Open clusters and the galactic disk

It is textbook knowledge that open clusters are conspicuous members of the thin disk of our Galaxy, but their role as contributors to the stellar population of the disk was regarded as minor. Starting from a homogenous stellar sky survey, the ASCC‐2.5, we revisited the population of open clusters in the solar neighbourhood from scratch. In the course of this enterprise we detected 130 formerly unknown open clusters, constructed volume‐ and magnitude‐limited samples of clusters, re‐determined distances, motions, sizes, ages, luminosities and masses of 650 open clusters. We derived the present‐day luminosity and mass functions of open clusters (not the stellar mass function in open clusters), the cluster initial mass function CIMF and the formation rate of open clusters. We find that open clusters contributed around 40 percent to the stellar content of the disk during the history of our Galaxy. Hence, open clusters are important building blocks of the Galactic disk (© 2010 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)     

The mass-to-light ratio of rich star clusters

We point out a strong time evolution of the mass-to-light conversion factor, η, commonly used to estimate masses of unresolved star clusters from observed cluster spectrophotometric measures. We present a series of gas-dynamical models, coupled with the Cambridge stellar evolution tracks, to compute line-of-sight velocity dispersions and half-light radii weighted by the luminosity. We explore a range of initial conditions, varying in turn the cluster mass and/or density, and the stellar population’s initial mass function. We find that η, and hence the estimated cluster mass, may increase by as much as a factor of three over time-scales of 50 million yr. We apply these results to an hypothetic cluster mass distribution function (d.f.), and show that the d.f. shape may be strongly affected at the low-mass end by this effect. Fitting truncated isothermal (Michie–King) models to the projected light profile leads to over-estimates of the concentration parameter, c, of δ c≈0.3 compared to the same functional fit applied to the projected mass density.     

Competitive accretion in embedded stellar clusters

We investigate the physics of gas accretion in young stellar clusters. Accretion in clusters is a dynamic phenomenon as both the stars and the gas respond to the same gravitational potential. Accretion rates are highly non-uniform with stars nearer the centre of the cluster, where gas densities are higher, accreting more than others. This competitive accretion naturally results in both initial mass segregation and a spectrum of stellar masses. Accretion in gas-dominated clusters is well modelled using a tidal-lobe radius instead of the commonly used Bondi–Hoyle accretion radius. This works as both the stellar and gas velocities are under the influence of the same gravitational potential and are thus comparable. The low relative velocity which results means that R _tidal< R _BH in these systems. In contrast, when the stars dominate the potential and are virialized, R _BH< R _tidal and Bondi–Hoyle accretion is a better fit to the accretion rates.     

On the mass of dense star clusters in starburst galaxies from spectrophotometry

The mass of unresolved young star clusters derived from spectrophotometric data may well be off by a factor of 2 or more once the migration of massive stars driven by mass segregation is accounted for. We quantify this effect for a large set of cluster parameters, including variations in the stellar initial mass function (IMF), the intrinsic cluster mass, and mean mass density. Gas-dynamical models coupled with the Cambridge stellar evolution tracks allow us to derive a scheme to recover the real cluster mass given measured half-light radius, one-dimensional velocity dispersion and age. We monitor the evolution with time of the ratio of real to apparent mass through the parameter η. When we compute η for rich star clusters, we find non-monotonic evolution in time when the IMF stretches beyond a critical cut-off mass of  25.5 M_⊙  . We also monitor the rise of colour gradients between the inner and outer volume of clusters: we find trends in time of the stellar IMF power indices overlapping well with those derived for the Large Magellanic Cloud cluster NGC 1818 at an age of 30 Myr. We argue that the core region of massive Antennae clusters should have suffered from much segregation despite their low ages. We apply these results to a cluster mass function, and find that the peak of the mass distribution would appear to observers shifted to lower masses by as much as 0.2 dex. The star formation rate derived for the cluster population is then underestimated by from 20 to 50 per cent.     

