Scaling of N-body calculations

We report results of collisional N -body simulations aimed at studying the N dependence of the dynamical evolution of star clusters. Our clusters consist of equal-mass stars and are in virial equilibrium. Clusters moving in external tidal fields and clusters limited by a cut-off radius are simulated. Our main focus is to study the dependence of the lifetimes of the clusters on the number of cluster stars and the chosen escape condition.
We find that star clusters in external tidal fields exhibit a scaling problem in the sense that their lifetimes do not scale with the relaxation time. Isolated clusters show a similar problem if stars are removed only after their distance to the cluster centre exceeds a certain cut-off radius. If stars are removed immediately after their energy exceeds the energy necessary for escape, the scaling problem disappears.
We show that some stars that gain the energy necessary for escape are scattered to lower energies before they can leave the cluster. As the efficiency of this process decreases with increasing particle number, it causes the lifetimes not to scale with the relaxation time. Analytic formulae are derived for the scaling of the lifetimes in the different cases.     

Continuum Energy Distribution of Bright Be Stars

This paper presents the spectrophotometric observations of five Be stars belonging to spectral type from B2.5 to B5 and luminosity class from III to V. The continuum energy distribution data of these stars are extracted from the spectrophotometric measurements over the wavelength range of λλ 3200–8000 Å. The observed data of continuum energy distribution are compared with the theoretical energy distribution curves to derive the value of effective temperatures of these stars. We have also examined the effect of circumstellar envelopes of Be stars on their continuum energy distribution. It has been found that the extended circumstellar envelope of Be stars affect the underlying continua in the near-ultraviolet and near-infrared regions. Three Be stars are found to exhibit near-ultraviolet and near-infrared flux deficiency in their continua. For one of the Be, namely star HR 1289, we report the first continuum energy distribution measurements. Another normal B star HR 1363, which was observed as comparison star, was found to exhibit near-ultraviolet and excess emission, which are signatures of a Be star, thus putting this star in the category of Be stars.     

On the onset of runaway stellar collisions in dense star clusters – I. Dynamics of the first collision

We study the circumstances under which first collisions occur in young and dense star clusters. The initial conditions for our direct N -body simulations are chosen such that the clusters experience core collapse within a few million years, before the most massive stars have left the main sequence. It turns out that the first collision is typically driven by the most massive stars in the cluster. Upon arrival in the cluster core, by dynamical friction, massive stars tend to form binaries. The enhanced cross-section of the binary compared to a single star causes other stars to engage the binary. A collision between one of the binary components and the incoming third star is then mediated by the encounters between the binary and other cluster members. Due to the geometry of the binary–single star engagement the relative velocity at the moment of impact is substantially different than in a two-body encounter. This may have profound consequences for the further evolution of the collision product.     

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.     

Final stages of N-body star cluster encounters

We performed numerical simulations of star cluster encounters with Hernquist's treecode on a CRAY YMP-2E computer. We used different initial conditions (relative positions and velocities, cluster sizes, masses and concentration degrees) with the total number of particles per simulation ranging from 4608 to 20 480. Long-term interaction stages (up to 1 Gyr) when the pair coalesces into a single cluster are compared with isolated LMC clusters. Evidence is found that, when seen in a favourable plane, these resulting clusters show elliptical shapes as a result of the disruption of one of the companions. These elliptical shapes are essentially time-independent, but they do depend on the initial structural parameters of the pair components. We also analysed the fraction of stars that are ejected to the field by the interaction. We found that this fraction can be almost 50 per cent for the disrupted cluster. These simulations can represent a possible mechanism with which to explain the ellipticity observed in several star clusters in the Magellanic Clouds.     

Numerical experiments on the escape from non-isolated clusters and the formation of multiple stars

Isolated and non isolated clusters with a mass distribution have been studied by numerical techniques. The rates of escape of stars and of kinetic energy are compared with Hénon's theoretical expressions. Multiple encounters play a very important role in the escape phenomenon, at least for clusters with a small number of stars. This leads to a theoretical underestimate of the rates of escape when the stars have equal masses and to an overestimate when masses are unequal.For non isolated clusters, the tidal field of the Galaxy is responsible for one half of the rate of escape of the stars. The energy of a star escaping because of the tidal effect grown slowly while that of a star escaping after an encounter increases very rapidly. The stars escaping because of the tidal effect leave the cluster in the vicinity of the equilibrium points.Encounters and the tidal field are not efficient enought to explain why very old open clusters are not observed. Other escape mechanisms have to be considered.Very stable subsystems are formed which are not destroyed under the influence of the galactic tide. Separation between stars can be as low as 100 UA.     

