Thermal Instability with Anisotropic Thermal Conduction and Adiabatic Cosmic Rays: Implications for Cold Filaments in Galaxy Clusters

Observations of the cores of nearby galaxy clusters show H$\alpha$ and molecular emission line filaments. We argue that these are the result of {\em local} thermal instability in a {\em globally} stable galaxy cluster core. We present local, high resolution, two-dimensional magnetohydrodynamic simulations of thermal instability for conditions appropriate to the intracluster medium (ICM); the simulations include thermal conduction along magnetic field lines and adiabatic cosmic rays. Thermal conduction suppresses thermal instability along magnetic field lines on scales smaller than the Field length ($\gtrsim$10 kpc for the hot, diffuse ICM). We show that the Field length in the cold medium must be resolved both along and perpendicular to the magnetic field in order to obtain numerically converged results. Because of negligible conduction perpendicular to the magnetic field, thermal instability leads to fine scale structure in the perpendicular direction. Filaments of cold gas along magnetic field lines are thus a natural consequence of thermal instability with anisotropic thermal conduction. Nonlinearly, filaments of cold ($\sim 10^4$ K) gas should have lengths (along the magnetic field) comparable to the Field length in the cold medium $\sim 10^{-4}$ pc! Observations show, however, that the atomic filaments in clusters are far more extended, $\sim 10$ kpc. Cosmic ray pressure support (or a small scale turbulent magnetic pressure) may resolve this discrepancy: even a small cosmic ray pressure in the diffuse ICM, $\sim 10^{-4}$ of the thermal pressure, can be adiabatically compressed to provide significant pressure support in cold filaments. This is qualitatively consistent with the large population of cosmic rays invoked to explain the atomic and molecular line ratios observed in filaments.