Turbulence and Mixing in the Intracluster Medium

Clusters of galaxies are the most massive gravitational entities in the universe (~10^{14} solar masses, dominated by the dark matter). The typical virial temperature (kT~GM/r) is ~ 1-10 keV, and the typical electron number density varies from ~ 0.001 /cc at outer radii to ~ 0.1 /cc in cluster cores. With this density and temperature, cooling time for most cluster cores is < Gyr, significantly shorter than the cluster lifetime. Thus, it was expected that the cluster cores will be cold (<< 1 keV) and dense. However, X-ray observations showed a drastic lack of cold plasma in cluster cores. This lack of cold plasma can only be explained only if there is an additional source of heating in cluster cores.

Two main classes of plasma heating have been proposed: first, the feedback heating mechanisms where heating is tightly coupled with cooling; and second, models where heating is basically independent of cooling. While heating by the central AGN due to accretion of cooling plasma is an example of the first class, heating due to thermal conduction from outer radii is an example of the second type. Both heating mechanisms are energetically feasible, but the real problem is to understand, in detail, how heating prevents cooling over ~ Hubble time. This is the still unresolved cooling flow problem.

The AGN feedback model is an attractive solution to the cooling flow problem but how, in detail, the accretion energy couples isotropically to the cooling ICM is unknown. Cosmic rays, produced by the AGN jets interacting with the ICM, have been proposed as a source of heating. Two mechanisms for heating, due to the damping of Alfven waves excited by cosmic rays, and due to turbulence driven by cosmic rays have been studied in some detail.

Stress To better understand cluster transport properties (mixing of metals and cosmic rays, turbulent velocities, etc.) we simulated (in 3D) a typical ICM with a centrally concentrated cosmic ray source term. Figure on right shows different timescales in the initial hydrostatic equilibrium. The spatial distribution of cosmic rays is poorly constrained so we use a simple isotropic cosmic ray source term. We do not include cooling; our focus here is on transport in cluster cores and not the cooling flow problem. Stress The Fig. on left shows a phi=constant snapshot of turbulent velocity with (left) and without (right) cosmic rays. Turbulent velocities~ 100 km/s are achieved in inner few tens of kpc with cosmic rays. Large turbulent velocities result in turbulent diffusion of metals with a diffusion coefficient~ 10^{29} cm^2/s. Turbulence is usually invoked to explain the broader distribution of metals as compared to the stellar light.

Cosmic rays, with entropy decreasing with radius, are able to mix inner cluster core when cosmic ray pressure is >~ 0.25 plasma pressure. The mechanism is analogous to Schwarzschild's convective instability in stars, but convection is driven by adiabatic (i.e., not diffusive; cosmic rays are likely to be effectively adiabatic due to scattering by self-excited magnetic irregularities) cosmic rays. This is different from weak convection in anisotropically conducting stratified plasmas, which shuts itself off by magnetic field reorientation.

The buoyancy force in a dilute plasma conducting heat along field lines is governed by temperature gradient and not by the usual entropy gradient. Thus, it is easier to mix the ICM, where temperature is rather smooth compared to the extremely stable entropy gradient. Check out the movies for comparison of convection (driven by cosmic rays confined in a narrow polar angle) and mixing in adiabatic and thermally conducting plasmas.

In this conference paper we show that forced convection (in contrast to natural convection [HBI/MTI] in anisotropically conducting plasmas) can be much more vigorous in a conducting ICM than in an adiabatic one. We argue that the anisotropic instabilities should be thought more of as buoyancy instabilities that relaxes the anisotropically conducting plasma to its stable state (horizontal field lines when dT/dz>0 and vertical field lines when dT/dz<0), rather than as convective intabilities. It is shown that a small disturbance in the saturated state of an anisotropically conducting plasma is stable, much like in a stably stratified adiabatic plasma. The mixing in anisotropically conducting and stably stratified adiabatic plasmas can be understood in terms of the Richardson number , the ratio of the stabilizing buoyancy force and the turbulent force (keeping in mind that the stable buoyancy force with anisotropically conducting plasma scales as dlnT/dz and for adiabatic plasma as dlnS/dz, where T is the tempearture and S=p/d^1.6666 is the entropy). Turbulent mixing is efficient when Ri< a critical value close to 1.

References:


Buoyancy Instabilities in Galaxy Clusters: Convection Due to Adiabatic Cosmic Rays and Anisotropic Thermal Conduction
Turbulence and Mixing in the Intracluster Medium