Shogo Inagaki

EVOLUTION OF TIDALLY TRUNCATED GLOBULAR CLUSTERS WITH ANISOTROPY

The evolution of tidally truncated globular clusters is investigated by integrating two-dimensional Fokker-Planck equation that allows the development of velocity anisotropy. We start from the isotropic Plummer model with tidal cut off and followed the evolution through the corecollapse. The heating by three-binary is included to obtain the evolution past the corecollapse. The anisotropy in velocity dispersion develops during the precollapse evolution. However, the anisotropy becomes highly depressed during the post-collapse evolution because of rapid loss of radial orbits. Maximum radial anisotropy appears just after the beginning of the expansion, and degree of anisotropy decreases slowly as the total mass of the cluster decreases. Thus it may be possible to determine the evolutionary status of a cluster if the velocity anisotropy can be measured in the sense that the postcollapse clusters always have very little degree of anisotropy. The structure of the post-collapse cluster can be well fitted to King models because the degree of anisotropy is rather small.

Gravitational clustering of galaxies : comparison between thermodynamic theory and N-body simulations. IV: The effects of continuous mass spectra

We compare quasi-equilibrium gravitational clustering theory with N-body simulations which have broad continuous mass spectra. For this, we generate new sets of 10,000-body experiments with Schechter-type mass spectra [dN∞(m/m * ) −p exp (−m/m * )d(m/m * )]. We examine the effects of different values of p, of mass range, and of cosmic densities. The resulting patterns have more structure than in the comparable single or two component simulations. There are several other differences between single-mass and multimass systems

Gravitational clustering of galaxies : comparison between thermodynamic theory and N-body simulations. III: Velocity distributions for different mass components

The radial velocity distribution function of galaxies as well as their three-dimensional velocity distributions predicted from the thermodynamic theory are compared with N-body simulations. We mainly consider systems with two mass components. The agreement between the thermodynamic theory and the N-body simulations is remarkably good, even for very large values of the mass ratios. When the mass ratio is large, this agreement is much better than for the spatial distribution functions. The velocity dispersion is found to be an excellent measure of the value of Ω 0

Dynamical Evolution of Multi-Component Clusters

Presence of stars with disparate masses causes great differences in the dynamical evolution of star clusters from the evolution of single component clusters. One remarkable effect is acceleration of the evolution. Another effect is destabilization or stabilization. In two-component clusters equipartition at the cluster centre is nearly achieved if Spitzer’s (1969) condition is satisfied. In multi-component clusters equipartition at the cluster centre is achieved if either the range of stellar mass is very narrow or the mass spectrum is very steep. Global equipartition is never achieved. Post-collapse evolution of multi-component clusters is discussed briefly and some remained problems are presented.

Distribution Of Stochastic Forces In Gravitationally Clustered System Of Galaxies

We are interested in examining the influence of nearest neighbor galactic encounters in gravitationally clustered systems by using cosmological N-body simulation.

Distribution of Forces in Gravitationally Clustered System

We have studied the distribution of forces in gravitational systems through numerical experiments. Data were taken from an N-body simulation in an expanding universe. Before clustering, the distribution of random forces was represented as a Holtsmark distribution; the nearest-neighbor distribution is also shown as a comparison. The analytical and simulation distributions are in good agreement. When clustering becomes strong, the simulation result showed that the contribution of the forces acting on each galaxy, which is generated from all other galaxies, is almost entirely due to the gravitational attraction of its nearest neighbor. This implies that nearest-neighbor galactic encounters may play the main role in the dynamics of galaxy clustering.

Force Distribution and Relaxation Time in Clusters of Galaxies

We examine the influence of nearest neighbor galactic encounters in gravi-tationally clustered systems by using cosmological N-body simulation and determine the two-body relaxation time in the expanding universe, which is based on the effect of two-body encounters in the clusters of galaxies.

Dynamical evolution of globular clusters

Abstract A brief review of pre- and post-collapse evolution of globular clusters is given. Particular attention is paid to gravothermal oscillations of cores of globular clusters.

Precollapse Evolution of Globular Clusters

Density profiles of most globular clusters are well fitted by a King (1966) model. The evolution of a King model in the tidal gravitational field of the Galaxy is first discussed. If the concentration parameter c (= log(rt/rc)) is small enough, the evolution is nearly along the King model sequence and c becomes larger. When c becomes large enough (about 2.1), gravothermal instability sets in. The basic properties of gravothermal instability is next discussed. The stability criterion and its interpretation are given. Globular clusters consist of stars with disparate masses, so that finally the evolution of multi-component clusters is discussed. Acceleration of evolution in multi-component clusters and equipartition of the kinetic energies among components are discussed, and conclusions and future problems are given.

Long-Term Evolution of Cores of Globular Clusters after Core Collapse

Fluctuations play an important role in the post-collapse evolution of cores of globular clusters. We present a simple model for the long-term evolution of a globular cluster which includes a realistic treatment of stochastic binary formation. We discuss some preliminary results concerning the number of binaries, their distribution through the cluster, their rate of evolution and their effect on the evolution of the cluster. At any time after core collapse few binaries are found in or near the core; most binaries describe orbits far outside the core, being slowly pulled in by dynamical friction after being kicked out of the core through the recoil effects of a strong three-body reaction.