Piet Hut

Missing Link Found? The "Runaway" Path to Supermassive Black Holes

Observations of stellar kinematics, gasdynamics, and masers around galactic nuclei have now firmly established that many galaxies host central supermassive black holes (SMBHs) with masses in the range of ~106-109 M☉. 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 ASCA and Chandra of the central region of the starburst galaxy M82. 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.

Formation of massive black holes through runaway collisions in dense young star clusters

A luminous X-ray source is associated with MGG 11—a cluster of young stars ∼200 pc from the centre of the starburst galaxy M 82 (refs 1, 2). The properties of this source are best explained by invoking a black hole with a mass of at least 350 solar masses (350 M[circdot]), which is intermediate between stellar-mass and supermassive black holes. A nearby but somewhat more massive 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 motion of stars within the clusters, where stars are allowed to merge with each other. We find that for MGG 11 dynamical friction leads to the massive stars sinking rapidly to the centre of the cluster, where they participate in a runaway collision. This produces a star of 800–3,000 M[circdot], which ultimately collapses to a 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.

HOP: A New Group-finding Algorithm for N-Body Simulations

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 Nhop 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 straightforward. 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.

Star cluster ecology – IV. Dissection of an open star cluster: photometry

The evolution of star clusters is studied using N-body simulations in which the evolution of single stars and binaries is 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 by the Galactic tidal field, and dissolve before deep core collapse occurs. The binary fraction decreases initially because of 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 white dwarfs formed 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 Centre. 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 effects of stellar mass-loss and evaporation of stars from the cluster potential drive the dissolution of a cluster on a much shorter time-scale 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. An observation of a blue straggler in an eccentric orbit around an unevolved star or a blue straggler of more than twice the turn-off mass might indicate past dynamical activity. We find two distinct populations of blue stragglers: those formed above the main-sequence turn-off, and those which appear as blue stragglers as the clusters turn-off drops below the mass of the rejuvenated star.

BINARIES IN GLOBULAR-CLUSTERS

Binary stars in a globular cluster (hereafter, GC) may be primordial (i.e. formed along with the cluster), or the result of cluster dynamics. “Dynamical” binaries can result from conservative three-body encounters (e.g. Spitzer, 1987) if a third star can carry away enough kinetic energy to leave two others bound, or from dissipative two-body encounters, if two stars happen to pass within a few stellar radii of one other (Fabian, Pringle, & Rees, 1975). Such non-primordial systems are likely to be found primarily in evolved GC cores, both because conditions are more favorable for making them there, and because of mass segregation. Knowledge of the formation process allows reasonable estimates to be made of their mass and energy distributions. The initial spatial, mass, and energy distributions of primordial binaries, on the other hand, are largely unknown.

The Equilibrium Tide Model for Tidal Friction

We derive from first principles the equations governing (a) the quadrupole tensor of a star distorted both by rotation and by 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 that rotates with the star; and (c) the equations governing the rates of change of the magnitude and the direction of the stellar rotation, 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 centers 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.

Dynamical Formation of Close Binary Systems in Globular Clusters

We know from observations that globular clusters are very efficient catalysts in forming unusual short-period binary systems or their offspring, such as low-mass X-ray binaries (LMXBs; neutron stars accreting matter from low-mass stellar companions), cataclysmic variables (white dwarfs accreting matter from stellar companions), and millisecond pulsars (rotating neutron stars with spin periods of a few milliseconds). Although there has been little direct evidence, the overabundance of these objects in globular clusters has been attributed by numerous authors to the high densities in the cores, which leads to an increase in the formation rate of exotic binary systems through close stellar encounters. Many such close binary systems emit X-radiation at low luminosities (LX 1034 ergs s-1) and are being found in large numbers through observations with the Chandra X-Ray Observatory. Here we present conclusive observational evidence of a link between the number of close binaries observed in X-rays in a globular cluster and the stellar encounter rate of the cluster. We also make an estimate of the total number of LMXBs in globular clusters in our Galaxy.

The gravitational million-body problem

We review what has been learned recently using N-body simulations about the evolution of globular clusters. While simulations of star clusters have become more realistic, and now include the evolution of single and binary stars, the prospect of reaching large enough N is still a distant one. Nevertheless more restricted kinds of simulations have recently brought valuable progress for certain problems of current observational interest, including the origin and structure of tidal tails of globular clusters. In addition, such simulations have forced us to rethink some basic aspects of stellar dynamics, including, in particular, the process of escape. Finally we turn to faster, approximate methods for studying star cluster dynamics, where the role of N-body simulations is one of calibration.

Merger Rate of Equal-Mass Spherical Galaxies

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 (~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 that is due to these tidal interactions.

On the Central Structure of M15

We present a detailed comparison between the latest observational data on the kinematical structure of the core of M15, obtained with the Hubble Space Telescope Space Telescope Imaging Spectrograph and Wide Field Planetary Camera 2 instruments, and the results of dynamical simulations carried out using the special purpose GRAPE-6 computer. The observations imply the presence of a significant amount of dark matter in the cluster core. In our dynamical simulations, neutron stars and/or massive white dwarfs concentrate to the center through mass segregation, resulting in a sharp increase in toward the center. While consistent with the presence of M/L a central black hole, the Hubble Space Telescope data can also be explained by this central concentration of stellar mass compact objects. The latter interpretation is more conservative, since such remnants result naturally from stellar evolution, although runaway merging leading to the formation of a black hole may also occur for some range of initial conditions. We conclude that no central massive object is required to explain the observational data, although we cannot conclusively exclude such an object at the level of. Our findings are similar to500-1000 M-circle dot. Our findings are unchanged when we reduce the assumed neutron star retention fraction in our simulations from 100% to 0%.