SIMBAD references

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, one needs to take into account important relativistic corrections. In this work, we present the first implementation of the effect of spin in mergers in a direct-summation code, nbody6. We employ non-spinning post-Newtonian (PN) corrections to the Newtonian accelerations up to 3.5PN order as well as the spin-orbit 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 find in particular the formation of a runaway black hole (BH) whose spin decays with the mass it wins, independently of the initial value of the spins of the BHs. We compare the result with 500 Monte Carlo realizations of the scenario and confirm the evolution observed with our direct-summation integrator. More remarkably, the subset of compact objects that does not undergo many mergers, and hence represent a more realistic system, has a correlation between the final 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 first detections have started.