On determining membership of open clusters from relative proper motion

We discuss the determination of membership of 42 open clusters. Our analysis shows that Vasilevskis' mathematical model can be reasonably applied to this case. Our improved version of Sanders' method and our definition of cluster member based on the principles of discriminatory analysis effectively exclude stars of low probabilities. It is important in the study of open cluster to use only those with high probabilities. The effectiveness of the statistical method is closely related to the velocity distributions of the member and field stars. For fields where the error rate is high, it is better to combine other data than proper motion in determining membership.     

Photometric membership and metallicities of red giant candidates in selected open clusters

As part of a long‐term project to determine abundances and astrophysical properties of evolved red stars in open clusters, we present high‐precision DDO photoelectric observations for a sample of 33 red giant candidates projected in the fields of nine Galactic open clusters. These data are supplemented with UBV photoelectric photometry of 24 of these stars as well as with CORAVEL radial‐velocity observations for 13 red giant candidates in four of the clusters. We also present Washington photoelectric photometry of a small sample of red giant candidates of the open cluster Ruprecht 97. The likelihood of cluster membership for each star photometrically observed and for 23 additional red giant candidates with UBV and DDO data available in the literature, is evaluated by using two independent photometric criteria. Nearly 82% of the analysed stars are found to have a high probability of being cluster giants. Photometric membership probabilities show very good agreement with those obtained from CORAVEL radial velocities. While E (B –V) colour excesses were determined from combined B – V and DDO colours, calibrations of the DDO system were used to derive MK spectral types, effective temperatures and metallicities. The derived DDO metallicities range between values typical of moderately metal‐poor clusters ([Fe/H] = –0.19) to moderately metal‐rich ([Fe/H] = 0.25) ones. (© 2008 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)     

The stellar three-body problem

Two applications of von Zeipel's method to the stellar three-body problem eliminate the short period terms and establish two new integrals of the motion beyond the classical integrals. The remaining time averaged problem with only the second order Hamiltonian has one additional integral and can be solved. The motion with the third order averaged Hamiltonian included is more complex, in that there may be additional resonances, and the additional integral does not exist in all cases.     

Discussion on the maximum likelihood method for determination of membership in open clusters

We suggest some objective criteria for pruning the vector point diagram, necessary when calculating the membership probabilities of stars in a cluster field from their proper motions. We present a staggered procedure of data pruning, and the determinations of the orientation of the field points and the distribution parameters of the two-component (cluster members and field stars) population.     

Binary formation in stellar clusters

We consider how the tidal potential of a stellar cluster or a dense molecular cloud affects the fragmentation of gravitationally unstable molecular cloud cores. We find that molecular cloud cores which would collapse to form a single star in the absence of tidal shear, can be forced to fragment if they are subjected to tides. This may enhance the frequency of binaries in star-forming regions such as Ophiuchus and the frequency of binaries with separations ≲100 au in the Orion Trapezium Cluster. We also find that clouds which collapse to form binary systems in the absence of a tidal potential will form bound binary systems if exposed to weak tidal shear. However, if the tidal shear is sufficiently strong, even though the cloud still collapses to form two fragments, the fragments are pulled apart while they are forming by the tidal shear and two single stars are formed. This sets an upper limit for the separation of binaries that form near dense molecular clouds or in stellar clusters.     

The lower mass function of young open clusters: clues to (sub)stellar formation

We report the present day mass functions (PDMFs) of 4 young open clusters over a mass range from 30 Jupiter masses to 3M_ . Three of these clusters have been chosen to have a similar age of ∼100 Myr. Their PDMFs are remarkably similar and are comparable to the field mass function. This suggests little impact of initial conditions (stellar density, metallicity) on the mass distribution and raises some issues concerning the currently debated star and brown dwarf formation theories. The fourth cluster is older (600 Myr) which allow us to investigate the effect of the cluster dynamical evolution on the shape of the mass function. (© 2005 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)     

Planetary dynamics in stellar clusters

We investigate how the formation and evolution of extrasolar planetary systems can be affected by stellar encounters that occur in the crowded conditions of a stellar cluster. Using plausible estimates of cluster evolution, we show how planet formation may be suppressed in globular clusters while planets wider than ≳0.1 au that do form in such environments can be ejected from their stellar system. Less crowded systems such as open clusters have a much reduced effect on any planetary system. Planet formation is unaffected in open clusters and only the wider planetary systems will be disrupted during the cluster's lifetime. The potential for free-floating planets in these environments is also discussed.     

