arXiv subjects

Piet Hut

Publications and source records attributed to Piet Hut.

At least 37 records · Page 2Linked to original sources

arXiv2005

The ecology of star clusters and intermediate mass black holes in the Galactic bulge

We simulate the inner 100pc of the Milky-Way Galaxy to study the formation and evolution of the population of star clusters and intermediate mass black holes. For this study we perform extensive direct N-body simulations of the star clusters which reside in the bulge, and of the inner few tenth of parsecs of the super massive black hole in the Galactic center. In our N-body simulations the dynamical friction of the star cluster in the tidal field of the bulge are taken into account via (semi)analytic soluations. The N-body calculations are used to calibrate a (semi)analytic model of the formation and evolution of the bulge. We find that about 10% of the clusters born within 100pc of the Galactic center undergo core collapse during their inward migration and form intermediate-mass black holes (IMBHs) via runaway stellar merging. After the clusters dissolve, these IMBHs continue their inward drift, carrying a few of the most massive stars with them. We predict that region within about 10 parsec of the SMBH is populated by about 50IMBHs of some 1000Msun. Several of these are expected to be accompanied still by some of the most massive stars from the star cluster. We also find that within a few milliparsec of the SMBH there is a steady population of several IMBHs. This population drives the merger rate between IMBHs and the SMBH at a rate of about one per 10Myr, sufficient to build the accumulate majority of mass of the SMBH. Mergers of IMBHs with SMBHs throughout the universe are detectable by LISA, at a rate of about two per week.

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arXiv2005

Three-Body Affairs in the Outer Solar System

Recent observations (Burnes2002,Veillet2002,Margot2002a) have revealed an unexpectedly high binary fraction among the Trans-Neptunian Objects (TNOs) that populate the Kuiper Belt. The TNO binaries are strikingly different from asteroid binaries in four respects (Veillet2002): their frequency is an order of magnitude larger, the mass ratio of their components is closer to unity, and their orbits are wider and highly eccentric. Two explanations have been proposed for their formation, one assuming large numbers of massive bodies (Weidenschilling2002), and one assuming large numbers of light bodies (Goldreich2002). We argue that both assumptions are unwarranted, and we show how TNO binaries can be produced from a modest number of intermediate-mass bodies of the type predicted by the gravitational instability theory for the formation of planetesimals (Goldreich and Ward1973). We start with a TNO binary population similar to the asteroid binary population, but subsequently modified by three-body exchange reactions, a process that is far more efficient in the Kuiper belt, because of the much smaller tidal perturbations by the Sun. Our mechanism can naturally account for all four characteristics that distinguish TNO binaries from main-belt asteroid binaries.

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arXiv2005

A New Time-Symmetric Block Time-Step Algorithm for N-Body Simulations

Time-symmetric integration schemes share with symplectic schemes the property that their energy errors show a much better behavior than is the case for generic integration schemes. Allowing adaptive time steps typically leads to a loss of symplecticity. In contrast, time symmetry can be easily maintained, at least for a continuous choice of time step size. In large-scale N-body simulations, however, one often uses block time steps, where all time steps are forced to take on values as powers of two. This greatly facilitates parallelization, and hence code efficiency. Straightforward implementation of time-symmetry, translated to block time steps, faces significant hurdles. For example, iteration can lead to oscillatory behavior, and even when such behavior is suppressed, energy errors show a linear drift in time. We present an approach that circumvents these problems.

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arXiv2005

Performance Tuning of N-Body Codes on Modern Microprocessors: I. Direct Integration with a Hermite Scheme on x86_64 Architecture

The main performance bottleneck of gravitational N-body codes is the force calculation between two particles. We have succeeded in speeding up this pair-wise force calculation by factors between two and ten, depending on the code and the processor on which the code is run. These speedups were obtained by writing highly fine-tuned code for x86_64 microprocessors. Any existing N-body code, running on these chips, can easily incorporate our assembly code programs. In the current paper, we present an outline of our overall approach, which we illustrate with one specific example: the use of a Hermite scheme for a direct N^2 type integration on a single 2.0 GHz Athlon 64 processor, for which we obtain an effective performance of 4.05 Gflops, for double precision accuracy. In subsequent papers, we will discuss other variations, including the combinations of N log N codes, single precision implementations, and performance on other microprocessors.

