The mass profile of A1413 observed with XMM-Newton:: Implications for the M-T relation

We present an XMM-Newton observation of A1413, a hot (kT = 6.5 keV) galaxy cluster at z = 0.143. We construct gas and temperature profiles over the radial range up to similar to1700 kpc. This radius corresponds to a density contrast delta similar to 500 with respect to the critical density at the redshift of the cluster, or equivalently similar to0.7r(200). The gas distribution is well described by a beta model in the outer regions, but is more concentrated in the inner similar to250 kpc. We introduce a new parameterisation for the inner regions, which allows a steeper gas density distribution. The radial temperature profile does not exhibit a sharp drop, but rather declines gradually towards the outer regions, by similar to20% between 0.1r(200) and 0.5r(200). The projected temperature profile is well described by a polytropic model with gamma = 1.07 +/- 0.01. We find that neither projection nor PSF effects change substantially the form of the temperature profile. Assuming hydrostatic equilibrium and spherical symmetry, we use the observed temperature profile and the new parametric form for the gas density profile to produce the total mass distribution of the cluster. The mass profile is remarkably well fitted with the Moore et al. (1999) parameterisation, implying a very centrally peaked matter distribution. The concentration parameter is in the range expected from numerical simulations. There are several indications that beyond a density contrast delta similar to 600, the gas may no longer be in hydrostatic equilibrium. There is an offset with respect to adiabatic numerical simulations in the virialised part of the cluster, in the sense that the predicted mass for the cluster temperature is similar to40% too high. The gas distribution is peaked in the centre primarily as a result of the cusp in the dark matter profile. The X-ray gas to total mass ratio rises with increasing radius to f(gas) similar to 0.2. These data strongly support the validity of the current approach for the modeling of the dark matter collapse, but confirm that understanding the gas specific physics is essential.