The binary second sequence in cluster colour–magnitude diagrams

We show how the second sequence seen lying above the main sequence in cluster colour–magnitude diagrams results from binaries with a large range of mass ratios and not just from those with equal masses. We conclude that the presence of a densely populated second sequence, with only sparse filling in between it and the single star main sequence, does not necessarily imply that binary mass ratios are close to unity.     

Single star scattering on an open cluster

We examine the scattering of single stars from an open star cluster. The probability of the capture of a star by a star cluster is dependent on the velocity and mass of the star, and the stars that are not captured experience a velocity change. For low-velocity stars there is an exponential decrease of the capture probability with the initial velocity, and the velocity change decreases almost linearly. For high-velocity stars there is a v ⁻⁶ dependence for the capture probability, and a v ⁻¹ dependence for the velocity change. Analytical estimations, Monte Carlo and full N -body simulations are all in good agreement.     

NGC 2587: a sparse open cluster projected on to a populous star field

We present CCD photometry in the Johnson U , B and V and Kron–Cousins I passbands for the open cluster NGC 2587. The sample consists of 4406 stars reaching down to   V ∼ 21.0  . We developed a new method to clean statistically the colour–magnitude diagrams. NGC 2587 appears to be a sparse, relatively bright open cluster, with a few tens of members projected on to a populous star field. The comparatively bright F7/8 II type star HD 70927, located close to the cluster centre, seems not to be a member. Our analysis suggests that NGC 2587 is slightly younger than the Hyades and probably of solar metallicity. A cluster radius of roughly 8 arcmin was estimated from the radial stellar density profile. From 18 probable cluster members with measured proper motions, we derive the following mean values for NGC 2587:  μ_α=−4.3 ± 3.6 mas yr⁻¹  and  μ_δ=−2.5 ± 3.4 mas yr⁻¹  . Adopting the theoretical metal content   Z = 0.02  , which provides the best global fit, we derive a cluster age of  500⁺⁶⁰₋₅₀  . Simultaneously, colour excesses   E ( B − V ) = 0.10  and   E ( V − I ) = 0.15  and an apparent distance modulus of   V − M_V = 12.50  are obtained. The interstellar extinction in the cluster direction is found to follow the normal law. NGC 2587 is located at a distance of (2.70 ± 0.70) kpc from the Sun and ∼9.8 kpc from the Galactic centre.     

On the Galactic disc age–metallicity relation

A comparison is made between the age–metallicity relations obtained from four different types of studies: F and G stars in the solar neighbourhood, analysis of open clusters, galactic structure studies with the stellar population synthesis technique and chemical evolution models. Metallicities of open clusters are corrected for the effects of the radial gradient, which we find to be −0.09 dex kpc⁻¹ and most likely constant in time. We do not correct for the vertical gradient, because its existence and value are not firmly established.
Stars and clusters trace a similar age–metallicity relation, showing an excess of rather metal-rich objects in the age range 5–9 Gyr. Galactic structure studies tend to give a more metal-poor relation than chemical evolution models. Neither relation explains the presence of old, relatively metal-rich stars and clusters. This might be caused by uncertainties in the ages of the local stars, or pre-enrichment of the disc with material from the bulge, possibly as a result of a merger event in the early phases of the formation of our Galaxy.     

Collaborative research of open star clusters

Preliminary results on observations of open clusters are presented. The project has been initiated in the framework of the Uzbek-Taiwan and Taiwan-Baltic collaboration, mainly to upgrade and make use of facilities at Maidanak Observatory. We present detailed, multiwavelength studies of the young cluster NGC 6823 and the associated complex nebulosity, to diagnose the young stellar population and star formation history in the region. In addition, 7 compact open clusters have been monitored for stellar variability. We show how observations like these could feasibly be used to look for exoplanet transit events. We also expect to join the Whole-Earth Telescope effort in future campaigns for asteroseismology.     