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arXiv2004

Black Holes in Massive Star Clusters

Close encounters and physical collisions between stars in young dense clusters can result in new channels for stellar evolution, and may lead to the formation of very massive stars and black holes via runaway merging. We present some details of this process, using the results of N-body simulations and simple analytical estimates to place limits on the cluster parameters for which it expected to occur. For small clusters, the mass of the runaway is effectively limited by the total number of high-mass stars in the system. For larger clusters, the runaway mass is determined by the fraction of stars that can mass-segregate to the cluster core while still on the main sequence. In typical cases, the result is in the range commonly cited for intermediate-mass black holes. This mechanism may therefore have important implications for the formation of massive black holes and black-hole binaries in dense cluster cores.

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arXiv2004

Which Globular Clusters contain Intermediate-mass Black Holes?

It has been assumed that intermediate-mass black holes (IMBHs) in globular clusters can only reside in the most centrally concentrated clusters, with a so-called `core-collapsed' density profile. While this would be a natural guess, it is in fact wrong. We have followed the evolution of star clusters containing IMBHs with masses between 125 \le M_{BH} \le 1000 M_{\odot} through detailed N-body simulations, and we find that a cluster with an IMBH, in projection, appears to have a relatively large `core' with surface brightness only slightly rising toward the center. This makes it highly unlikely that any of `core-collapsed' clusters will harbor an IMBH. On the contrary, the places to look for an IMBH are those clusters that can be fitted well by medium-concentration King models. The velocity dispersion of the visible stars in a globular cluster with an IMBH is nearly constant well inside the apparent core radius. For a cluster of mass M_C containing an IMBH of mass M_{BH}, the influence of the IMBH becomes significant only at a fraction 2.5 M_{BH}/M_C of the half-mass radius, deep within the core, where it will affect only a small number of stars. In conclusion, observational detection of an IMBH may be possible, but will be challenging.

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arXiv2004

The formation of massive black holes through collision runaway in dense young star clusters

A luminous X-ray source is associated with a cluster (MGG-11) of young stars \~200pc from the center of the starburst galaxy M82. The properties of the X-ray source are best explained by a black hole with a mass of at least 350Msun, which is intermediate between stellar-mass and supermassive black holes. A nearby but somewhat more massive star cluster (MGG-9) shows no evidence of such an intermediate mass black hole, 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 the motions of stars within the clusters, where stars are allowed to mergers with each other. We find that for MGG-11 dynamical friction leads to the massive stars sinking rapidly to the center of the cluster to participate in a runaway collision, thereby producing a star of 800-3000Msun, which ultimately collapses to an 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.

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arXiv2004

The formation of Kuiper-belt Binaries through Exchange Reactions

Recent observations have revealed an unexpectedly high binary fraction among the Trans-Neptunian Objects (TNOs) that populate the Kuiper-belt. The discovered binaries have four characteristics they comprise a few percent of the TNOs, the mass ratio of their components is close to unity, their internal orbits are highly eccentric, and the orbits are more than 100 times wider than the primary's radius. In contrast, theories of binary asteroid formation tend to produce close, circular binaries. Therefore, a new approach is required to explain the unique characteristics of the TNO binaries. Two models have been proposed. Both, however, require extreme assumptions on the size distribution of TNOs. Here we show a mechanism which is guaranteed to produces binaries of the required type during the early TNO growth phase, based on only one plausible assumption, namely that initially TNOs were formed through gravitational instabilities of the protoplanetary dust layer.

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arXiv2003

MODEST: modeling stellar evolution and (hydro)dynamics

Simulations of dense stellar systems currently face two major hurdles, one astrophysical and one computational. The astrophysical problem lies in the fact that several major stages in binary evolution, such as common envelope evolution, are still poorly understood. The best we can do in these cases is to parametrize our ignorance, in a way that is reminiscent of the introduction of a mixing length to describe convection in a single star, or an alpha parameter in modeling an accretion disk. The hope is that by modeling a whole star cluster in great detail, and comparing the results to the wealth of observational data currently available, we will be able to constrain the parameters that capture the unknown physics. The computational problem is one of composition: while we have accurate computer codes for modeling stellar dynamics, stellar hydrodynamics, and stellar evolution, we currently have no good way to put all this knowledge together in a single software environment. A year ago, a loosely-knit organization was founded to address these problems, MODEST for MOdeling DEnse STellar systems, with nine working groups and a series of meetings that are held every half year. This report reviews the first year of this initiative. Much more detail can be found on the MODEST web site http://www.manybody.org/modest.html .

