Thermal conduction in the stochastic magnetic fields in clusters of galaxies
Abstract
We consider two effects that reduce electron thermal conduction in the stochastic magnetic fields in clusters of galaxies. First, the parallel conduction along magnetic field lines may be reduced because the heat conducting electrons become trapped and detrapped between regions of strong magnetic field (magnetic mirrors). This problem reduces to a simple but realistic model for parallel diffusion of monoenergetic electrons based on the fact that when there is a reduction of diffusion, it is controlled by a subset of the mirrors, the principle mirrors. The reduction of parallel diffusion can be considered as equivalent to an enhancement of the pitch angle scattering rate. Therefore, in deriving the full perturbed electronelectron and electronproton collision integral, we modify the pitch angle scattering term, and then find the effective parallel thermal conductivity as a function of the ratio of the magnetic field decorrelation length l_{0} to the electron mean free path at the electron thermal speed V_{T=√ {2kT/m_e}}. The second effect is that conducting electrons have to travel along tangled magnetic field lines, and as a result, they have to go larger distances between hot and cold regions of space. This effect leads to further reduction of electron thermal conduction, which is given by the product of (l_{0/X_0)2} and a function of a single parameter β =2(X_{0/l_0) <} B>big /<δ B>. Here, X_{0} is the cluster size (or the temperature gradient scale), < B> is the mean magnetic field component (assumed to be homogeneous), and <δ B> is the averaged absolute value of the random field component. We discuss the application of our final results to clusters of galaxies. Leonid Malyshkin would like to thank the Department of Astrophysical Sciences at Princeton University and Professor Bruce Draine for financial support.
 Publication:

American Astronomical Society Meeting Abstracts
 Pub Date:
 December 2000
 Bibcode:
 2000AAS...197.8906M