the terminal velocity, the bubble detaches from the parent AGN and floats upwards.
The Perseus galaxy cluster in X rays. Bubbles can reach a significant distance from their origin without breaking up.
It is seen in hydro simulations of rising bubbles that the velocity shear at the bubble boundary is unstable, and that the top of the bubble is subject to the Rayleigh-Tayler instability as the less dense gas is pushed against the denser surroundings. This results in disintegration of the bubble once the bubble has risen by a distance equal to its own radius. This, however, is contrary to observations of intact bubbles located at larges distances from their parent AGN. An obvious candidate for preventing this bubble shredding is a magnetic field, which could inhibit these instabilities. One might expect the bubble to contain an initially disordered magnetic field which reconnects to form a `helical ball' which stabilises the bubble. Preliminary calculations suggest that the formation of a helical ball takes place on somewhat less than the buoyant-rise timescale of the bubble. Numerical simulations can be used to resolve this problem, first without and then with gravity and an accompanying stratification of the external intergalactic medium. This should shed some light on, amongst other things, the process of chemical and magnetic enrichment of the primordial gas and more generally on the formation and evolution of galaxy clusters and on the history of star formation. Moreover, this work should answer a more fundamental question: what happens to a magnetised region embedded in a non-magnetised region, how does the magnetic reconnection process proceed and what is the end result? In this project, the student will use a mixture of analytic and numerical methods to investigate this process of magnetic relaxation in bubbles, using the results to make predictions about the stability and composition of these large bubbles which can be tested with radio observations over the next few years.