Thermal conduction in cosmological SPH simulations

Thermal conduction in the intracluster medium has been proposed as a possible heating mechanism for offsetting central cooling losses in rich clusters of galaxies. However, because of the coupled non-linear dynamics of gas subject to radiative cooling and thermal conduction, cosmological hydrodynamical simulations are required to predict reliably the effects of heat conduction on structure formation. In this study, we introduce a new formalism to model conduction in a diffuse ionized plasma using smoothed particle hydrodynamics (SPH), and we implement it in the parallel TreePM/SPH-code GADGET-2. We consider only isotropic conduction and assume that magnetic suppression can be described in terms of an effective conductivity, taken as a fixed fraction of the temperature-dependent Spitzer rate. We also account for saturation effects in low-density gas. Our formulation manifestly conserves thermal energy even for individual and adaptive time-steps, and is stable in the presence of small-scale temperature noise. This allows us to evolve the thermal diffusion equation with an explicit time integration scheme along with the ordinary hydrodynamics. We use a series of simple test problems to demonstrate the robustness and accuracy of our method. We then apply our code to spherically symmetric realizations of clusters, constructed under the assumptions of hydrostatic equilibrium and a local balance between conduction and radiative cooling. While we confirm that conduction can efficiently suppress cooling flows for an extended period of time in these isolated systems, we do not find a similarly strong effect in a first set of clusters formed in self-consistent cosmological simulations. However, their temperature profiles are significantly altered by conduction, as is the X-ray luminosity.