The Dynamical Implications of Multiple Stellar Formation Events in Galactic Globular Clusters

Various galactic globular clusters display abundance anomalies that affect the morphology of their colour-magnitude diagrams. In this paper we consider the possibility of helium enhancement in the anomalous horizontal branch of NGC 2808. We examine the dynamics of a self-enrichment scenario in which an initial generation of stars with a top-heavy initial mass function enriches the interstellar medium with helium via the low-velocity ejecta of its asymptotic giant branch stars. This enriched medium then produces a second generation of stars which are themselves helium-enriched. We use a direct N-body approach to perform five simulations and conclude that such two-generation clusters are both possible and would not differ significantly from their single-generation counterparts on the basis of dynamics. We find, however, that the stellar populations of such clusters would differ from single-generation clusters with a standard initial mass function and in particular would be enhanced in white dwarf stars. We conclude, at least from the standpoint of dynamics, that two-generation globular clusters are feasible.Comment: 24 pages, 7 figures, 3 tables. Accepted for publication in Ap

Structure of Dark Matter Halos From Hierarchical Clustering

We investigate the structure of the dark matter halo formed in the cold dark matter scenario using $N$-body simulations. We simulated 12 halos with the mass of $6.6\times 10^{11}M_{\odot}$ to $8.0\times 10^{14}M_{\odot}$. In almost all runs, the halos have density cusps proportional to $r^{-1.5}$ developed at the center, which is consistent with the results of recent high-resolution calculations. The density structure evolves in a self-similar way, and is universal in the sense that it is independent of the halo mass and initial random realization of density fluctuation. The density profile is in good agreement with the profile proposed by Moore et al. (1999), which has central slope proportional to $r^{-1.5}$ and outer slope proportional to $r^{-3}$. The halo grows through repeated accretion of diffuse smaller halos. We argue that the cusp is understood as a convergence slope for the accretion of tidally disrupted matter.Comment: 34 including 23 figures, revised version, accepted for publication in Ap

Modeling the dynamical evolution of the M87 globular cluster system

We study the dynamical evolution of the M87 globular cluster system (GCS) with a number of numerical simulations. We explore a range of different initial conditions for the GCS mass function (GCMF), for the GCS spatial distribution and for the GCS velocity distribution. We confirm that an initial power-law GCMF like that observed in young cluster systems can be readily transformed through dynamical processes into a bell-shaped GCMF. However,only models with initial velocity distributions characterized by a strong radial anisotropy increasing with the galactocentric distance are able to reproduce the observed constancy of the GCMF at all radii.We show that such strongly radial orbital distributions are inconsistent with the observed kinematics of the M87 GCS. The evolution of models with a bell-shaped GCMF with a turnover similar to that currently observed in old GCS is also investigated. We show that models with this initial GCMF can satisfy all the observational constraints currently available on the GCS spatial distribution,the GCS velocity distribution and on the GCMF properties.In particular these models successfully reproduce both the lack of a radial gradient of the GCS mean mass recently found in an analysis of HST images of M87 at multiple locations, and the observed kinematics of the M87 GCS.Our simulations also show that evolutionary processes significantly affect the initial GCS properties by leading to the disruption of many clusters and changing the masses of those which survive.The preferential disruption of inner clusters flattens the initial GCS number density profile and it can explain the rising specific frequency with radius; we show that the inner flattening observed in the M87 GCS spatial distribution can be the result of the effects of dynamical evolution on an initially steep density profile. (abridged)Comment: 15 pages,14 figures;accepted for publication in The Astrophysical Journa

Evaporation of Compact Young Clusters near the Galactic Center

We investigate the dynamical evolution of compact young clusters (CYCs) near the Galactic center (GC) using Fokker-Planck models. CYCs are very young (< 5 Myr), compact (< 1 pc), and only a few tens of pc away from the GC, while they appear to be as massive as the smallest Galactic globular clusters (~10^4 Msun). A survey of cluster lifetimes for various initial mass functions, cluster masses, and galactocentric radii is presented. Short relaxation times due to the compactness of CYCs, and the strong tidal fields near the GC make clusters evaporate fairly quickly. Depending on cluster parameters, mass segregation may occur on a time scale shorter than the lifetimes of most massive stars, which accelerates the cluster's dynamical evolution even more. When the difference between the upper and lower mass boundaries of the initial mass function is large enough, strongly selective ejection of lighter stars makes massive stars dominate even in the outer regions of the cluster, so the dynamical evolution of those clusters is weakly dependent on the lower mass boundary. The mass bins for Fokker-Planck simulations were carefully chosen to properly account for a relatively small number of the most massive stars. We find that clusters with a mass <~ 2x10^4 Msun evaporate in <~ 10 Myr. A simple calculation based on the total masses in observed CYCs and the lifetimes obtained here indicates that the massive CYCs comprise only a fraction of the star formation rate (SFR) in the inner bulge estimated from Lyman continuum photons and far-IR observations.Comment: 20 pages in two-column format, accepted for publication in Ap

