Simon Portegies Zwart

The Runaway Growth of Intermediate-Mass Black Holes in Dense Star Clusters

We study the growth rate of stars via stellar collisions in dense star clusters, calibrating our analytic calculations with direct N-body simulations of up to 65,536 stars, performed on the GRAPE family of special-purpose computers. We find that star clusters with initial half-mass relaxation times 25 Myr are dominated by stellar collisions, the first collisions occurring at or near the point of core collapse, which is driven by the segregation of the most massive stars to the cluster center, where they end up in hard binaries. The majority of collisions occur with the same star, resulting in the runaway growth of a supermassive object. This object can grow up to ~0.1% of the mass of the entire star cluster and could manifest itself as an intermediate-mass black hole (IMBH). The phase of runaway growth lasts until mass loss by stellar evolution arrests core collapse. Star clusters older than about 5 Myr and with present-day half-mass relaxation times 100 Myr are expected to contain an IMBH.

Star cluster ecology – IV. Dissection of an open star cluster: photometry

The evolution of star clusters is studied using N-body simulations in which the evolution of single stars and binaries is taken self-consistently into account. Initial conditions are chosen to represent relatively young Galactic open clusters, such as the Pleiades, Praesepe and the Hyades. The calculations include a realistic mass function, primordial binaries and the external potential of the parent Galaxy. n n n nOur model clusters are generally significantly flattened by the Galactic tidal field, and dissolve before deep core collapse occurs. The binary fraction decreases initially because of the destruction of soft binaries, but increases later because lower mass single stars escape more easily than the more massive binaries. At late times, the cluster core is quite rich in giants and white dwarfs. There is no evidence for preferential evaporation of old white dwarfs. On the contrary, the white dwarfs formed are likely to remain in the cluster. Stars tend to escape from the cluster through the first and second Lagrange points, in the direction of and away from the Galactic Centre. n n n nMass segregation manifests itself in our models well within an initial relaxation time. As expected, giants and white dwarfs are much more strongly affected by mass segregation than main-sequence stars. n n n nOpen clusters are dynamically rather inactive. However, the combined effects of stellar mass-loss and evaporation of stars from the cluster potential drive the dissolution of a cluster on a much shorter time-scale than if these effects are neglected. The often-used argument that a star cluster is barely older than its relaxation time and therefore cannot be dynamically evolved is clearly in error for the majority of star clusters. n n n nAn observation of a blue straggler in an eccentric orbit around an unevolved star or a blue straggler of more than twice the turn-off mass might indicate past dynamical activity. We find two distinct populations of blue stragglers: those formed above the main-sequence turn-off, and those which appear as blue stragglers as the clusters turn-off drops below the mass of the rejuvenated star.

High performance direct gravitational N-body simulations on graphics processing units II: An implementation in CUDA

We present the results of gravitational direct N-body simulations using the graphics processing unit (GPU) on a commercial NVIDIA GeForce 8800GTX designed for gaming computers. The force evaluation of the N-body problem is implemented in ‘‘Compute Unified Device Architecture’’ (CUDA) using the GPU to speedup the calculations. We tested the implementation on three different N-body codes: two direct N-body integration codes, using the 4th order predictor–corrector Hermite integrator with block time-steps, and one Barnes-Hut treecode, which uses a 2nd order leapfrog integration scheme. The integration of the equations of motions for all codes is performed on the host CPU. We find that for N > 512 particles the GPU outperforms the GRAPE-6Af, if some softening in the force calculation is accepted. Without softening and for very small integration time-steps the GRAPE still outperforms the GPU. We conclude that modern GPUs offer an attractive alternative to GRAPE-6Af special purpose hardware. Using the same time-step criterion, the total energy of the N-body system was conserved better than to one in 10 6 on the GPU, only about an order of magnitude worse than obtained with GRAPE-6Af. For N J 10 5 the 8800GTX outperforms the host CPU by a factor of about 100 and runs at about the same speed as the GRAPE-6Af.

Dynamical Formation of Close Binary Systems in Globular Clusters

We know from observations that globular clusters are very efficient catalysts in forming unusual short-period binary systems or their offspring, such as low-mass X-ray binaries (LMXBs; neutron stars accreting matter from low-mass stellar companions), cataclysmic variables (white dwarfs accreting matter from stellar companions), and millisecond pulsars (rotating neutron stars with spin periods of a few milliseconds). Although there has been little direct evidence, the overabundance of these objects in globular clusters has been attributed by numerous authors to the high densities in the cores, which leads to an increase in the formation rate of exotic binary systems through close stellar encounters. Many such close binary systems emit X-radiation at low luminosities (LX 1034 ergs s-1) and are being found in large numbers through observations with the Chandra X-Ray Observatory. Here we present conclusive observational evidence of a link between the number of close binaries observed in X-rays in a globular cluster and the stellar encounter rate of the cluster. We also make an estimate of the total number of LMXBs in globular clusters in our Galaxy.

