Evolution of globular cluster systems in elliptical galaxies. I. Log-normal initial mass function

We study the evolution of globular cluster systems (GCS) in elliptical galaxies and explore the dependence of their main properties on the mass and the size of the host galaxy.The dependence of the evolution of the GCS mass function (GCMF), of the fraction of surviving clusters and of the ratio of the final to initial mass in clusters on the structure of the host galaxy as well as their variation with the galactocentric distance inside individual host galaxies has been thoroughly investigated.After a survey over a large number of different host galaxies we have restricted our attention to a sample of galaxies with effective masses and radii equal to those observed for dwarf,normal and giant ellipticals. We show that, in spite of large differences in the fraction of surviving clusters, the final mean masses of the GCMF in massive galaxies are very similar to each other with a small galaxy-to-galaxy dispersion;low-mass compact galaxies tend to have smaller values of the final mean mass and a larger galaxy-to-galaxy dispersion. These findings are in agreement with those of recent observational analyses. The fraction of surviving clusters increases with the mass of the host galaxy. We show that a small difference between the initial and the final mean mass and dispersion of the GCMF and the lack of a significant radial dependence of the mean mass inside individual galaxies do not necessarily imply that evolutionary processes have been unimportant in the evolution of the initial population of clusters. For giant galaxies most disruption occurs within the effective radius while for low-mass galaxies a significant disruption of clusters takes place also at larger galactocentric distances. The dependence of the results obtained on the initial mean mass of the GCMF is investigated. (abridged)Comment: 17 pages, accepted for publication in MNRA

Star Formation in Violent and Normal Evolutionary Phases

Mergers of massive gas-rich galaxies trigger violent starbursts that - over timescales of $> 100$ Myr and regions $> 10$ kpc - form massive and compact star clusters comparable in mass and radii to Galactic globular clusters. The star formation efficiency is higher by 1 - 2 orders of magnitude in these bursts than in undisturbed spirals, irregulars or even BCDs. We ask the question if star formation in these extreme regimes is just a scaled-up version of the normal star formation mode of if the formation of globular clusters reveals fundamentally different conditions.Comment: 4 pages To appear in The Evolution of Galaxies. II. Basic building blocks, eds. M. Sauvage, G. Stasinska, L. Vigroux, D. Schaerer, S. Madde

Gravothermal Catastrophe in Anisotropic Spherical Systems

In this paper we investigate the gravothermal instability of spherical stellar systems endowed with a radially anisotropic velocity distribution. We focus our attention on the effects of anisotropy on the conditions for the onset of the instability and in particular we study the dependence of the spatial structure of critical models on the amount of anisotropy present in a system. The investigation has been carried out by the method of linear series which has already been used in the past to study the gravothermal instability of isotropic systems. We consider models described by King, Wilson and Woolley-Dickens distribution functions. In the case of King and Woolley-Dickens models, our results show that, for quite a wide range of amount of anisotropy in the system, the critical value of the concentration of the system (defined as the ratio of the tidal to the King core radius of the system) is approximately constant and equal to the corresponding value for isotropic systems. Only for very anisotropic systems the critical value of the concentration starts to change and it decreases significantly as the anisotropy increases and penetrates the inner parts of the system. For Wilson models the decrease of the concentration of critical models is preceded by an intermediate regime in which critical concentration increases, it reaches a maximum and then it starts to decrease. The critical value of the central potential always decreases as the anisotropy increases.Comment: 7pages, 5figures, to appear in MNRAS (figures have been replaced with their corrected versions

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

Evolution of the Mass Function of the Galactic Globular Cluster System

In this work we investigate the evolution of the mass function of the Galactic globular cluster system (GCMF) taking into account the effects of stellar evolution, two-body relaxation, disk shocking and dynamical friction on the evolution of individual globular clusters. We have adopted a log-normal initial GCMF and considered a wide range of initial values for the dispersion, , and the mean value, hlogMi. We have studied in detail the dependence on the initial conditions of the final values of , hlogMi, of the fraction of the initial number of clusters surviving after one Hubble time, and of the difference between the properties of the GCMF of clusters closer to the Galactic center and the properties of those located in the outer regions of the Galaxy. In most of the cases considered evolutionary processes alter significantly the initial population of globular clusters and the disruption of a significant number of globular clusters leads to a flattening in the spatial distribution of clusters in the central regions of the Galaxy. The initial log-normal shape of the GCMF is preserved in most cases and if a power-law in M is adopted for the initial GCMF, evolutionary processes tend to modify it into a log-normal GCMF. The difference between initial and final values of σ and (log M) as well as the difference between the final values of these parameters for inner and outer clusters can be positive or negative depending on initial conditions. A significant effect of evolutionary processes does not necessarily give rise to a strong trend of hlogMi with the galactocentric distance. The existence of a particular initial GCMF able to keep its initial shape and parameters unaltered during the entire evolution through a subtle balance between disruption of clusters and evolution of the masses of those which survive, suggested in Vesperini (1997), is confirmed

