The population of variable stars in M54 (NGC6715)

We present new B, V and I CCD time-series photometry for 177 variable stars in a 13'X 13' field centered on the globular cluster M54 (lying at the center of the Sagittarius dwarf spheroidal galaxy), 94 of which are newly identified variables. The total sample is composed of 2 anomalous Cepheids, 144 RR Lyrae stars (108 RR0 and 36 RR1), 3 SX Phoenicis, 7 eclipsing binaries (5 W UMA and 2 Algol binaries), 3 variables of uncertain classification and 18 long-period variables. The large majority of the RR Lyrae variables likely belong to M54. Ephemerides are provided for all the observed short-period variables. The pulsational properties of the M54 RR Lyrae variables are close to those of Oosterhoff I clusters, but a significant number of long-period ab type RR Lyrae are present. We use the observed properties of the RR Lyrae to estimate the reddening and the distance modulus of M54, E(B-V)=0.16 +/- 0.02 and (m-M)_0=17.13 +/- 0.11, respectively, in excellent agreement with the most recent estimates. The metallicity has been estimated for a subset of 47 RR Lyrae stars, with especially good quality light curves, from the Fourier parameters of the V light curve. The derived metallicity distribution has a symmetric bell shape, with a mean of =-1.65 and a standard deviation sigma=0.16 dex. Seven stars have been identified as likely belonging to the Sagittarius galaxy, based on their too high or too low metallicity. This evidence, if confirmed, might suggest that old stars in this galaxy span a wide range of metallicities.Comment: 15 pages, 11 figures, accepted for publication by MNRA

Synthetic properties of bright metal-poor variables. I. "Anomalous" Cepheids

We present new grids of evolutionary models for the so-colled ``Anomalous'' Cepheids (ACs), adopting Z=0.0001 and various assumptions on the progenitor mass and mass-loss efficiency. These computations are combined with the results of our previous set of pulsation models and used to build synthetic populations of the predicted pulsators as well as to provide a Mass-Luminosity relation in the absence of mass-loss. We investigate the effect of mass-loss on the predicted boundaries of the instability strip and we find that the only significant dependence occurs in the Period-Magnitude plane, where the synthetic distribution of the pulsators is, on average, brighter by about 0.1 mag than the one in absence of mass-loss. Tight Period-Magnitude relations are derived in the K band for both fundamental and first overtone pulsators, providing a useful tool for distance evaluations with an intrinsic uncertainty of about 0.15 mag, which decreases to about 0.04 mag if the mass term is taken into account. The constraints provided by the evolutionary models are used to derive evolutionary (i.e, mass-independent) Period-Magnitude-Color relations which provide distance determinations with a formal uncertainty of the order of about 0.1 mag, once the intrinsic colors are well known. We also use model computations from the literature to investigate the effect of metal content both on the instability strip and on the evolutionary Period-Magnitude-Color relations. Finally, we compare our theoretical predictions with observed variables and we confirm that a secure identification of actual ACs requires the simultaneous information on period, magnitude and color, that also provide constraints on the pulsation mode.Comment: accepte

The effect of heavy element opacity on pre-main sequence Li depletion

Recent 3-D analysis of the solar spectrum data suggests a significant change of the solar chemical composition. This may affect the temporal evolution of the surface abundance of light elements since the extension of the convective envelope is largely affected by the internal opacity value. We analyse the influence of the adopted solar mixture on the opacity in the convective envelope of pre-main sequence (PMS) stars and thus on PMS lithium depletion. The surface Li abundance depends on the relative efficiency of several processes, some of them still not known with the required precision; this paper thus analyses one of the aspects of this ``puzzle''. Focusing on PMS evolution, where the largest amount of Li burning occurs, we computed stellar models for three selected masses (0.8, 1.0 and 1.2 Msun, with Z=0.013, Y=0.27, alpha=1.9) by varying the chemical mixture, that is the internal element distribution in Z. We analysed the contribution of the single elements to the opacity at the temperatures and densities of interest for Li depletion. Several mixtures were obtained by varying the abundance of the most important elements one at a time; we then calculated the corresponding PMS Li abundance evolution. We found that a mixture variation does change the Li abundance: at fixed total metallicity, the Li depletion increases when increasing the fraction of elements heavier than O.Comment: A&A accepted, 11 pages, 18 eps figure