Origin and dynamical evolution of young mass-segregated clusters

A significant degree of mass segregation inconsistent with the effects of standard two-body relaxation has been observed in a number of young star clusters. In this paper we present the results of a survey of N-body simulations aimed at exploring the origin and the dynamical evolution of young mass-segregated star clusters. Our simulations show that large segregated clusters can form from the merger of small clumps that are either initially segregated or in which segregation is produced before the merger is complete; the large cluster produced at the end of the merger process inherits the progenitor clumps’ segregation. We show that, in a young mass-segregated cluster, the effect of early mass loss associated with stellar evolution is, in general, more destructive than for an unsegregated cluster with the same density profile, and leads to shorter lifetimes, a faster initial evolution towards less-concentrated structure and a faster flattening of the stellar initial mass function.     

Recurrent gas accretion by massive star clusters, multiple stellar populations and mass thresholds for spheroidal stellar systems

We explore the gravitational influence of pressure-supported stellar systems on the internal density distribution of a gaseous environment. We conclude that compact massive star clusters with masses  ≳10⁶ M_⊙  act as cloud condensation nuclei and are able to accrete gas recurrently from a warm interstellar medium which may cause further star formation events and account for multiple stellar populations in the most massive globular and nuclear star clusters. The same analytical arguments can be used to decide whether an arbitrary spherical stellar system is able to keep warm or hot interstellar material or not. These mass thresholds coincide with transition masses between pressure supported galaxies of different morphological types.     

On the initial cluster mass distribution inferred from synthesis models

In this contribution we examine the problem of inferring ages and initial cluster masses from synthesis models at the limit of low-mass clusters (M≤ a few ×10⁴ M_⊙). We show that it is not possible to apply directly synthesis models using standard methods to such clusters, since the basic hypothesis implicit in the models (a fixed proportionality between the number of stars in different evolutionary phases) is not fulfilled due to an insufficient number of stars for a reliable sampling of the stellar initial mass function. The consequence of this incomplete sampling is a non-Gaussian distribution of the mass–luminosity relation for clusters that share the same evolutionary conditions (age, metallicity and stellar initial mass distribution function). We review some tests, that can be performed before the start of the analysis, to estimate if the observed cluster can be analyzed with synthesis models following traditional procedures (like χ ² minimization) or if it is necessary make use of synthesis models in a probabilistic framework. Finally, we show the implications of these results for estimating the low-mass tail in the initial cluster mass distribution function.     

The Mass Function of Young Star Clusters in the "Antennae" Galaxies

We determine the mass function of young star clusters in the merging galaxies known as the "Antennae" (NGC 4038/9) from deep images taken with the Wide Field Planetary Camera 2 on the refurbished Hubble Space Telescope. This is accomplished by means of reddening-free parameters and a comparison with stellar population synthesis tracks to estimate the intrinsic luminosity and age, and hence the mass, of each cluster. We find that the mass function of the young star clusters (with ages less, similar160 Myr) is well represented by a power law of the form psi&parl0;M&parr0;~M-2 over the range 104 less, similarM less, similar106 M middle dot in circle. This result may have important implications for our understanding of the origin of globular clusters during the early phases of galactic evolution.     

Faint stars in the Ursa Minor dwarf spheroidal galaxy: implications for the low-mass stellar initial mass function at high redshift

The stellar initial mass function at high redshift is an important defining property of the first stellar systems to form and may also play a role in various dark matter problems. We here determine the faint stellar luminosity function in an apparently dark-matter-dominated external galaxy in which the stars formed at high redshift. The Ursa Minor dwarf spheroidal galaxy is a system with a particularly simple stellar population—all of the stars being old and metal-poor—similar to that of a classical halo globular cluster. A direct comparison of the faint luminosity functions of the UMi dSph and of similar metallicity, old globular clusters is equivalent to a comparison of the initial mass functions and is presented here, based on deep HST WFPC2 and STIS imaging data. We find that these luminosity functions are indistinguishable, down to a luminosity corresponding to ∼0.3 M_⊙. Our results show that the low-mass stellar IMF for stars that formed at very high redshift is apparently invariant across environments as diverse as those of an extremely low-surface-brightness, dark-matter-dominated dwarf galaxy and a dark-matter-free, high-density globular cluster within the Milky Way.     