Evolution of the mass function of the Galactic globular cluster system

We investigate the evolution of the mass function of the Galactic globular cluster system (GCMF) taking into account the effects of stellar evolution, two-body relaxation, disk shocking and dynamical friction on the evolution of individual globular clusters.We have adopted a log-normal initial GCMF and we have studied in detail the dependence on the initial dispersion and mean value of the GCMF of the fraction of the initial number of clusters surviving after one Hubble time, of the final GCMF, and of the difference between the properties of the GCMF of clusters closer to the Galactic center and of those in the outer regions of the Galaxy.The initial log-normal shape of the GCMF is preserved in most cases and if a power-law in M is adopted for the initial GCMF, evolutionary processes tend to modify it into a log-normal GCMF. The difference between initial and final values of dispersion and mean value of the GCMF as well as the difference between the final values of these parameters for inner and outer clusters can be positive or negative depending on initial conditions.A significant effect of evolutionary processes does not necessarily give rise to a strong trend of the mean value of the GCMF with the galactocentric distance.The existence of a particular initial GCMF able to keep its initial shape and parameters unaltered during the entire evolution through a subtle balance between disruption of clusters and evolution of the masses of those which survive,suggested in Vesperini(1997),is confirmed. (abridged)Comment: 16 pages LaTeX(MNRAS style) 22 figures, (MNRAS in press

On the evolution of the galactic globular cluster system

In this paper we address the issue of the origin of some observational properties of the galactic globular cluster system. After a preliminary study of some general properties of the main evolutionary processes, we investigate the evolution of systems of globular clusters located in a model of the Milky Way starting from different initial conditions. We study the role of the evolutionary processes in changing the spatial distribution and mass function of the cluster system, in establishing and/or preserving some of the observed correlations and trends between internal properties of globular clusters and between internal properties and location inside the host galaxy and we provide an estimate for the rates of core collapse and disruption of globular clusters. The initial mass function and spatial distribution of the cluster system evolve quite significantly in one Hubble time and the evolution is toward a final state similar to the observed one. If the mass function is initially taken to be a log-normal distribution similar to the one currently observed in our galaxy, its shape is not significantly altered during the entire simulation even though a significant number of clusters are disrupted before one Hubble time, which suggests that the present mass function might represent a sort of 'quasi-equilibrium' distribution.Comment: accepted for publication in MNRAS, 12 pages LaTeX (MNRAS style), 14 figures available on request from [email protected]

Dynamical evolution of the mass function and radial profile of the Galactic globular cluster system

Evolution of the mass function (MF) and radial distribution (RD) of the Galactic globular cluster (GC) system is calculated using an advanced and a realistic Fokker-Planck (FP) model that considers dynamical friction, disc/bulge shocks and eccentric cluster orbits. We perform hundreds of FP calculations with different initial cluster conditions, and then search a wide-parameter space for the best-fitting initial GC MF and RD that evolves into the observed present-day Galactic GC MF and RD. By allowing both MF and RD of the initial GC system to vary, which is attempted for the first time in the present Letter, we find that our best-fitting models have a higher peak mass for a lognormal initial MF and a higher cut-off mass for a power-law initial MF than previous estimates, but our initial total masses in GCs, M_{T,i} = 1.5-1.8x10^8 Msun, are comparable to previous results. Significant findings include that our best-fitting lognormal MF shifts downward by 0.35 dex during the period of 13 Gyr, and that our power-law initial MF models well-fit the observed MF and RD only when the initial MF is truncated at >~10^5 Msun. We also find that our results are insensitive to the initial distribution of orbit eccentricity and inclination, but are rather sensitive to the initial concentration of the clusters and to how the initial tidal radius is defined. If the clusters are assumed to be formed at the apocentre while filling the tidal radius there, M_{T,i} can be as high as 6.9x10^8 Msun, which amounts to ~75 per cent of the current mass in the stellar halo.Comment: To appear in May 2008 issue of MNRAS, 386, L6