Thermal Conduction in Magnetized Turbulent Gas

Using numerical methods, we systematically study in the framework of ideal MHD the effect of magnetic fields on heat transfer within a turbulent gas. We measure the rates of passive scalar diffusion within magnetized fluids and make the comparisons a) between MHD and hydro simulations, b) between different MHD runs with different values of the external magnetic field (up to the energy equipartition value), c) between thermal conductivities parallel and perpendicular to magnetic field. We do not find apparent suppression of diffusion rates by the presence of magnetic fields, which implies that magnetic fields do not suppress heat diffusion by turbulent motions. Subject headings: turbulence – ISM: general – galaxies: clusters: general – MHD 1. astrophysical motivation It is well known that Astrophysical fluids are turbulent and that magnetic fields are dynamically important. One characteristic of the medium that magnetic fields and turbulence may substantially change is the heat transfer. There are many instances when heat transfer through thermal conductivity is important. For instance, thermal conductivity is essential in rarefied gases where radiative heat transfer is suppressed. This is exactly the situation that is present in clusters of galaxies. It is widely accepted that ubiquitous X-ray emission due to hot gas in clusters of galaxies should cool significant amounts of the intracluster medium (ICM) and this must result in cooling flows (Fabian 1994). However, observations do not support the evidence for the cool gas (see Fabian et al. 2001) which is suggestive of the existence of heating that replenishes the energy lost via X-ray emission. Heat transfer from the outer hot regions can do the job, provided that the heat transfer is sufficiently efficient. Gas in clusters of galaxies is magnetized and the conventional wisdom suggests that the magnetic fields strongly suppress thermal conduction perpendicular to their direction. Realistic magnetic fields are turbulent and the issue of the thermal conduction in such a situation has been long debated. A recent paper by Narayan & Medvedev (2001) obtained estimates for the thermal conductivity of turbulent magnetic fields, but those estimates happen to be too low to explain the absence of cooling flows for many of the clusters of galaxies (Zakamska & Narayan 2002). Narayan & Medvedev (2001) treat the turbulent magnetic fields as static. In hydrodynamical turbulence it is possible to neglect plasma turbulent motions only when the diffusion of electrons which is the product of the electron thermal velocity velect and the electron mean free path in plasma lmfp, i.e. velectlmfp, is greater than the turbulent velocity vturb times the turbulent injection scale linj , i.e. vturblinj . If such scaling estimates are applicable to heat transport in magnetized plasma, the turbulent heat transport should be accounted for heat transfer within clusters of galaxies. Indeed, data for velectlmfp given in Zakamska & Narayan (2002; Narayan &Medvedev 2001) provide the classical Spitzer (1962) diffusion coefficient κSp ≡ velectlmfp ∼ 6.2×10 cm sec for the inner region of R ∼ 100kpc and κSp ≡ velectlmfp ∼ 3.6 × 10 cm sec for the very inner region of R ∼ 10kpc (for Hydra A). If turbulence in the cluster of galaxies is of the order of the velocity dispersion of galaxies, while the injection scale is of the order of 20 kpc, the diffusion coefficient is ∼ vturblinj ∼ 3.1 × 10 cm sec, where we take vturb ∼ 500 km/sec. Earlier numerical studies by Cho, Lazarian & Vishniac (2002) revealed a good correspondence between hydrodynamic motions and motions of fluid perpendicular to the local direction of magnetic field. To what extend heat transfer in a turbulent medium is affected by a magnetic field is the subject of the present study. To solve this problem we shall systematically study the passive scalar diffusion in a magnetized turbulent medium, compare results of MHD and hydrodynamic calculations, and investigate the heat transfer perpendicular and parallel to the mean magnetic field for magnetic fields of different intensities. This work has a broad astrophysical impact. Clusters of galaxies is just one of the examples where non-radiative heat transfer is essential. This process, however, is important for many regions within galactic interstellar medium, e.g. for supernova remnants. 2. numerical methods We use a 3rd-order hybrid essentially non-oscillatory (ENO) upwind shock-capturing scheme to solve the ideal MHD equations. To reduce spurious oscillations near shocks, we combine two ENO schemes. When variables are sufficiently smooth, we use the 3rd-order Weighted ENO scheme (Jiang & Wu 1999) without characteristic mode decomposition. When the opposite is true, we use 1