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 up to ~1700 kpc, equivalent to ~0.7 r_200. The gas distribution is well described by a beta model in the outer regions, but is more concentrated in the inner ~250 kpc. We introduce a new parameterisation for the inner regions, allowing a steeper gas density distribution. The projected radial temperature profile declines gradually towards the outer regions, by ~20% between 0.1 r_200 and 0.5 r_200, and 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 (HE) 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. The mass profile is remarkably well fitted with the Moore et al. (1999) parameterisation with a concentration parameter in the range expected from numerical simulations. There are several indications that beyond a density contrast delta \~600, the gas may no longer be in HE. There is an offset with respect to adiabatic numerical simulations in the virialised part of the cluster, in that the predicted mass for the cluster temperature is ~40% 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 ~ 0.2. These data strongly support the validity of the current approach for the modelling of the dark matter collapse, but confirm that understanding the gas specific physics is essential. (Abridged)