Piet Hut

Bio: Piet Hut is an academic researcher from Institute for Advanced Study. The author has contributed to research in topics: Star cluster & Globular cluster. The author has an hindex of 58, co-authored 248 publications receiving 16143 citations. Previous affiliations of Piet Hut include Princeton University & University of California, Berkeley.

A hierarchical O(N log N) force-calculation algorithm

Abstract: Until recently the gravitational N-body problem has been modelled numerically either by direct integration, in which the computation needed increases as N2, or by an iterative potential method in which the number of operations grows as N log N. Here we describe a novel method of directly calculating the force on N bodies that grows only as N log N. The technique uses a tree-structured hierarchical subdivision of space into cubic cells, each of which is recursively divided into eight subcells whenever more than one particle is found to occupy the same cell. This tree is constructed anew at every time step, avoiding ambiguity and tangling. Advantages over potential-solving codes are: accurate local interactions; freedom from geometrical assumptions and restrictions; and applicability to a wide class of systems, including (proto-)planetary, stellar, galactic and cosmological ones. Advantages over previous hierarchical tree-codes include simplicity and the possibility of rigorous analysis of error. Although we concentrate here on stellar dynamical applications, our techniques of efficiently handling a large number of long-range interactions and concentrating computational effort where most needed have potential applications in other areas of astrophysics as well.

Formation of massive black holes through runaway collisions in dense young star clusters.

Abstract: A luminous X-ray source is associated with MGG 11—a cluster of young stars ∼200 pc from the centre of the starburst galaxy M 82 (refs 1, 2). The properties of this source are best explained3,4 by invoking a black hole with a mass of at least 350 solar masses (350 M⊙), which is intermediate between stellar-mass and supermassive black holes. A nearby but somewhat more massive cluster (MGG 9) shows no evidence of such an intermediate-mass black hole1,3, raising the issue of just what physical characteristics of the clusters can account for this difference. Here we report numerical simulations of the evolution and motion of stars within the clusters, where stars are allowed to merge with each other. We find that for MGG 11 dynamical friction leads to the massive stars sinking rapidly to the centre of the cluster, where they participate in a runaway collision. This produces a star of 800–3,000 M⊙, which ultimately collapses to a black hole of intermediate mass. No such runaway occurs in the cluster MGG 9, because the larger cluster radius leads to a mass segregation timescale a factor of five longer than for MGG 11.

HOP: A New group finding algorithm for N body simulations

Abstract: We describe a new method (HOP) for identifying groups of particles in N-body simulations. Having assigned to every particle an estimate of its local density, we associate each particle with the densest of the Nhop particles nearest to it. Repeating this process allows us to trace a path, within the particle set itself, from each particle in the direction of increasing density. The path ends when it reaches a particle that is its own densest neighbor; all particles reaching the same such particle are identified as a group. Combined with an adaptive smoothing kernel for finding the densities, this method is spatially adaptive, coordinate-free, and numerically straightforward. One can proceed to process the output by truncating groups at a particular density contour and combining groups that share a (possibly different) density contour. While the resulting algorithm has several user-chosen parameters, we show that the results are insensitive to most of these, the exception being the outer density cutoff of the groups.

Binaries in globular-clusters

Abstract: Binary stars in a globular cluster (hereafter, GC) may be primordial (i.e. formed along with the cluster), or the result of cluster dynamics. “Dynamical” binaries can result from conservative three-body encounters (e.g. Spitzer, 1987) if a third star can carry away enough kinetic energy to leave two others bound, or from dissipative two-body encounters, if two stars happen to pass within a few stellar radii of one other (Fabian, Pringle, & Rees, 1975). Such non-primordial systems are likely to be found primarily in evolved GC cores, both because conditions are more favorable for making them there, and because of mass segregation. Knowledge of the formation process allows reasonable estimates to be made of their mass and energy distributions. The initial spatial, mass, and energy distributions of primordial binaries, on the other hand, are largely unknown.

