Internal dynamics of globular clusters

Summary. Galactic globular clusters, which are ancient building blocks of our Galaxy, represent a very interesting family of stellar systems in which some fundamental dynamical processes have taken place on time scales shorter than the age of the universe. In contrast with galaxies, these clusters represent unique laboratories for learning about two-body relaxation, mass segregation from equipartition of energy, stellar collisions, stellar mergers, and core collapse. In the present review, we summarize the tremendous developments, as much theoretical as observational, that have taken place during the last two decades, and which have led to a quantum jump in our understanding of these beautiful dynamical systems. Received 3 August 1996     

Evolution of Population II stars

The current knowledge of the evolution of Population II stars, as observed in galactic halos and globular clusters, is outlined. The recent theoretical results provided by an improved physical understanding of the stars are reported, with a particular emphasis upon those stellar evolutionary phases which are the keystones of the interpretation of globular cluster stars. Within the up–to–date theoretical scenario, the luminosity of the turn–off stars and horizontal branch stars, which are of fundamental importance for distance and age determinations, turns out to be fainter and brighter, respectively, in comparison with previous theoretical computations. The predicted absolute magnitude of RR Lyrae stars is consistent with the bright values suggested from the long distance scale (Sandage 1993), but the slope of the relation between and metallicity ([Fe/H]) agrees with that suggested from the short distance scale (see, e.g., Carney et al. 1992, Clementini et al. 1995), at least with [Fe/H]-1.3. As to the globular cluster ages, the new computations provide younger ages ( 10 Gyr–13 Gyr), weakening the conflict with current cosmological estimates. The recent results derived from the fitting of HIPPARCOS parallaxes of field subdwarfs to the fiducial main sequence of globular clusters are consistent with the up–to–date theoretical models. However, the direct determinations of , which are based on the HIPPARCOS proper motions and trigonometric parallaxes of field RR Lyrae stars, give fainter absolute magnitudes than those obtained from the improved evolutionary models. This seems to suggest that the problem of the globular cluster distance and age is still open. Received 6 April 1998     

Merging Massive Star Clusters as Building Blocks of Dwarf Galaxies?

Recent spectroscopic observations of galaxies in the Fornax-Cluster reveal nearly unresolved ‘star-like’ objects with red-shifts appropriate to the Fornax-Cluster. These objects have intrinsic sizes of ≈ 100 pc and absolute B-band magnitudes in the range - 14 < M_B < -11.5 mag and lower limits for the central surface brightness μ_B ≥ 23 mag/arcsec² (Phillipps et al., 2001, Hilker et al., 1999), and so appear to constitute a new population of ultra-compact dwarf galaxies (UCDs). Such compact dwarfs were predicted to form from the amalgamation of stellar super-clusters (= clusters of star clusters; not to confuse with super stellar clusters (SSC)) by P. Kroupa (1998), which are rich aggregates of young massive star clusters (YMCs) that can form in collisions between gas-rich galaxies. Here we present the evolution of super-clusters in a tidal field. The YMCs merge on a few super-cluster crossing times. Super-clusters that are initially as concentrated and massive as Knot S in the interacting Antennae galaxies (Whitmore et al., 1999) evolve to merger objects that are long-lived and show properties comparable to the newly discovered UCDs. This revised version was published online in September 2006 with corrections to the Cover Date.     

Stellar models for very low-mass main-sequence stars: the role of model atmospheres

We present very low-mass stellar models as computed using non-grey model atmospheres for selected assumptions about the stellar metallicities. The role of atmospheres is discussed and the models are compared with models based on the Eddington approximation, and with similar models that have appeared in the recent literature. Theoretical predictions concerning both the HR diagram location and the mass–luminosity relation are presented and discussed in terms of expectations in selected photometric bands. Comparison with available observational data concerning both galactic globular clusters and dwarfs in the solar neighbourhood reveals a satisfactory agreement together with the existence of some residual mismatches.     

