Multi-Phase Fluids

Evidence is mounting that a lot of the energy released by AGN jets is funneled into sound waves that traverse the cluster and, without some form of dissipation, will take their energy with them to the outskirts of the cluster - not ideal for heating the centers of galaxy clusters.The presence of relativistic gas itself makes the the intergalactic medium (IGM) a multi-phase gas. These bubbles and filaments of hot, relativistic gas react very differently to the passage of sound and shocks waves: Their high internal sound speed makes them act like hydraulic pistons that broadcast the arrival of the wave immediately over their entire surface. They also present much lower inertia to the arriving wave. The result is that that the wave transforms a stationary bubble into a rotating vortex ring - not unlike a smoke ring.

This process of vorticity creation through the interaction of waves with multi-phase gases is known in the fluid dynamics community as the Richtmyer-Meshkov instability. We are studying the efficiency of the Richtmyer-Meshkov instability in the context of galaxy clusters using hydrodynamic and magneto-hydrodynamic simulations.

In order to calculate the energy in the vortex field, we developed an algorithm to split the velocity field into a purely potential and a purely rotational component. The former has zero vorticity, the latter has zero divergence. We can then use the vorticity equation ω=curl(curl v) to calculate the vector potential that gives the rotational velocity component, from which we calculate vrot.

The implication is that the IGM, which is filled with filaments and bubbles of relativistic plasma, is very good at converting energy carried by sound waves and shock waves into kinetic energy in a vortex field that stays behind. Dissipative processes then have much more time to act on this energy and heat the cluster gas. The amount of energy that can be extracted is directly proportional to the volume filled by relativistic plasma. We estimate that for a typical cluster, a volume filling fraction of a few percent should be sufficient to extract enough energy to heat the cluster.


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