arXiv subjects

N. V. Kharchenko

Publications and source records attributed to N. V. Kharchenko.

At least 19 recordsLinked to original sources

arXiv2022

The evolutionary state of the chemically peculiar members of the open cluster NGC2516

We aim at establishing safe membership and evolutionary status of 11 chemically peculiar (CP) stars that are residing in the domain of the open cluster NGC2516 and are frequently referred to as cluster members. We queried the Gaia EDR3 catalogue in an area with a radius of 1deg and selected 37508 stars brighter than G=19mag. The cluster membership was determined in parallax-proper motion-space and 719 probable and 764 possible members were found. The obtained average astrometric and photometric parameters of the cluster are in good agreement with the most recent literature data. The evolutionary status of the target stars was determined with respect to Padova isochrones. After minor adjustments including the metallicity, the reddening, and the transformation scale variation, a perfect fit of the model to the observations over the whole observed magnitude range was achieved. Only 5 of the 11 considered CP stars could be classified as highly probable cluster members. Among the Ap/Bp stars with previously detected magnetic fields HD65987 and HD65712 have a high membership probability and the magnetic star CPD-60 944B is a possible cluster member. Further we discuss the blue straggler nature of HD66194 and the magnetic star HD65987. To our knowledge, HD65987 is currently the only known blue straggler, with a field of the order of a few hundred Gauss. The most striking result of our study is that the strongly magnetic A0p star HD66318 with previously reported very low fractional age does not belong to the NGC2516 cluster at a high level of confidence.

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arXiv2018

Global survey of star clusters in the Milky Way VI. Age distribution and cluster formation history

The all-sky Milky Way Star Clusters (MWSC) survey provides uniform and precise ages and other parameters for a variety of clusters in the Solar Neighbourhood. We construct the cluster age distribution, investigate its spatial variations, and discuss constraints on cluster formation scenarios of the Galactic disk during the last 5 Gyrs. Due to the spatial extent of the MWSC, we consider spatial variations of the age distribution along galactocentric radius $R_G$, and along $Z$-axis. For the analysis of the age distribution we use 2242 clusters, which all lie within roughly 2.5 kpc of the Sun. To connect the observed age distribution to the cluster formation history we build an analytical model based on simple assumptions on the cluster initial mass function and on the cluster mass-lifetime relation, fit it to the observations, and determine the parameters of the cluster formation law. Comparison with the literature shows that earlier results strongly underestimated the number of evolved clusters with ages $t\gtrsim 100$ Myr. Recent studies based on all-sky catalogues agree better with our data, but still lack the oldest clusters with ages $t\gtrsim 1$ Gyr. We do not observe a strong variation in the age distribution along $R_G$, though we find an enhanced fraction of older clusters ($t>1$ Gyr) in the inner disk. In contrast, the distribution strongly varies along $Z$. The high altitude distribution practically does not contain clusters with $t<1$ Gyr. With simple assumptions on the cluster formation history, cluster initial mass function and cluster lifetime we can reproduce the observations. Cluster formation rate and cluster lifetime are strongly degenerate, which does not allow us to disentangle different formation scenarios. In all cases the cluster formation rate is strongly declining with time, and the cluster initial mass function is very shallow at the high mass end. (abridged)

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arXiv2016

A spectral and photometric study of 102 star forming regions in seven spiral galaxies

We present a study of complexes of young massive star clusters (YMCs), embedded in extragalactic giant HII regions, based on the coupling of spectroscopic with photometric and spectrophotometric observations of about 100 star forming regions in seven spiral galaxies (NGC 628, NGC 783, NGC 2336, NGC 6217, NGC 6946, NGC 7331, and NGC 7678). The complete observational database has been observed and accumulated within the framework of our comprehensive study of extragalactic star forming regions. The current paper presents the last part of either unpublished or refreshed photometric and spectrophotometric observations of the galaxies NGC 6217, NGC 6946, NGC 7331, and NGC 7678. We derive extinctions, chemical abundances, continuum and line emissions of ionised gas, ages and masses for cluster complexes. We find the young massive cluster complexes to have ages no greater than 10 Myr and masses between 10^4Msol and 10^7Msol, and the extinctions A(V) vary between ~ 0 and 3 mag, while the impact of the nebular emission on integrated broadband photometry mainly is not greater than 40% of the total flux and is comparable with accuracies of dereddened photometric quantities.We also find evidence of differential extinction of stellar and gas emissions in some clusters, which hinders the photometric determination of ages and masses in these cases. Finally, we show that young massive cluster complexes in the studied galaxies and open clusters in the Milky Way form a continuous sequence of luminosities/masses and colour/ages.