The early evolution of the star cluster mass function

Several recent studies have shown that the star cluster initial mass function (CIMF) can be well approximated by a power law, with indications for a steepening or truncation at high masses. This contribution considers the evolution of such a mass function due to cluster disruption, with emphasis on the part of the mass function that is observable in the first ∼1 Gyr. A Schechter type function is used for the CIMF, with a power-law index of −2 at low masses and an exponential truncation at M _*. Cluster disruption due to the tidal field of the host galaxy and encounters with giant molecular clouds flattens the low-mass end of the mass function, but there is always a part of the 'evolved Schechter function' that can be approximated by a power law with index −2. The mass range for which this holds depends on age, τ, and shifts to higher masses roughly as  τ^0.6  . Mean cluster masses derived from luminosity-limited samples increase with age very similarly due to the evolutionary fading of clusters. Empirical mass functions are, therefore, approximately power laws with index −2, or slightly steeper, at all ages. The results are illustrated by an application to the star cluster population of the interacting galaxy M51, which can be well described by a model with   M _*= (1.9 ± 0.5) × 10⁵ M_⊙  and a short (mass-dependent) disruption time destroying M _* clusters in roughly a Gyr.     

Measurement of the epicycle frequency in the Galactic disc and initial velocities of open clusters

A new method to measure the epicycle frequency κ in the Galactic disc is presented. We make use of the large data base on open clusters completed by our group to derive the observed velocity vector (amplitude and direction) of the clusters in the Galactic plane. In the epicycle approximation, this velocity is equal to the circular velocity given by the rotation curve, plus a residual or perturbation velocity, of which the direction rotates as a function of time with the frequency κ. Due to the non-random direction of the perturbation velocity at the birth time of the clusters, a plot of the present-day direction angle of this velocity as a function of the age of the clusters reveals systematic trends from which the epicycle frequency can be obtained. Our analysis considers that the Galactic potential is mainly axis-symmetric, or in other words, that the effect of the spiral arms on the Galactic orbits is small; in this sense, our results do not depend on any specific model of the spiral structure. The values of κ that we obtain provide constraints on the rotation velocity of the disc; in particular, V ₀ is found to be  230 ± 15 km s⁻¹  even if the short scale  ( R ₀= 7.5 kpc)  of the Galaxy is adopted. The measured κ at the solar radius is  43 ± 5 km s⁻¹ kpc ⁻¹  . The distribution of initial velocities of open clusters is discussed.     

Quantitative analysis of clumps in the tidal tails of star clusters

Tidal tails of star clusters are not homogeneous but show well-defined clumps in observations as well as in numerical simulations. Recently, an epicyclic theory for the formation of these clumps was presented. A quantitative analysis was still missing. We present a quantitative derivation of the angular momentum and energy distribution of escaping stars from a star cluster in the tidal field of the Milky Way and derive the connection to the position and width of the clumps. For the numerical realization we use star-by-star N -body simulations. We find a very good agreement of theory and models. We show that the radial offset of the tidal arms scales with the tidal radius, which is a function of cluster mass and the rotation curve at the cluster orbit. The mean radial offset is 2.77 times the tidal radius in the outer disc. Near the Galactic Centre the circumstances are more complicated, but to lowest order the theory still applies. We have also measured the Jacobi energy distribution of bound stars and showed that there is a large fraction of stars (about 35 per cent) above the critical Jacobi energy at all times, which can potentially leave the cluster. This is a hint that the mass loss is dominated by a self-regulating process of increasing Jacobi energy due to the weakening of the potential well of the star cluster, which is induced by the mass loss itself.     

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.     

Analysing the structure of elongated star clusters

We have previously reported a measure     which both quantifies and distinguishes between a (relatively smooth) large-scale radial density gradient and multiscale (fractal) subclustering. Here, we extend the applicability of     to clusters which deviate significantly from an overall circular shape.
    varies systematically as clusters assume a more elongated shape, and it is therefore possible to correct for the effect, if the elongation of the cluster is also quantified.     therefore remains a useful and robust analytical technique for classifying and quantifying the internal structure of star clusters, even when their overall shape is far from circular.
The corrections required are small for individual clusters which are not extremely elongated (not more than three times longer than they are wide) of the same order as the uncertainty in the value of     for a particular cluster type. We therefore recommend that no correction be applied to the calculation of     for individual clusters, unless they are more than three times longer than their width, but that correction for elongation be applied when     is used for statistical analyses of large numbers of observed or simulated clusters.