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.     

Galactic rotation parameters from data on open star clusters

Currently available data on the field of velocities V _r , V _l , V _b for open star clusters are used to perform a kinematic analysis of various samples that differ by heliocentric distance, age, and membership in individual structures (the Orion, Carina-Sagittarius, and Perseus arms). Based on 375 clusters located within 5 kpc of the Sun with ages up to 1 Gyr, we have determined the Galactic rotation parameters ω ₀ = ?26.0 ± 0.3 km s^?1 kpc^?1, ω′₀ = 4.18 ± 0.17 km s^?1 kpc^?2, ω″₀ = ?0.45 ± 0.06 km s^?1 kpc^?3, the system contraction parameter K = ?2.4 ± 0.1 km s^?1 kpc^?1, and the parameters of the kinematic center R ₀ = 7.4 ± 0.3 kpc and l ₀ = 0° ± 1°. The Galactocentric distance R ₀ in the model used has been found to depend significantly on the sample age. Thus, for example, it is 9.5 ± 0.7 and 5.6 ± 0.3 kpc for the samples of young (≤50 Myr) and old (>50 Myr) clusters, respectively. Our study of the kinematics of young open star clusters in various spiral arms has shown that the kinematic parameters are similar to the parameters obtained from the entire sample for the Carina-Sagittarius and Perseus arms and differ significantly from them for the Orion arm. The contraction effect is shown to be typical of star clusters with various ages. It is most pronounced for clusters with a mean age of ≈100 Myr, with the contraction velocity being Kr = ?4.3 ± 1.0 km s^?1.     

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.     

Weak Elliptical Distortion of the Milky Way Potential traced by Open Clusters

From photometric observations and star counts, the existence of a bar in the cen-tral few kpc of the Galaxy is suggested. It is generally thought that our Galaxy is surrounded by a massive invisible halo. The gravitational potential of the Galaxy is therefore made non-axisymmetric generated by the central tfiaxial bar, by the outer triaxial halo, and/or by the spiral structures. Selecting nearly 300 open clusters with complete spatial velocity measure-ments and ages, we were able to construct the rotation curve of the Milky Way within a range of 3 kpc of the Sun. Using a dynamic model for an assumed elliptical disk, a clear weak el-liptical potential of the disk with ellipticity of ε(R0) = 0.060 ± 0.012 is detected, the Sun is found to be near the minor axis, displaced by 30°± 3°. The motion of the clusters is suggested to be on an oval orbit rather than on a circular one.     

Open clusters and the galactic disk

It is textbook knowledge that open clusters are conspicuous members of the thin disk of our Galaxy, but their role as contributors to the stellar population of the disk was regarded as minor. Starting from a homogenous stellar sky survey, the ASCC‐2.5, we revisited the population of open clusters in the solar neighbourhood from scratch. In the course of this enterprise we detected 130 formerly unknown open clusters, constructed volume‐ and magnitude‐limited samples of clusters, re‐determined distances, motions, sizes, ages, luminosities and masses of 650 open clusters. We derived the present‐day luminosity and mass functions of open clusters (not the stellar mass function in open clusters), the cluster initial mass function CIMF and the formation rate of open clusters. We find that open clusters contributed around 40 percent to the stellar content of the disk during the history of our Galaxy. Hence, open clusters are important building blocks of the Galactic disk (© 2010 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)     

