Evolution of compact groups of galaxies .1. Merging rates

We discuss the merging rates in compact groups of five identical elliptical galaxies. All groups have the same mass and binding energy. We consider both cases with individual haloes and cases where the halo is common to all galaxies and enveloping the whole group. In the latter situation the merging rate is lower if the halo is more massive. The mass of individual haloes has little influence on the merging rates, due to the fact that all galaxies in our simulations have the same mass, and so the mure extended ones have a smaller velocity dispersion. Groups with individual haloes merge faster than groups with common haloes if the configuration is centrally concentrated. Like a King distribution of index Psi = 10. On the other hand, for less concentrated configurations the merging is initially faster for individual halo cases than for common halo cases, and slower after part of the group has merged. In cases with a common halo, centrally concentrated configurations merge faster for high halo-to-total mass ratios and more slowly for low halo-to-total mass ratios. Groups with a virial ratio initially less than 1 merge faster than groups in virial equilibrium, while groups that have initially cylindrical rotation merge more slowly than groups starting with no rotation. In order to test how long a virialized group can survive before merging, we follow the evolution of a group with a high halo-to-total mass ratio and a density distribution with very little central concentration. We find that the first merging occurred only after a large number of crossing times. A reasonable calibration of our computer units shows that this time should be larger than a Hubble time. Therefore our simulations suggest that, at least for appropriate initial conditions, the longevity of compact groups is not necessarily a problem, thus presenting an alternative explanation of why we observe so many compact groups despite the fact that their lifetimes seem short.