Confidence limits of evolutionary synthesis models. IV Moving forward to a probabilistic formulation

Synthesis models predict the integrated properties of stellar populations. Several problems exist in this field, mostly related to the fact that integrated properties are distributed. To date, this aspect has been either ignored (as in standard synthesis models, which are inherently deterministic) or interpreted phenomenologically (as in Monte Carlo simulations, which describe distributed properties rather than explain them). We approach population synthesis as a problem in probability theory, in which stellar luminosities are random variables extracted from the stellar luminosity distribution function (sLDF). We derive the population LDF (pLDF) for clusters of any size from the sLDF, obtaining the scale relations that link the sLDF to the pLDF. We recover the predictions of standard synthesis models, which are shown to compute the mean of the sLDF. We provide diagnostic diagrams and a simplified recipe for testing the statistical richness of observed clusters, thereby assessing whether standard synthesis models can be safely used or a statistical treatment is mandatory. We also recover the predictions of Monte Carlo simulations, with the additional bonus of being able to interpret them in mathematical and physical terms. We give examples of problems that can be addressed through our probabilistic formalism. Though still under development, ours is a powerful approach to population synthesis. In an era of resolved observations and pipelined analyses of large surveys, this paper is offered as a signpost in the field of stellar populations.Comment: Accepted by A&A. Substantially modified with respect to the 1st draft. 26 pages, 14 fig

Calibrated stellar models for metal-poor population

We extend to lower metallicities recent evolutionary computations devoted to Magellanic Clouds stars, presenting and discussing new stellar models with Z=0.0002, 0.0004, 0.0006, 0.001 and suitable assumptions about the original He content. As in the previous paper, evolutionary results are compared with observational data to properly calibrate the assumptions about the efficiency of the surface convection. On this basis, we follow the evolution of stellar models in the mass range 0.6 to 11Mo from the Main Sequence (MS) to the C ignition or the onset of thermal pulses in the advanced Asymptotic Giant Branch (AGB) phase, presenting cluster isochrones covering the range of ages from 20 Myr to 20 Gyr. Selected predictions constraining the cluster ages are discussed, presenting a calibration of the difference in magnitude between the luminous MS termination and the He burning giants in terms of the cluster age. Both evolutionary tracks and isochrones are available at the URL http://astro.df.unipi.it/SAA/PEL/Z0.html. Data files are also available at the CDS.Comment: In publication on Astronomy and Astrophysic

The second and third parameters of the Horizontal Branch in Globular Clusters

The Horizontal Branch (HB) second parameter of Globular Clusters (GCs) is a major open issue in stellar evolution. Large photometric and spectroscopic databases allow a re-examination of this issue. We derive median and extreme (90% of the distribution) colours and magnitudes of stars along the HB for about a hundred GCs. We transform these into median and extreme masses of stars on the HB taking into account evolutionary effects, and compare these masses with those expected at the tip of the Red Giant Branch to derive the total mass lost by the stars. A simple linear dependence on metallicity of this total mass lost explains well the median colours of HB stars. Adopting this mass loss law as universal, we find that age is the main second parameter. However, at least a third parameter is clearly required. The most likely candidate is the He abundance, which might be different in GCs stars belonging to the different stellar generations whose presence was previously derived from the Na-O and Mg-Al anticorrelations. Variations in the median He abundance allow explaining the extremely blue HB of some GCs; such variations are correlated with the R-parameter. Suitable He abundances allow deriving ages from the HB which are consistent with those obtained from the Main Sequence. Small corrections to these latter ages are then proposed, producing a tight age-metallicity relation for disk and bulge GCs. Star-to-star variations in the He content explain the extension of the HB. There is a strong correlation between this extension and the interquartile of the Na-O anticorrelation. The main driver for the variations in the He-content within GCs seems the total cluster mass. 47 Tuc and M3 exhibit exceptional behaviours; however, they can be accommodated in a scenario for the formation of GCs that relates their origin to cooling flows generated after very large episodes of star formation.Comment: 30 pages, 31 figures. In press on Astronomy and Astrophysics, version after language editin

