The evolution of luminosity, colour and the mass-to-luminosity ratio of Galactic open clusters: comparison of discrete vs. continuous IMF models

(abridged) We found in previous studies that standard Simple Stellar Population (SSP) models are unable to describe or explain the colours of Galactic open clusters both in the visible and in the NIR spectral range. (...) We construct a numerical SSP-model, with an underlying Salpeter IMF, valid within an upper $m_u$ and lower $m_l$ stellar mass range, and with total masses $M_c=10^2...10^4\,m_\odot$ typical of open clusters. We assume that the mass loss from a cluster is provided by mass loss from evolved stars and by the dynamical evaporation of low-mass members due to two-body relaxation. The data for the latter process were scaled to the models from high-resolution N-body calculations. We also investigate how a change of the $m_l$-limit influences magnitudes and colours of clusters of a given mass and derive a necessary condition for a luminosity and colour flash. The discreteness of the IMF leads to bursts in magnitude and colour of model clusters at moments when red supergiants or giants appear and then die. The amplitude of the burst depends on the cluster mass and on the spectral range; it is strongly increased in the NIR compared to optical passbands. In the discrete case, variations of the parameter $m_l$ are able to substantially change the magnitude-age and $M/L$-age relations. For the colours, the lowering of $m_l$ considerably amplifies the discreteness effect. The influence of dynamical mass loss on colour and magnitude is weak, although it provides a change of the slopes of the considered relations, improving their agreement with observations. For the Galactic open clusters we determined luminosity and tidal mass independent of each other. The derived mass-to-luminosity ratio shows, on average, an increase with cluster age in the optical, but gradually declines with age in the NIR. The observed flash statistics can be used to constrain $m_l$ in open clusters.Comment: 15 pages, 13 figures, accepted for publication in Astronomy and Astrophysic

On the determination of age and mass functions of stars in young open star clusters from the analysis of their luminosity functions

Based on the CCD observations of remote young open clusters NGC 2383, NGC 2384, NGC 4103, NGC 4755, NGC 7510 and Hogg 15, we constructed their observed luminosity functions (LFs). The observed LFs are corrected for field star contamination determined with the help of galactic star count model. In the case of Hogg 15 and NGC 2383 we also considered the additional contamination from neighbouring clusters NGC 4609 and NGC 2384 respectively. These corrections provided the realistic pattern of cluster LF in the vicinity of the MS turn on point and at fainter magnitudes, revealed the so called H-feature arising due to transition of the Pre-MS phase to MS, which is dependent on the cluster age. The theoretical LFs were constructed representing a cluster population model with continuous star formation for a short time scale and a power law Initial Mass Function (IMF) and these were fitted to the observed LF. As a result we are able to determine for each cluster a set of parameters, describing cluster population (the age, duration of star formation, IMF slope and percentage of field star contamination). It was found that in spite of the non-monotonic behaviour of observed LFs, cluster IMFs can be described as the power law functions with slopes similar to Salpeter's value. The present MS turn on cluster ages are several times lower than those derived from the fitting of theoretical isochrones to the turn off region of the upper Main Sequences.Comment: 17 pages, 5 figures, To appear in MNRA

Global survey of star clusters in the Milky Way II. The catalogue of basic parameters

Although they are the main constituents of the Galactic disk population, for half of the open clusters in the Milky Way reported in the literature nothing is known except the raw position and an approximate size. The main goal of this study is to determine a full set of uniform spatial, structural, kinematic, and astrophysical parameters for as many known open clusters as possible. On the basis of stellar data from PPMXL and 2MASS, we used a dedicated data-processing pipeline to determine kinematic and photometric membership probabilities for stars in a cluster region. For an input list of 3784 targets from the literature, we confirm that 3006 are real objects, the vast majority of them are open clusters, but associations and globular clusters are also present. For each confirmed object we determined the exact position of the cluster centre, the apparent size, proper motion, distance, colour excess, and age. For about 1500 clusters, these basic astrophysical parameters have been determined for the first time. For the bulk of the clusters we also derived the tidal radius. We estimated additionally average radial velocities for more than 30% of the confirmed clusters. The present sample (called MWSC) reaches both the central parts of the Milky Way and its outer regions. It is almost complete up to 1.8 kpc from the Sun and also covers neighbouring spiral arms. However, for a small subset of the oldest open clusters ($\log t \gtrsim 9$) we found some evidence of incompleteness within about 1 kpc from the Sun.Comment: 8 pages, 5 figures, accepted for publication in Astronomy and Astrophysic

