Encounters of binaries – II. Unequal energies

Gravitational encounters of pairs of hard binaries with unequal energies, but equal mass stars, have been studied numerically. Special attention was drawn to the phenomenon called collision, which cannot be treated as a fly-by. A semi-analytical theory for obtaining the collision cross-section and outcome distributions was developed and the free parameters fitted to numerical observations. Good agreement between theory and experiments confirms the theoretical assumption that the class of interactions, which results in a disruption into one binary and two separately escaping stars, can be treated in terms of two independent random ejections. The energy distribution of the first ejection is approximately scaled by the harmonic mean of the binding energies of the binaries as corrected somewhat for the impact energy, while the disruption of the remaining three-body system has its total energy as the scaling factor. With increasing binding energy ratio the number of hierarchical three-body systems, resulting from collisions, becomes larger. For equal energies it is 20 per cent and gets the value 50 per cent if the binding energies differ by a factor of about 4.