Fast parallel algorithms for short-range molecular dynamics

Abstract: Three parallel algorithms for classical molecular dynamics are presented. The first assigns each processor a fixed subset of atoms; the second assigns each a fixed subset of inter-atomic forces to compute; the third assigns each a fixed spatial region. The algorithms are suitable for molecular dynamics models which can be difficult to parallelize efficiently—those with short-range forces where the neighbors of each atom change rapidly. They can be implemented on any distributed-memory parallel machine which allows for message-passing of data between independently executing processors. The algorithms are tested on a standard Lennard-Jones benchmark problem for system sizes ranging from 500 to 100,000,000 atoms on several parallel supercomputers--the nCUBE 2, Intel iPSC/860 and Paragon, and Cray T3D. Comparing the results to the fastest reported vectorized Cray Y-MP and C90 algorithm shows that the current generation of parallel machines is competitive with conventional vector supercomputers even for small problems. For large problems, the spatial algorithm achieves parallel efficiencies of 90% and a 1840-node Intel Paragon performs up to 165 faster than a single Cray C9O processor. Trade-offs between the three algorithms and guidelines for adapting them to more complex molecular dynamics simulations are also discussed.

On the variation of the initial mass function

Abstract: A universal initial mass function (IMF) is not intuitive, but so far no convincing evidence for a variable IMF exists. The detection of systematic variations of the IMF with star-forming conditions would be the Rosetta Stone for star formation. In this contribution an average or Galactic-field IMF is defined, stressing that there is evidence for a change in the power-law index at only two masses: near 0.5 M⊙ and near 0.08 M⊙. Using this supposed universal IMF, the uncertainty inherent in any observational estimate of the IMF is investigated by studying the scatter introduced by Poisson noise and the dynamical evolution of star clusters. It is found that this apparent scatter reproduces quite well the observed scatter in power-law index determinations, thus defining the fundamental limit within which any true variation becomes undetectable. The absence of evidence for a variable IMF means that any true variation of the IMF in well-studied populations must be smaller than this scatter. Determinations of the power-law indices α are subject to systematic errors arising mostly from unresolved binaries. The systematic bias is quantified here, with the result that the single-star IMFs for young star clusters are systematically steeper by Δα≈0.5 between 0.1 and 1 M⊙ than the Galactic-field IMF, which is populated by, on average, about 5-Gyr-old stars. The MFs in globular clusters appear to be, on average, systematically flatter than the Galactic-field IMF (Piotto & Zoccali; Paresce & De Marchi), and the recent detection of ancient white-dwarf candidates in the Galactic halo and the absence of associated low-mass stars (Ibata et al.; Mendez & Minniti) suggest a radically different IMF for this ancient population. Star formation in higher metallicity environments thus appears to produce relatively more low-mass stars. While still tentative, this is an interesting trend, being consistent with a systematic variation of the IMF as expected from theoretical arguments.

The Cosmological simulation code GADGET-2

Abstract: We discuss the cosmological simulation code GADGET-2, a new massively parallel TreeSPH code, capable of following a collisionless fluid with the N-body method, and an ideal gas by means of smoothed particle hydrodynamics (SPH). Our implementation of SPH manifestly conserves energy and entropy in regions free of dissipation, while allowing for fully adaptive smoothing lengths. Gravitational forces are computed with a hierarchical multipole expansion, which can optionally be applied in the form of a TreePM algorithm, where only short-range forces are computed with the ‘tree’ method while long-range forces are determined with Fourier techniques. Time integration is based on a quasi-symplectic scheme where long-range and short-range forces can be integrated with different time-steps. Individual and adaptive short-range time-steps may also be employed. The domain decomposition used in the parallelization algorithm is based on a space-filling curve, resulting in high flexibility and tree force errors that do not depend on the way the domains are cut. The code is efficient in terms of memory consumption and required communication bandwidth. It has been used to compute the first cosmological N-body simulation with more than 10 10 dark matter particles, reaching a homogeneous spatial dynamic range of 10 5 per dimension in a three-dimensional box. It has also been used to carry out very large cosmological SPH simulations that account for radiative cooling and star formation, reaching total particle numbers of more than 250 million. We present the algorithms used by the code and discuss their accuracy and performance using a number of test problems. GADGET-2 is publicly released to the research community. Ke yw ords: methods: numerical ‐ galaxies: interactions ‐ dark matter.