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arXiv2016

Study of young stellar groupings in HII regions based on the spectral and photometric data

We studied 102 star forming regions in seven spiral galaxies (NGC 628, NGC 783, NGC 2336, NGC 6217, NGC 6946, NGC 7331, and NGC 7678) on the basis of complex spectroscopic, photometric (UBVRI) and spectrophotometric (H alpha line) observations. Using data on the chemical composition and absorption in HII regions, obtained from spectroscopic observations, and using evolutionary models, we estimated physical parameters (ages and masses) of young stellar groupings embedded in HII regions. We found that the gas extinction, A(gas), which determined from the Balmer decrement, does not correspond in some cases to the absorption A(stars) in the young stellar associations (complexes). This is due to the spatial offset relative HII cloud the stellar group related to him. It has been found that the condition A(gas) = A(stars) does not satisfied for the star forming regions, in which: 1) the contribution to the total emission of gas in the B and/or V bands is higher than 40%, and 2) EW(H alpha) > 1500A. Extinction A(V) in studied star forming regions corrected for the Galactic absorption A(V)Gal ranges from 0 to 3 mag with a mean value A(V)-A(V)Gal = 1.18+-0.84 mag. We estimated masses and ages for 63 star forming regions. The regions have ages from 1 to 10 Myr, the most part of them are younger than 6 Myr. The derived masses of young stellar groupings range from 10^4Msun in the nearby galaxies NGC 628 and NGC 6946 to 10^7Msun in the most distant NGC 7678. More than 80% of groupings have masses between 10^5Msun and 10^6Msun. The lowest mass estimate of 1x10^4Msun for the objects in NGC 628 and NGC 6946 belongs to the mass interval of the youngest Galactic open clusters.

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arXiv2015

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)

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arXiv2014

Global survey of star clusters in the Milky Way III. 139 new open clusters at high Galactic latitudes

An earlier analysis of the Milky Way Star Cluster (MWSC) catalogue revealed an apparent lack of old (> 1 Gyr) open clusters in the solar neighbourhood (< 1 kpc). To fill this gap we undertook a search for hitherto unknown star clusters, assuming that the missing old clusters reside at high Galactic latitudes |b|> 20°. We were looking for stellar density enhancements using a star count algorithm on the 2MASS point source catalogue. To increase the contrast between potential clusters and the field, we applied filters in colour-magnitude space according to typical colour-magnitude diagrams of nearby old open clusters. The subsequent comparison with lists of known objects allowed us to select thus far unknown cluster candidates. For verification they were processed with the standard pipeline used within the MWSC survey for computing cluster membership probabilities and for determining structural, kinematic, and astrophysical parameters. In total we discovered 782 density enhancements, 522 of which were classified as real objects. Among them 139 are new open clusters with ages 8.3 < log (t [yr]) < 9.7, distances d < 3 kpc, and distances from the Galactic plane 0.3 < Z < 1 kpc. This new sample has increased the total number of known high latitude open clusters by about 150%. Nevertheless, we still observe a lack of older nearby clusters up to 1 kpc from the Sun. This volume is expected to still contain about 60 unknown clusters that probably escaped our detection algorithm, which fails to detect sparse overdensities with large angular size.

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arXiv2014

B fields in OB stars (BOB): The discovery of a magnetic field in a multiple system in the Trifid Nebula, one of the youngest star forming regions

Recent magnetic field surveys in O- and B-type stars revealed that about 10% of the core-hydrogen-burning massive stars host large-scale magnetic fields. The physical origin of these fields is highly debated. To identify and model the physical processes responsible for the generation of magnetic fields in massive stars, it is important to establish whether magnetic massive stars are found in very young star-forming regions or whether they are formed in close interacting binary systems. In the framework of our ESO Large Program, we carried out low-resolution spectropolarimetric observations with FORS2 in 2013 April of the three most massive central stars in the Trifid nebula, HD164492A, HD164492C, and HD164492D. These observations indicated a strong longitudinal magnetic field of about 500-600G in the poorly studied component HD164492C. To confirm this detection, we used HARPS in spectropolarimetric mode on two consecutive nights in 2013 June. Our HARPS observations confirmed the longitudinal magnetic field in HD164492C. Furthermore, the HARPS observations revealed that HD164492C cannot be considered as a single star as it possesses one or two companions. The spectral appearance indicates that the primary is most likely of spectral type B1-B1.5V. Since in both observing nights most spectral lines appear blended, it is currently unclear which components are magnetic. Long-term monitoring using high-resolution spectropolarimetry is necessary to separate the contribution of each component to the magnetic signal. Given the location of the system HD164492C in one of the youngest star formation regions, this system can be considered as a Rosetta Stone for our understanding of the origin of magnetic fields in massive stars.

