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 con duction. Neglecting cooling and heating terms, the stationary energy conser vation equation reduces to a second-order differential equation, the resolu tion of which requires two boundary conditions, taken here as the inner rad ius and the ratio between the inner and outer temperature. Thus a two-param eter family of analytical models for the TP is obtained. Once these two con stants are chosen, the TP has a fixed analytical expression, which reproduc es nicely the observed 'universal' TP obtained by Markevitch et al. from AS CA data. Using observed X-ray surface brightnesses for two hot clusters wit h spatially resolved TP, the local polytropic index and the hot gas fractio n 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 struct ure of galactic or cluster haloes in numerical simulations of collisionless matter. With the forthcoming availability of spatially resolved high-quali ty spectroscopic data, the predicted shape of the TP (related to the temper ature dependence of the heat flux for a collisionally ionized plasma) will be tested directly against observations.