A Weak Gravitational Lensing and X-ray Analysis of Abell 2163

We report on the detection of dark matter in the cluster of galaxies Abell~2163 using the weak gravitational distortion of background galaxies, and an analysis of the cluster X-ray emission. We find that while the qualitative distributions of the cluster light and the dark matter are similar -- shallow and extended, with significant substructure -- the X-ray morphology shows a more regular overall appearance. We interpret the joint lensing and X-ray observations as a signature of a merger event in the cluster. We present new ROSAT/HRI data and reanalyze ROSAT/PSPC data, accounting for the effect of a varying background to determine the best fit parameters in the $\beta$-model formalism. We combine the surface brightness fits with two determinations of the radial temperature profile to determine the total mass. Although there are slight variations in the total mass determinations introduced by the uncertainties in the $\beta$-fit, the main contributor to the error arises from the uncertainties in the temperature determinations. Even though the morphologies of the dark matter/light and X-ray gas are quite different, we find that the total mass determined from the X-ray and weak lensing estimates are consistent with each other within the $2\sigma$ error bars, with the X-ray inferred mass a factor of $\simeq 2$ larger. However, as the lensing mass estimates are differential (the surface density at any point is determined relative to the mean in a control annulus), the shallow, extended nature of the mass profile biases the lensing inferred mass downwards. We estimate the correction for this effect and find very good agreement between the corrected lensing and X-ray results. We determine the gas mass fraction and find $f_g \simeq 0.07h^{-3/2}$ at all radii and a constant mass-to-light ratio of $M/L_V