Core radii of globular clusters in the Large and Small Magellanic Clouds show an increasing trend with age. We propose that this trend is a dynamical effect resulting from the accumulation of massive stars and stellar-mass black holes at the cluster centers. The black holes are remnants of stars with initial masses exceeding 20-25 solar masses; as their orbits decay by dynamical friction, they heat the stellar background and create a core. Using analytical estimates and N-body experiments, we show that the sizes of the cores so produced and their growth rates are consistent with what is observed. We propose that this mechanism is responsible for the formation of cores in all globular clusters and possibly in other systems as well.Comment: 5 page

A systolic algorithm rhythmically computes and passes data through a network of processors. We investigate the performance of systolic algorithms for implementing the gravitational N -body problem on distributedmemory computers. Systolic algorithms minimize memory requirements by distributing the particles between processors. We show that the performance of systolic routines can be greatly enhanced by the use of nonblocking communication, which allows particle coordinates to be communicated at the same time that force calculations are being carried out. The performance enhancement is particularly great when block sizes are small, i.e. when only a small fraction of the N particles need their forces computed in each time step. Hyper-systolic algorithms reduce the communication complexity from O(N p), with p the processor number, to O(N √ p), at the expense of increased memory demands. We describe a hyper-systolic algorithm that will work with a block time step algorithm and analyze its performance. As an example of an application requiring large N , we use the systolic algorithm to carry out direct-summation simulations using 10 6 particles of the Brownian motion of the supermassive black hole at the center of the Milky Way galaxy. We predict a 3D random velocity of ∼ 0.4 km s −1 for the black hole.

We use a systolic N-body algorithm to evaluate the linear stability of the gravitational N-body problem for N up to 1:3 Â 10 5 , 2 orders of magnitude greater than in previous experiments. For the first time, a clear N-dependence of the perturbation growth rate is seen, l e $ ln N. The e-folding time for N ¼ 10 5 is roughly 1/20 of a crossing time.

We follow the sinking of two massive black holes in a spherical stellar system where the black holes become bound under the influence of dynamical friction. Once bound, the binary hardens by three-body encounters with surrounding stars. We find that the binary wanders inside the core, providing an enhanced supply of reaction partners for the hardening. The binary evolves into a highly eccentric orbit leading to coalescence well beyond a Hubble time. These are the first results from a hybrid '' self-consistent field '' (SCF) and direct Aarseth N-body integrator (NBODY6), which combines the advantages of the direct force calculation with the efficiency of the field method. The code is designed for use on parallel architectures and is therefore applicable to collisional N-body integrations with extraordinarily large particle numbers (>10 5 ). This creates the possibility of simulating the dynamics of both globular clusters with realistic collisional relaxation and stellar systems surrounding supermassive black holes in galactic nuclei.