Merger Rate of Equal-Mass Spherical Galaxies
  We present cross sections and reaction rates for merging to occur during encounters of equal-mass spherical galaxies. As an application, we determine the rate of galaxy merging in clusters of galaxies. We present results for two types of Plummer models (a full and a truncated one), two King models and the Hernquist model. Cross sections are determined on the basis of a large number ($\sim 500$) of simulations of galaxy encounters, using the 10-Gigaflops GRAPE 3A special-purpose computer. We characterize the overall merger rate of galaxies in a galaxy cluster by a single number, derived from our cross sections by an integration over galaxy encounter velocities in the limit of a constant density in velocity space. For small clusters, where the cluster velocity dispersion may not significantly exceed the internal velocity dispersion of the individual galaxies, this constant-density approximation may not be valid. For those cases, we present separate results, based on integrations of our cross sections over Maxwellian velocity distributions. Finally, tidal effects from the cluster potential as well as from neighboring galaxies may prevent a barely bound galaxy pair from spiraling in after their first encounter. We give a quantitative estimate of the resulting reduction in the actual merger rate, due to these tidal interactions. 
Junichiro Makino and Piet Hut