The distribution of ejected brown dwarfs in clusters

We examine the spatial distribution of brown dwarfs produced by the decay of small‐N stellar systems as expected from the embryo ejection scenario. We model a cluster of several hundred stars grouped into ‘cores’ of a few stars/brown dwarfs. These cores decay, preferentially ejecting their lowest‐mass members. Brown dwarfs are found to have a wider spatial distribution than stars, however once the effects of limited survey areas and unresolved binaries are taken into account it can be difficult to distinguish between clusters with many or no ejections. A large difference between the distributions probably indicates that ejections have occurred, however similar distributions sometimes arise even with ejections. Thus the spatial distribution of brown dwarfs is not necessarily a good discriminator between ejection and non‐ejection scenarios. (© 2005 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)     

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 most metal-poor galaxies

Summary. Metallicity is a key parameter that controls many aspects in the formation and evolution of stars and galaxies. In this review we focus on the metal deficient galaxies, in particular the most metal-poor ones, because they play a crucial r?le in the cosmic scenery. We first set the stage by discussing the difficult problem of defining a global metallicity and how this quantity can be measured for a given galaxy. The mechanisms that control the metallicity in a galaxy are reviewed in detail and involve many aspects of modern astrophysics: galaxy formation and evolution, massive star formation, stellar winds, chemical yields, outflows and inflows etc. Because metallicity roughly scales as the galactic mass, it is among the dwarfs that the most metal-poor galaxies are found. The core of our paper reviews the considerable progress made in our understanding of the properties and the physical processes that are at work in these objects. The question on how they are related and may evolve from one class of objects to another is discussed. While discussing metal-poor galaxies in general, we present a more detailed discussion of a few very metal-poor blue compact dwarf galaxies like IZw18. Although most of what is known relates to our local universe, we show that it pertains to our quest for primeval galaxies and is connected to the question of the origin of structure in the universe. We discuss what do QSO absorption lines and known distant galaxies tell us already? We illustrate the importance of star-forming metal-poor galaxies for the determination of the primordial helium abundance, their use as distance indicator and discuss the possibility to detect nearly metal-free galaxies at high redshift from Ly emission. Received 19 August 1999 / Published online: 15 February 2000     

Resonant excitation of white dwarf oscillations in compact object binaries – I. The no back reaction approximation

We consider the evolution of white dwarfs with compact object companions (specifically black holes with masses up to  ∼10⁶  M_⊙  , neutron stars, and other white dwarfs). We suppose that the orbits are initially quite elliptical and then shrink and circularize under the action of gravitational radiation. During this evolution, the white dwarfs will pass through resonances when harmonics of the orbital frequency match the stellar oscillation eigenfrequencies. As a star passes through these resonances, the associated modes will be excited and can be driven to amplitudes that are so large that there is a back reaction on the orbit which, in turn, limits the growth of the modes. A formalism is presented for describing this dynamical interaction for a non-rotating star in the linear approximation when the orbit can be treated as non-relativistic. A semi-analytical expression is found for computing the resonant energy transfer as a function of stellar and orbital parameters for the regime where back reaction may be neglected. This is used to calculate the results of passage through a sequence of resonances for several hypothetical systems. It is found that the amplitude of the  ℓ= m = 2  f -mode can be driven into the non-linear regime for appropriate initial conditions. We also discuss where the no back reaction approximation is expected to fail, and the qualitative effects of back reaction.     

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.     

Finding Faint Intermediate-Mass Black Holes in the Radio Band

We discuss the prospects for detecting faint intermediate-mass black holes, such as those predicted to exist in the cores of globular clusters and dwarf spheroidal galaxies. We briefly summarize the difficulties of stellar dynamical searches, then show that recently discovered relations between black hole mass, X-ray luminosity and radio luminosity imply that in most cases, these black holes should be more easily detected in the radio than in the X-rays. Finally, we show upper limits from some radio observations of globular clusters, and discuss the possibility that the radio source in the core of the Ursa Minor dwarf spheroidal galaxy might be a ∼10,000–100,000 M⊙ black hole.     

IRTF observations of white dwarfs with possible near-infrared excess

Near-infrared photometry and spectroscopy are obtained for a heterogeneous sample of nearby white dwarfs with possible excess flux as identified primarily in the Two Micron All Sky Survey. Among the sample of 43 stars are a number of white dwarfs that are either metal-rich, magnetic or binary suspects. With a few notable exceptions in four (or possibly five) distinct categories, the newly obtained JHK photometric data fail to corroborate the putative excesses, with  〈 K _IRTF− K _2MASS〉=+0.31  mag. Where available, Galaxy Evolution Explorer photometric data are used to better constrain the overall spectral energy distribution of the white dwarfs, enabling any excess near-infrared flux to stand out more readily against the expected stellar photosphere.
With superior data, a near-infrared photometric excess is confirmed at three metal-rich white dwarfs and ruled out at nine others. Several new binaries are confirmed or suggested; five white dwarf–red dwarf pairs and five double degenerates. Four apparently single magnetic white dwarfs – two DA and two DQp – display modest to strong near-infrared excess (relative to non-magnetic models), which may be better described as two effective temperatures owing to a redistribution of energy in highly magnetic or peculiar atmospheres.     