Blue Straggler Stars in Globular Clusters: a powerful tool to probe the internal dynamical evolution of stellar systems

This chapter presents an overview of the main observational results obtained to date about Blue Straggler Stars (BSSs) in Galactic Globular Clusters (GCs). The BSS specific frequency, radial distribution, chemical composition and rotational properties are presented and discussed in the framework of using this stellar population as probe of GC internal dynamics. In particular, the shape of the BSS radial distribution has been found to be a powerful tracer of the dynamical age of stellar systems, thus allowing the definition of the first empirical "dynamical clock".Comment: Chapter 5, in Ecology of Blue Straggler Stars, H.M.J. Boffin, G. Carraro & G. Beccari (Eds), Astrophysics and Space Science Library, Springe

Two distinct sequences of blue straggler stars in the globular cluster M30

Stars in globular clusters are generally believed to have all formed at the same time, early in the Galaxy's history. 'Blue stragglers' are stars massive enough that they should have evolved into white dwarfs long ago. Two possible mechanisms have been proposed for their formation: mass transfer between binary companions and stellar mergers resulting from direct collisions between two stars. Recently, the binary explanation was claimed to be dominant. Here we report that there are two distinct parallel sequences of blue stragglers in M30. This globular cluster is thought to have undergone 'core collapse', during which both the collision rate and the mass transfer activity in binary systems would have been enhanced. We suggest that the two observed sequences arise from the cluster core collapse, with the bluer population arising from direct stellar collisions and the redder one arising from the evolution of close binaries that are probably still experiencing an active phase of mass transfer.Comment: Published on the 24th December 2009 issue of Natur

The photometric evolution of dissolving star clusters: II. Realistic models. Colours and M/L ratios

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)Comment: MNRAS, in press, data are available at http://www.phys.uu.nl/~anders/data/SSP_varMF/, http://data.galev.org and soon also from CDS ... sorry for the sometimes strange layout, that's LaTe

Monte Carlo Simulations of Metal-Poor Star Clusters

Metal-poor globular clusters (GCs) can provide a probe of the earliest epoch of star formation in the Universe, being the oldest stellar systems observable. In addition, young and intermediate-age low-metallicity GCs are present in external galaxies. Nevertheless, inferring their evolutionary status by using integrated properties may suffer from large \emph{intrinsic} uncertainty caused by the discrete nature of stars in stellar systems, especially in the case of faint objects. In this paper, we evaluate the \emph{intrinsic} uncertainty (due to statistical effects) affecting the integrated colours and mass--to--light ratios as a function of the cluster integrated visual magnitude ($M_V^{tot}$), which represents a quantity directly measured. Our approach is based on Monte Carlo techniques for randomly generating stars distributed according to the cluster's mass function. Integrated colours and mass--to--light ratios in different photometric bands are checked to be in good agreement with the observational values of low-metallicity Galactic clusters. We present integrated colours and mass--to--light ratios as a function of age for different assumptions on the cluster total $V$ magnitude. We find that the emph{intrinsic} uncertainty cannot be neglected. In particular, in models with $M_V^{tot}=-4$ the broad-band colours show an \emph{intrinsic} uncertainty so high as to prevent precise age evaluation of the cluster. Finally, the present predictions are compared with recent results available in the literature, showing in some cases non-negligible differences.Comment: 18 pages, 12 figures, A&A accepte