Relativistic mergers of compact binaries in clusters: the fingerprint of the spin

Dense stellar systems such as globular clusters and dense nuclear clusters are the breeding ground of sources of gravitational waves for the advanced detectors LIGO and Virgo. The stellar densities reached in these systems lead to the dynamical formation of binaries at a rate superior to what one can expect in regions of the galaxy with lower densities. Hence, these systems deserve a close study to estimate rates and parameter distribution. This is not an easy task, since the evolution of a dense stellar cluster involves the integration of N bodies with high resolution in time and space and including hard binaries and their encounters and, in the case of gravitational waves (GWs), one needs to take into account important relativistic corrections. In this work we present the rst implementation of the eect of spin in mergers in a directsummation code, NBODY6. We employ non-spinning post-Newtonian corrections to the Newtonian accelerations up to 3.5 post-Newtonian (PN) order as well as the spinorbit coupling up to next-to-lowest order and the lowest order spin-spin coupling. We integrate spin precession and add a consistent treatment of mergers. We analyse the implementation by running a set of two-body experiments and then we run a set of 500 simulations of a stellar cluster with a velocity dispersion set to a high value to induce relativistic mergers to set a proving ground of the implementation. In spite of the large number of mergers in our tests, the application of the algorithm is robust. We nd in particular the formation of a runaway star whose spin decays with the mass it wins, independently of the initial value of the spins of the stars. We compare the result with 500 Monte Carlo realisations of the scenario and conrm the evolution observed with our direct-summation integrator. More remarkably, the subset of compact objects that do not undergo many mergers, and hence represent a more realistic system, has a correlation between the nal absolute spin and the initial choice for the initial distribution, which could provide us with information about the evolution of spins in dense clusters once the rst detections have started.