We have computed simplified globular cluster evolutionary tracks which take into account the effects of internal relaxation, of the cluster rotation, of the galactic tidal field, and, in a cruder way, of stellar evolution and of gravitational shocking. The objectives are first to quantify the influence of rotation in the dynamical evolution of globular clusters; and second, to investigate the evolution of globular cluster angular momentum and flattening (Lagoute and Longaretti 1995a, Longaretti and Lagoute 1995b,c).

Searches of low-mass stars have become possible in globular clusters, and the first results suggest that the mass function turns up below ∼ 0.4 M⊙ (Fahlman et al. 1989; Richer et al., 1990; Richer et al. 1991; G. Piotto, these proceedings). This conclusion is independently supported by the non-parametric dynamical analysis of four clusters by Gebhardt and Fisher 1995.

We examine critically the properties of the large-amplitude oscillations seen in Fokker-Planck simulations of globular clusters, with both continuous and stochastic binary heating, and compare them to the defining characteristics of gravothermal oscillations.

We study tidal shocking on globular clusters by N-body simulation. The results, which cover a range of cluster and disk parameters, are compared with the impulsive approximation.

Low-mass binary millisecond pulsars are born with very small orbital eccentricities, typically of order ei ∼ 10−6−10−3. In globular clusters, however, higher eccentricities ef ≫ ei can be induced by dynamical interactions with passing stars. Using both analytical perturbation calculations and numerical integrations, we have shown (Heggie & Rasio 1996) that the cross section for this process is much larger than previously estimated. This is because, even for initially circular binaries, the induced eccentricity ef for an encounter with pericentre separation rp beyond a few times the binary semi-major axis a declines only as a power-law, ef ∝ (rp/a)−5/2, and not as an exponential. We find that all currently known low-mass binary millisecond pulsars in globular clusters must have been affected by interactions, with their current eccentricities being at least an order of magnitude larger than at birth (Rasio & Heggie 1995).

One-dimensional self-gravitating many-body systems consist of N identical parallel sheets which have uniform mass density m and infinite in extent in the (y, z) plane. We call the sheets particles in this paper. The particles are free to move along x axis and accelerate as a result of their mutual gravitational attraction. The Hamiltonian of this system has a form of where m, vi, and xi are the mass (surface density), velocity, and position of ith particle respectively.

We investigate whether or not the energy exchange occurs between two species groups of particles in an expanding two-component gravitating system, and we derive the relaxation time scale for energy exchange in such a phase. This is accomplished by solving the dynamic equation coupled with Poisson's equation. We derive a characteristic time determined by the various mass and velocity ratios. When the expansion time does not exceed the characteristic time, energy exchange between the two components is possible and depends on the mass ratio. Once the characteristic time is exceeded, there is virtually no relaxation at all in system. When m2 ≫ m1, the transfer of energy becomes inefficient. Therefore, energy exchange between two species of particle in an expanding two-component gravitating system depends not only on the mass ratio but also on the expansion time.

The young open star clusters (OCl) with ages of 107 − 108 years in the overwhelming majority of cases are located in the regions of a star formation which are the massive and extensive gas - star complexes (GSC) in our Galaxy. The typical sizes of GSCs are near 600 pc in projection at the Galaxy plane and the masses of such complexes are in range ∼ (105 − 107) M⊙ (Efremov (1989)). It is well known that the old open clusters avoid the regions of an active star formation in our Galaxy. As a result the structural and dynamical parameters of OCls depend on their ages and their locations relatively the nearest GSCs centres.

NGC 4472 (M49) is a giant elliptical galaxy in the Virgo cluster, and has a rich GCS. Radial surface density profiles of the GCS in this galaxy are well-known (Cohen 1988, Harris 1986). However, little information is available for the ellipticity (e) and position angles of the GCS in NGC 4472. In this study we have investigated in detail the spatial structures of the GCS in NGC 4472 (the surface density, the ellipticity, the color, and the position angle) in comparison with those of the halo, using a large sample of the globular clusters located in a wide field (16′ × 16′) of NGC 4472.

NGC 4472, the brightest elliptical galaxy in the Virgo cluster, has a rich globular cluster system. We present a study of the metallicity and luminosity functions of a large number of globular clusters in NGC 4472. Deep Washington CT1 photometry of a wide (16′ × 16′) field of NGC 4472 was obtained using Tek 2048 × 2048 CCD at the KPNO 4m telescope.

The central concentration of the luminosity distribution in dwarf elliptical galaxies (dEs) is weaker than that of giant elliptical galaxies (Es). In other words, the luminosity profiles in Es follow the de Vaucouleurs' law whereas dEs have exponential luminosity profiles. Athanassoula(1994) describes the one dimensional simulations of the formation of dEs that include the feedback effects from supernovae. The model with no dark matter halo is shown to be much better agreements with the observations than with dark matter halo. However no attempt has yet been made to reproduce much lower heavy element abundances in dEs than in Es. We calculate the chemodynamical evolution of a less massive gas cloud with an SPH+N-body three dimensional simulation code to explore the luminosity profile and chemical abundances in dEs.

We examine two globular cluster formation scenarios with SPH simulations, using GRAPE-3AF. First model is the spontaneous collapse, which is found to induce a disruption of the system. However, the system can survive when sufficiently high external pressure exists. Second model is the collision of the two proto-cluster clouds, which can form a bound stellar system due to efficient cooling and a burst of star formation.

In the last decade several scenarios for the formation of globular clusters have been suggested. One of these models starts with an OB-association exploding near the center of a molecular cloud (Brown et al., ApJ 376, 115 (1991)): The expanding shell sweeps up the cloud material and later the expansion will be decelerated or stopped by the external pressure of the ambient hot gas. The shell itself can break into fragments and form stars. If the total energy of these stars is negative, they will recollapse and eventually form a bound system. According to this idea the dynamics of a thin stellar shell has been studied.

Recent surveys of the observational properties of galactic globular clusters have shown the existence of interesting correlations and trends between structural parameters and between structural parameters and location inside the Galaxy (Chernoff & Djorgovski 1989, Djorgovski & Meylan 1994). The origin of most of these correlations is not clear yet and it is not clear to what extent they reflect the primordial conditions or the result of evolution. We have carried out a set of simulations following the evolution of the properties of a globular cluster system (mass function, spatial distribution, correlations between structural parameters) starting from given initial conditions. The evolution of each individual cluster has been followed by the same method applied by Chernoff et al. (1986) and Chernoff & Shapiro (1987). The effects of internal relaxation, disk shocking and dynamical friction have been considered. The main goal of the analysis is that of establishing the role of initial conditions and evolutionary processes in determining the present observational properties.

Recent observational searches suggest that the frequency of primordial binaries in globular clusters may reach ~ 10% (see Hut et al. 1992 for a review). Several different treatments conclude that primordial binaries are effective in halting core collapse, supporting the core and driving the post-core collapse expansion phase (Goodman & Hut 1989, McMillan et al. 1990, 1991, Gao et al. 1991, Heggie & Aarseth 1992, McMillan & Hut 1994). The abundance and binding energy distribution have a direct impact on observable characteristics of globular clusters such as the size of the core radius (Vesperini & Chernoff 1994). In this analysis we have investigated how the initial binary distribution function may be altered in the formation of a cluster; the key question we have addressed is whether it is possible for binaries, assumed to be primordial, to survive the birth of the cluster. A detailed description of our results is in Vesperini & Chernoff (1995).