A principal component analysis of the equivalent widths of spectral lines of star clusters

Using principal component analysis, we have studied the equivalent widths of optical spectral lines of 41 Galactic globular clusters and 22 young stellar clusters. We have discovered that some characteristic spectral lines, such as the CN, Ca IIK, Ca IIH and MgI+MgII lines, are rather sensitive to metallicity. We have also found some lines that may be used as indicators of age, e.g. Hδ, Hγ, Hβ and H. These lines can help us to disentangle the coupling effects of age and metallicity in the clusters.     

Galaxy evolution in the high-redshift, colour-selected cluster RzCS 052 at z= 1.02

We present deep I and z ' imaging of the colour-selected cluster RzCS 052 and study the colour–magnitude relation of this cluster, its scatter, the morphological distribution on the red sequence, the luminosity and stellar mass functions of red galaxies and the cluster blue fraction. We find that the stellar populations of early-type galaxies in this cluster are uniformly old and that their luminosity function does not show any sign of evolution other than the passive evolution of their stellar populations. We rule out a significant contribution from mergers in the build-up of the red sequence of RzCS 052. The cluster has a large (∼30 per cent) blue fraction and we infer that the evolution of the blue galaxies is faster than an exponentially declining star formation model and that these objects have probably experienced starburst episodes. Mergers are unlikely to be the driver of the observed colour evolution, because of the measured constancy of the mass function, as derived from near-infrared photometry of 32 clusters, including RzCS 052, presented in a related paper. Mechanisms with clustercentric radial dependent efficiencies are disfavoured as well, because of the observed constant blue fraction with clustercentric distance.     

Stellar Mass—Halo Mass Relation and Star Formation Efficiency in High-Mass Halos

We study relation between stellar mass and halo mass for high-mass halos using a sample of galaxy clusters with accurate measurements of stellar masses from optical and ifrared data and total masses from X-ray observations. We find that stellar mass of the brightest cluster galaxies (BCGs) scales as M_*,BCG ∝ M ₅₀₀ ^αBCG with the best fit slope of α_BCG ≈ 0.4 ± 0.1. We measure scatter of M_*,BCG at a fixed M₅₀₀ of ≈0.2 dex. We show that stellar mass-halo mass relations from abundance matching or halo modelling reported in recent studies underestimate masses of BCGs by a factor of ～2?4. We argue that this is because these studies used stellar mass functions (SMF) based on photometry that severely underestimates the outer surface brightness profiles of massive galaxies. We show that M_*?M relation derived using abundance matching with the recent SMF calibration by Bernardi et al. (2013) based on improved photometry is in a much better agreement with the relation we derive via direct calibration for observed clusters. The total stellar mass of galaxies correlates with total mass M₅₀₀ with the slope of ≈0.6 ± 0.1 and scatter of 0.1 dex. This indicates that efficiency with which baryons are converted into stars decreases with increasing cluster mass. The low scatter is due to large contribution of satellite galaxies: the stellar mass in satellite galaxies correlates with M₅₀₀ with scatter of ≈0.1 dex and best fit slope of α_sat ≈ 0.8 ± 0.1. We show that for a fixed choice of the initial mass function (IMF) total stellar fraction in clusters is only a factor of 3?5 lower than the peak stellar fraction reached in M ≈ 10¹²M_⊙ halos. The difference is only a factor of ～1.5?3 if the IMF becomes progressively more bottom heavy with increasing mass in early type galaxies, as indicated by recent observational analyses. This means that the overall efficiency of star formation in massive halos is only moderately suppressed compared to L_* galaxies and is considerably less suppressed than previously thought. The larger normalization and slope of the M_*?M relation derived in this study shows that feedback and associated suppression of star formation in massive halos should be weaker than assumed in most of the current semi-analytic models and simulations.     