Type Ia supernovae and remnant neutron stars

On the basis of the current observational evidence, we put forward the case that the merger of two CO white dwarfs produces both a Type Ia supernova explosion and a stellar remnant, the latter in the form of a magnetar. The estimated occurrence rates raise the possibility that many, if not most, Type Ia supernovae might result from white dwarf mergers.     

Astrophysical supplements to the ASCC‐2.5: Ia. Radial velocities of ∼55000 stars and mean radial velocities of 516 Galactic open clusters and associations

We present the 2nd version of the Catalogue of Radial Velocities with Astrometric Data (CRVAD‐2). This is the result of the cross‐identification of stars from the All‐Sky Compiled Catalogue of 2.5 Million Stars (ASCC‐2.5) with the General Catalogue of Radial Velocities and with other recently published radial velocity lists and catalogues. The CRVAD‐2 includes accurate J2000 equatorial coordinates, proper motions and trigonometric parallaxes in the Hipparcos system, B, V photometry in the Johnson system, spectral types, radial velocities (RVs), multiplicity and variability flags for 54907 ASCC‐2.5 stars. We have used the CRVAD‐2 for a new determination of mean RVs of 363 open clusters and stellar associations considering their established members from proper motions and photometry in the ASCC‐2.5. For 330 clusters and associations we compiled previously published mean RVs from the literature, critically reviewed and partly revised them. The resulting Catalogue of Radial Velocities of Open Clusters and Associations (CRVOCA) contains about 460 open clusters and about 60 stellar associations in the Solar neighbourhood. These numbers still represent less than 30% of the total number of about 1820 objects currently known in the Galaxy. The mean RVs of young clusters are generally better known than those of older ones. (© 2007 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)     

Identifying star clusters in a field: A comparison of different algorithms

Star clusters are often hard to find, as they may lie in a dense field of background objects or, because in the case of embedded clusters, they are surrounded by a more dispersed population of young stars. This paper discusses four algorithms that have been developed to identify clusters as stellar density enhancements in a field, namely stellar density maps from star counts, the nearest neighbour method and the Voronoi tessellation, and the separation of minimum spanning trees. These methods are tested and compared to each other by applying them to artificial clusters of different sizes and morphologies. While distinct centrally concentrated clusters are detected by all methods, clusters with low overdensity or highly hierarchical structure are only reliably detected by methods with inherent smoothing (star counts and nearest neighbour method). Furthermore, the algorithms differ strongly in computation time and additional parameters they provide. Therefore, the method to choose primarily depends on the size and character of the investigated area and the purpose of the study (© 2011 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)     

The globular clusters–stellar haloes connection in early-type galaxies

This paper explores if, and to what an extent, the stellar populations of early-type galaxies can be traced through the colour distribution of their globular cluster (GC) systems. The analysis, based on a galaxy sample from the Virgo Advanced Camera for Surveys data, is an extension of a previous approach that has been successful in the cases of the giant ellipticals NGC 1399 and NGC 4486, and assumes that the two dominant GC populations form along diffuse stellar populations sharing the cluster chemical abundances and spatial distributions. The results show that (a) integrated galaxy colours can be matched to within the photometric uncertainties and are consistent with a narrow range of ages; (b) the inferred mass to luminosity ratios and stellar masses are within the range of values available in the literature; (c) most GC systems occupy a thick plane in the volume space defined by the cluster formation efficiency, total stellar mass and projected surface mass density. The formation efficiency parameter of the red clusters shows a dependency with projected stellar mass density that is absent for the blue globulars. In turn, the brightest galaxies appear clearly detached from that plane as a possible consequence of major past mergers; (d) the stellar mass–metallicity relation is relatively shallow but shows a slope change at   M _*≈ 10¹⁰ M_⊙  . Galaxies with smaller stellar masses show predominantly unimodal GC colour distributions. This result may indicate that less massive galaxies are not able to retain chemically enriched interstellar matter.     

