1 Introduction

The simple first-order formation scenario for galaxy clusters, in which they grow through the gravitational infall and subsequent merging of smaller subunits, provides a remarkably good description of the large-scale properties of these objects. Within this hierarchical model, the gas trapped in the potential well of a cluster is heated to the observed X-ray emitting temperatures by the shocks due to the formation process; merger features in the gas distribution are then erased in roughly a sound crossing time ($\sim$few Gyr), leaving the gas in hydrostatic equilibrium (HE).

Observation of this gas is a powerful tool for uncovering the physical characteristics and formation history of a cluster. Substructure in X-ray images, combined with optical data, can give clues to the dynamical state (e.g., Buote 2001). Direct (temperature maps) and indirect (hardness ratio maps) methods can give an indication of where (and if) interactions and mergers are still occurring (e.g., Markevitch et al. 1999; Neumann et al. 2001). In addition, for clusters in reasonably relaxed state, the assumption of HE and spherical symmetry allow the derivation of the spatial distribution of both the gas and total cluster mass by using the information from the X-ray surface brightness and temperature profiles. This approach, which is of fundamental use in cluster studies, has been shown to give masses which are accurate to about $\pm 20\%$ when applied to simulated clusters (e.g., Evrard et al. 1996 (EMN96); Schindler 1996).

Numerical simulations based on gravitational collapse are an essential counterpoint to the observations, being as they are ideal scenarios with exactly measurable quantities, thus offering a direct comparison with the real data. A crucial result from these simulations is the suggestion that CDM haloes with masses spanning several orders of magnitude follow a universal density profile independent of halo mass or cosmology (Navarro et al. 1997 (NFW)). As the X-ray emitting gas lies in the potential well of the CDM halo, this suggests that many directly measurable cluster properties should display self-similarity. This is observationally testable and indeed, regularity in the local cluster population has been found in previous ROSAT, ASCA and BeppoSAX studies, where the gas density and temperature profiles of hot, relaxed clusters do appear similar when scaled to units of the virial radius (Markevitch et al. 1998; Neumann & Arnaud 1999; Vikhlinin et al. 1999; Irwin & Bregman 2000; De Grandi & Molendi 2002; Arnaud et al. 2002). The very existence of these similarities gives strong support to an underlying universality in the dark matter distribution, leading to a pleasing convergence between the observed and simulated properties of galaxy clusters.

However, the temperature profiles in particular have generated much discussion, as rather different profile shapes have been found for similar samples observed by the same satellite (e.g., Markevitch et al. 1998; White 2000 (ASCA); Irwin & Bregman 2000; De Grandi & Molendi 2002 (BeppoSAX)). These studies have been hampered somewhat by both PSF issues and sensitivity limits. The former has an inevitable effect on the spatial resolution and is a possible source of systematic uncertainty, the derivation of the profiles being potentially sensitive to the exact correction for the PSF and the detailed modelling of the non-resolved cooling flow component. The latter leads to an inability really to constrain parameters beyond the supposedly isothermal regime, which is expected, from simulations, to extend to $\sim$ 0.5 r₂₀₀. As a direct consequence of this, there are relatively few galaxy clusters for which sufficiently high quality data were available for an accurate determination of the total mass and the corresponding density profile. Furthermore, any systematic uncertainty in the shape of the radial temperature distribution can have a direct effect on the derived mass. For example, the temperature profile obtained by Markevitch et al. (1998) gives mass values that are 1.35 and 0.7 times that derived assuming isothermality at 1 and 6 core radii respectively. As a result, the actual form of the density profile is still a largely untested quantity, at least from an observational point of view.

Clusters can also be used to provide cosmological constraints. For any given cosmology and initial density fluctuation, the mass distribution of virialized objects can be predicted for any given redshift. Constraints on cosmological parameters, $\sigma_{8}$ and $\Omega$, can be found by comparing the predictions with the observed cluster mass function and its evolution (Perrenod 1980). For this, however, a great number of accurate observational masses are needed. In the calculation of the observed cluster mass function, the standard way to overcome the paucity of data is to use average cluster temperatures, taking advantage of the tight mass-temperature relation predicted by numerical simulations, where $M \propto T^{3/2}$ (e.g., EMN96). While observations have, for hot clusters at least, recovered the slope of this relation, observed masses imply a normalisation consistently lower than found by simulations (e.g., Horner et al. 1999; Nevalainen et al. 2000; Finoguenov et al. 2001). However, these total cluster mass estimates, except in a few cases, required an extrapolation of the data and the level of the discrepancy is sensitive to the assumed temperature profile (e.g. see Horner et al. 1999; Neumann & Arnaud 1999).

XMM-Newton and Chandra offer, for the first time, sufficiently good spatial and spectral resolution for self-consistent determinations of global cluster observables such as gas density, temperature and mass profiles. We are now observing clusters with unsurpassed clarity. Chandra, with higher resolution, is the instrument best-suited for the study of cluster cores. In the most recent Chandra study by Allen et al. (2001a), mass-temperature data from 6 clusters are measured up to r ₂₅₀₀, and compared to the reference simulations of EMN96 and Mathiesen & Evrard (2001). Once again, a systematic offset of $\sim$$40\%$ is found between the observed and simulated M-T curves, in the sense that the predicted temperatures are too low for a given mass. XMM-Newton, with its high throughput and large field of view, is the satellite best-matched for the study of the larger scale structure of these objects, and for the determination of essential quantities out to a good fraction of the virial radius. With this capability it is possible to test for other effects, such as potential variations of the normalisation with radius.

In this paper, we use XMM-Newton observations of the relaxed cluster A1413 at z = 0.143 to derive the large scale properties to high resolution, and compare the results to those obtained from both observations and simulations. We address several questions which have been the subject of a large amount of debate in the literature. In particular, we compare our temperature profile with previously derived composite profiles from large samples observed with ASCA and BeppoSAX, and we compare both the form and normalisation of our mass profile with that expected from numerical simulations.

Throughout this paper we use H₀ = 50 km s^-1 Mpc^-1, and unless otherwise stated, $\Omega_{\rm m} = 1$ and $\Omega_\Lambda = 0$(q₀ = 0.5). In this cosmology, at the cluster redshift of z = 0.143, one arcminute corresponds to 196 kpc.