The steady-state conduction-driven temperature profile in clusters of galaxies

In this paper, I present a theoretical model of a relaxed cluster where the temperature profile (hereafter TP) is structured by electronic thermal conduction. Neglecting cooling and heating terms, the stationary energy conservation equation reduces to a second-order differential equation, the resolution of which requires two boundary conditions, taken here as the inner radius and the ratio between the inner and outer temperature. Thus a two-parameter family of analytical models for the TP is obtained. Once these two constants are chosen, the TP has a fixed analytical expression, which reproduces nicely the observed 'universal' TP obtained by Markevitch et al. from ASCA data. Using observed X-ray surface brightnesses for two hot clusters with spatially resolved TP, the local polytropic index and the hot gas fraction profile are predicted and compared with ASCA observations (Markevitch et al. 1999). Moreover, the total density profile derived from observed X-ray surface brightness, hydrostatic equilibrium and the conduction-driven TP is very well fitted by three analytical profiles found to describe the structure of galactic or cluster haloes in numerical simulations of collisionless matter. With the forthcoming availability of spatially resolved high-quality spectroscopic data, the predicted shape of the TP (related to the temperature dependence of the heat flux for a collisionally ionized plasma) will be tested directly against observations.