The formation of a bound star cluster: from the Orion nebula cluster to the Pleiades

Direct N -body calculations are presented of the formation of Galactic clusters using GasEx , which is a variant of the code Nbody6 . The calculations focus on the possible evolution of the Orion nebula cluster (ONC) by assuming that the embedded OB stars explosively drove out 2/3 of its mass in the form of gas about 0.4 Myr ago. A bound cluster forms readily and survives for 150 Myr despite additional mass loss from the large number of massive stars, and the Galactic tidal field. This is the very first time that cluster formation is obtained under such realistic conditions. The cluster contains about 1/3 of the initial 10⁴ stars, and resembles the Pleiades cluster to a remarkable degree, implying that an ONC-like cluster may have been a precursor of the Pleiades. This scenario predicts the present expansion velocity of the ONC, which will be measurable by upcoming astrometric space missions. These missions should also detect the original Pleiades members as an associated expanding young Galactic-field subpopulation. The results arrived at here suggest that Galactic clusters form as the nuclei of expanding OB associations.
The results have wide implications, also for the formation of globular clusters and the Galactic-field and halo stellar populations. In view of this, the distribution of binary orbital periods and the mass function within and outside the model ONC and Pleiades is quantified, finding consistency with observational constraints. Advanced mass segregation is evident in one of the ONC models. The calculations show that the primordial binary population of both clusters could have been much the same as is observed in the Taurus–Auriga star-forming region. The computations also demonstrate that the binary proportion of brown dwarfs is depleted significantly for all periods, whereas massive stars attain a high binary fraction.     

White dwarf stars as strange quark matter detectors – III

We continue the study of the properties of non-radial pulsations of strange dwarfs. These stars are essentially white dwarfs with a strange quark matter (SQM) core. We have previously shown that the spectrum of oscillations should be formed by several, well-detached clusters of modes inside which the modes are almost evenly spaced. Here, we study the relation between the characteristics of these clusters and the size of the SQM core. We do so assuming that, for a given cluster, the kinetic energy of the modes is constant. For a constant amplitude of the oscillation at the stellar surface, we find that the kinetic energy of the modes is very similar for the cases of models with Log Q _SQM=−2, −3 and −4, while it is somewhat lower for  Log Q _SQM=−5  (here   Q _SQM≡ M _SQM/ M ; M _SQM  and M are the masses of the SQM core and the star, respectively). Remarkably, the shape (amplitude of the modes versus period of oscillation) of the clusters of periods is very similar. However, the number of modes inside each cluster is strongly (and non-monotonously) dependent upon the size of the SQM core.
The characteristics of the spectrum of oscillations of strange dwarf stars are very different from the ones corresponding to normal white dwarfs and should be, in principle, observable. Consequently, the stars usually considered as white dwarfs may indeed provide an interesting and affordable way to detect SQM in an astrophysical environment.     

Low mass companions to white dwarfs

This paper summarizes the results of over 17 years of work searching for low mass stellar and substellar companions to more than 370 nearby white dwarfs. Roughly 60 low mass, unevolved companions were found and studied all together, with over 20 discovered in the last few years, including the first unambiguous brown dwarf companion to a white dwarf, GD 1400B. The resulting spectral type distributions for companions to white dwarfs and nearby cool field dwarfs are compared, and the implications for binary star formation are discussed. A brief analysis of GD 1400B, including new data, is also presented. (© 2005 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)     

Brown dwarf populations in open clusters

We present the results of multiple simulations of open clusters, modelling the dynamics of a population of brown dwarf members. We consider the effects of a large range of primordial binary populations, including the possibilities of having brown dwarf members contained within a binary system. We also examine the effects of various cluster diameters and masses. Our examination of a population of wide binary systems containing brown dwarfs, reveals evidence for exchange reactions whereby the brown dwarf is ejected from the system and replaced by a heavier main-sequence star. We find that there exists the possibility of hiding a large fraction of the brown dwarfs contained within the primordial binary population. We conclude that it is probable that the majority of brown dwarfs are contained within primordial binary systems which then hides a large proportion of them from detection.     

Non-Radial Pulsations in Components of Symbiotic Stars

Photometric observations of symbiotic stars in the blue and in the red spectral regions make it possible to reveal non-radial oscillations both of the cool and of the hot components. Light variations of red giants in the symbiotic systems CI Cyg and AG Peg show several periods in the 10–80^d range, interpreted as p-mode pulsations. These modes are excited by a bright spot produced by radiation flux from the hot component. The spot moves on the red giant’s photosphere at a velocity close to the sound speed. During the active phase of the symbiotic star CH Cyg, at least 25 frequencies of oscillations in the 150–6000 s range of periods were found in the light of the white dwarf. Their features correspond to non-radial g-modes. In the frame of 2D gas dynamical non-adiabatic models, the interaction between gas flows and the accretion disk leads to formation of a system of shock waves propagating towards the compact object, which is one of possible mechanisms to excite non-radial pulsations of white dwarfs in symbiotic systems.