Projection effects in cluster mass estimates: the case of MS2137-23

We revisit the mass properties of the lensing cluster of galaxies MS2137-23 and assess the mutual agreement between cluster mass estimates based on strong/weak lensing, X-rays and stellar dynamics. We perform a thorough elliptical lens modelling using arcs and their counter-images in the range $20\lesssim R\lesssim100$ kpc and weak lensing ($100\lesssim R\lesssim1000$ kpc). We confirm that the dark matter distribution is consistent with an NFW profile (Navarro et al., 1997, ApJ, 490, 493) with high concentration $c\sim11.7\pm0.6$. We further analyse stellar kinematics data with a detailed modelling of the line-of-sight velocity distribution (LOSVD) of stars in the cD galaxy and quantify the small bias due to the non-Gaussian shape of the LOSVD. After correction, the NFW lens model is unable to properly fit kinematical data and is a factor of ~2 more massive than suggested by X-rays analysis. The discrepancy between projected (lensing) and tridimensional (X-rays, dynamics) mass estimates is studied by assuming prolate (triaxial) halos with the major axis oriented toward the line-of-sight. This model well explains the high concentration and the misalignement between stellar and dark matter components $(\Delta \psi \sim 13^\circ)$. We then calculate the systematic and statistical uncertainties in the relative normalization between the cylindric $M_2({<}r)$ and spherical $M_3({<}r)$ mass estimates for triaxial halos. These uncertainties prevent any attempt to couple 2D and 3D constraints without undertaking a complete tridimensional analysis. Such asphericity/projection effects should be a major concern for comparisons between lensing and X-rays/dynamics mass estimates