Intermediate-age Galactic open clusters: fundamental parameters of NGC 2627

Charge-coupled device (CCD) photometry in the Johnson V , Kron–Cousins I and Washington CMT ₁ systems is presented in the field of the poorly known open cluster NGC 2627. Four independent Washington abundance indices yield a mean cluster metallicity of  [Fe/H]=−0.12 ± 0.08  , which is compatible with the existence of a radial gradient in the Galactic disc. The resultant colour–magnitude diagrams indicate that the cluster is an intermediate-age object of 1.4 Gyr. Based on the best fits of the Geneva group's isochrones to the ( V , V − I ) and  ( T ₁, C − T ₁)  diagrams, we estimate   E ( V − I ) = 0.25 ± 0.05  and   V − M_V = 11.80 ± 0.25  for  log  t = 9.15  , and   E ( C − T ₁) = 0.23 ± 0.07  and   T ₁− M _{T 1}= 11.85 ± 0.25  for  log  t = 9.10  , respectively, assuming solar metal content. The derived reddening value   E ( C − T ₁)  implies   E ( B − V ) = 0.12 ± 0.07  and a distance from the Sun of  2.0 ± 0.4 kpc  . Using the WEBDA data base and the available literature, we re-examined the overall properties of all the open clusters with ages between 0.6 and 2.5 Gyr. We identified peaks of cluster formation at 0.7–0.8, 1.0–1.1, 1.6–1.7 and 2.0–2.1 Gyr, separated by relative quiescent epochs of ∼0.2–0.3 Gyr. We also estimated a radial abundance gradient of  −0.08 ± 0.02  , which is consistent with the most recent determinations for the Galactic disc, but no clear evidence for a gradient perpendicular to the Galactic plane is found.     

Kinematics of the Open Cluster System in the Galaxy

Absolute proper motions and radial velocities of 202 open clusters in the solar neighborhood, which can be used as tracers of the Galactic disk, are used to investigate the kinematics of the Galaxy in the solar vicinity, including the mean heliocentric velocity components (u_1,u_2,u_3) of the open cluster system, the characteristic velocity dispersions (σ_1,σ_2,σ_3), Oort constants (A, B) and the large-scale radial motion parameters (C,D) of the Galaxy. The results derived from the observational data of proper motions and radial velocities of a subgroup of 117 thin disk young open clusters by means of a maximum likelihood algorithm are: (u_1,u2,u3) = (-16.1±1.0, -7.9±1.4,-10.4±1.5) kms~(-1), (σ_1,σ_2,σ_3) = (17.0 ±0.7,12.2±0.9,8.0±1.3) kms~(-1),(A,B) = (14.8±1.0,-13.0±2.7) kms~(-1) kpc~(-1) ,and(C,D) = (1.5±0.7,-1.2±1.5) kms~(-1) kpc~(-1) . A discussion on the results and comparisons with what was obtained by other authors is given.     

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.     

A Kinematical Calibration of the Galactocentric Distance

1 INTRODUCTION The distance to the Galactic center R0 is a fundamental constant for astronomy and astrophysics. Most determinations of astronomical quantities are directly connected with the Galactic distance scale, e.g., the rotational speed of our Galax…     

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.     

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 6404 and 6583: two neglected intermediate-age open clusters located in the Galactic Centre direction

We report on VI charge-coupled device photometry of two fields centred in the region of the open clusters NGC 6404 and 6583 down to   V = 22.0  . So far these clusters have never been studied, and we provide for the first time estimates of their fundamental parameters, namely, radial extent, age, distance and reddening. We find that the radius of NGC 6404 is 2.0 arcmin, as previously proposed, while the radius of NGC 6583 is 1.0 arcmin, significantly lower than previous estimates. Both clusters turn out to be of intermediate age (0.5–1.0 Gyr old), and located inside the solar ring, at a Galactocentric distance of about 6.5 kpc. These results make these objects very interesting targets for spectroscopic follow-up to measure their metallicity. In fact, they might allow us to enlarge by more than 1 kpc the baseline of the radial abundance gradient in the Galactic disc towards the Galactic Centre direction. This baseline is currently rather narrow especially for clusters of this age.     

Morphological analysis of open clusters’ properties: II. Relationships projected onto the galactic plane

A morphological analysis study of open clusters’ properties has been achieved for a sample of 160 UBVCCD open star clusters of approximately 128,000 stars near the galactic plane. The data was obtained and reduced from Tadross (2001) using the same reduction procedures, which makes this catalogue the largest homogeneous source of open clusters’ parameters.