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Since we cannot put stars in a laboratory, astrophysicists had to wait till the invention of computers before becoming laboratory scientists. For half a century now, we have been conducting experiments in our virtual laboratories. However, we ourselves have remained behind the keyboard, with the screen of the monitor separating us from the world we are simulating. Recently, 3D on-line technology, developed first for games but now deployed in virtual worlds like Second Life, is beginning to make it possible for astrophysicists to enter their virtual labs themselves, in virtual form as avatars. This has several advantages, from new possibilities to explore the results of the simulations to a shared presence in a virtual lab with remote collaborators on different continents. I will report my experiences with the use of Qwaq Forums, a virtual world developed by a new company (see http://www.qwaq.com), Comment: 10 pages, 2 figures, Conference proceedings for IAUS246 'Dynamical Evolution of Dense Stellar Systems', ed. E. Vesperini (Chief Editor), M. Giersz, A. Sills, Capri, Sept. 2007

Black holes and neutron stars present extreme forms of matter that cannot be created as such in a laboratory on Earth. Instead, we have to observe and analyze the experiments that are ongoing in the Universe. The most telling observations of black holes and neutron stars come from dense stellar systems, where stars are crowded close enough to each other to undergo frequent interactions. It is the interplay between black holes, neutron stars and other objects in a dense environment that allows us to use observations to draw firm conclusions about the properties of these extreme forms of matter, through comparisons with simulations. The art of modeling dense stellar systems through computer simulations forms the main topic of this review., Comment: 23 pages, to appear in Prog. Theor. Phys

(Simplified) We present a theoretical framework which establishes how the core radius of a star cluster varies with the mass of an assumed central black hole. Our result is that the ratio of core to half-mass radius varies as the 3/4 power of the ratio of the black hole to cluster mass, when the system is well relaxed. The theory compares favourably with a number of simulations of this problem, which extend to black hole masses of order 10% of the cluster mass. Though strictly limited as yet to clusters with stars of equal mass, our conclusion strengthens the view that clusters with large core radii are the most promising candidates in which to find a massive black hole., Comment: 4 pages, 2 figures, to appear in PASJ Letters, PASJ Vol. 59, No. 3. (to be issued on June 25, 2007). Minor revisions

I provide some background about recent efforts made in modeling dense stellar systems, within the context of the MODEST initiative. During the last four years, we have seen more than fifteen MODEST workshops, with an attendance between twenty and a hundred participants, and topics ranging from very specialized discussions to rather general overviews., Comment: to appear in the proceedings for JD06, IAU Highlights of Astronomy, Volume 14, ed. K. van der Hucht

At the frontier of most areas in science, computer simulations play a central role. The traditional division of natural science into experimental and theoretical investigations is now completely outdated. Instead, theory, simulation, and experimentation form three equally essential aspects, each with its own unique flavor and challenges. Yet, education in computational science is still lagging far behind, and the number of text books in this area is minuscule compared to the many text books on theoretical and experimental science. As a result, many researchers still carry out simulations in a haphazard way, without properly setting up the computational equivalent of a well equipped laboratory. The art of creating such a virtual laboratory, while providing proper extensibility and documentation, is still in its infancy. A new approach is described here, Open Knowledge, as an extension of the notion of Open Source software. Besides open source code, manuals, and primers, an open knowledge project provides simulated dialogues between code developers, thus sharing not only the code, but also the motivations behind the code., Comment: to appear in Prog. Theor. Phys

The Gravity Tractor (GT) is a fully controlled asteroid deflection concept using the mutual gravity between a robotic spacecraft and an asteroid to slowly accelerate the asteroid in the direction of the "hovering" spacecraft. Based on early warning, provided by ground tracking and orbit prediction, it would be deployed a decade or more prior to a potential impact. Ion engines would be utilized for both the rendezvous with the asteroid and the towing phase. Since the GT does not dock with or otherwise physically contact the asteroid during the deflection process there is no requirement for knowledge of the asteroid's shape, composition, rotation state or other "conventional" characteristics. The GT would first reduce the uncertainty in the orbit of the asteroid via Earth tracking of its radio transponder while station keeping with the asteroid. If, after analysis of the more precise asteroid orbit a deflection is indeed indicated, the GT would "hover" above the surface of the asteroid in the direction of the required acceleration vector for a duration adequate to achieve the desired velocity change. The orbit of the asteroid is continuously monitored throughout the deflection process and the end state is known in real time. The performance envelope for the GT includes most NEOs which experience close gravitational encounters prior to impact and those below 150-200 meters in diameter on a direct Earth impact trajectory., Comment: Submitted to NASA Workshop on Near-Earth Objects, Vail, Colorado, June 2006

