Statistical analysis of the motion of globular clusters in the galaxy

The laws of motion of globular stellar clusters, capable of answering many interesting questions about their evolution and the overall structure of the Galaxy, are investigated. Solving the problem of the orbits of these objects requires knowledge of the initial conditions of their motion and assigning an expression for the gravitational potential of the Galaxy’s regular field. The situation here is complicated, in general by the fact that, despite some progress in determining the proper motions of globular clusters, only their radial velocities can be estimated from observations. One must therefore apply statistical methods of analysis of the possible shapes of the Galactic orbits of these formations. In the present work, on the basis of new, relatively rich observational material, we have carried out statistical investigations of the possible shapes of orbits for about 100 globular clusters and studied the influence of a change in the Galaxy’s gravitational potential on the results of the investigations. Translated from Astrofizika, Vol. 41, No. 1, pp. 101–112, January-March, 1998.     

Stellar Relics from the Early Galaxy

We reviewed the recent progress in the field of stellar/galactic archeology, which is a study of the relics from the early galaxy. The oldest and most pristine objects that can be observed in the galaxy are the low mass metal poor stars of the Milky Way. They were formed during the early phases, when the ISM might have been polluted only by the Pop-III supernovae. With the recent large spectroscopic surveys (e.g. HK survey by Beers and collaborators, the Hamburg-ESO survey by Christlieb and collaborators and Sloan Digital Sky Survey) it has been possible to get clues on the nature of the first stars that has contributed to the heavy elements. Most of these metal-poor low mass stars also retain their signature of the early dynamical evolution of the galaxy, which can be studied through their orbits around the galaxy and spatial distribution. Here, we discuss the connection between the chemical and the kinematical properties of metal-poor stars in order to probe the early galaxy formation. We also discuss about the globular clusters, the satellite galaxies around the Milky Way and its possible contribution to the formation of the galaxy halo.     

Test of the hypothesis of circular motion of interstellar clouds

The study of the motion of interstellar clouds by direct dynamical methods is hindered by the lack of a complete set of initial conditions of the motion. The hypothesis of the circular motion of interstellar matter of various composition is tested on the basis of the catalog of Brand and Blitz. A modification of the method proposed by Edmondson and Hoerner, which was successfully used for a statistical investigation of the shapes of the orbits of globular clusters, is used. It is established that interstellar clouds move in nearly circular orbits with small deviations, so that data on the spiral structure of the Galaxy obtained by radio-astronomical methods should be considered as close to reality. Translated from Astrofizika, Vol. 43, No. 2, pp. 239–246, April-June, 2000.     

蓝离散星研究现状(Ⅱ):观测特性

不同恒星系统(银河系晕、疏散星团、球状星团、矮星系)中蓝离散星所表现出的观测特性各不相同,这与恒星系统动力学环境及相应的蓝离散星主导形成机制直接相关。因此,分析研究蓝离散星的不同观测特性,也就成为研究蓝离散星形成机制、恒星及双星系统演化以及恒星系统动力学演化的有效方法。     

The evolution of helium-rich subdwarf-B stars

Helium-rich subdwarf-B (He-sdB) stars are extremely rare hot subluminous stars found in the field of our Galaxy as well as in some globular clusters. The existence of these hot helium stars cannot be explained by canonical stellar evolution theories nor can it be explained by normal sdB evolution. We discuss the existing evolutionary models for the formation of He-sdB stars—the flash mixing model and the binary white dwarf merger model in the light of new observational results. Spectral classification of objects as He-sdB stars by various authors has resulted in a range of objects, including white dwarfs, being classified as He-sdB stars. We propose a homogeneous definition for this class of objects based on the original classification scheme used in the PG catalogue. Spectral analysis of He-sdB stars in the last 15 years is also briefly reviewed.     

