Dark mass-to-luminous mass coupling in Virgo

The empirical relation of coupling in M-d= gamma M(1/2)r between the halo dark mass distribution M-d and visible mass M at radius r, previously shown in spiral galaxies and in the core of MS 2137-2353, is tested for the inner 150 h(-1) kpc Virgo Cluster core. If the stellar mass-to-light ratio in M87 is treated as a free parameter, the density distribution predicted by this relation is found to be consistent with that derived from published surface photometry, stellar and globular cluster dynamics, and X-ray observations. The best fit is obtained for Y*(M87) = 6 (M/L-B)., but a wide range of stellar mass-to-light ratios are possible. At r > 50 kpc, the relation of coupling and the equation of dynamical equilibrium of the gas are the same. The extrapolated dark mass is also consistent with the kinematics of early-type galaxies on a larger, megaparsec scale for Y* (M87) = 8-11 (M/L-B).. The cluster dark mass halo and the stellar mass in M87 have equal weight at similar to 1/2-3/4 effective radius.