Hypersonic Swizzle Sticks: Protostellar Turbulence, Outflows and Fossil Outflow Cavities

The expected lifetimes for molecular clouds has become a topic of considerable debate as numerical simulations have shown that MHD turbulence, the nominal means of support for clouds against self-gravity, will decay on short timescales. Thus it appears that either molecular clouds are transient features or they are resupplied with turbulent energy through some means. Jets and molecular outflows are recognized as a ubiquitous phenomena associated with star formation. Stars however form not isolation but in clusters of different density and composion. The ubiquity and high density of outflows from young stars in clusters make them an intriguing candidate for the source of turbulence energy in molecular clouds. In this contribution we present new studies, both observational and theoretical, which address the issue of jet/outflow interactions and their abilityto drive turbulent flows in molecular clouds. Our studies focus on scales associated with young star forming clusters. In particular we first show that direct collisions between active outflows are not effective at stirring the ambient medium. We then show that fossil cavities from “extinct” outflows may provide the missing link in terms of transferring momentum and energy to the cloud.     

Be phenomenon in open clusters: results from a survey of emission-line stars in young open clusters

Emission-line stars in young open clusters are identified to study their properties, as a function of age, spectral type and evolutionary state. 207 open star clusters were observed using the slitless spectroscopy method and 157 emission stars were identified in 42 clusters. We have found 54 new emission-line stars in 24 open clusters, out of which 19 clusters are found to house emission stars for the first time. About 20 per cent clusters harbour emission stars. The fraction of clusters housing emission stars is maximum in both the 0–10 and 20–30 Myr age bin (∼40 per cent each). Most of the emission stars in our survey belong to Classical Be class (∼92 per cent) while a few are Herbig Be stars (∼6 per cent) and Herbig Ae stars (∼2 per cent). The youngest clusters to have Classical Be stars are IC 1590, NGC 637 and 1624 (all 4 Myr old) while NGC 6756 (125–150 Myr) is the oldest cluster to have Classical Be stars. The Classical Be stars are located all along the main sequence (MS) in the optical colour–magnitude diagrams (CMDs) of clusters of all ages, which indicates that the Be phenomenon is unlikely due to core contraction near the turn-off. The distribution of Classical Be stars as a function of spectral type shows peaks at B1–B2 and B6–B7 spectral types. The Be star fraction [N(Be)/N(B+Be)] is found to be less than 10 per cent for most of the clusters and NGC 2345 is found to have the largest fraction (∼26 per cent). Our results indicate there could be two mechanisms responsible for the Classical Be phenomenon. Some are born Classical Be stars (fast rotators), as indicated by their presence in clusters younger than 10 Myr. Some stars evolve to Classical Be stars, within the MS lifetime, as indicated by the enhancement in the fraction of clusters with Classical Be stars in the 20–30 Myr age bin.     

Dynamical evolution of two-component star clusters

The dynamical evolution of two-component star clusters, each of which is enclosed within a perfectly reflecting sphere, is investigated by numerically solving moment equations derived from the Boltzmann equation. One of the two adopted model clusters evolves, starting from a state of no mass segregation, toward an equilibrium state at a quite slow rate. The other one evolves away from an equilibrium state and its central density increases without limit. The different evolutionary behaviors of the two model clusters are explained by the fact that there exists no equilibrium state for such clusters if the total energy is less than a certain critical value. The critical value increases with increasing total mass fraction of the heavier stars. This is qualitatively the same as Spitzer's theorem (1969) expressed in another way.     

Relative content of Be stars in young open star clusters

Based on high- and medium-resolution spectra, we analyze the population of Be stars in eight young open star clusters. We have found a clear dependence of the relative content of early-type (B0-B3) Be stars on the cluster age. The relative concentration of Be stars of spectral types B0?CB3 gradually increases with cluster age, reaching its maximum value of 0.46 in clusters with ages of 12?C20 Myr. The almost complete absence of Be stars in older clusters can be easily explained by the fact that B stars leave the main sequence. The few emission objects in clusters with ages of 1?C7 Myr are most likely Herbig Be stars. Such a distribution of Be stars in clusters unequivocally points to the evolutionary status of the Be phenomenon. We also briefly consider the causes of this pattern.     

