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.     

Stellar contents and star formation in the young star cluster Be 59

We present   UBV  I _c   CCD photometry of the young open cluster Be 59 with the aim to study the star formation scenario in the cluster. The radial extent of the cluster is found to be ∼10 arcmin (2.9 pc). The interstellar extinction in the cluster region varies between   E ( B − V ) ≃ 1.4  to 1.8 mag. The ratio of total-to-selective extinction in the cluster region is estimated as  3.7 ± 0.3  . The distance of the cluster is found to be  1.00 ± 0.05 kpc  . Using near-infrared (NIR) colours and slitless spectroscopy, we have identified young stellar objects (YSOs) in the open cluster Be 59 region. The ages of these YSOs range between <1 and ∼2 Myr, whereas the mean age of the massive stars in the cluster region is found to be ∼2 Myr. There is evidence for second-generation star formation outside the boundary of the cluster, which may be triggered by massive stars in the cluster. The slope of the initial mass function, Γ, in the mass range  2.5 < M /M_⊙≤ 28  is found to be  −1.01 ± 0.11  which is shallower than the Salpeter value (−1.35), whereas in the mass range  1.5 < M /M_⊙≤ 2.5  the slope is almost flat. The slope of the K -band luminosity function is estimated as  0.27 ± 0.02  , which is smaller than the average value (∼0.4) reported for young embedded clusters. Approximately 32 per cent of Hα emission stars of Be 59 exhibit NIR excess indicating that inner discs of the T Tauri star (TTS) population have not dissipated. The Midcourse Space Experiment (MSX) and IRAS-HIRES images around the cluster region are also used to study the emission from unidentified infrared bands and to estimate the spatial distribution of optical depth of warm and cold interstellar dust.     

L dwarfs in the Hyades

We present the results of a proper motion survey of the Hyades to search for brown dwarfs, based on UKIRT Deep Sky Survey (UKIDSS) and Two-Micron All Sky Survey (2MASS) data. This survey covers  ∼275 deg²  to a depth of   K ∼ 15  mag, equivalent to a mass of  ∼0.05 M_⊙  assuming a cluster age of 625 Myr. The discovery of 12 L dwarf Hyades members is reported. These members are also brown dwarfs, with masses between  0.05 < M < 0.075 M_⊙  . A high proportion of these L dwarfs appear to be photometric binaries.     

Galactic clusters with associated Cepheid variables – VII. Berkeley 58 and CG Cassiopeiae

Photoelectric, photographic and CCD UBV photometry, spectroscopic observations and star counts are presented for the open cluster Berkeley 58 to examine a possible association with the 4.37 d Cepheid CG Cas. The cluster is difficult to separate from the early-type stars belonging to the Perseus spiral arm, in which it is located, but has reasonably well-defined parameters: an evolutionary age of ∼10⁸ yr, a mean reddening of   E ( B − V ) (B0) = 0.70 ± 0.03  s.e. and a distance of  3.03 ± 0.17 kpc ( V ₀− M _V = 12.40 ± 0.12  s.d.). CG Cas is a likely cluster coronal member on the basis of radial velocity, and its period increase of  +0.170 ± 0.014 s yr⁻¹  and large light amplitude describe a Cepheid in the third crossing of the instability strip lying slightly blueward of strip centre. Its inferred reddening and luminosity are   E ( B − V ) = 0.64 ± 0.02  s.e. and  〈 M _V 〉=−3.06 ± 0.12  . A possible K supergiant may also be a cluster member.     

The initial–final mass relationship of white dwarfs revisited: effect on the luminosity function and mass distribution

The initial–final mass relationship connects the mass of a white dwarf with the mass of its progenitor in the main sequence. Although this function is of fundamental importance to several fields in modern astrophysics, it is not well constrained either from the theoretical or from the observational points of view. In this work, we revise the present semi-empirical initial–final mass relationship by re-evaluating the available data. The distribution obtained from grouping all our results presents a considerable dispersion, which is larger than the uncertainties. We have carried out a weighted least-squares linear fit of these data and a careful analysis to give some clues on the dependence of this relationship on some parameters such as metallicity or rotation. The semi-empirical initial–final mass relationship arising from our study covers the range of initial masses from 1.0 to  6.5 M_⊙  , including in this way the low-mass domain, poorly studied until recently. Finally, we have also performed a test of the initial–final mass relationship by studying its effect on the luminosity function and on the mass distribution of white dwarfs. This was done by using different initial–final mass relationships from the literature, including the expression derived in this work, and comparing the results obtained with the observational data from the Palomar Green Survey and the Sloan Digital Sky Survey. We find that the semi-empirical initial–final mass relationship derived here gives results in good agreement with the observational data, especially in the case of the white dwarf mass distribution.     

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.     

Do binaries in clusters form in the same way as in the field?

We examine the dynamical destruction of binary systems in star clusters of different densities. We find that at high densities  (10⁴– 10⁵ M_⊙ pc⁻³)  almost all binaries with separations  >10³  au are destroyed after a few crossing times. At low densities [     ], many binaries with separations  >10³  au are destroyed, and no binaries with separations  >10⁴  au survive after a few crossing times. Therefore, the binary separations in clusters can be used as a tracer of the dynamical age and past density of a cluster.
We argue that the central region of the Orion nebula cluster was ∼100 times denser in the past with a half-mass radius of only 0.1–0.2 pc as (i) it is expanding, (ii) it has very few binaries with separations  >10³  au and (iii) it is well mixed and therefore dynamically old.
We also examine the origin of the field binary population. Binaries with separations  <10²  au are not significantly modified in any cluster, therefore at these separations the field reflects the sum of all star formation. Binaries with separations in the range  10²– 10⁴  au are progressively more and more heavily affected by dynamical disruption in increasingly dense clusters. If most star formation is clustered, these binaries must be overproduced relative to the field. Finally, no binary with a separation  >10⁴  au can survive in any cluster and so must be produced by isolated star formation, but only if all isolated star formation produces extremely wide binaries.     

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.     

How well do starlab and nbody4 compare? I. Simple models

N -body simulations are widely used to simulate the dynamical evolution of a variety of systems, among them star clusters. Much of our understanding of their evolution rests on the results of such direct N -body simulations. They provide insight in the structural evolution of star clusters, as well as into the occurrence of stellar exotica. Although the major pure N -body codes starlab/kira and nbody4 are widely used for a range of applications, there is no thorough comparison study yet.
Here, we thoroughly compare basic quantities as derived from simulations performed either with starlab/kira or nbody4 .
We construct a large number of star cluster models for various stellar mass function settings (but without stellar/binary evolution, primordial binaries, external tidal fields, etc.), evolve them in parallel with starlab/kira and nbody4 , analyse them in a consistent way and compare the averaged results quantitatively. For this quantitative comparison, we develop a bootstrap algorithm for functional dependencies.
We find an overall excellent agreement between the codes, both for the clusters' structural and energy parameters as well as for the properties of the dynamically created binaries. However, we identify small differences, like in the energy conservation before core collapse and the energies of escaping stars, which deserve further studies.
Our results reassure the comparability and the possibility to combine results from these two major N -body codes, at least for the purely dynamical models (i.e. without stellar/binary evolution) we performed. Further detailed comparison studies for more complex systems, e.g. including stellar/binary evolution, are required.