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

Abstract

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.

Thermal Conduction in Clusters of Galaxies

“…Only in the inner regions of some clusters (e.g., 3C 295; see Table 1) might there be significant dropout. It is worth noting that some authors have discussed potential problems with invoking such strong conduction (Binney & Cowie 1981;Bregman & David 1988), while others have rebutted these arguments (Rosner & Tucker 1989;Dos Santos 2001). …”

“…The inner region of a cluster (R ∼ few ×10 kpc) where mass dropout appears to be occurring is typically cooler than the rest of the cluster. Therefore, an often-discussed source of heat is thermal conduction from the hot outer regions of the cluster to the center (Binney & Cowie 1981;Tucker & Rosner 1983;Bertschinger & Meiksin 1986;Bregman & David 1988;Gaetz 1989;Rosner & Tucker 1989;Pistinner & Shaviv 1996;Santos 2001). While the idea is attractive, it requires extremely efficient conduction, which is considered problematic.…”

Competition between shocks and entropy floor: Unifying groups and clusters of galaxies

“…To this purpose, we will use a semi-analytic model (hereafter SAM) developped independently by one of us (Dos Santos 2001, in preparation). This particular model uses the conduction-structured temperature profile (which was shown by Dos Santos (2001) to describe very well the temperature and surface brightness profile of clusters of galaxies), together with an NFW profile for the dark matter density profile. A shock model at the virial radius, together with entropic constraints at the center allow to predict the temperature profile without the hypothesis of isothermality or the unphysical polytropic link between temperature and density.…”

Are X-ray clusters cooled by heat conduction to the surrounding intergalactic medium?

“…Recently, the old idea that heat conduction may suppress cooling flows in X-ray clusters (Binney & Cowie 1981;Tucker & Rosner 1983;Bertschinger & Meiksin 1986;Bregman & David 1988;Gaetz 1989;Rosner & Tucker 1989;David et al 1992;Pistinner & Shaviv 1996;Dos Santos 2001) has been revived due to the apparent lack of strong cooling flows in Chandra and XMM-Newton data (Fabian et al 2001;Böhringer et al 2001;Molendi & Pizolato 2001). It was argued that if the heat conductivity is not suppressed by more than a factor of a few relative to the Spitzer value, then the inward heat flow due to the positive temperature gradient in cluster cores would be sufficient to compensate for the energy loss caused by Bremsstrahlung cooling of the gas (Narayan & Medvedev 2001;Gruzinov 2002;Voigt et al 2002).…”