Shapiro effect as a possible cause of the low-frequency pulsar timing noise in globular clusters

A prolonged timing of millisecond pulsars has revealed low-frequency uncorrelated (infrared) noise, presumably of astrophysical origin, in the pulse arrival time (PAT) residuals for some of them. Currently available pulsar timing methods allow the statistical parameters of this noise to be reliably measured by decomposing the PAT residual function into orthogonal Fourier harmonics. In most cases, pulsars in globular clusters show a low-frequency modulation of their rotational phase and spin rate. The relativistic time delay of the pulsar signal in the curved spacetime of randomly distributed and moving globular cluster stars (the Shapiro effect) is suggested as a possible cause of this modulation. Extremely important (from an astrophysical point of view) information about the structure of the globular cluster core, which is inaccessible to study by other observational methods, could be obtained by analyzing the spectral parameters of the low-frequency noise caused by the Shapiro effect and attributable to the random passages of stars near the line of sight to the pulsar. Given the smallness of the aberration corrections that arise from the nonstationarity of the gravitational field of the randomly distributed ensemble of stars under consideration, a formula is derived for the Shapiro effect for a pulsar in a globular cluster. The derived formula is used to calculate the autocorrelation function of the low-frequency pulsar noise, the slope of its power spectrum, and the behavior of the σ_z statistic that characterizes the spectral properties of this noise in the form of a time function. The Shapiro effect under discussion is shown to manifest itself for large impact parameters as a low-frequency noise of the pulsar spin rate with a spectral index of n = −1.8 that depends weakly on the specific model distribution of stars in the globular cluster. For small impact parameters, the spectral index of the noise is n = −1.5.     

Intermediate-mass black holes in globular clusters

The mass of central bodies in a number of Milky-Way globular clusters is estimated based on the stellar radial-velocity dispersion data. It is assumed that stars located close to the center of the cluster (i.e., to the black hole) rotate about it, have masses on the order of the solar mass, and that the mass of the gravitating center is greater by a factor of 1000. The radial velocities of stars in the vicinity of cluster centers are analyzed for two hypothetical extreme cases: (1) ordered orbital motion of stars about the gravitating center and (2) chaotic orbital motions. The masses inferred for most of the clusters (10²–10⁴ M _⊙) correspond to intermediate-mass black holes. Another important result of this study consists in the determination of the quantity l, the characteristic scale length of the additional spatial dimension. Given the age and mass of the globular cluster NGC 6397 we estimate l to be between 0.02 and 0.14 mm.     

Gravitational interactions between globular and open clusters: an introduction

Historically, it has been assumed that globular and open clusters never interact. However, recent evidence suggests that: globular clusters passing through the disk may be able to perturb giant molecular clouds (GMCs) triggering formation of open clusters and some old open clusters may be linked to accreted globulars. Here, we further explore the existence of possible dynamical connections between globular and open clusters, and realize that the most obvious link must be in the form of gravitational interactions. If open clusters are born out of GMCs, they have to move in similar orbits. If we accept that globulars can interact with GMCs, triggering star formation, it follows that globular and open clusters must also interact. Consistently, theoretical arguments as well as observational evidence, show that globular and open clusters certainly are interacting populations and their interactions are far more common than usually thought, especially for objects part of the bulge/disk. Monte Carlo calculations confirm that conclusion. Globular clusters seem capable of not only inducing formation of open clusters but, more often, their demise. Relatively frequent high speed cluster encounters or cluster harassment may also cause, on the long-term, slow erosion and tidal truncation on the globulars involved. The disputed object FSR 1767 (2MASS-GC04) may be, statistically speaking, the best example of an ongoing interaction.     

