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 Piet Hut Physics , 1998, Abstract: 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.
 Piet Hut Physics , 2006, Abstract: 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.
 Physics , 2010, DOI: 10.1111/j.1365-2966.2010.17925.x Abstract: Two coalescing black holes (BHs) represent a conspicuous source of gravitational waves (GWs). The merger involves 17 parameters in the general case of Kerr BHs, so that a successful identification and parameter extraction of the information encoded in the waves will provide us with a detailed description of the physics of BHs. A search based on matched-filtering for characterization and parameter extraction requires the development of some $10^{15}$ waveforms. If a third additional BH perturbed the system, the waveforms would not be applicable, and we would need to increase the number of templates required for a valid detection. In this letter, we calculate the probability that more than two BHs interact in the regime of strong relativity in a dense stellar cluster. We determine the physical properties necessary in a stellar system for three black holes to have a close encounter in this regime and also for an existing binary of two BHs to have a strong interaction with a third hole. In both cases the event rate is negligible. While dense stellar systems such as galactic nuclei, globular clusters and nuclear stellar clusters are the breeding grounds for the sources of gravitational waves that ground-based detectors like Advanced LIGO and Advanced VIRGO will be exploring, the analysis of the waveforms in full general relativity needs only to evaluate the two-body problem. This reduces the number of templates of waveforms to create by orders of magnitude.
 Natalia Ivanova Physics , 2011, DOI: 10.1063/1.3536357 Abstract: In contrast to the field, the binaries in dense stellar systems are frequently not primordial, and could be either dynamically formed or significantly altered from their primordial states. Destruction and formation of binaries occur in parallel all the time. The destruction, which constantly removes soft binaries from a binary pool, works as an energy sink and could be a reason for cluster entering the binary-burning phase. The true binary fraction is greater than observed, as a result, the observable binary fraction evolves differently from the predictions. Combined measurements of binary fractions in globular clusters suggest that most of the clusters are still core-contracting. The formation, on other hand, affects most the more evolutionary advanced stars, which significantly enhances the population of X-ray sources in globular clusters. The formation of binaries with a compact objects proceeds mainly through physical collisions, binary-binary and single-binary encounters; however, it is the dynamical formation of triples and multiple encounters that principally determine whether the formed binary will become an X-ray source.
 Physics , 2009, DOI: 10.1111/j.1745-3933.2009.00777.x Abstract: We compile observations of the surface mass density profiles of dense stellar systems, including globular clusters in the Milky Way and nearby galaxies, massive star clusters in nearby starbursts, nuclear star clusters in dwarf spheroidals and late-type disks, ultra-compact dwarfs, and galaxy spheroids spanning the range from low-mass cusp bulges and ellipticals to massive core ellipticals. We show that in all cases the maximum stellar surface density attained in the central regions of these systems is similar, Sigma_max ~ 10^11 M_sun/kpc^2 (~20 g/cm^2), despite the fact that the systems span 7 orders of magnitude in total stellar mass M_star, 5 in effective radius R_e, and have a wide range in effective surface density M_star/R_e^2. The surface density limit is reached on a wide variety of physical scales in different systems and is thus not a limit on three-dimensional stellar density. Given the very different formation mechanisms involved in these different classes of objects, we argue that a single piece of physics likely determines Sigma_max. The radiation fields and winds produced by massive stars can have a significant influence on the formation of both star clusters and galaxies, while neither supernovae nor black hole accretion are important in star cluster formation. We thus conclude that feedback from massive stars likely accounts for the observed Sigma_max, plausibly because star formation reaches an Eddington-like flux that regulates the growth of these diverse systems. This suggests that current models of galaxy formation, which focus on feedback from supernovae and active galactic nuclei, are missing a crucial ingredient.