Monte Carlo Simulations of Globular Cluster Evolution - II. Mass Spectra, Stellar Evolution and Lifetimes in the Galaxy

We study the dynamical evolution of globular clusters using our new 2-D Monte Carlo code, and we calculate the lifetimes of clusters in the Galactic environment. We include the effects of a mass spectrum, mass loss in the Galactic tidal field, and stellar evolution. We consider initial King models containing N = 10^5 - 3x10^5 stars, and follow the evolution up to core collapse, or disruption, whichever occurs first. We find that the lifetimes of our models are significantly longer than those obtained using 1-D Fokker-Planck (F-P) methods. We also find that our results are in very good agreement with recent 2-D F-P calculations, for a wide range of initial conditions. Our results show that the direct mass loss due to stellar evolution can significantly accelerate the mass loss through the tidal boundary, causing most clusters with a low initial central concentration (Wo <~ 3) to disrupt quickly in the Galactic tidal field. Only clusters born with high initial central concentrations (Wo >~ 7) or steep initial mass functions are likely to survive to the present and undergo core collapse. We also study the orbital characteristics of escaping stars, and find that the velocity distribution of escaping stars in collapsing clusters looks significantly different from the distribution in disrupting clusters. We calculate the lifetime of a cluster on an eccentric orbit in the Galaxy, such that it fills its Roche lobe only at perigalacticon. We find that such an orbit can extend the lifetime by at most a factor of a few compared to a circular orbit in which the cluster fills its Roche lobe at all times.Comment: 32 pages, including 10 figures, to appear in ApJ, minor corrections onl

Star cluster dynamics

Dynamical evolution plays a key role in shaping the current properties of star clusters and star cluster systems. A detailed understanding of the effects of evolutionary processes is essential to be able to disentangle the properties which result from dynamical evolution from those imprinted at the time of cluster formation. In this review, we focus our attention on globular clusters and review the main physical ingredients driving their early and long-term evolution, describe the possible evolutionary routes and show how cluster structure and stellar content are affected by dynamical evolution.Comment: 20 pages, 2 figures. To appear as invited review article in a special issue of the Phil. Trans. Royal Soc. A: Ch. 7 "Star clusters as tracers of galactic star-formation histories" (ed. R. de Grijs). Fully peer reviewed. LaTeX, requires rspublic.cls style fil

Ejection of Supermassive Black Holes from Galaxy Cores

[Abridged] Recent numerical relativity simulations have shown that the emission of gravitational waves during the merger of two supermassive black holes (SMBHs) delivers a kick to the final hole, with a magnitude as large as 4000 km/s. We study the motion of SMBHs ejected from galaxy cores by such kicks and the effects on the stellar distribution using high-accuracy direct N-body simulations. Following the kick, the motion of the SMBH exhibits three distinct phases. (1) The SMBH oscillates with decreasing amplitude, losing energy via dynamical friction each time it passes through the core. Chandrasekhar's theory accurately reproduces the motion of the SMBH in this regime if 2 < ln Lambda < 3 and if the changing core density is taken into account. (2) When the amplitude of the motion has fallen to roughly the core radius, the SMBH and core begin to exhibit oscillations about their common center of mass. These oscillations decay with a time constant that is at least 10 times longer than would be predicted by naive application of the dynamical friction formula. (3) Eventually, the SMBH reaches thermal equilibrium with the stars. We estimate the time for the SMBH's oscillations to damp to the Brownian level in real galaxies and infer times as long as 1 Gyr in the brightest galaxies. Ejection of SMBHs also results in a lowered density of stars near the galaxy center; mass deficits as large as five times the SMBH mass are produced for kick velocities near the escape velocity. We compare the N-body density profiles with luminosity profiles of early-type galaxies in Virgo and show that even the largest observed cores can be reproduced by the kicks, without the need to postulate hypermassive binary SMBHs. Implications for displaced AGNs and helical radio structures are discussed.Comment: 18 pages, The Astrophysical Journal, in press. Replaced with revised versio

The radial structure of galaxy groups and clusters

Simple self-consistent models of galaxy groups and clusters are tested against the results of high-resolution adiabatic gasdynamical simulations. We investigate two models based on the existence of a 'universal' dark matter density profile and two versions of the beta-model. The mass distribution of relaxed clusters can be fitted by phenomenological formulae proposed in the literature. Haloes that have experienced a recent merging event are systematically less concentrated and show steeper profiles than relaxed objects near the centre. The hot X-ray emitting gas is found to be in approximate hydrostatic equilibrium with the dark matter potential, and it is well described by a polytropic equation of state. Analytic formulae for the gas density and temperature can be derived from these premises. Though able to reproduce the X-ray surface brightness, the beta-model is shown to provide a poor description of our numerical clusters. We find strong evidence of a 'universal' temperature profile that decreases by a factor of 2-3 from the centre to the virial radius, whereas baryon fraction and entropy are monotonically increasing functions. Numerical resolution and entropy conservation play a key role in the shapes of the profiles at small radii.Comment: 16 pages, 19 figures, minor changes to match published versio