Lensing from the Light-Traces-Mass Map of MS1224+20

The MS1224+20 cluster of galaxies is a high luminosity X-ray source at z=0.325. To compare the lensing mass to the virial mass we have completed a uniform, high precision redshift survey over a field of $7\text{arcm}\times 9\text{arcm}$, obtaining 75 redshifts. The velocity dispersion of 30 cluster galaxies is $775$ \kms\ and the projected harmonic radius is 0.32 \hmpc. The virial mass is $2.1\times {10}^{14}{h}^{-1}\text{msun}$. Correcting for faint cluster galaxies without redshifts and allowing for a modest evolution in the galaxy luminosity function gives a current epoch mass-to-light ratio $M\mathrm{/}{L}_V(0)=255h\text{msun}\mathrm{/}\text{lsun}$. The same field contains a $z=0.225$ cluster with ${\sigma }_v\simeq 500$ \kms, and a group at $z=0.412$ with ${\sigma }_v\simeq 400$ \kms. The clusters’ gravitational field induces image ellipticities that are calculated from the light-traces-mass density distribution and compared to the observed average tangential distortions from Fahlman \et (1994). Between 1.5 and 3 virial radii, the observed lensing distortions are $4\pm 2$ times stronger than the light-traces-mass model and the virial M/L predict.