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arXiv2003

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 WFPC2 and STIS instruments, and the results of dynamical simulations carried out using the special-purpose computer GRAPE-6. We have obtained good fits for models starting with single cluster King-model initial conditions and even better fits when starting our simulations with a dynamically constructed merger remnant 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 $M/L = 4.0 \pm 0.4$ and a total cluster mass of $M=(8\pm 1)\times 10^6 M_\odot$. 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.

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arXiv2003

Kuiper-belt Binary Formation through Exchange Reactions

Recent observations (Burnes et al 2002,Veillet et al 2002, Margot et al 2002a) have revealed an unexpectedly high binary fraction among the Trans-Neptunian Objects (TNOs) that populate the Kuiper Belt. The TNO binaries are strikingly different from asteroid binaries in four respects (Veillet et al 2002): their frequency is an order of magnitude larger, the mass ratio of their components is closer to unity, and their orbits are wider and highly eccentric. Two explanations have been proposed for their formation, one assuming large numbers of massive bodies (Weidenschilling 2002), and one assuming large numbers of light bodies (Goldreich et al 2002). We argue that both assumptions are unwarranted, and we show how TNO binaries can be produced from a modest number of intermediate-mass bodies of the type predicted by the gravitational instability theory for the formation of planetesimals (Goldreich and Ward 1973). We start with a TNO binary population similar to the asteroid binary population, but subsequently modified by three-body exchange reactions, a process that is far more efficient in the Kuiper belt, because of the much smaller tidal perturbations by the Sun. Our mechanism can naturally account for all four characteristics that distinguish TNO binaries from main-belt asteroid binaries.

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arXiv2003

Parameters of core-collapse

This paper considers the phenomenon of deep core collapse in collisional stellar systems, with stars of equal mass. The collapse takes place on some multiple, $ξ^{-1}$, of the central relaxation time, and produces a density profile in which $ρ\propto r^{-α}$, where $α$ is a constant. The parameters $α$ and $ξ$ have usually been determined from simplified models, such as gas and Fokker-Planck models, often with the simplification of isotropy. Here we determine the parameters directly from N-body simulations carried out using the newly completed GRAPE-6.

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arXiv2003

Star cluster ecology V: Dissection of an open star cluster--spectroscopy

We have modeled in detail the evolution of rich open star clusters such as the Pleiades, Praesepe and Hyades, using simulations that include stellar dynamics as well as the effects of stellar evolution. The dynamics is modeled via direct N-body integration, while the evolution of single stars and binaries is followed through the use of fitting formulae and recipes. The feedback of stellar and binary evolution on the dynamical evolution of the stellar system is taken into account self-consistently. Our model clusters dissolve in the tidal field of the Galaxy in a time span on the order of a billion years. The rate of mass loss is rather constant, about 1Msun per million years. The binary fraction at first is nearly constant in time, then increases slowly near the end of a cluster's lifetime. For clusters which are more than about 100 million years old the fractions of stars in the form of binaries, giants and collision products in the inner few core radii are considerably higher than in the outer regions, beyond the cluster's half mass radius. When stars with masses >2Msun escape from the cluster, they tend to do so with velocities higher than average....

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arXiv2002

MODEST-1: Integrating Stellar Evolution and Stellar Dynamics

We summarize the main results from MODEST-1, the first workshop on MOdeling DEnse STellar systems. Our goal is to go beyond traditional population synthesis models, by introducing dynamical interactions between single stars, binaries, and multiple systems. The challenge is to define and develop a software framework to enable us to combine in one simulation existing computer codes in stellar evolution, stellar dynamics, and stellar hydrodynamics. With this objective, the workshop brought together experts in these three fields, as well as other interested astrophysicists and computer scientists. We report here our main conclusions, questions and suggestions for further steps toward integrating stellar evolution and stellar (hydro)dynamics.

