Cluster mass estimate and a cusp of the mass-density distribution in clusters of galaxies

We study density cusps in the center of clusters of galaxies in order to re concile X-ray mass estimates with gravitational lensing masses. For various mass-density models with cusps, we compute X-ray surface brightness distri butions and fit them to observations to measure the range of parameters in the density models. The Einstein radii estimated from these density models are compared with Einstein radii derived from the observed arcs for Abell 2 163, Abell 2218, and RX J1347.5 - 1145. The X-ray masses and lensing masses corresponding to these Einstein radii are also compared. While steeper cus ps give smaller ratios of lensing mass to X-ray mass, the X-ray surface bri ghtnesses estimated from flatter cusps are better fits to the observations. For Abell 2163 and Abell 2218, although the isothermal sphere with a finit e core cannot produce giant are images, a density model with a central cusp can produce a finite Einstein radius that is smaller than the observed rad ii. We find that a total mass-density profile that declines as similar to r (-1.4) produces the largest radius in models that are consistent with the X -ray surface brightness profile. As a result, the extremely large ratio of the lensing mass to the X-ray mass is improved from 2.2 to 1.4 for Abell 21 63 and from 3 to 2.4 for Abell 2218. For RX J1347.5 - 1145, which is a cool ing flow cluster, we cannot reduce the mass discrepancy.