Given a primary interest in "mitigation of the potential hazard" of near-Earth objects impacting the Earth, the subject of characterization takes on an aspect not normally present when considering asteroids as abstract bodies. Many deflection concepts are interested in the classic geophysical characteristics of asteroids when considering the physical challenge of modifying their orbits in order to cause them to subsequently miss an impact with Earth. Yet for all deflection concepts there are characteristics of the threat which overwhelm these traditional factors. For example, a close gravitational encounter with Earth some years or decades prior to impact can reduce the velocity change necessary for deflection by several orders of magnitude if the deflection precedes the close encounter (or encounters). Conversely this "benefit" comes at a "price"; a corresponding increase in the accuracy of tracking required to determine the probability of impact. Societal issues, both national and international, also characterize the NEO deflection process and these may strongly contend with the purely technical issues normally considered. Therefore critical factors not normally considered must be brought into play as one characterizes the threat of NEO impacts., Comment: Submitted to NASA Workshop on Near-Earth Objects, Vail, Colorado, June 2006

The Asteroid Tugboat (AT) is a fully controlled asteroid deflection concept using a robotic spacecraft powered by a high efficiency, electric propulsion system (ion or plasma) which docks with and attaches to the asteroid, conducts preliminary operations, and then thrusts continuously parallel to the asteroid velocity vector until the desired velocity change is achieved. Based on early warning, provided by ground tracking and orbit prediction, it would be deployed a decade or more prior to a potential impact. On completion of the initial rendezvous with the near-Earth object (NEO) the AT would first reduce the uncertainty in the orbit of the asteroid via Earth tracking of its radio transponder while it is station keeping with the asteroid. If on analysis of tracking data a deflection is required the AT would execute a reconnaissance phase collecting and processing information about the physical characteristics of the asteroid to support subsequent operations. The AT would then dock at the appropriate pole (i.e. on the spin axis), attach to the asteroid surface, and initiate a NEO reorientation maneuver. Following completion of the NEO reorientation the AT would initiate the deflection phase by thrusting continuously parallel to the asteroid velocity vector until the resultant target orbit is achieved. The orbit of the asteroid is continuously monitored throughout the deflection process and the end state is known in real time. If one assumes a nuclear-electric propulsion (NEP) system similar to that formerly under development in the recently canceled Prometheus Program, the AT would be capable of deflecting threatening NEOs up to 800 meters in diameter or more., Comment: Submitted to NASA Workshop on Near-Earth Objects, Vail, Colorado, June 2006

We answer the long-standing question of which production mechanism is responsible for the cataclysmic variables (CVs) in globular clusters. Arguments have been given that range from mostly primordial presence to a significant contribution of later dynamical formation in close stellar encounters. We conclude, based on a thorough analysis of a homogeneous {\it Chandra} data set, that the majority of CVs in globulars has a dynamical origin., Comment: submitted to ApJL; comments welcome

The method of choice for integrating the equations of motion of the general N-body problem has been to use an individual time step scheme. For the sake of efficiency, block time steps have been the most popular, where all time step sizes are smaller than a maximum time step size by an integer power of two. We present the first successful attempt to construct a time-symmetric integration scheme, based on block time steps. We demonstrate how our scheme shows a vastly better long-time behavior of energy errors, in the form of a random walk rather than a linear drift. Increasing the number of particles makes the improvement even more pronounced.

