Search

At the moment of deepest core collapse, a star cluster core contains less than ten stars. This small number makes the traditional treatment of hard binary formation, assuming a homogeneous background density, suspect. In a previous paper, we have found that indeed the conventional wisdom of binary formation, based on three-body encounters, is incorrect. Here we refine that insight, by further dissecting the subsequent steps leading to hard binary formation. For this purpose, we add some analysis tools in order to make the study less subjective. We find that the conventional treatment does remain valid for direct three-body scattering, but fails for resonant three-body scattering. Especially democratic resonance scattering, which forms an important part of the analytical theory of three-body binary formation, takes too much space and time to be approximated as being isolated, in the context of a cluster core around core collapse. We conclude that, while three-body encounters can be analytically approximated as isolated, subsequent strong perturbations typically occur whenever those encounters give rise to democratic resonances. We present analytical estimates postdicting our numerical results. If we only had been a bit more clever, we could have predicted this qualitative behaviour., Comment: 44 pages, 18 figures, 1 table

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

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

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

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

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)

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 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

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)

Blue stragglers are natural phenomena in star clusters. They originate through mass transfer in isolated binaries, as well as through encounters between two or more stars, in a complex interplay between stellar dynamics and stellar evolution. While this interplay cannot be modeled quantitatively at present, we will be able to do so in one or two years time. With this prospect, the present paper is written largely as a preview., Comment: LaTeX file, 22 pages, Institute for Advanced Study number 93/11

We report the preliminary results of a surface photometry survey of globular cluster cores. Two new cores with post-collapse morphology have been found, and two possible candidates. The estimated fraction of clusters with this core morphology in the Galaxy is only a few percent. Most clusters do not show a morphology similar to the predictions of the central black hole models.