A Neutron Star with a Massive Progenitor in Westerlund 1

We report the discovery of an X-ray pulsar in the young, massive Galactic star cluster Westerlund 1. We detected a coherent signal from the brightest X-ray source in the cluster, CXO J164710.2–455216, during two Chandra observations on 2005 May 22 and June 18. The period of the pulsar is 10.6107(1) s. We place an upper limit to the period derivative of u P 1M⊙. Taken together, the properties of the pulsar indicate that it is a magnetar. The rarity of slow X-ray pulsars and the position of CXO J164710.2–455216 only 1.6 ′ from the core of Westerlund 1 indicates that it is a member of the cluster with >99.97% confidence. Westerlund 1 contains 07V stars with initial masses Mi�35M⊙ and >50 post-main-sequence stars that indicate the cluster is 4±1 Myr old. Therefore, the progenitor to this pulsar had an initial mass Mi>40M⊙. This is the most secure result among a handful of observational limits to the masses of the progenitors to neutron stars. Subject headings: X-rays: stars — neutron stars — open clusters and associations: individual (Westerlund 1)

Performance Analysis of Direct N-body Algorithms on Special-Purpose Supercomputers

Abstract Direct-summation N-body algorithms compute the gravitational interaction between stars in an exact way and have a computational complexity of O ( N 2 ) . Performance can be greatly enhanced via the use of special-purpose accelerator boards like the GRAPE-6A. However, the memory of the GRAPE boards is limited. Here, we present a performance analysis of direct N-body codes on two parallel supercomputers that incorporate special-purpose boards, allowing as many as four million particles to be integrated. Both computers employ high-speed, Infiniband interconnects to minimize communication overhead, which can otherwise become significant due to the small number of “active” particles at each time step. We find that the computation time scales well with processor number; for 2xa0×xa0106 particles, efficiencies greater than 60% and speeds in excess of ∼3xa0TFlops are reached.

SAPPORO: A way to turn your graphics cards into a GRAPE-6

We present Sapporo, a library for performing high-precision gravitationalN-body simulations on NVIDIA Graphical Processing Units (GPUs). Our library mimics the GRAPE-6 library, and N-body codes currently running on GRAPE-6 can switch to Sapporo by a simple relinking of the library. The precision of our library is comparable to that of GRAPE-6, even though internally the GPU hardware is limited to single precision arithmetics. This limitation is effectively overcome by emulating double precision for calculating the distance between particles. The performance loss of this operation is small ( < ∼ 20%) compared to the advantage of being able to run at high precision. We tested the library using several GRAPE-6-enabled N-body codes, in particular with Starlab and phiGRAPE. We measured peak performance of 800Gflop/s for running with 10 6 particles on a PC with four commercial G92 architecture GPUs (two GeForce 9800GX2). As a production test, we simulated a 32k Plummer model with equal mass stars well beyond core collapse. The simulation took 41 days, during which the mean performance was 113Gflop/s. The GPU did not show any problems from running in a production environment for such an extended period of time.

On the Central Structure of M15

We present a detailed comparison between the latest observational data on the kinematical structure of the core of M15, obtained with the Hubble Space Telescope Space Telescope Imaging Spectrograph and Wide Field Planetary Camera 2 instruments, and the results of dynamical simulations carried out using the special purpose GRAPE-6 computer. The observations imply the presence of a significant amount of dark matter in the cluster core. In our dynamical simulations, neutron stars and/or massive white dwarfs concentrate to the center through mass segregation, resulting in a sharp increase in toward the center. While consistent with the presence of M/L a central black hole, the Hubble Space Telescope data can also be explained by this central concentration of stellar mass compact objects. The latter interpretation is more conservative, since such remnants result naturally from stellar evolution, although runaway merging leading to the formation of a black hole may also occur for some range of initial conditions. We conclude that no central massive object is required to explain the observational data, although we cannot conclusively exclude such an object at the level of. Our findings are similar to500-1000 M-circle dot. Our findings are unchanged when we reduce the assumed neutron star retention fraction in our simulations from 100% to 0%.

A Dynamical Origin for Early Mass Segregation in Young Star Clusters

Some young star clusters show a degree of mass segregation that is inconsistent with the effects of standard two-body relaxation from an initially unsegregated system without substructure, in virial equilibrium, and it is unclear whether current cluster formation models can account for this degree of initial segregation in clusters of significant mass. In this Letter we demonstrate that mergers of small clumps that are initially mass segregated, or in which mass segregation can be produced by two-body relaxation before they merge, generically lead to larger systems that inherit the progenitor clumps segregation. We conclude that clusters formed in this way are naturally mass segregated, accounting for the anomalous observations and suggesting that this process of prompt mass segregation due to initial clumping should be taken into account in models of cluster formation and dynamics.

A Dynamical Model for the Globular Cluster G1

We present a comparison between the observational data on the kinematical structure of G1 in M31, obtained with the Hubble Space Telescope Wide Field Planetary Camera 2 and Space Telescope Imaging Spectrograph instruments, and the results of dynamical simulations carried out using the special purpose computer GRAPE-6. We have obtained good fits for models starting from single-cluster King model initial conditions and even better fits when starting our simulations with a dynamically constructed merger product of two star clusters. In the latter case, the results from our simulations are in excellent agreement with the observed profiles of luminosity, velocity dispersion, rotation, and ellipticity. We obtain a mass-to-light ratio of M/L = 4.0 ± 0.4 and a total cluster mass of M = (8 ± 1) × 106 M☉. Given that our dynamical model can fit all available observational data very well, there seems to be no need to invoke the presence of an intermediate-mass black hole in the center of G1.