Post‐Newtonian N ‐body simulations

We report on the first fully consistent conventional cluster simulation which includes terms up to the third‐order post‐Newtonian approximation. Numerical problems for treating extremely energetic binaries orbiting a single massive object are circumvented by employing the special ‘wheel‐spoke’ regularization method of Zare which has not been used in large‐ N simulations before. Idealized models containing N = 1 × 10 5 particles of mass 1 M ⊙ with a central black hole (BH) of 300 M ⊙ have been studied on GRAPE‐type computers. An initial half‐mass radius of r h ≃ 0.1 pc is sufficiently small to yield examples of relativistic coalescence. This is achieved by significant binary shrinkage within a density cusp environment, followed by the generation of extremely high eccentricities which are induced by Kozai cycles and/or resonant relaxation. More realistic models with white dwarfs and 10 times larger half‐mass radii also show evidence of general relativity effects before disruption. An experimentation with the post‐Newtonian terms suggests that reducing the time‐scales for activating the different orders progressively may be justified for obtaining qualitatively correct solutions without aiming for precise predictions of the final gravitational radiation wave form. The results obtained suggest that the standard loss‐cone arguments underestimate the swallowing rate in globular clusters containing a central BH.