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 less than or similar to R less than or similar to 100 kpc and weak lensing (100 less than or similar to R less than or similar to 1000 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 similar to 11.7 +/- 0.6. 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 similar to 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 similar to 13 degrees). 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.