Mass loss of stars in star clusters: an energy source for dynamical evolution

Dense star clusters expand until their sizes are limited by the tidal field of their host galaxy. During this expansion phase the member stars evolve and lose mass. We show that for clusters with short initial relaxation time scales (<~100 Myr) the dynamical expansion is largely powered by mass loss from stars in the core, but happens on a relaxation time scale. That is, the energy release following stellar mass loss is in balance with the amount of energy that is transported outward by two-body relaxation.Comment: 4 pages, to appear in the proceedings of the conference "370 years of Astronomy in Utrecht", eds. G. Pugliese, A. de Koter and M. Wijbur

The mass and radius evolution of globular clusters in tidal fields

We present a simple theory for the evolution of initially compact clusters in a tidal field. The fundamental ingredient of the model is that a cluster conducts a constant fraction of its own energy through the half-mass radius by two-body interactions every half-mass relaxation time. This energy is produced in a self-regulative way in the core by an (unspecified) energy source. We find that the half-mass radius increases during the first part (roughly half) of the evolution and decreases in the second half, while the escape rate is constant and set by the tidal field. We present evolutionary tracks and isochrones for clusters in terms of cluster half-mass density, cluster mass and galacto-centric radius. We find substantial agreement between model isochrones and Milky Way globular cluster parameters, which suggests that there is a balance between the flow of energy and the central energy production for almost all globular clusters. We also find that the majority of the globular clusters are still expanding towards their tidal radius. Finally, a fast code for cluster evolution is presented.Comment: 5 pages, 1 figure. To appear in the proceedings of the conference `Reading the book of globular clusters with the lens of stellar evolution', Rome, Nov. 26-28, 2012, to be published in Memorie della Societa Astronomica Italiana, Eds. Paolo Ventura and Corinne Charbonne

Dynamical evolution of stellar clusters

The evolution of star clusters is determined by several internal and external processes. Here we focus on two dominant internal effects, namely energy exchange between stars through close encounters (two-body relaxation) and mass-loss of the member stars through stellar winds and supernovae explosions. Despite the fact that the former operates on the relaxation timescale of the cluster and the latter on a stellar evolution timescale, these processes work together in driving a nearly self-similar expansion, without forming (hard) binaries. Low-mass clusters expand more, such that after some time the radii of clusters depend very little on their masses, even if all clusters have the same (surface) density initially. Throughout it is assumed that star clusters are in virial equilibrium and well within their tidal boundary shortly after formation, motivated by observations of young (few Myrs) clusters. We start with a discussion on how star clusters can be distinguished from (unbound) associations at these young ages.Comment: 6 pages, 4 figures, proceedings of "Stellar Clusters and Associations - A RIA workshop on GAIA", 23-27 May 2011, Granada, Spai

A family of lowered isothermal models

We present a family of self-consistent, spherical, lowered isothermal models, consisting of one or more mass components, with parameterised prescriptions for the energy truncation and for the amount of radially biased pressure anisotropy. The models are particularly suited to describe the phase-space density of stars in tidally limited, mass-segregated star clusters in all stages of their life-cycle. The models extend a family of isotropic, single-mass models by Gomez-Leyton and Velazquez, of which the well-known Woolley, King and Wilson (in the non-rotating and isotropic limit) models are members. We derive analytic expressions for the density and velocity dispersion components in terms of potential and radius, and introduce a fast model solver in PYTHON (LIMEPY), that can be used for data fitting or for generating discrete samples.Comment: 17 pages, 10 figures, 4 appendices, MNRAS, updated to match final journal styl

A flexible method to evolve collisional systems and their tidal debris in external potentials

We introduce a numerical method to integrate tidal effects on collisional systems, using any definition of the external potential as a function of space and time. Rather than using a linearisation of the tidal field, this new method follows a differential technique to numerically evaluate the tidal acceleration and its time derivative. Theses are then used to integrate the motions of the components of the collisional systems, like stars in star clusters, using a predictor-corrector scheme. The versatility of this approach allows the study of star clusters, including their tidal tails, in complex, multi-components, time-evolving external potentials. The method is implemented in the code nbody6 (Aarseth 2003).Comment: MNRAS accepted. Code available here: http://personal.ph.surrey.ac.uk/~fr0005/nbody6tt.ph

The distinction between star clusters and associations

In Galactic studies a distinction is made between (open) star clusters and associations. For barely resolved objects at a distance of several Mpc this distinction is not trivial to make. Here we provide an objective definition by comparing the age of the stars to the crossing time of nearby stellar agglomerates. We find that a satisfactory separation can be made where this ratio equals unity. Stellar agglomerates for which the age of the stars exceeds the crossing time are bound, and are referred to as star clusters. Alternatively, those for which the crossing time exceeds the stellar age are unbound and are referred to as associations. This definition is useful whenever reliable measurements for the mass, radius and age are available.Comment: 2 pages, 2 figures, accepted for MNRAS Letter

The origin of the Milky Way globular clusters

We present a cosmological zoom-in simulation of a Milky Way-like galaxy used to explore the formation and evolution of star clusters. We investigate in particular the origin of the bimodality observed in the colour and metallicity of globular clusters, and the environmental evolution through cosmic times in the form of tidal tensors. Our results self-consistently confirm previous findings that the blue, metal-poor clusters form in satellite galaxies which are accreted onto the Milky Way, while the red, metal-rich clusters form mostly in situ or, to a lower extent in massive, self-enriched galaxies merging with the Milky Way. By monitoring the tidal fields these populations experience, we find that clusters formed in situ (generally centrally concentrated) feel significantly stronger tides than the accreted ones, both in the present-day, and when averaged over their entire life. Furthermore, we note that the tidal field experienced by Milky Way clusters is significantly weaker in the past than at present-day, confirming that it is unlikely that a power-law cluster initial mass function like that of young massive clusters, is transformed into the observed peaked distribution in the Milky Way with relaxation-driven evaporation in a tidal field.Comment: MNRAS accepte

Evolution of star clusters in arbitrary tidal fields

We present a novel and flexible tensor approach to computing the effect of a time-dependent tidal field acting on a stellar system. The tidal forces are recovered from the tensor by polynomial interpolation in time. The method has been implemented in a direct-summation stellar dynamics integrator (NBODY6) and test-proved through a set of reference calculations: heating, dissolution time and structural evolution of model star clusters are all recovered accurately. The tensor method is applicable to arbitrary configurations, including the important situation where the background potential is a strong function of time. This opens up new perspectives in stellar population studies reaching to the formation epoch of the host galaxy or galaxy cluster, as well as for star-burst events taking place during the merger of large galaxies. A pilot application to a star cluster in the merging galaxies NGC 4038/39 (the Antennae) is presented.Comment: 12 pages, 8 figures. Accepted for publication in MNRA