Mass function study of open star clusters Haffner 11 and Czernik 31

We analysis VI CCD data of two open clusters Haffner 11 and Czernik 31 in order to determine their luminosity function, mass function and mass-segregation for the first time. The observed luminosity function is corrected for both data incompleteness and field star contamination. Theoretical stellar evolutionary isochrones are used to convert luminosity function into mass function. The Mass function slopes are derived as 1.22 ± 0.42 and 1.55 ± 0.38 for Haffner 11 and Czernik 31 respectively. They agree with the Salpeter value ($x=$1.35) within the errors. The effect of mass segregation are observed in both the clusters. The estimated dynamical relaxation time is less than age of the clusters. This indicates that they are dynamically relaxed. The cause of relaxation may be due to the dynamical evolution or imprint of star formation or both.     

Nuclear star formation in the hotspot galaxy NGC 2903

We present high-resolution near-infrared imaging obtained using adaptive optics and HST /NICMOS, and ground-based spectroscopy of the hotspot galaxy NGC 2903. Our near-infrared resolution imaging enables us to resolve the infrared hotspots into individual young stellar clusters or groups of these. The spatial distribution of the stellar clusters is not coincident with that of the bright H  ii regions, as revealed by the HST /NICMOS Pa α image. Overall, the circumnuclear star formation in NGC 2903 shows a ring-like morphology with an approximate diameter of 625 pc.
The star formation properties of the stellar clusters and H  ii regions have been studied using the photometric and spectroscopic information in conjunction with evolutionary synthesis models. The population of bright stellar clusters shows a very narrow range of ages, 4–7×10⁶ yr after the peak of star formation, or absolute ages 6.5–9.5×10⁶ yr (for the assumed short-duration Gaussian bursts), and luminosities similar to the clusters found in the Antennae interacting galaxy. This population of young stellar clusters accounts for some 7–12 per cent of the total stellar mass in the central 625 pc of NGC 2903. The H  ii regions in the ring of star formation have luminosities close to that of the supergiant H  ii region 30 Doradus, they are younger than the stellar clusters, and they will probably evolve into bright infrared stellar clusters similar to those observed today. We find that the star formation efficiency in the central regions of NGC 2903 is higher than in normal galaxies, approaching the lower end of infrared luminous galaxies.     

On the potential of transit surveys in star clusters: impact of correlated noise and radial velocity follow-up

We present an extension of the formalism recently proposed by Pepper and Gaudi to evaluate the yield of transit surveys in homogeneous stellar systems, incorporating the impact of correlated noise on transit time-scales on the detectability of transits, and simultaneously incorporating the magnitude limits imposed by the need for radial velocity (RV) follow-up of transit candidates. New expressions are derived for the different contributions to the noise budget on transit time-scales and the least-squares detection statistic for box-shaped transits, and their behaviour as a function of stellar mass is re-examined. Correlated noise that is constant with apparent stellar magnitude implies a steep decrease in detection probability at the high -mass end which, when considered jointly with the RV requirements, can severely limit the potential of otherwise promising surveys in star clusters. However, we find that small-aperture, wide-field surveys may detect hot Neptunes whose RV signal can be measured with present-day instrumentation in very nearby (<100 pc) clusters.     

Analysis of the structure and dynamics of the stellar tails of open star clusters

We have analyzed the formation, structure, and dynamical evolution of the population of stars that escaped from open clusters by numerical simulations using S. Aarseth’s modified NBODY6 code. In the Galactic tidal field, the population of stars that escaped from a cluster is shown to be elongated along the orbit of the cluster symmetrically about its core in the form of stellar tails of increasing sizes. We analyze the parameters of stellar tails as a function of such initial simulation conditions as the number of stars, the cluster density, the eccentricity of the Galactic cluster orbit in the plane of the Galactic disk, and the z velocity component. As a result, we constructed a grid of model stellar tails of open clusters. The grid includes such time-dependent parameters of the stellar tails as the length, the cross section, the number of stars, the velocity distribution, etc. Our simulations allow us to clarify the origin of moving clusters and stellar streams and to assess the role of star clusters in forming the stellar velocity field in the solar neighborhood.     

How special are brightest group and cluster galaxies?