Global survey of star clusters in the Milky Way IV. 63 new open clusters detected by proper motions

AIMS: In their 1st extension to the Milky Way Star Clusters (MWSC) survey, Schmeja et al. applied photometric filters to the 2MASS to find new cluster candidates that were subsequently confirmed or rejected by the MWSC pipeline. To further extend the MWSC census, we aimed at discovering new clusters by conducting an almost global search in proper motion catalogues as a starting point. METHODS: We first selected high-quality samples from the PPMXL and UCAC4 for comparison and verification of the proper motions. For 441 circular proper motion bins (radius 15 mas/yr) within $\pm$50 mas/yr, the sky outside a thin Galactic plane zone ($|b|$$<$5$^{\circ}$) was binned in small areas ('sky pixels') of 0.25$\times$0.25 deg$^2$. Sky pixels with enhanced numbers of stars with a certain common proper motion in both catalogues were considered as cluster candidates. After visual inspection of the sky images, we built an automated procedure that combined these representations of the sky for neighbouring proper motion subsamples after a background correction. RESULTS: About half of our 692 candidates overlapped with known clusters (46 globular and 68 open clusters in the Galaxy, about 150 known clusters of galaxies) or the Magellanic Clouds. About 10% of our candidates turned out to be 63 new open clusters confirmed by the MWSC pipeline. They occupy predominantly the two inner Galactic quadrants and have apparent sizes and numbers of high-probable members slightly larger than those of the typically small MWSC clusters, whereas their other parameters (ages, distances, tidal radii) fall in the typical ranges. As our search aimed at finding compact clusters, we did not find new very nearby (extended) clusters. (abridged)Comment: 14 pages, 14 figures, accepted for publication in Astronomy and Astrophysic

Why Simple Stellar Population models do not reproduce the colours of Galactic open clusters

(...) We search for an explanation of the disagreement between the observed integrated colours of 650 local Galactic clusters and the theoretical colours of present-day SSP models. We check the hypothesis that the systematic offsets between observed and theoretical colours, which are $(B$$-$$V)\approx 0.3$ and $(J$$-$$K_s)\approx 0.8$, are caused by neglecting the discrete nature of the underlying mass function. Using Monte Carlo simulations, we construct artificial clusters of coeval stars taken from a mass distribution defined by an Salpeter initial mass function (IMF) and compare them with corresponding "continuous-IMF" SSP models. If the discreteness of the IMF is taken into account, the model fits the observations perfectly and is able to explain naturally a number of red "outliers" observed in the empirical colour-age relation. We find that the \textit{systematic} offset between the continuous- and discrete-IMF colours reaches its maximum of about 0.5 in $(B$$-$$V)$ for a cluster mass $M_c=10^2 m_\odot$ at ages $\log t\approx 7$, and diminishes substantially but not completely to about one hundredth of a magnitude at $\log t >7.9$ at cluster masses $M_c> 10^5 m_\odot$. At younger ages, it is still present even in massive clusters, and for $M_c \leqslant 10^4 m_\odot$ it is larger than 0.1 mag in $(B$$-$$V)$. Only for very massive clusters ($M_c>10^6 m_\odot$) with ages $\log t< 7.5$ is the offset small (of the order of 0.04 mag) and smaller than the typical observational error of colours of extragalactic clusters.Comment: 4 pages, 3 figures, accepted for publication in Astronomy and Astrophysics Letters, revised version after language editing and with an additional reference to Cervino and Luridiana (2004