Galactic nuclei and globular clusters act as laboratories in which nature experiments with normal stars, neutron stars and black holes, through collisions and through the formation of bound states, in the form of binaries. The main difference with the usual Earth-based laboratories is that we cannot control the experiments. Instead, we have no choice but to create virtual laboratories on Earth, in order to simulate all the relevant physics in large-scale computational experiments. This implies a realistic treatment of stellar dynamics, stellar evolution, and stellar hydrodynamics. Each of these three fields has its own legacy codes, workhorses that are routinely used to simulate star clusters, stars, and stellar collisions, respectively. I outline the main steps that need to be taken in order to embed and where needed transform these legacy codes in order to produce a far more modular and robust environment for modeling dense stellar systems. The time is right to do so: within a few years computers will reach the required speed, in the Petaflops range, to follow a star cluster with a million stars for ten billion years, while resolving the internal binary and multiple star motions. By that time simulation software will be the main bottleneck in our ability to analyze dense stellar systems. Only through full-scale simulations will we be able to critically test our understanding of the `microphysics' of stellar collisions and their aftermath, in a direct comparison with observations., Comment: review paper, presented at A Life With Stars (Conference in Honor of Ed van den Heuvel), Amsterdam, August, 2005

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., Comment: Published in 2003 in the proceedings of the 35th Symposium on Celestial Mechanics. 8 pages

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., Comment: 26 pages, ApJ in press. Old title: The Galactic center welcomes black hole immigrants

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., Comment: 14 pages, 3 figures, submitted for publication in New Astronomy

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., Comment: 32 pages, 2 figures

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., Comment: 8 pages, 2 figures; to appear in "Formation and Evolution of Massive Young Star Clusters," eds. H.J.G.L.M. Lamers, A. Nota & L.J. Smith

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., Comment: 13 pages, 3 figures, Accepted ofr publication in ApJ (scheduled for February 2005)

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., Comment: Accepted for publication in Nature (Including supplementary information)

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., Comment: 12pages, 4 figures

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 ., Comment: 4 pages, review talk presented at JD-11, IAU General Assembly XXV, Sydney, July 2003, to be included in Highlights of Astronomy, Vol. 13

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., Comment: 11 pages, 3 Figures

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., Comment: 12 pages, 3 figures, ApJL accepted, minor changes

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, $\xi ^{-1}$, of the central relaxation time, and produces a density profile in which $\rho \propto r^{-\alpha}$, where $\alpha$ is a constant. The parameters $\alpha$ and $\xi$ 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., Comment: 5 pages, 3 figures, accepted by MNRAS. Reference added to Table 1

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.... , Comment: 17 pages, submitted to MNRAS

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., Comment: workshop summary, to appear in New Astronomy, 36 pages, 3 figures; this slightly revised version mainly contains more references

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., Comment: 14 pages, 20 figures, MNRAS in press, V2: Order of authors changed in author-field

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., Comment: 12 pages, 1 figure, to appear in "Astrophysical Supercomputing Using Particle Simulations", eds. P. Hut and J. Makino, IAU Symposium 208, Tokyo, July 2001

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., Comment: 4 pages, ADASS-XI conference, http://bima.astro.umd.edu/nemo/nvo/

Observations of stellar kinematics, gas dynamics and masers around galactic nuclei have now firmly established that many galaxies host central supermassive black holes (SMBHs) with masses in the range $10^6 \sim 10^9$M$_{\odot}$. However, how these SMBHs formed is not well understood. One reason for this situation is the lack of observations of intermediate-mass BHs (IMBHs), which could bridge the gap between stellar-mass BHs and SMBHs. Recently, this missing link (i.e., an IMBH) has been found in observations made by the ASCA and the Chandra of the central region of the starburst galaxy M82 \citep{MT99, PG99, MT01, Ka01}. Subsequent observations by SUBARU have revealed that this IMBH apparently coincides with a young compact star cluster. Based on these findings, we suggest a new formation scenario for SMBHs. In this scenario, IMBHs first form in young compact star clusters through runaway merging of massive stars. While these IMBHs are forming, the host star clusters sink toward the galactic nucleus through dynamical friction, and upon evaporation deposit their IMBHs near the galactic center. The IMBHs then form binaries and eventually merge via gravitational radiation, forming an SMBH., Comment: 12 pages 2 figuresm submitted to Astrophysical Journal, Letters

