Blocking low-eccentricity EMRIs: A statistical direct-summation N-body study of the schwarzschild barrier

The capture of a compact object in a galactic nucleus by a massive black hole (MBH), an extreme-mass ratio inspiral (EMRI), is the best way to map space and time around it. Recent work on stellar dynamics has demonstrated that there seems to be a complot in phase space acting on low-eccentricity captures, since their rates decrease significantly by the presence of a blockade in the rate at which orbital angular momenta change takes place. This so-called 'Schwarzschild barrier' is a result of the impact of relativistic precession on to the stellar potential torques, and thus it affects the enhancement on lower eccentricity EMRIs that one would expect from resonant relaxation. We confirm and quantify the existence of this barrier using a large number of direct-summation N-body simulations with both a post-Newtonian and also, for the first time in a direct-summation code, a geodesic approximation for the relativistic orbits. The existence of the barrier prevents low-eccentricity EMRIs from approaching the central MBH via resonant relaxation.We confirm that the event rates for capture thus increase with the square of the distributed mass, in agreement with two-body relaxation. However, for nuclei with more than a few thousand M⊙ in the inner 10 mpc, two-body relaxation is so efficient that compact objects do not decouple into gravitational wave-driven inspirals but are mostly driven into direct plunges, if the centralMBH is not spinning. This leads to an apparent maximum event rate of about 1 Myr-1 for EMRIs originating from the inner 10 mpc. © 2013 The Authors Published by Oxford University Press on behalf of the Royal Astronomical Society.