PPM-Extended (PPMX) - a catalogue of positions and proper motions

Aims: We build a catalogue PPM-Extended (PPMX) on the ICRS system which is complete down to a well-defined limiting magnitude and contains the best presently available proper motions to be suited for kinematical studies in the Galaxy. Methods: We perform a rigorous weighted least-squares adjustment of individual observations, spread over more than a century, to determine mean positions and proper motions. The stellar content of PPMX is taken from GSC 1.2 supplemented by catalogues like ARIHIP, PPM and Tycho-2 at the bright end. All observations have been weighted according to their individual accuracy. The catalogue has been screened towards rejecting false entries in the various source catalogues. Results: PPM-Extended (PPMX) is a catalogue of 18,088,920 stars containing astrometric and photometric information. Its limiting magnitude is about 15.2 in the GSC photometric system. PPMX consists of three parts: a) a survey complete down to R_U = 12.8 in the magnitude system of UCAC2; b) additional stars of high-precision proper motions, and c) all other stars from GSC 1.2 identified in 2MASS. The typical accuracy of the proper motions is 2mas/y for 66 percent of the survey stars (a) and the high-precision stars (b), and about 10 mas/y for all other stars. PPMX contains photometric information from ASCC-2.5 and 2MASS.Comment: 9 pages, 8 figures, accepted for publication in Astronomy and Astrophysic

Shape parameters of Galactic open clusters

(abridged) In this paper we derive observed and modelled shape parameters (apparent ellipticity and orientation of the ellipse) of 650 Galactic open clusters identified in the ASCC-2.5 catalogue. We provide the observed shape parameters of Galactic open clusters, computed with the help of a multi-component analysis. For the vast majority of clusters these parameters are determined for the first time. High resolution ("star by star") N-body simulations are carried out with the specially developed $\phi$GRAPE code providing models of clusters of different initial masses, Galactocentric distances and rotation velocities. The comparison of models and observations of about 150 clusters reveals ellipticities of observed clusters which are too low (0.2 vs. 0.3), and offers the basis to find the main reason for this discrepancy. The models predict that after $\approx 50$ Myr clusters reach an oblate shape with an axes ratio of $1.65:1.35:1$, and with the major axis tilted by an angle of $q_{XY} \approx 30^\circ$ with respect to the Galactocentric radius due to differential rotation of the Galaxy. Unbiased estimates of cluster shape parameters require reliable membership determination in large cluster areas up to 2-3 tidal radii where the density of cluster stars is considerably lower than the background. Although dynamically bound stars outside the tidal radius contribute insignificantly to the cluster mass, their distribution is essential for a correct determination of cluster shape parameters. In contrast, a restricted mass range of cluster stars does not play such a dramatic role, though deep surveys allow to identify more cluster members and, therefore, to increase the accuracy of the observed shape parameters.Comment: 13 pages, 12 figures, accepted for publication in Astronomy and Astrophysic

Risk-oriented internal control: The essence, management methods at small enterprises

The research topic relevance is inspired by necessity to develop theoretical and methodical provisions on the internal control system, risk-based management at small enterprises and to prove application feasibility, using economic-mathematical methods its implementation. The purpose of this research is to develop theoretical and methodical approaches to internal control system formation in small businesses, generating reliable and relevant information on the commercial organization activities, enabling risks identification. The leading approach to study this problem is situational and systematic in the frame of theory and methodology internal control at small businesses in the risk-based management system, allowing to analyze the impact of various risks on small enterprises activity and to systematize obtained results. According to the study results, there were proved the implementing internal control feasibility at small businesses, presenting the author's systematization and classification of internal and external risks in small companies, identifying organizational and methodological approaches to risk-based internal control development; implemented the adaptation of existing economic-mathematical methods within risk-based internal control at small businesses. The article can be useful for practical and scientific workers in the field of company’s internal control, teachers, postgraduates, undergraduates and students, studying Economics and Management at higher educational institutions. © 2016 Piskunov et al

A Possible Bifurcation in Atmospheres of Strongly Irradiated Stars and Planets

We show that under certain circumstances the differences between the absorption mean and Planck mean opacities can lead to multiple solutions for an LTE atmospheric structure. Since the absorption and Planck mean opacities are not expected to differ significantly in the usual case of radiative equilibrium, non-irradiated atmospheres, the most interesting situations where the effect may play a role are strongly irradiated stars and planets, and also possibly structures where there is a significant deposition of mechanical energy, such as stellar chromospheres and accretion disks. We have presented an illustrative example of a strongly irradiated giant planet where the bifurcation effect is predicted to occur for a certain range of distances from the star.Comment: 22 pages, 6 figures, submitted to Ap