N-body simulations of star cluster evolution have reached a high degree of realism, by incorporating more and more elements of stellar dynamics, stellar evolution, and hydrodynamics. At the end of this conference, six participants discussed how to present the increasingly realistic data from star cluster simulations in a way that is most useful for a direct comparison with observations., Comment: 7 pages, LaTeX, to appear in the proceedings for the conference on Stellar Collisions, Mergers, and their Consequences, held in New York, June 2000, ed.: M. Shara [ASP Conference Series]

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., Comment: 21 pages, to be published on Januari 1, 2001 in ApJ v564

In dense clusters a bewildering variety of interactions between stars can be observed, ranging from simple encounters to collisions and other mass-transfer encounters. With faster and special-purpose computers like GRAPE, the amount of data per simulation is now exceeding 1TB. Visualization of such data has now become a complex 4D data-mining problem, combining space and time, and finding interesting events in these large datasets. We have recently starting using the virtual reality simulator, installed in the Hayden Planetarium in the American Museum for Natural History, to tackle some of these problem. This work (http://www.astro.umd.edu/nemo/amnh/) reports on our first ``observations'', modifications needed for our specific experiments, and perhaps field ideas for other fields in science which can benefit from such immersion. We also discuss how our normal analysis programs can be interfaced with this kind of visualization., Comment: 4 pages, 1 figure, ADASS-X conference proceedings

We study the occurrence of physical collisions between stars in young and compact star cluster. The calculations are performed on the GRAPE-4 with the starlab software environment which include the dynamical evolution and the nuclear evolution of all stars and binaries. The selection of the initial conditions is based on existing and well observed star clusters, such as R136 in the 30 Doradus region in the Large Magellanic Cloud and the Arches and Quintuplet star clusters in the vicinity of the Galactic center. Collisions between stars occurred rather frequently in our models. At any time a single star dominates the collision history of the system. The collision rate of this runaway merger scales with the initial relaxation time of the cluster and is independent on other cluster parameters, such as the initial mass function or the initial density profile of the cluster. Subsequent encounters result in a steady grow in mass of the coagulating star, until it escapes or explodes in a supernova. The collision rate in these models is about 0.00022 collisions per star per Myr for a cluster with an initial relaxation time of 1 Myr., Comment: 15 pages, to be published in 'Stellar Collisions, Mergers, and their Consequences', ASP Conference Series (ed. M. Shara)

We study the evolution and observability of young compact star clusters within about 200pc of the Galactic center. Calculations are performed using direct N-body integration on the GRAPE-4, including the effects of both stellar and binary evolution and the external influence of the Galaxy. The results of these detailed calculations are used to calibrate a simplified model applicable over a wider range of cluster initial conditions. We find that clusters within 200 pc from the Galactic center dissolve within about 70 Myr. However, their projected densities drop below the background density in the direction of the Galactic center within 20 Myr, effectively making these clusters undetectable after that time. Clusters farther from the Galactic center but at the same projected distance are more strongly affected by this selection effect, and may go undetected for their entire lifetimes. Based on these findings, we conclude that the region within 200 pc of the Galactic center could easily harbor some 50 clusters with properties similar to those of the Arches or the Quintuplet systems., Comment: ApJ Letters in press

The evolution of star clusters is studied using N-body simulations in which the evolution of single stars and binaries are 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. Our model clusters are generally significantly flattened in the Galactic tidal field, and dissolve before deep core collapse occurs. The binary fraction decreases initially due to 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 formed white dwarfs 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 center. Mass 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. Open clusters are dynamically rather inactive. However, the combined effect of stellar mass loss and evaporation of stars from the cluster potential drives its dissolution on a much shorter timescale 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., Comment: reduced abstract, 33 pages (three separate color .jpg figures), submitted to MNRAS

