arXiv subjects

R. Spurzem

Publications and source records attributed to R. Spurzem.

43 records · Page 3Linked to original sources

arXiv1999

A stochastic Monte Carlo approach to model real star cluster evolution, II. Self-consistent models and primordial binaries

The new approach outlined in Paper I (Spurzem \& Giersz 1996) to follow the individual formation and evolution of binaries in an evolving, equal point-mass star cluster is extended for the self-consistent treatment of relaxation and close three- and four-body encounters for many binaries (typically a few percent of the initial number of stars in the cluster). The distribution of single stars is treated as a conducting gas sphere with a standard anisotropic gaseous model. A Monte Carlo technique is used to model the motion of binaries, their formation and subsequent hardening by close encounters, and their relaxation (dynamical friction) with single stars and other binaries. The results are a further approach towards a realistic model of globular clusters with primordial binaries without using special hardware. We present, as our main result, the self-consistent evolution of a cluster consisting of 300.000 equal point-mass stars, plus 30.000 equal mass binaries over several hundred half-mass relaxation times, well into the phase where most of the binaries have been dissolved and evacuated from the core. In a self-consistent model it is the first time that such a realistically large number of binaries is evolving in a cluster with an even ten times larger number of single stars. Due to the Monte Carlo treatment of the binaries we can at every moment analyze their external and internal parameters in the cluster as in an N-body simulation.

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arXiv1999

AHA-GRAPE: Adaptive Hydrodynamic Architecture - GRAvity PipE

In astrophysics numerical star cluster simulations and hydrodynamical methods like SPH require computational performance in the petaflop range. The GRAPE family of ASIC-based accelerators improves the cost-performance ratio compared to general purpose parallel computers, however with limited flexibility. The AHA-GRAPE architecture adds a reconfigurable FPGA-processor to accelerate the SPH computation. The basic equations of the algorithm consist of three parts each scaling with the order of O(N), O(N*Nn), and O(N**2) respectively, where N is in the range of 10**4 to 10**7 and Nn approximately 50. These equations can profitably be distributed across a host workstation, an FPGA processor, and a GRAPE subsystem. With the new ATLANTIS FPGA processor we expect a scalable SPH performance of 1.5 Gflops per board. The first prototype AHA-GRAPE system will be available in mid-2000. This 3-layered system will deliver an increase in performance by a factor of 10 as compared to a pure GRAPE solution.

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arXiv1999

Direct N-body Simulations

Special high-accuracy direct force summation N-body algorithms and their relevance for the simulation of the dynamical evolution of star clusters and other gravitating N-body systems in astrophysics are presented, explained and compared with other methods. Other methods means here approximate physical models based on the Fokker-Planck equation as well as other, approximate algorithms to compute the gravitational potential in N-body systems. Questions regarding the parallel implementation of direct ``brute force'' N-body codes are discussed. The astrophysical application of the models to the theory of relaxing rotating and non-rotating collisional star clusters is presented, briefly mentioning the questions of the validity of the Fokker-Planck approximation, the existence of gravothermal oscillations and of rotation and primordial binaries.

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arXiv1999

Towards the million body problem on the computer - no news since the three-body problem?

Astrophysical Challenges which demand the solution of the one million (or more) gravitating body problem are briefly discussed for the fields of cosmology, galactic nuclei and globular star clusters. Results from the classical three-body problem are to be combined with methods of statistical mechanics or thermodynamics in order to provide a reasonable model for astrophysically relevant particle numbers of the order 10**4-10**8. For high-precision modelling of star clusters and galactic nuclei over the required hundreds and thousands of crossing times specially tailored ``brute-force'' N-body integration methods are used together with special purpose hardware. A recent implementation of such code on a general purpose parallel computer is presented. After a comparison of the relevance of different N-body algorithms a new concept for a more flexible customized special purpose computer based on a combination of GRAPE and FPGA is proposed. It is an ideal machine for all kinds of N-body simulations using neighbour schemes, as the Ahmad-Cohen direct N-body codes and smoothed particle hydrodynamics (SPH) for systems including interstellar gas dynamics.

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arXiv1998

On the evolution of shape in N-body simulations

A database on shape evolution of direct N-body models formed out of cold, dissipationless collapse is generated using GRAPE and HARP special purpose computers. Such models are important to understand the formation of elliptical galaxies. Three dynamically distinct phases of shape evolution were found, first a fast dynamical collapse which gives rise to the radial orbit instability (ROI) and generates at its end the maximal triaxiality of the system. Subsequently, two phases of violent and two-body shape relaxation occur, which drive the system first towards axisymmetry, finally to spherical symmetry (the final state, however, is still much more concentrated than the initial model). In a sequence of models the influence of numerical and physical parameters, like particle number, softening, initial virial ratio, timestep choice, different N-body codes, are examined. We find that an improper combination of softening and particle number can produce erroneous results. Selected models were evolved on the secular timescale until they became spherically symmetric again. The secular shape relaxation time scale is shown to agree very well with the two-body relaxation time, if softening is properly taken into account for the latter. Finally, we argue, that the intermediate phase of violent shape relaxation after collapse is induced by strong core oscillations in the centre, which cause potential fluctuations, dampening out the triaxiality.

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arXiv1997

Dynamical Simulations: Methods and Comparisons

We review recent progress in computational methods for studying the dynamical evolution of large star clusters. After describing some highlights of a new comparison of different models, including N-body models, we mention in detail recent developments in three codes which allow models with anisotropic distributions of velocity to be studied: (i) a Fokker-Planck code using finite differences, (ii) a Monte Carlo code and (iii) a gaseous model code.

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arXiv1997

Dynamical evolution of rotating stellar systems: I pre-collapse, equal mass systems

The influence of rotation on the dynamical evolution of collisional stellar systems is investigated by solving the orbit-averaged Fokker-Planck equation in (E,J_z)-space. We find that large amounts of initial rotation drive the system into a phase of strong mass loss while it is moderately contracting. The core is rotating even faster than before although angular momentum is transported outwards. At the same time the core is heating. Given these features this phase can be associated with the gravo-gyro 'catastrophe' found by Hachisu (1979). The increase in central angular momentum levels off after about 2-3 initial half-mass relaxation times indicating that the source of this `catastrophe' is depleted. Finally, the central angular velocity increases again, but with a rather small power of the central density -- the same power as for the central velocity dispersion during self-similar contraction towards the collapse. The rotation curves flatten and the ellipticity variations decrease with time, but their shapes are very similar. These results suggest the existence of a self-similar solution for a rotating cluster as well. The maximum values of rotational velocity and ellipticity occur at about the half mass radius.

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