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arXiv2013

A RAVE Investigation on Galactic open Clusters I. Radial velocities and metallicities

Context. Galactic open clusters (OCs) mainly belong to the young stellar population in the Milky Way disk, but are there groups and complexes of OCs that possibly define an additional level in hierarchical star formation? Current compilations are too incomplete to address this question, especially regarding radial velocities (RVs) and metallicities ($[M/H]$). Aims. Here we provide and discuss newly obtained RV and $[M/H]$ data, which will enable us to reinvestigate potential groupings of open clusters and associations. Methods.We extracted additional RVs and $[M/H]$ from the RAdial Velocity Experiment (RAVE) via a cross-match with the Catalogue of Stars in Open Cluster Areas (CSOCA). For the identified OCs in RAVE we derived RV and $[M/H]$ from a cleaned working sample and compared the results with previous findings. Results. Although our RAVE sample does not show the same accuracy as the entire survey, we were able to derive reliable RV for 110 Galactic open clusters. For 37 OCs we publish RV for the first time. Moreover, we determined $[M/H]$ for 81 open clusters, extending the number of OCs with $[M/H]$ by 69.

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arXiv2013

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.

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arXiv2013

Exploring the origin of magnetic fields in massive stars: II. New magnetic field measurements in cluster and field stars

Theories on the origin of magnetic fields in massive stars remain poorly developed, because the properties of their magnetic field as function of stellar parameters could not yet be investigated. To investigate whether magnetic fields in massive stars are ubiquitous or appear only in stars with a specific spectral classification, certain ages, or in a special environment, we acquired 67 new spectropolarimetric observations for 30 massive stars. Among the observed sample, roughly one third of the stars are probable members of clusters at different ages, whereas the remaining stars are field stars not known to belong to any cluster or association. Spectropolarimetric observations were obtained during four different nights using the low-resolution spectropolarimetric mode of FORS2 (FOcal Reducer low dispersion Spectrograph) mounted on the 8-m Antu telescope of the VLT. Furthermore, we present a number of follow-up observations carried out with the high-resolution spectropolarimeters SOFIN mounted at the Nordic Optical Telescope (NOT) and HARPS mounted at the ESO 3.6m between 2008 and 2011. To assess the membership in open clusters and associations, we used astrometric catalogues with the highest quality kinematic and photometric data currently available. The presence of a magnetic field is confirmed in nine stars previously observed with FORS1/2: HD36879, HD47839, CPD-282561, CPD-472963, HD93843, HD148937, HD149757, HD328856, and HD164794. New magnetic field detections at a significance level of at least 3sigma were achieved in five stars: HD92206c, HD93521, HD93632, CPD-468221, and HD157857. Among the stars with a detected magnetic field, five stars belong to open clusters with high membership probability. According to previous kinematic studies, five magnetic O-type stars in our sample are candidate runaway stars.

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arXiv2012

Global survey of star clusters in the Milky Way I. The pipeline and fundamental parameters in the second quadrant

Aims: On the basis of the PPMXL star catalogue we performed a survey of star clusters in the second quadrant of the Milky Way. Methods: From the PPMXL catalogue of positions and proper motions we took the subset of stars with near-infrared photometry from 2MASS and added the remaining 2MASS stars without proper motions (called 2MAst, i.e. 2MASS with astrometry). We developed a data-processing pipeline including interactive human control of a standardised set of multi-dimensional diagrams to determine kinematic and photometric membership probabilities for stars in a cluster region. The pipeline simultaneously produced the astrophysical parameters of a cluster. From literature we compiled a target list of presently known open and globular clusters, cluster candidates, associations, and moving groups. From established member stars we derived spatial parameters (coordinates of centres and radii of the main morphological parts of clusters) and cluster kinematics (average proper motions and sometimes radial velocities). For distance, reddening, and age determination we used specific sets of theoretical isochrones. Tidal parameters were obtained by a fit of three-parameter King profiles to the observed density distributions of members. Results: We investigated all 871 objects in the 2nd Galactic quadrant, of which we successfully treated 642 open clusters, 2 globular clusters, and 8 stellar associations. The remaining 219 objects (24%) were recognised by us to be nonexistent clusters, duplicate entries, or clusters too faint for 2MAst. We found that our sample is complete in the 2nd quadrant up to a distance of 2 kpc, where the average surface density is 94 clusters per kpc$^{2}$. Compared with literature values we found good agreement in spatial and kinematic data, as well as for optical distances and reddening. Small, but systematic offsets were detected in the age determination.

