GRAVITATIONAL LENSING BY A CLUSTER OF GALAXIES AND THE CENTRAL CD GALAXY - MEASURING THE MASS PROFILE

We study the constraints on the density profile of the mass in a clust er of galaxies that can be obtained when a radial are produced by grav itational lensing is observed. We apply this to the cluster MS 2137-23 , which contains a radial are, a tangential are, and three other arcle ts. As shown by Mellier and coworkers, the positions and elongations o f all these five images are well reproduced as arising from two differ ent background galaxies, if the mass distribution in the cluster is el liptical, is exactly centered on the brightest duster galaxy, and has the same ellipticity and position angle as this galaxy. The galaxy is therefore identified as the center of the cluster potential well. We s how that the ratio theta(r)/theta(i) of the distance from the radial a re to the center of the cluster to the distance from the other image o f the same source to the center gives a powerful constraint on the for m of the dark matter density profile. Models that are favored have wel l-defined core radii of similar to 30 h(-1) kpc, with the slope changi ng rapidly from almost flat to roughly isothermal around this radius. Density profiles that remain steeper than r(-1) all the way to the cen ter are probably ruled out, since they predict theta(r)/theta(i) to be smaller than observed. We also show that theta(r)/theta(i) is signifi cantly affected by the mass in stars in the central galaxy. The stella r mass tends to move the radial are closer to the center, since its pr ofile is very steep. This implies an upper limit to the mass-to-light ratio of the stars, similar to the dynamical measurements of the mass- to-light ratio of elliptical galaxies. The constraints on the profile will be improved once the position of the radial are is measured more accurately and the are redshifts are determined. All the models for th e density profile that are consistent with the observed position of th e radial are predict a velocity dispersion for the cluster galaxies of similar to 1200 km s(-1) and a central velocity dispersion for the st ars of similar to 350 km s(-1), consistent with the observed velocity dispersions in other cD galaxies. The models also predict that the vel ocity dispersion of the cD halo should rise rapidly with radius and th at the two sources producing the five arcs should be at similar redshi fts. This can be tested by future observations.