B and Be-stars in the young open stellar clusters NGC 659 and NGC 7419

The populations of B and Be-stars in the young open clusters NGC 7419 and NGC 659 are studied. Lowresolution spectral observations in the region of the Hα line are used to study 34 members of NGC 7419 and additional spectra in the range λ3700-6200 ? are obtained for 12 stars. During the period of our observations, four previously identified Be-stars manifested an absorption profile for the Hα line. Emission in the Hα line is observed in the spectra of 21 objects. The members of the cluster NGC 7419 are classified as to spectral type. The position of the Be-stars on a two-color IR diagram and a comparison with the position of the objects in other clusters with similar ages cast doubt on the existence of two starformation waves. Moderate resolution spectra were obtained for 22 stars in the cluster NGC 659 over wavelengths of λ4050-5200 ? and for 7 objects in the neighborhood of the Hα line. Emission is observed in both the Hα and Hβ lines for two of the five Be-stars that were studied, while faint emission appears only in the Hα line in one of the stars. The other members of the cluster show no signs of emission in these spectra. T_eff, log g, and Vsini are estimated for the observed stars. It is found that 5 of the objects are not members of the cluster.     

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.     

Mass segregation in young stellar clusters

We investigate the evolutionary effect of dynamical mass segregation in young stellar clusters. Dynamical mass segregation acts on a time-scale of order the relaxation time of a cluster. Although some degree of mass segregation occurs earlier, the position of massive stars in rich young clusters generally reflects the cluster's initial conditions. In particular, the positions of the massive stars in the Trapezium cluster in Orion cannot be due to dynamical mass segregation, but indicate that they formed in, or near, the centre of the cluster. Implications of this for cluster formation and for the formation of high-mass stars are discussed.     

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.     

The stellar content of binary star clusters in the LMC

The bright stellar content for fifteen binary star clusters and their adjoining fields in the Large Magellanic Cloud (LMC) were studied here. Film copies of plates taken with the 1.2 U.K. Schmidt telescope were used for deriving the spectral types of the stars in the studied regions. All classified stars are brighter thanV=17.5 mag and situated in large areas around each pair and in a neighbouring field. Seven of the pairs, the brightest and most populous are young clusters (located mainly at the north part of the parent galaxy). The derived distributions of spectral types of their stars give strong evidence that each pair consists of similar stellar content with ages 0.6–8×10⁷ yr.Eight more binary star clusters were studied as well, selected among the rest of the binaries in the LMC. It is found that their stars were faint for our limit of detection so the poor statistics did not allow a comparison among the two cluster members of each pair. However the bright limit of their stars implies ages >6×10⁸ yr. Considering that these objects were randomly selected it is unlikely that all are projected pairs. So it seems that binarity in star clusters is a phenomenon (favourable in the LMC) which did not happen only once in the life of this galaxy.     

Classification of stellar populations in globular clusters

Possessing multiple stellar populations has been accepted as a common feature of globular clusters(GCs). Different stellar populations manifest themselves with different chemical features,e.g. the well-known O-Na anti-correlation. Generally, the first(primordial) population has O and Na abundances consistent with those of field stars with similar metallicity; while the second(polluted) population is identified by their Na overabundance and O deficiency. The fraction of the populations is an important constraint on the GC formation scenario. Several methods have been proposed for the classification of GC populations. Here we examine a criterion derived based on the distribution of Galactic field stars, which relies on Na abundance as a function of [Fe/H], to distinguish first and second stellar populations in GCs. By comparing the first population fractions of 17 GCs estimated by the field star criterion with those in the literature derived by methods related to individual GCs, we find that the field star criterion tends to overestimate the first population fractions. The population separation methods,which are related to an individual GC sample, are recommended because the diversity of GCs can be taken into consideration. Currently, more caution should be exercised if one wants to regard field stars as a reference for the identification of a GC population. However, further study on the connection between field stars and GCs populations is still needed.     