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arXiv2011

Magnetic field studies of massive main sequence stars

We report on the status of our spectropolarimetric observations of massive stars. During the last years, we have discovered magnetic fields in many objects of the upper main sequence, including Be stars, beta Cephei and Slowly Pulsating B stars, and a dozen O stars. Since the effects of those magnetic fields have been found to be substantial by recent models, we are looking into their impact on stellar rotation, pulsation, stellar winds, and chemical abundances. Accurate studies of the age, environment, and kinematic characteristics of the magnetic stars are also promising to give us new insight into the origin of the magnetic fields. Furthermore, longer time series of magnetic field measurements allow us to observe the temporal variability of the magnetic field and to deduce the stellar rotation period and the magnetic field geometry. Studies of the magnetic field in massive stars are indispensable to understand the conditions controlling the presence of those fields and their implications on the stellar physical parameters and evolution.

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arXiv2011

A deep all-sky census of the Hyades

On the basis of the PPMXL catalogue we perform an all-sky census of the Hyades down to masses of about 0.2 m_sun in a region up to 30 pc from the cluster centre. We use the proper motions from PPMXL in the convergent point method to determine probable kinematic members. From 2MASS photometry and CMC14 r'-band photometry, we derive empirical colour-absolute magnitude diagrams and, finally, determine photometric membership for all kinematic candidates. This is the first deep (r' < 17) all-sky survey of the Hyades allowing a full three-dimensional analysis of the cluster. The survey is complete down to at least M_{K_s} = 7.3 or 0.25 m_sun. We find 724 stellar systems co-moving with the bulk Hyades space velocity, which represent a total mass of 435 m_sun. The tidal radius is about 9 pc, and 275 m_sun (364 systems) are gravitationally bound. This is the cluster proper. Its mass density profile is perfectly fitted by a Plummer model with a central density of 2.21 m_sun*pc^-3 and a core radius of r_co = 3.10 pc, while the half-mass radius is r_h = 4.1 pc. There are another 100 m_sun in a volume between one and two tidal radii (halo), and another 60 m_sun up to a distance of 30 pc from the centre. Strong mass segregation is inherent in the cluster. The present-day luminosity and mass functions are noticeably different in various parts of the cluster (core, corona, halo, and co-movers). They are strongly evolved compared to presently favoured initial mass functions. The analysis of the velocity dispersion of the cluster shows that about 20% of its members must be binaries. As a by-product, we find that presently available theoretical isochrones are not able to adequately describe the near-infrared colour-absolute magnitude relation for those cluster stars that are less massive than about 0.6 m_sun.

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arXiv2011

Exploring the origin of magnetic fields in massive stars: A survey of O-type stars in clusters and in the field

To investigate statistically whether magnetic fields in massive stars are ubiquitous or appear in stars with specific spectral classification, certain ages, or in a special environment, we acquired 41 new spectropolarimetric observations for 36 stars. Among the observed sample roughly half of the stars are probable members of clusters at different ages, whereas the remaining stars are field stars not known to belong to any cluster or association. Spectropolarimetric observations were obtained during three different nights using the low-resolution spectropolarimetric mode of FORS2 (FOcal Reducer low dispersion Spectrograph) mounted on the 8-m Antu telescope of the VLT. To assess the membership in open clusters and associations, we used astrometric catalogues with the best currently available kinematic and photometric data. A field at a significance level of 3sigma was detected in ten O-type stars. Importantly, the largest longitudinal magnetic fields were measured in two Of?p stars: =-381+-122G for CPD-282561 and =-297+-62G for HD148937, previously detected by us as magnetic. The obtained observations of HD148937 on three different nights indicate that the magnetic field is slightly variable. Our new measurements support our previous conclusion that large-scale organized magnetic fields with polar field strengths in excess of 1kG are not widespread among O-type stars. Among the stars with a detected magnetic field, only one star, HD156154, belongs to an open cluster at high membership probability. According to previous kinematic studies, four magnetic O-type stars in the sample are well-known candidate runaway stars.

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arXiv2010

The kinematic characteristics of magnetic O-type stars

Although magnetic fields have been discovered in ten massive O-type stars during the last years, the origin of their magnetic fields remains unknown. Among the magnetic O-type stars, two stars, HD36879 and HD57682, were identified as candidate runaway stars in the past, and theta^1 Ori C was reported to move rapidly away from its host cluster. We search for an explanation for the occurrence of magnetic fields in O-type stars by examining the assumption of their runaway status. We use the currently best available astrometric, spectroscopic, and photometric data to calculate the kinematical status of seven magnetic O-type stars with previously unknown space velocities. The results of the calculations of space velocities suggest that five out of the seven magnetic O-type stars can be considered as candidate runaway stars. Only two stars, HD155806 and HD164794, with the lowest space velocities, are likely members of Sco OB4 and NGC6530, respectively. However, the non-thermal radio emitter HD164794 is a binary system with colliding winds, for which the detected magnetic field has probably a different origin in comparison to other magnetic O-type stars.

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arXiv2010

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.

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arXiv2009

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.

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arXiv2008

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 $ϕ$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.

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