Globular Clusters: Absolute Proper Motions and Galactic Orbits

We cross-match objects from several different astronomical catalogs to determine the absolute proper motions of stars within the 30-arcmin radius fields of 115 Milky-Way globular clusters with the accuracy of 1–2 mas yr^?1. The proper motions are based on positional data recovered from the USNO-B1, 2MASS, URAT1, ALLWISE, UCAC5, and Gaia DR1 surveys with up to ten positions spanning an epoch difference of up to about 65 years, and reduced to Gaia DR1 TGAS frame using UCAC5 as the reference catalog. Cluster members are photometrically identified by selecting horizontal- and red-giant branch stars on color–magnitude diagrams, and the mean absolute proper motions of the clusters with a typical formal error of about 0.4 mas yr^?1 are computed by averaging the proper motions of selected members. The inferred absolute proper motions of clusters are combined with available radial-velocity data and heliocentric distance estimates to compute the cluster orbits in terms of the Galactic potential models based on Miyamoto and Nagai disk, Hernquist spheroid, and modified isothermal dark-matter halo (axisymmetric model without a bar) and the same model + rotating Ferre’s bar (non-axisymmetric). Five distant clusters have higher-than-escape velocities, most likely due to large errors of computed transversal velocities, whereas the computed orbits of all other clusters remain bound to the Galaxy. Unlike previously published results, we find the bar to affect substantially the orbits of most of the clusters, even those at large Galactocentric distances, bringing appreciable chaotization, especially in the portions of the orbits close to the Galactic center, and stretching out the orbits of some of the thick-disk clusters.     

On the existence of differences in luminosity between horizontal branch stars in globular clusters and in the field

The discrepancy between a long distance-scale derived from Hipparcos -based distances to globular clusters via main-sequence fitting to local subdwarfs, and a short distance-scale derived from the absolute magnitude of field RR Lyraes via statistical parallaxes and the Baade–Wesselink method could be accounted for whether an intrinsic difference of about ∼0.1–0.2 mag was found to exist between horizontal branch (HB) stars populating the sparse general field and the dense globular clusters. In this paper we discuss the possible existence of such a systematic difference comparing the period-shifts observed for field and cluster RR Lyraes. Various approaches based on different parameters and data sets for both cluster and field variables were used in order to establish the size of such a hypothetical difference, if any. We find that on the whole very small not significant differences exist between the period–metallicity distributions of field and cluster RR Lyraes, thus confirming with a more quantitative approach, the qualitative conclusions by Catelan . This observational evidence translates into a very small difference between the horizontal branch luminosity of field and cluster stars, unless RR Lyraes in globular clusters are about 0.06 M_⊙ more massive than field RR Lyraes at same metallicity, which is to be proven.     

Light‐element abundance variations in globular clusters

Star‐to‐star variations in abundances of the light elements carbon, nitrogen, oxygen, and sodium have been observed in stars of all evolutionary phases in all Galactic globular clusters that have been thoroughly studied. The data available for studying this phenomenon, and the hypotheses as to its origin, have both co‐evolved with observing technology; once high‐resolution spectra were available even for main‐sequence stars in globular clusters, scenarios involving multiple closely spaced stellar generations enriched by feedback from moderate‐ and high‐mass stars began to gain traction in the literature. This paper briefly reviews the observational history of globular cluster abundance inhomogeneities, discusses the presently favored models of their origin, and considers several aspects of this problem that require further study (© 2011 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)     

Two populations of open star clusters in the Galaxy

Based on our compiled catalogue of fundamental astrophysical parameters for 593 open clusters, we analyze the relations between the chemical composition, spatial positions, Galactic orbital elements, age, and other physical parameters of open star clusters. We show that the population of open clusters is heterogeneous and is divided into two groups differing by their mean parameters, properties, and origin. One group includes the Galactic clusters formed mainly from the interstellar matter of the thin disk with nearly solarmetallicities ([Fe/H] > ?0.2) and having almost circular orbits a short distance away from the Galactic plane, i.e., typical of the field stars of the Galactic thin disk. The second group includes the peculiar clusters formed through the interaction of extragalactic objects (such as high-velocity clouds, globular clusters, or dwarf galaxies) with the interstellar matter of the thin disk, which, as a result, derived abnormally low (for field thin-disk stars) metallicities and/or Galactic orbits typical of objects of the older Galactic subsystems. About 70% of the clusters older than 1Gyr have been found to be peculiar, suggesting a slower disruption of clusters with noncircular high orbits. Analysis of orbital elements has shown that the bulk of the clusters from both groups were formed within a Galactocentric radius of ??10.5 kpc and closer than ??180 pc from the Galactic plane, but owing to their high initial velocities, the peculiar clusters gradually took up the volumes occupied by the objects of the thick disk, the halo, and even the accreted halo of the Galaxy. Analysis of the relative abundances of magnesium (a representative of the ??-elements) in clusters that, according to their kinematical parameters, belong to different Galactic subsystems has shown that all clusters are composed of matter incorporating the interstellar matter of a single protogalactic cloud in different proportions, i.e., reprocessed in genetically related stars of the Galaxy. The [Mg/Fe] ratios for the clusters with thick-disk kinematics are, on average, overestimated, just as for the field stars of the socalled ??metal-rich wing?? of the thick disk. For the clusters with halo kinematics, these ratios exhibit a very large spread, suggesting that they were formed mainly from matter that experienced a history of chemical evolution different from the Galactic one. We point out that a large fraction of the open clusters with thindisk kinematics have also been formed from matter of an extragalactic nature within the last ??30 Myr.     