The evolution of young compact star clusters is studied using N-body simulations in which both stellar evolution and physical collisions between stars are taken into account. The initial conditions are chosen to represent R136, a compact star cluster in the 30 Doradus region of the Large Magellanic Cloud. The present runs do not include the effects of primordial binaries. We find that physical collisions between stars in these models are frequent, and that the evolution of the most massive stars and the dynamical evolution of the cluster are closely coupled. In all cases, a single star grows steadily in mass through mergers with other stars, forming a very massive (>100 Msun) star in less than 3-4 Myr. The growth rate of this runaway merger is much larger than estimates based on simple cross-section arguments, mainly because the star is typically found in the core and tends to form binaries with other massive stars there. The runaway is ``rejuvenated'' by each new collision, and its lifetime is extended considerably as a consequence. Observationally, such a star will appear in the Hertzsprung-Russell diagram as a blue straggler. When the runaway forms a black hole, the binary in which it is found is usually dissociated., Comment: A&A in press: 11 pages, 13 figures and one MPEG animation at http://www.sns.ias.edu/~starlab/research/30Doradus/

The next decade will be an exciting time for computational physicists. After 50 years of being forced to use standardized commercial equipment, it will finally become relatively straightforward to adapt one's computing tools to one's own needs. The breakthrough that opens this new era is the now wide-spread availability of programmable chips that allow virtually every computational scientist to design his or her own special-purpose computer., Comment: 5 pages, to apper in IEEE Computing in Science and Engineering

The GRAPE-4, the world's fastest computer in 1995-1997, has produced some major scientific results, through a wide diversity of large-scale simulations in astrophysics. Applications have ranged from planetary formation, through the evolution of star clusters and galactic nuclei, to the formation of galaxies and clusters of galaxies., Comment: 15 pages, to apper in Science

Stellar dynamics is almost unreasonably well suited for an implementation in terms of special-purpose hardware. Unlike the case of molecular dynamics, stellar dynamics deals exclusively with a long-range force, gravity, which leads to a computational cost scaling as the square of the number of stars involved. While special tricks can lead to a reduction of this cost from $\sim N^2$ to $\sim N\log N$ in the case of very large particle numbers, such tricks are not suitable for all areas within stellar dynamics. When a stellar system is close to equilibrium, and has a very high density, it still pays to compute all interactions on a star by star basis, even for $N=10^5$. Any $cN\log N$ approach would either gloss over the subtle net effects of near-canceling interactions, driving the evolution of such a system, or would carry a prohibitively large coefficient $c$. This paper presents a brief introduction to the stellar dynamics of dense stellar systems, aimed at researchers using special purpose computers in other branches of physics., Comment: 10 pages, LaTeX, to appear in the proceedings for the International Symposium on Supercomputing, held in Tokyo, Japan, September 1-3, 1997

Using direct N-body simulations which include both the evolution of single stars and the tidal field of the parent galaxy, we study the dynamical evolution of globular clusters and rich open clusters. We compare our results with other N-body simulations and Fokker-Planck calculations. Our simulations, performed on the GRAPE-4, employ up to 32,768 stars. The results are not in agreement with Fokker-Planck models, in the sense that the lifetimes of stellar systems derived using the latter are an order of magnitude smaller than those obtained in our simulations. For our standard run, Fokker-Plank calculations obtained a lifetime of 0.28 Gyr, while our equivalent N-body calculations find about 4 Gyr. The principal reason for the discrepancy is that a basic assumption of the Fokker-Plank approach is not valid for typical cluster parameters. The stellar evolution timescale is comparable to the dynamical timescale, and therefore the assumption of dynamical equilibrium leads to an overestimate of the dynamical effects of mass loss. Our results suggest that the region in parameter space for which Fokker-Planck studies of globular cluster evolution, including the effects of both stellar evolution and the galactic tidal field, are valid is limited. The discrepancy is largest for clusters with short lifetimes., Comment: 10 pages including 9 figures, Latex; A&A in press