We use the Sloan Digital Sky Survey (SDSS) to construct a sample of 625 brightest group and cluster galaxies (BCGs) together with control samples of non-BCGs matched in stellar mass, redshift and colour. We investigate how the systematic properties of BCGs depend on stellar mass and on their privileged location near the cluster centre. The groups and clusters that we study are drawn from the C4 catalogue of Miller et al. but we have developed improved algorithms for identifying the BCG and for measuring the cluster velocity dispersion. Since the SDSS photometric pipeline tends to underestimate the luminosities of large galaxies in dense environments, we have developed a correction for this effect which can be readily applied to the published catalogue data. We find that BCGs are larger and have higher velocity dispersions than non-BCGs of the same stellar mass, which implies that BCGs contain a larger fraction of dark matter. In contrast to non-BCGs, the dynamical mass-to-light ratio of BCGs does not vary as a function of galaxy luminosity. Hence BCGs lie on a different Fundamental Plane than ordinary elliptical galaxies. BCGs also follow a steeper Faber–Jackson relation than non-BCGs, as suggested by models in which BCGs assemble via dissipationless mergers along preferentially radial orbits. We find tentative evidence that this steepening is stronger in more massive clusters. BCGs have similar mean stellar ages and metallicities to non-BCGs of the same mass, but they have somewhat higher α/Fe ratios, indicating that star formation may have occurred over a shorter time-scale in the BCGs. Finally, we find that BCGs are more likely to host radio-loud active galactic nuclei than other galaxies of the same mass, but are less likely to host an optical active galactic nucleus (AGN). The differences we find are more pronounced for the less massive BCGs, i.e. they are stronger at the galaxy group level.     

A robust statistical estimation of the basic parameters of single stellar populations – I. Method

The colour–magnitude diagrams of resolved single stellar populations, such as open and globular clusters, have provided the best natural laboratories to test stellar evolution theory. Whilst a variety of techniques have been used to infer the basic properties of these simple populations, systematic uncertainties arise from the purely geometrical degeneracy produced by the similar shape of isochrones of different ages and metallicities. Here we present an objective and robust statistical technique which lifts this degeneracy to a great extent through the use of a key observable: the number of stars along the isochrone. Through extensive Monte Carlo simulations we show that, for instance, we can infer the four main parameters (age, metallicity, distance and reddening) in an objective way, along with robust confidence intervals and their full covariance matrix. We show that systematic uncertainties due to field contamination, unresolved binaries, initial or present-day stellar mass function are either negligible or well under control. This technique provides, for the first time, a proper way to infer with unprecedented accuracy the fundamental properties of simple stellar populations, in an easy-to-implement algorithm.     

The astrophysical consequences of the bimodal hydrodynamic solution of the super star cluster winds

The mass reinserted by young stars in an emerging massive compact cluster shows a bimodal hydrodynamic behaviour. In the inner parts of the cluster, it is thermally unstable, while in its outer parts it forms an outflowing wind. The chemical homogeneity/inhomogeneity of low/high-mass clusters demonstrates the relevance of this solution to the presence of single/multiple stellar populations. We show the consequences which the thermal instability of the reinserted mass has on galactic superwinds and discuss the open issues raised by the bimodal solution of stellar winds of massive clusters.     

The influence of gas expulsion and initial mass segregation on the stellar mass function of globular star clusters

Recently, De Marchi, Paresce & Pulone studied a sample of 20 globular clusters and found that all clusters with high concentrations have steep stellar mass functions while clusters with low concentration have comparatively shallow mass functions. No globular clusters were found with a flat mass function and high concentration. This seems curious since more concentrated star clusters are believed to be dynamically more evolved and should have lost more low-mass stars via evaporation, which would result in a shallower mass function in the low-mass part.
We show that this effect can be explained by residual-gas expulsion from initially mass segregated star clusters, and is enhanced further through unresolved binaries. If gas expulsion is the correct mechanism to produce the observed trend in the   c –α  -plane, then observation of these parameters would allow to constrain cluster starting conditions such as star formation efficiency and the time-scale of gas expulsion.