白矮星演化与宇宙纪年学

近几年白矮星研究在理论与观测方面都取得了很大进展，这推动了白矮星宇宙纪年学的应用和发展。白矮星宇宙纪年学，即利用白矮星的演化结果计算白矮星理论光度函数，并通过与现测光度函数的对比来确定天体年龄。简要描述了白矮星的基本性质，回顾了白矮星演化研究的历史和基本方法；介绍了白矮星宇宙纪年学研究的基本原理及其在银盘、球状星团、疏散星团以及银晕年龄确定方面的应用现状。白矮星宇宙纪年学是一个很新的研究领域，但它已经在确定天体年龄方面显示出很大的潜力。最后讨论了目前研究中存在的问题，并提出今后需要进一步研究的几项工作。     

On the number ratio of horizontal branch stars to red giant stars in globular clusters

The number ratios of horizontal branch stars to red giant stars were obtained for globular clusters and Draco dwarf galaxy and the helium abundance was estimated using model results without semiconvection zone (SCZ) and with fully developed one. The analysis was confined to the four clusters (M4, M5, M13, and 47 Tuc) and the Draco galaxy, for which fairly precise star counts had been carried out. The effect of the difference in radial distribution between horizontal and red giant branch stars were taken into account, if necessary. The statistically significant difference inR exists among these objects. The cause may be the difference in the helium abundance and/or in the development of the SCZ. In the case of the fully developed SCZ, the helium abundance for M5 and Draco is appreciably smaller than the value given by the big-bang cosmology. It may be taken as an evidence against the full development of the SCZ for the horizontal branch stars in these objects.     

Effects of external tidal field on the evolution of the outer regions of multi-mass star clusters

We present N -body simulations (including an initial mass function) of globular clusters in the Galaxy in order to study effects of the tidal field systematically on the properties of the outer parts of globular clusters. Using nbody6 , which correctly takes into account the two-body relaxation, we investigate the development of tidal tails of globular clusters in the Galactic tidal field. For simplicity, we have employed only the spherical components (bulge and halo) of the Galaxy, and ignored the effects of stellar evolution which could have been important in the very early phase of the cluster evolution. The total number of stars in our simulations is about 20 000, which is much smaller than the realistic number of stars. All simulations had been done for several orbital periods in order to understand the development of the tidal tails. In our scaled-down models, the relaxation time is sufficiently short to show the mass segregation effect, but we did not go far enough to see the core collapse, and the fraction of stars lost from the cluster at the end of the simulations is only ∼10 per cent. The radial distribution of extra-tidal stars can be described by a power law with a slope around −3 in surface density. The directions of tidal tails are determined by the orbits and locations of the clusters. We find that the length of tidal tails increases towards the apogalacticon and decreases towards the perigalacticon. This is an anti-correlation with the strength of the tidal field, caused by the fact that the time-scale for the stars to respond to the potential is similar to the orbital time-scale of the cluster. The escape of stars in the tidal tails towards the pericentre could be another reason for the decrease of the length of tidal tails. We find that the rotational angular velocity of tidally induced clusters shows quite different behaviour from that of initially rotating clusters.     