We derive from first principles equations governing (a) the quadrupole tensor of a star distorted by both rotation and the presence of a companion in a possibly eccentric orbit, (b) a functional form for the dissipative force of tidal friction, based on the concept that the rate of energy loss from a time-dependent tide should be a positive-definite function of the rate of change of the quadrupole tensor as seen in the frame which rotates with the star, and (c) the equations governing the rates of change of the magnitude and direction of the stellar rotation, and the orbital period and eccentricity, based on the concept of the Laplace-Runge-Lenz vector. Our analysis leads relatively simply to a closed set of equations, valid for arbitrary inclination of the stellar spin to the orbit. The results are equivalent to classical results based on the rather less clear principle that the tidal bulge lags behind the line of centres by some time determined by the rate of dissipation; our analysis gives the effective lag time as a function of the dissipation rate and the quadrupole moment. We discuss briefly some possible applications of the formulation., Comment: LaTeX, 1 postscript figure included, ApJ, accepted

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 N_hop 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 straight-forward. 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., Comment: LaTeX, 18 pages, 7 Postscript figures included. ApJ, in press. Source code available from http://www.sns.ias.edu/~eisenste/hop/hop.html

We present the results from a two-day study in which we discussed various implementations of Smooth Particle Hydrodynamics (SPH), one of the leading methods used across a variety of areas of large-scale astrophysical simulations. In particular, we evaluated the suitability of designing special hardware extensions, to further boost the performance of the high-end general purpose computers currently used for those simulations. We considered a range of hybrid architectures, consisting of a mix of custom LSI and reconfigurable logic, combining the extremely high throughput of Special-Purpose Devices (SPDs) with the flexibility of reconfigurable structures, based on Field Programmable Gate Arrays (FPGAs). The main findings of our workshop consist of a clarification of the decomposition of the computational requirements, together with specific estimates for cost/performance improvements that can be obtained at each stage in this decomposition, by using enabling hardware technology to accelerate the performance of general purpose computers., Comment: 12 pages, TeX, report of a workshop, held on June 18-19, 1997, at the Institute for Advanced Study, Princeton

Three-body effects greatly complicate stellar evolution. We model the effects of encounters of binaries with single stars, based on parameters chosen from conditions prevalent in the cores of globular clusters. For our three-body encounters, we start with a population of primordial binaries, and choose incoming stars from the evolving single star populations of Portgies Zwart, Hut and Verbunt (1997). In addition, we study the formation of new binaries through tidal capture among the single stars. In subsequent papers in this series, we will combine stellar evolution with the dynamics of a full N-body system., Comment: 16 pages including 11 figures, Latex

The gravitational N-body problem, for $N>2$, is the oldest unsolved problem in mathematical physics. Some of the most ideal examples that can be found in nature are globular star clusters, with $N \sim 10^6$. In this overview, I discuss six types of fundamental sources of unpredictability, each of which poses a different challenge to attempts to determine the long-term behavior of these systems, governed by a peculiar type of thermodynamics., Comment: 19 pages, 5 included figures, Tex, uses psfig.tex. To appear in `Complexity', as part of the Proceedings of the Workshop on Fundamental Sources of Unpredictability, held at the Santa Fe Institute, March 28-30, 1996, eds. James Hartle, Piet Hut, and Joseph Traub

We present two types of meta-algorithm that can greatly improve the accuracy of existing algorithms for integrating the equations of motion of dynamical systems. The first meta-algorithm takes an integrator that is time-symmetric only for constant time steps, and ensures time-symmetry even in the case of varying time steps. The second meta-algorithm can be applied to any self-starting integration scheme to create time-symmetry, both for constant and for variable time steps, even if the original scheme was not time-symmetric. Our meta-algorithms are most effective for Hamilton systems or systems with periodic solutions. If the system is not Hamiltonian (for example, if some dissipative force exists), our methods are still useful so long as the dissipation is small., Comment: 6 pages, 2 included figures, LaTeX, uses paspconf.sty. To appear in `Computational Astrophysics', the Proceedings of the 12th `Kingston meeting' on Theoretical Astrophysics, eds. D. A. Clarke and M. J. West, ASP Conference Series, Vol. XXX (San Francisco: ASP)