Close encounters in young stellar clusters: implications for planetary systems in the solar neighbourhood

The stars that populate the solar neighbourhood were formed in stellar clusters. Through N -body simulations of these clusters, we measure the rate of close encounters between stars. By monitoring the interaction histories of each star, we investigate the singleton fraction in the solar neighbourhood. A singleton is a star which formed as a single star, has never experienced any close encounters with other stars or binaries, or undergone an exchange encounter with a binary. We find that, of the stars which formed as single stars, a significant fraction is not singletons once the clusters have dispersed. If some of these stars had planetary systems, with properties similar to those of the Solar System, the planets' orbits may have been perturbed by the effects of close encounters with other stars or the effects of a companion star within a binary. Such perturbations can lead to strong planet–planet interactions which eject several planets, leaving the remaining planets on eccentric orbits. Some of the single stars exchange into binaries. Most of these binaries are broken up via subsequent interactions within the cluster, but some remain intact beyond the lifetime of the cluster. The properties of these binaries are similar to those of the observed binary systems containing extrasolar planets. Thus, dynamical processes in young stellar clusters will alter significantly any population of Solar System-like planetary systems. In addition, beginning with a population of planetary systems exactly resembling the Solar System around single stars, dynamical encounters in young stellar clusters may produce at least some of the extrasolar planetary systems observed in the solar neighbourhood.     

Numerical simulations of protostellar encounters — I. Star–disc encounters

It appears that most stars are born in clusters, and that at birth most stars have circumstellar discs which are comparable in size to the separations between the stars. Interactions between neighbouring stars and discs are therefore likely to play a key role in determining disc lifetimes, stellar masses, and the separations and eccentricities of binary orbits. Such interactions may also cause fragmentation of the discs, thereby triggering the formation of additional stars.   We have carried out a series of simulations of star–disc interactions using an SPH code which treats self-gravity, hydrodynamic and viscous forces. We find that interactions between discs and stars provide a mechanism for removing energy from, or adding energy to, the orbits of the stars, and for truncating the discs. However, capture during such encounters is unlikely to be an important binary formation mechanism.   A more significant consequence of such encounters is that they can trigger fragmentation of the disc, via tidally and compressionally induced gravitational instabilities, leading to the formation of additional stars and substellar objects. When the disc spins and stellar orbits are randomly oriented, encounters lead to the formation of new companions to the original star in 20 per cent of encounters. If most encounters are prograde and coplanar, as suggested by simulations of dynamically triggered star formation, then new companions are formed in approximately 50 per cent of encounters.     

Dynamical evolution of clusters with two stellar groups

The generalization of the fluid-dynamical approach from one-component star clusters to clusters with several stellar groups (as far as the star masses are concerned) has been applied to the study of two-component clusters. Rather extreme values of stellar masses and masses of groups were chosen in order to emphasize the different dynamical evolutions and asymptotic behaviours. Escape of stars from clusters and the problem of equipartition of kinetic energy among the two star groups are discussed. Comparisons of the main features of our results with those obtained by other authors have shown a good agreement. Some characteristic properties of the last computed models with an age of 18×10⁹ yr have been pointed out and discussed in relation with some observed features of galactic globular clusters.     

振动Kuzmin盘中恒星的运动性质

本文研究振动盘中恒星的运动性质．所采用的势模型为它由一种具简单径向振动模态的Kuzmin盘和一种对数晕共同产生．得到的主要结论是：（1）恒星存在稳定且有序的近圆轨道；（2）盘振动对角动量较小的恒星及远离近圆轨道的恒星影响较大；（3）盘中大部分恒星的运动是有序的；（4）远离近圆轨道的恒星一般作混沌运动，并且最终可能逃逸，但在一个Hubble时间内实际逃逸的恒星比例较小；（5）盘振动可能是振动Kurmin盘中某些星团形成并长期维持的机制之一，盘振动幅度越大，盘中星团数目可能越多；在同一个星系盘中，角动量越大的星团数目可能越少．     

Numerical simulations of protostellar encounters — III. Non-coplanar disc–disc encounters

It is expected that an average protostar will undergo at least one impulsive interaction with a neighbouring protostar whilst a large fraction of its mass is still in a massive, extended disc. If protostars are formed individually within a cluster before falling together and interacting, there should be no preferred orientation for such interactions. As star formation within clusters is believed to be coeval, it is probable that, during interactions, both protostars possess massive, extended discs.   We have used an SPH code to carry out a series of simulations of non-coplanar disc–disc interactions. We find that non-coplanar interactions trigger gravitational instabilities in the discs, which may then fragment to form new companions to the existing stars. (This is different from coplanar interactions, in which most of the new companion stars form after material in the discs has been swept up into a shock layer, and this then fragments.) The original stars may also capture each other, leading to the formation of a small- N cluster. If every star undergoes a randomly oriented disc–disc interaction, then the outcome will be the birth of many new stars and substellar objects. Approximately two-thirds of the stars will end up in multiple systems.     