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arXiv2002

Long-term evolution of isolated N-body sytems

We report results of N-body simulations of isolated star clusters, performed up to the point where the clusters are nearly completely dissolved. Our main focus is on the post-collapse evolution of these clusters. We find that after core collapse, isolated clusters evolve along nearly a single sequence of models whose properties are independent of the initial density profile and particle number. Due to the slower expansion of high-N clusters, relaxation times become almost independent of the particle number after several core collapse times, at least for the particle range of our study. As a result, the dissolution times of isolated clusters exhibit a surprisingly weak dependence on N. We find that most stars escape due to encounters between single stars inside the half-mass radius of the cluster. Encounters with binaries take place mostly in the cluster core and account for roughly 15% of all escapers. Encounters between single stars at intermediate radii are also responsible for the build up of a radial anisotropic velocity distribution in the halo. For clusters undergoing core oscillations, escape due to binary stars is efficient only when the cluster center is in a contracted phase. Our simulations show that it takes about 10^5 N-body time units until the global anisotropy reaches its maximum value. The anisotropy increases with particle number and it seems conceivable that isolated star clusters become vulnerable to radial orbit instabilities for large enough N. However, no indication for the onset of such instabilities was seen in our runs.

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arXiv2002

The Starlab Environment for Dense Stellar Systems

Traditionally, a simulation of a dense stellar system required choosing an initial model, running an integrator, and analyzing the output. Almost all of the effort went into writing a clever integrator that could handle binaries, triples and encounters between various multiple systems efficiently. Recently, the scope and complexity of these simulations has increased dramatically, for three reasons: 1) the sheer size of the data sets, measured in Terabytes, make traditional `awking and grepping' of a single output file impractical; 2) the addition of stellar evolution data brings qualitatively new challenges to the data reduction; 3) increased realism of the simulations invites realistic forms of `SOS': Simulations of Observations of Simulations, to be compared directly with observations. We are now witnessing a shift toward the construction of archives as well as tailored forms of visualization including the use of virtual reality simulators and planetarium domes, and a coupling of both with budding efforts in constructing virtual observatories. This review describes these new trends, presenting Starlab as the first example of a full software environment for realistic large-scale simulations of dense stellar systems.

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arXiv2001

Theory in a Virtual Observatory

During the last couple of years, observers have started to make plans for a Virtual Observatory, as a federation of existing data bases, connected through levels of software that enable rapid searches, correlations, and various forms of data mining. We propose to extend the notion of a Virtual Observatory by adding archives of simulations, together with interactive query and visualization capabilities, as well as ways to simulate observations of simulations in order to compare them with observations. For this purpose, we have already organized two small workshops, earlier in 2001, in Tucson and Aspen. We have also provided concrete examples of theory data, designed to be federated with a Virtual Observatory. These data stem from a project to construct an archive for our large-scale simulations using the GRAPE-6 (a 32-Teraflops special purpose computer for stellar dynamics). We are constructing interfaces by which remote observers can observe these simulations. In addition, these data will enable detailed comparisons between different simulations.

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arXiv2001

The lives and deaths of star clusters near the Galactic center

We study the evolution and observability of young, compact star clusters near the Galactic center, such as the Arches and Quintuplet systems. The clusters are modeled by integrating the equations of motion of all stars while accounting for the internal evolution of stars and binaries, as well as the effect of the Galactic tidal field. We find that clusters within 150 pc of the Galactic center dissolve within ~55 Myr, but their projected densities drop below the background density in the direction of the Galactic center within only a few Myr, effectively making these clusters undetectable after that time. Detailed observations of the Arches cluster, taken at face value, suggest that its mass function is unusually flat and that the cluster contains an overabundance of stars more massive than 20 Msun. Our dynamical analysis, however, shows that the observed characteristics of the Arches cluster are consistent with a perfectly normal initial mass function. The observed anomalies are then caused by a combination of observational selection effects and the dynamical evolution of the cluster. We calibrate the current parameters of the Arches cluster using a normal initial mass function and conclude that the cluster is more massive than 40000 Msun, has a half mass radius of about 0.35 pc and is located between 50 and 90 pc from the Galactic center.

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