The core collapse of globular clusters with stellar evolution

The orbit averaged Fokker-Planck equation is used to study the dynamical evolution of globular clusters. Stellar evolutions according to their masses are incorporated in the model. The initial density distribution is chosen by Plummer's model with the initial mass function index =0.65, 1.35, 2.35, and 3.35. The mass-loss rate is given by the model of Fusi-Pecci and Renzini. It is found that the stellar mass loss acts as an energy source, and thereby affects the dynamical evolution of globular clusters by slowing down the evolution rate and extending the core collapse time. Also, the dynamical length scale is extended.     

Triggered planet formation in young stellar clusters

Conventional planet formation models via coagulation of planetesimals require timescales in the range of several 10 or even 100 Myr in the outer regions of a protoplanetary disk. But according to observational data, the lifetime of a protoplanetary disk is limited to about 6 Myr. Therefore the existence of Uranus and Neptune poses a problem. Planet formation via gravitational instability may be a solution for this discrepancy. We present a parameter study of the possibility of gravitationally triggered disk instability. Using a restricted N‐body model which allows for a survey of an extended parameter space, we show that a passing dwarf star with a mass between 0.1 and 1 M_⊙ can probably induce gravitational instabilities in the pre‐planetary solar disk for prograde passages with minimum separations below 80‐170 AU. Inclined and retrograde encounters lead to similar results but require slightly closer passages. Such encounter distances are quite likely in young moderately massive star clusters. The induced gravitational instabilities may lead to enhanced planetesimal formation in the outer regions of the protoplanetary disk, and could therefore be relevant for the formation of Uranus and Neptune. (© 2005 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)     

The starburst-AGN connection: the role of stellar clusters in AGNs

Nuclear stellar clusters are a common phenomenon in spirals and in starburst galaxies, and they may be a natural consequence of the star formation processes in the central regions of galaxies. HST UV imaging of a few Seyfert 2 galaxies have resolved nuclear starbursts in Seyfert 2 revealing stellar clusters as the main components of the extended emission. However, we do not know whether stellar clusters are always associated with all types of nuclear activity. We present HST NUV and optical images to study the role that stellar clusters play in different types of AGNs. Also with these images, we study the circumnuclear dust morphology as a probe of the circumnuclear environment of AGNs.     

The formation and evolution of massive stellar clusters in IC4662

We present a multiwavelength study of the formation of massive stellar clusters, their emergence from cocoons of gas and dust, and their feedback on surrounding matter. Using data that span from radio to optical wavelengths, including Spitzer and Hubble Space Telescope ACS observations, we examine the population of young star clusters in the central starburst region of the irregular Wolf–Rayet galaxy IC4662. We model the radio-to-infrared (IR) spectral energy distributions of embedded clusters to determine the properties of their Hii regions and dust cocoons (sizes, masses, densities, temperatures), and use near-IR and optical data with mid-IR spectroscopy to constrain the properties of the embedded clusters themselves (mass, age, extinction, excitation, abundance). The two massive star-formation regions in IC4662 are excited by stellar populations with ages of ～4 Myr and masses of ～3×10⁵ M_⊙ (assuming a Kroupa initial mass function). They have high excitation and subsolar abundances, and they may actually be comprised of several massive clusters rather than the single monolithic massive compact objects known as ‘super star clusters’ (SSCs). Mid-IR spectra reveal that these clusters have very high extinction values, A _V ～20–25 mag, and that the dust in IC4662 is well mixed with the emitting gas, not in a foreground screen.     

The orbits of open clusters in the Galaxy

We present and analyse the kinematics and orbits for a sample of 488 open clusters (OCs) in the Galaxy. The velocity ellipsoid for our present sample is derived as  (σ _U , σ _V , σ _W ) = (28.7, 15.8, 11.0) km s⁻¹  which represents a young thin-disc population. We also confirm that the velocity dispersions increase with the age of a cluster subsample. The orbits of OCs are calculated with three Galactic gravitational potential models. The errors of orbital parameters are also calculated considering the intrinsic variation of the orbital parameters and the effects of observational uncertainties. The observational uncertainties dominate the errors of derived orbital parameters. The vertical motions of clusters calculated using different Galactic disc models are rather different. The observed radial metallicity gradient of clusters is derived with a slope of   b =−0.070 ± 0.011   dex kpc⁻¹. The radial metallicity gradient of clusters based on their apogalactic distances is also derived with a slope of   b =−0.082 ± 0.014   dex kpc⁻¹. The distribution of derived orbital eccentricities for OCs is very similar to that derived for the field population of dwarfs and giants in the thin disc.