Powerful CMD:a tool for color-magnitude diagram studies

We present a new tool for color-magnitude diagram(CMD) studies, Powerful CMD. This tool is built based on the advanced stellar population synthesis(ASPS) model, in which single stars, binary stars, rotating stars and star formation history have been taken into account. Via Powerful CMD, the distance modulus, color excess, metallicity, age, binary fraction, rotating star fraction and star formation history of star clusters can be determined simultaneously from observed CMDs. The new tool is tested via both simulated and real star clusters. Five parameters of clusters NGC 6362, NGC 6652, NGC 6838 and M67 are determined and compared to other works. It is shown that this tool is useful for CMD studies, in particular for those utilizing data from the Hubble Space Telescope(HST). Moreover, we find that inclusion of binaries in theoretical stellar population models may lead to smaller color excess compared to the case of single-star population models.     

OB星协和年轻星团的形成与早期演化

ＯＢ星协和年轻星团是恒星形成与早期演化的“化石”，同时也是研究初始重质量函数（ＩＭＦ）的最好场所；文中就ＯＢ星协和年轻星团的形成和早期演化方面的研究进展作了一评述，还论述了ＩＭＦ的测定和研究情况，并对相关的速逃ＯＢ星及蓝离散星问题作了简要介绍。     

The period–luminosity relation for type II Cepheids in globular clusters

We report the result of our near-infrared observations ( JHK _s) for type II Cepheids (including possible RV Tau stars) in galactic globular clusters. We detected variations of 46 variables in 26 clusters (10 new discoveries in seven clusters) and present their light curves. Their periods range from 1.2 d to over 80 d. They show a well-defined period–luminosity relation at each wavelength. Two type II Cepheids in NGC 6441 also obey the relation if we assume the horizontal branch stars in NGC 6441 are as bright as those in metal-poor globular clusters in spite of the high metallicity of the cluster. This result supports the high luminosity which has been suggested for the RR Lyr variables in this cluster. The period–luminosity relation can be reproduced using the pulsation equation     assuming that all the stars have the same mass. Cluster RR Lyr variables were found to lie on an extrapolation of the period–luminosity relation. These results provide important constraints on the parameters of the variable stars.
Using Two Micron All-Sky Survey (2MASS) data, we show that the type II Cepheids in the Large Magellanic Cloud (LMC) fit our period–luminosity relation within the expected scatter at the shorter periods. However, at long periods (   P > 40  d, i.e. in the RV Tau star range) the LMC field variables are brighter by about one magnitude than those of similar periods in galactic globular clusters. The long-period cluster stars also differ from both these LMC stars and galactic field RV Tau stars in a colour–colour diagram. The reasons for these differences are discussed.     

Chromospheric activity in the late A- and early F-type stars of open clusters – II. Pleiades and Alpha Persei

We report observations of the He  i λ 5876 (D3) line in the late A- and early F-type stars in the Pleiades and Alpha Persei star clusters used to determine chromospheric activity levels. This represents the first sample of young stars in this temperature range with chromospheric activity measurements. We find the same average activity level in the young early F stars as in Hyades-age stars and field stars. In addition, the young star sample shows the same large star-to-star variation in activity as seen in the older stars. Thus, as a whole, chromospheric activity in this photospheric temperature range remains the same over nearly a factor of 100 in stellar age (50 Myr to 3 Gyr), in striking contrast to the behaviour of later-type stars. In the five late A stars we find three certain detections of D3 and one likely detection. This includes the bluest star yet observed with a chromospheric D3 line, Pleiades star HII 1362 at ( B − V )₀=0.22, making it one of the earliest stars with an observed chromosphere. The late A stars have D3 equivalent widths comparable to the weakest early F stars. However, when comparing D3 measurements in the young late A stars with older late A stars, we find evidence for a slight decrease in activity with age based on the large number of non-detections in the older stars. We find an apparently linear relationship between the activity upper limit and B − V over our entire range of B − V . Extrapolated blueward, this relationship predicts that the chromospheric D3 line would disappear for all stars at B − V ≈0.13.     

Neutron star retention and millisecond pulsar production in globular clusters

We investigate the conditions by which neutron star retention in globular clusters is favoured. We find that neutron stars formed in massive binaries are far more likely to be retained. Such binaries are likely to then evolve into contact before encountering other stars, possibly producing a single neutron star after a common envelope phase. A large fraction of the single neutron stars in globular clusters are then likely to exchange into binaries containing moderate-mass main-sequence stars, replacing the lower-mass components of the original systems. These binaries will become intermediate-mass X-ray binaries (IMXBs), once the moderate-mass star evolves off the main sequence, as mass is transferred on to the neutron star, possibly spinning it up in the process. Such systems may be responsible for the population of millisecond pulsars (MSPs) that has been observed in globular clusters. Additionally, the period of mass-transfer (and thus X-ray visibility) in the vast majority of such systems will have occurred 5–10 Gyr ago, thus explaining the observed relative paucity of X-ray binaries today, given the MSP population.