银河系中球状星团的空间运动

球状星团是银河系中最古老的天体类型之一,其累积光度很大,是银晕中重要的示踪天体。已以发现的银河系球状星团有１４０多个,其中１２０个银心距Ｒ〈４０Ｋｐｃ的星团已被准确地测定了视向速度。根据结数据以及球状星团金属度的统计分析,可以把球状星团次系再进一步分成某些不同的族群。目前已经测定过绝对自行的球状星团只有３８个,尽管这些自行的精度比视向速度和距离的精度差很多,然而,由此可以得出三维的空间速度,在统计     

Can a globular cluster formed in the galactic disk be raised into the halo?

The classical assumption that most globular clusters (hereafter GC) formed in situ in galactic halos is examined in an approximate, empirical way. Although this viewpoint is not rejected per se, an alternative possibility is investigated: the presence of multiple resonances in the galactic disk, together with the concurrent action of a resonant internal bar or distortion, may stir these resonances. This may lead to chaotic motion which breaks the action of the third integral for moderately eccentric orbits. These circumstances may consequently allow the formation of some GC’s in the disk with moderate to highly eccentric orbits, with the action of the resonant bar subsequently gradually driving them (as well as other stars with similar orbits) to spend most of their time in the Galaxy’s halo. The size of the resonant region and the probable effectiveness of the various agents in the associated phase space in the axisymmetric model are listed. An n-body simulation would be required to establish this proposal in a fully self-consistent way. Paper presented at the Division of Dynamical Astronomy Meetings in Halifax, N.S., Canada, June 2006.     

Kinematical and orbital properties for selected southern high — Velocity stars

Using the model of the Galaxy presented by Eggen, Lynden-Bell and Sandage (1962), plane galactic orbits have been calculated for several southern high-velocity stars which possess parallax, proper motion, and radial velocity data. Extensive lists of both raw and computed data for these stars are included. Published values ofU-B andB-V for some of these stars were used in plots of each of the orbital parameters versusU-B, B-V, or the ultraviolet excess (U-B). Also, a comparison is made between the H-R diagrams for the southern high-velocity star group and that of M3, a globular cluster, and again for M67, an old open cluster. The high-velocity star group is found to resemble an old open cluster more than a globular cluster.     

Distribution of gamma-ray bursts in halo neutron star-comet models

The motions of comets and neutron stars have been integrated over five billion years in the Galactic potential to determine a gamma-ray burst distribution, presuming that bursts are the result of interactions between these two families of objects. The comets originate in two distinct populations - one from ejection by stars in the Galactic disk, and the other from ejection by stars in globular clusters. No choice of the free parameters resulted in agreement with both the isotropy data and the log(N >F)-log(F) data.     

Dynamics of very rich open clusters

The oldest open clusters in our Galaxy set the lower limit to the age of the Galactic Disk (9–10 Gyr). Although they appear to be very rich now, it is clear that their primordial populations were much larger. Often considered as transitional objects, these populous open clusters show structural differences with respect to globular clusters so their dynamics and characteristic evolutionary time scales can also be different. On the other hand, their large membership lead to different dynamical evolution as compared with average open clusters. In this paper, the differential features of the evolution of rich open clusters are studied using N-body simulations, including several of the largest (10⁴ stars) published direct collisional N-body calculations so far, which were performed on a CRAY YMP. The disruption rate of rich open clusters is analysed in detail and the effect of the initial spatial distribution of the stars in the cluster on its dynamics is studied. The results show that cluster life-time depends on this initial distribution, decreasing when it is more concentrated. The effect of stellar evolution on the dynamical evolution of rich clusters is an important subject that also has been considered here. We demonstrate that the cluster's life-expectancy against evaporation increases because of mass loss by evolving high-mass stars. This revised version was published online in July 2006 with corrections to the Cover Date.