THE MASS-DISTRIBUTION OF CL-0939+4713 OBTAINED FROM A WEAK LENSING ANALYSIS OF A WFPC2 IMAGE

The image distortions of high-redshift galaxies caused by gravitationa l light deflection of foreground clusters of galaxies can be used to r econstruct the two-dimensional surface mass density of these clusters. We apply an unbiased parameter-free reconstruction technique to the c luster CL 0939+4713 (Abell 851), observed with the WFPC2 on board of t he HST. We demonstrate that a single deep WFPC2 observation can be use d for cluster mass reconstruction despite its small field of view and the irregular shape of the data field (especially for distant clusters ). For CL 0939, we find a strong correlation between the reconstructed mass distribution and the bright cluster galaxies indicating that mas s follows light on average. The detected anti-correlation between the faint galaxies and the reconstructed mass is most likely an effect of the magnification (anti) bias, which was detected previously in the cl uster A1689. Because of the high redshift of CL 0939 (z(d) = 0.41), th e redshift distribution of the lensed, faint galaxies has to be accoun ted for in the reconstruction technique. We derive an approximate glob al transformation for the surface mass density which leaves the mean i mage ellipticities invariant, resulting in an uncertainty in the norma lization of the mass. From the non-negativity of the surface mass dens ity, we derive lower limits on the mass inside the observed field of 0 .75 (h(50)(-1) Mpc)(2) ranging from M > 3.6 x 10(14)h(50)(-1) M. to M > 6.3 x 10(14)h(50)(-1) M. for a mean redshift of [z] = 1 to [z] = 0.6 of the faint galaxy images with R is an element of (23, 25.5). Howeve r, we can break the invariance transformation for the mass using the m agnification effect on the observed number density of the background g alaxies. Assuming a mean redshift of [z] = 0.8 and a fraction of x = 1 5% (x = 20%) of cluster galaxies in the observed galaxy sample with R is an element of (23, 25.5) we obtain for the mass inside the field M approximate to 5 x 10(14)h(50)(-1) M. (M approximate to 7 x 10(14)h(50 )(-1) M.) which corresponds to M/L approximate to 100h(50) (M/L approx imate to 140h(50)).