Dynamics of compact object clusters: a post-Newtonian study

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Abstract
Compact object clusters are likely to exist in the centres of some galaxies because of mass segregation. The high densities and velocities reached in them need a better understanding. The formation of binaries and their subsequent merging by gravitational radiation emission are important to the evolution of such clusters. We address the evolution of such a system in a relativistic regime. The recurrent mergers at high velocities create an object with a mass much larger than the average. For this purpose we modified the direct Nbody6++ code to include post-Newtonian effects on the force during two-body encounters. We adjusted the equations of motion to include for the first time the effects of both periastron shift and energy loss by emission of gravitational waves, and so to study the eventual decay and merger of radiating binaries. The method employed allows us to give here an accurate post-Newtonian description of the formation of a runaway compact object by successive mergers with surrounding particles, as well as the distribution of characteristic eccentricities in the events. This study should be envisaged as a first step towards a detailed, accurate study of possible gravitational wave sources, thanks to the combination of the direct Nbody numerical tool with the implementation of post-Newtonian terms.

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