In this paper a cluster is modelled as a smooth potential (due to the cluster stars) plus the steady tidal field of the Galaxy. In this model there is a minimum energy below which stars cannot escape. Above this energy, however, the time‐scale on which a star escapes varies with the orbital parameters of the star (mainly its energy) in a way which we attempt to quantify, with both theoretical arguments and computer simulations. Within the limitations of the model we show that the time‐scale is long enough to complicate the interpretation of full N‐body simulations of clusters, and that stars above the escape energy may remain bound to the cluster for about a Hubble time.

Observed cusps with density profiles $\rho\propto r^{-1}$ or shallower, in the central regions of galaxies, cannot be reproduced in the standard Cold Dark Matter (CDM) picture of hierarchical clustering. Previous claims to the contrary were based on simulations with relatively few particles, and substantial softening. We present simulations with particle numbers an order of magnitude higher, and essentially no softening, and show that typical central density profiles are clearly steeper than $\rho\propto r^{-1}$. The observed shallower profiles may have formed through the smoothing effect of the spiral-in of central black holes in previous merger phases. In addition, we confirm the presence of a temperature inversion in the inner 5 kpc of massive galactic halos, and illustrate its formation as a natural result of the merging of unequal progenitors.Comment: 5 pages, 4 figures, figure 1 available at http://grape.c.u-tokyo.ac.jp/pub/people/fukushig/paper/list.html, ApJ Letters, in pres

We investigate the structure of the dark matter halo formed in the cold dark matter scenario using N-body simulations. We simulated 12 halos with masses of 6.6 ] 1011È8.0 ] 1014In all runs, the M _ . halos have density cusps proportional to r~1.5 developed at their centers, which is consistent with the results of recent high-resolution calculations. The density structure evolves in a self-similar way and is universal in the sense that it is independent of the halo mass and initial random realization of density Ñuctuation. The density proÐle is in good agreement with the proÐle proposed by Moore et al., which has a central slope proportional to r~1.5 and an outer slope proportional to r~3. The halo grows through repeated accretion of di †use smaller halos. We argue that the cusp is understood as a convergence slope for the accretion of tidally disrupted matter.

In this paper, we describe the architecture and performance of the GRAPE-6 system, a massivelyparallel special-purpose computer for astrophysical N -body simulations. GRAPE-6 is the successor of GRAPE-4, which was completed in 1995 and achieved the theoretical peak speed of 1.08 Tflops. As was the case with GRAPE-4, the primary application of GRAPE-6 is simulation of collisional systems, though it can be used for collisionless systems. The main differences between GRAPE-4 and GRAPE-6 are (a) The processor chip of GRAPE-6 integrates 6 force-calculation pipelines, compared to one pipeline of GRAPE-4 (which needed 3 clock cycles to calculate one interaction), (b) the clock speed is increased from 32 to 90 MHz, and (c) the total number of processor chips is increased from 1728 to 2048. These improvements resulted in the peak speed of 64 Tflops. We also discuss the design of the successor of GRAPE-6.

We investigate the structure of the dark matter halo formed in the cold dark matter scenarios by N-body simulations with a parallel tree code on GRAPE cluster systems. We simulated eight halos with the mass of 4:4 ; 10 14 to 1:6 ; 10 15 M in SCDM and LCDM models using up to 30 million particles. With the resolution of our simulations, the density profile is reliable down to 0.2% of the virial radius. Our results show that the slope of inner cusp within 1% virial radius is shallower than À1.5, and the radius where the shallowing starts exhibits run-to-run variation, which means that the innermost profile is not universal.