 Physics , 2014, DOI: 10.1103/PhysRevD.90.103008 Abstract: TeV gamma-ray emission has been recently observed from direction of a few open clusters containing massive stars. We consider the high energy processes occurring within massive binary systems and in their dense environment by assuming that nuclei, from the stellar winds of massive stars, are accelerated at the collision region of the stellar winds. We calculate the rates of injection of protons and neutrons from fragmentation of these nuclei in collisions with stellar radiation and matter of the winds from the massive companions in binary system. Protons and neutrons can interact with the matter, within the stellar wind cavity and within the open cluster, producing pions which decay into $\gamma$-rays and neutrinos. We discuss the detectability of such $\gamma$-ray emission by the present and future Cherenkov telescopes for the case of two binary systems Eta Carinae, within the Carina Nebula, and WR 20a, within the Westerlund 2 open cluster. We also calculate the neutrino fluxes produced by protons around the binary systems and within the open clusters. This neutrino emission is confronted with ANTARES upper limits on the neutrino fluxes from discrete sources and with the sensitivity of IceCube.
 Physics , 2009, DOI: 10.1088/0004-637X/696/1/298 Abstract: We present the chemistry, temperature, and dynamical state of a sample of 193 dense cores or core candidates in the Perseus Molecular cloud and compare the properties of cores associated with young stars and clusters with those which are not. The combination of our NH3 and CCS observations with previous millimeter, sub-millimeter, and Spitzer data available for this cloud enable us both to determine core properties precisely and to accurately classify cores as starless or protostellar. The properties of cores in different cluster environments and before-and-after star formation provide important constraints on simulations of star-formation, particularly under the paradigm that the essence of star formation is set by the turbulent formation of prestellar cores. We separate the influence of stellar content from that of cluster environment and find that cores within clusters have (1) higher kinetic temperatures and (2) lower fractional abundances of CCS and NH3. Cores associated with protostars have (1) slightly higher kinetic temperatures (2) higher NH3 excitation temperatures), (3) are at higher column density, have (4) slightly more non-thermal/turbulent NH3 linewidths, have (5) higher masses and have (6) lower fractional abundance of CCS. We find that neither cluster environment nor protostellar content makes a significant difference to the dynamical state of cores as estimated by the virial parameter -- most cores in each category are gravitationally bound. Overall, cluster environment and protostellar content have a smaller influence on the properties of the cores than is typically assumed, and the variation within categories is larger than the differences between categories.
 Physics , 2011, Abstract: We describe AMUSE, the Astrophysical Multipurpose Software Environment, a programming framework designed to manage multi-scale, multi-physics simulations in a hierarchical, extensible, and internally consistent way. Constructed as a collection of individual modules, AMUSE allows computational tools for different physical domains to be easily combined into a single task. It facilitates the coupling of modules written in different languages by providing inter-language tools and a standard programming interface that represents a balance between generality and computational efficiency. The framework currently incorporates the domains of stellar dynamics, stellar evolution, gas dynamics, and radiative transfer. We present some applications of the framework and outline plans for future development of the package.
 Physics , 2013, Abstract: The central regions of galaxies show the presence of massive black holes and/or dense stellar systems. The question about their modes of formation is still under debate. A likely explanation of the formation of the central dense stellar systems in both spiral and elliptical galaxies is based on the orbital decay of massive globular clusters in the central region of galaxies due to kinetic energy dissipation by dynamical friction. Their merging leads to the formation of a nuclear star cluster, like that of the Milky Way, where a massive black hole (Sgr A*) is also present. Actually, high precision N-body simulations (Antonini, Capuzzo-Dolcetta et al. 2012, ApJ, 750, 111) show a good fit to the observational characteristics of the Milky Way nuclear cluster, giving further reliability to the cited migratory' model for the formation of compact systems in the inner galaxy regions.
 Junichiro Makino Physics , 2000, Abstract: In this paper we describe the current status of the GRAPE-6 project to develop a special-purpose computer with a peak speed exceeding 100 Tflops for the simulation of astrophysical N-body problems. One of the main targets of the GRAPE-6 project is the simulation of dense stellar systems. In this paper, therefore, we overview the basic algorithms we use for the simulation of dense stellar systems and their characteristics. We then describe how we designed GRAPE hardwares to meet the requirements of these algorithms. GRAPE-6 will be completed by the year 2001. As an example of what science can be done on GRAPE-6, we describe our work on the galactic center with massive black holes performed on GRAPE-4, the predecessor of GRAPE-6.
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