Recently, special-purpose computers have surpassed general-purpose computers in the speed with which large-scale stellar dynamics simulations can be performed. Speeds up to a Teraflops are now available, for simulations in a variety of fields, such as planetary formation, star cluster dynamics, galactic nuclei, galaxy interactions, galaxy formation, large scale structure, and gravitational lensing. Future speed increases for special-purpose computers will be even more dramatic: a Petaflops version, tentatively named the GRAPE-6, could be built within a few years, whereas general-purpose computers are expected to reach this speed somewhere in the 2010-2015 time frame. Boards with a handful of chips from such a machine could be made available to individual astronomers. Such a board, attached to a fast workstation, will then deliver Teraflops speeds on a desktop, around the year 2000., Comment: 12 pages, LaTex, uses paspconf.sty. To appear in `Computational Astrophysics', the Proceedings of the 12th `Kingston meeting' on Theoretical Astrophysics, eds. D. A. Clarke and M. J. West, ASP Conference Series, Vol. XXX (San Francisco: ASP)

We present the outline of a research project aimed at designing and constructing a hybrid computing system that can be easily scaled up to petaflops speeds. As a first step, we envision building a prototype which will consist of three main components: a general-purpose, programmable front end, a special-purpose, fully hardwired computing engine, and a multi-purpose, reconfigurable system. The driving application will be a suite of particle-based large-scale simulations in various areas of physics. The prototype system will achieve performance in the $\sim 50 - 100$ teraflops range for a broad class of applications in this area. The combination of a hardwired petaflops-class computational engine and a front end with sustained speed on the order of 10 gigaflops can produce extremely high performance, but only for the limited class of problems in which there exists a single bottleneck with computing cost dominating the total. While the calculation for which the Grape-4 (our system's immediate predecessor) was designed is a prime example of such a problem, in many other applications the primary computational bottleneck, while still related to an inverse-square (gravitational, Coulomb, etc.) force, requires less than 99% of the computing power. Although the remainder of the CPU time is typically dominated by just one secondary bottleneck, its nature varies greatly from problem to problem. It is not cost-effective to attempt to design custom chips for each new problem that arises. FPGA-based systems can restore the balance, guaranteeing scalability from the teraflops to the petaflops domain, while still retaining significant flexibility. (abbreviated abstract), Comment: LaTeX, 16 pages, to appear in the proceedings of the 1997 Petaflops Algorithms Workshop (PAL'97), held on April 13-18, 1997 in Williamsburg, Virginia

Star clusters with a high central density contain an ecological network of evolving binaries, affected by interactions with passing stars, while in turn affecting the energy budget of the cluster as a whole by giving off binding energy. This is the first paper in a series aimed at providing the tools for increasingly realistic simulations of these ecological networks., Comment: 14 pages including 7 figures, Accepted for publication in Astronomy and Astrophysics

We present cross sections and reaction rates for merging to occur during encounters of equal-mass spherical galaxies. As an application, we determine the rate of galaxy merging in clusters of galaxies. We present results for two types of Plummer models (a full and a truncated one), two King models and the Hernquist model. Cross sections are determined on the basis of a large number ($\sim 500$) of simulations of galaxy encounters, using the 10-Gigaflops GRAPE 3A special-purpose computer. We characterize the overall merger rate of galaxies in a galaxy cluster by a single number, derived from our cross sections by an integration over galaxy encounter velocities in the limit of a constant density in velocity space. For small clusters, where the cluster velocity dispersion may not significantly exceed the internal velocity dispersion of the individual galaxies, this constant-density approximation may not be valid. For those cases, we present separate results, based on integrations of our cross sections over Maxwellian velocity distributions. Finally, tidal effects from the cluster potential as well as from neighboring galaxies may prevent a barely bound galaxy pair from spiraling in after their first encounter. We give a quantitative estimate of the resulting reduction in the actual merger rate, due to these tidal interactions., Comment: To appear in ApJ (May 20, 1997 issue) 22 pages, 14 figures, Postscript (or GIF) version available at http://grape.c.u-tokyo.ac.jp/pub/people/makino/papers/rate.ps or http://grape.c.u-tokyo.ac.jp/pub/people/makino/papers/rate.html