No Arabic abstract
We calculated the broad-band photometric evolution of unresolved star clusters, including the preferential loss of low-mass stars due to mass segregation. The stellar mass function of a cluster evolves due to three effects: (a) the evolution of massive stars; (b) early tidal effects reduce the mass function independently of the stellar mass; (c) after mass segregation has completed, tidal effects preferentially remove the lowest-mass stars from the cluster. Results: (1) During the first ~40% of the lifetime of a cluster the cluster simply gets fainter due to the loss of stars by tidal effects. (2) Between ~40 and ~80% of its lifetime the cluster gets bluer due to the loss of low-mass stars. This will result in an underestimate of the age of clusters if standard cluster evolution models are used (0.15 -- 0.5 dex). (3) After ~80% of the total lifetime of a cluster it will rapidly get redder. This is because stars at the low-mass end of the main sequence, which are preferentially lost, are bluer than the AGB stars that dominate the light at long wavelengths, resulting in an age overestimate. (4) Clusters with mass segregation and the preferential loss of low-mass stars evolve along almost the same tracks in colour-colour diagrams as clusters without mass segregation. Therefore it will be difficult to distinguish this effect from that due to the cluster age for unresolved clusters, unless the total lifetime of the clusters can be estimated. (5) The changes in the colour evolution of unresolved clusters due to the preferential loss of low-mass stars will affect the determination of the SFHs. (6) The preferential loss of low-mass stars might explain the presence of old (~13 Gyr) clusters in NGC 4365 which are photometrically disguised as intermediate-age clusters (2 - 5 Gyr). [Abridged]
Evolutionary synthesis models are the prime method to construct models of stellar populations, and to derive physical parameters from observations. One of the assumptions for such models so far has been the time-independence of the stellar mass function. However, dynamical simulations of star clusters in tidal fields have shown the mass function to change due to the preferential removal of low-mass stars from clusters. Here we combine the results from dynamical simulations of star clusters in tidal fields with our evolutionary synthesis code GALEV to extend the models by a new dimension: the total cluster disruption time. We reanalyse the mass function evolution found in N-body simulations of star clusters in tidal fields, parametrise it as a function of age and total cluster disruption time and use this parametrisation to compute GALEV models as a function of age, metallicity and the total cluster disruption time. We study the impact of cluster dissolution on the colour (generally, they become redder) and magnitude (they become fainter) evolution of star clusters, their mass-to-light ratios (off by a factor of ~2 -- 4 from standard predictions), and quantify the effect on the cluster age determination from integrated photometry (in most cases, clusters appear to be older than they are, between 20 and 200%). By comparing our model results with observed M/L ratios for old compact objects in the mass range 10^4.5 -- 10^8 Msun, we find a strong discrepancy for objects more massive than 10^7 Msun (higher M/L). This could be either caused by differences in the underlying stellar mass function or be an indication for the presence of dark matter in these objects. Less massive objects are well represented by the models. The models for a range of total cluster disruption times are available online. (shortened)
The existence of star-to-star light-element abundance variations (multiple populations, MPs) in massive Galactic and extragalactic star clusters older than about 2 Gyr is by now well established. Photometry of red giant branch (RGB) stars has been and still is instrumental in enabling the detection and characterization of cluster MPs, through the appropriate choices of filters, colours and colour combinations, that are mainly sensitive to N and --to a lesser degree-- C stellar surface abundances. An important issue not yet properly addressed is that the translation of the observed widths of the cluster RGBs to abundance spreads must account for the effect of the first dredge-up on the surface chemical patterns, hence on the spectral energy distributions of stars belonging to the various MPs. We have filled this gap by studying theoretically the impact of the dredge-up on the predicted widths of RGBs in clusters hosting MPs. We find that for a given initial range of N abundances, the first dredge up reduces the predicted RGB widths in N-sensitive filters compared to the case when its effect on the stellar spectral energy distributions is not accounted for. This reduction is a strong function of age and has also a dependence on metallicity. The net effect is an underestimate of the initial N-abundance ranges from RGB photometry if the first dredge-up is not accounted for in the modelling, and also the potential determination of spurious trends of N-abundance spreads with age.
We study the evolution of embedded clusters. The equations of motion of the stars in the cluster are solved by direct N-body integration while taking the effects of stellar evolution and the hydrodynamics of the natal gas content into account. The gravity of the stars and the surrounding gas are coupled self consistently to allow the realistic dynamical evolution of the cluster. While the equations of motion are solved, a stellar evolution code keeps track of the changes in stellar mass, luminosity and radius. The gas liberated by the stellar winds and supernovae deposits mass and energy into the gas reservoir in which the cluster is embedded. We examine cluster models with 1000 stars, but we varied the star formation efficiency (between 0.05-0.5), cluster radius (0.1-1.0 parsec), the degree of virial support of the initial population of stars (0-100%) and the strength of the feedback. We find that an initial star fraction $M_star/M_{rm tot} > 0.05$ is necessary for cluster survival. Survival is more likely if gas is not blown out violently by a supernova and if the cluster has time to approach virial equilibrium during out-gassing. While the cluster is embedded, dynamical friction drives early and efficient mass segregation in the cluster. Stars of $m gtrsim 2,M_odot$ are preferentially retained, at the cost of the loss of less massive stars. We conclude that the degree of mass segregation in open clusters such as the Pleiades is not the result of secular evolution but a remnant of its embedded stage.
$UBVRI$ photometry of the five open clusters Czernik 4, Berkeley 7, NGC 2236, NGC 7226 and King 12 has been carried out using ARIES 104 cm telescope, Nainital. Fundamental cluster parameters such as foreground reddening $E(B-V)$, distance, and age have been derived by means of the observed two colour and colour-magnitude diagrams, coupled to comparisons with theoretical models. $E(B-V)$ values range from 0.55 to 0.74 mag, while ages derived for these clusters range from $sim$10 to $sim$500 Myr. We have also studied the spatial structure, mass function and mass segregation effects. The present study shows that evaporation of low mass stars from the halo of the clusters increases as they evolve.
Two-body relaxation times of nuclear star clusters are short enough that gravitational encounters should substantially affect their structure in 10 Gyr or less. In nuclear star clusters without massive black holes, dynamical evolution is a competition between core collapse, which causes densities to increase, and heat input from the surrounding galaxy, which causes densities to decrease. The maximum extent of a nucleus that can resist expansion is derived numerically for a wide range of initial conditions; observed nuclei are shown to be compact enough to resist expansion, although there may have been an earlier generation of low-density nuclei that were dissolved. An evolutionary model for NGC 205 is presented which suggests that the nucleus of this galaxy has already undergone core collapse. Adding a massive black hole to a nucleus inhibits core collapse, and nuclear star clusters with black holes always expand, due primarily to heat input from the galaxy and secondarily to heating from stellar disruptions. The expansion rate is smaller for larger black holes due to the smaller temperature difference between galaxy and nucleus when the black hole is large. The rate of stellar tidal disruptions and its variation with time are computed for a variety of initial models. The disruption rate generally decreases with time due to the evolving nuclear density, particularly in the faintest galaxies, assuming that scaling relations derived for luminous galaxies can be extended to low luminosities.