Thermal Conduction and Particle Transport in Strong Magnetohydrodynamic Turbulence, with Application to Galaxy Cluster Plasmas

• Published in: The Astrophysical journal 2004-02, Vol.602 (1), p.170-180
• Main Authors: Chandran, Benjamin D. G, Maron, Jason L
• Format: Article
• Language: English
• ISSN: 0004-637X; 1538-4357
• DOI: 10.1086/380897

Galaxy clusters possess turbulent magnetic fields with a dominant scale length l[sub]B ~ 1-10 kpc. In the static magnetic field approximation, the thermal conductivity Kappa [sub]T for heat transport over distances >l[sub]B in clusters is ~ Kappa [sub]Sl[sub]B/L[sub]S(rho[sub]e), where Kappa [sub]S is the Spitzer thermal conductivity for a nonmagnetized plasma, the length L[sub]S(r[sub]0) is a characteristic distance that a pair of field lines separated by a distance r[sub]0 < l[sub]B at one location must be followed before they separate by a distance l[sub]B, and rho[sub]e is the electron gyroradius. We introduce an analytic Fokker-Planck model and a numerical Monte Carlo model of field-line separation in strong magnetohydrodynamic (MHD) turbulence to calculate L[sub]S(r[sub]0). We also determine L[sub]S(r[sub]0) using direct numerical simulations of MHD turbulence with zero mean magnetic field. All three approaches, like earlier models, predict that L[sub]S asymptotes to a value of order several l[sub]B as r[sub]0 is decreased toward l[sub]d in the large- l[sub]B/l[sub]d limit, where l[sub]d is the dissipation scale, which is taken to be the proton gyroradius. When the turbulence parameters used in the Fokker-Planck and Monte Carlo models are evaluated using direct numerical simulations, the Fokker-Planck model yields L[sub]S(rho[sub]e) ~ 4.5l[sub]B and the Monte Carlo model yields L[sub]S(rho[sub]e) ~ 6.5l[sub]B in the large- l[sub]B/l[sub]d limit. Extrapolating from our direct numerical simulations to the large-l[sub]B/l[sub]d limit, we find that L[sub]S(rho[sub]e) ~ 5l[sub]B-10l[sub]B, implying that Kappa [sub]T ~ 0.1 Kappa [sub]S-0.2 Kappa [sub]S in galaxy clusters in the static field approximation. We also discuss the phenomenology of thermal conduction and particle diffusion in the presence of time-varying turbulent magnetic fields. Under the questionable assumption that turbulent resistivity completely reconnects field lines on the timescale l[sub]B/u, where u is the rms turbulent velocity, we find that Kappa [sub]T is enhanced by a moderate amount relative to the static field estimate for typical cluster conditions.