A Numerical Simulation Study of Mass Segregation in Embedded Stellar Clusters

The initial condition of the formation of massive stars is still unclear at present. In particular, it is still debatable whether or not massive stars are formed in the cluster center. Some people considered from the viewpoint of time scale and thought that the mass segregation phenomena in embedded clusters means that the massive stars can only be born in the cluster center. In this paper we used the Monte Carlo method to make numerical simulation of the dynamical evolution of embedded clusters and the result is compared with the observations. It is assumed that at the initial time massive stars are randomly distributed. It was found that, due to the random motions of massive stars, temporary mass segregation may exist at certain times in the course of evolution of a given embedded cluster, and this phenomenon may be very prominent in some of them. It is pointed out that massive star formation in the center is not the only explanation for mass segregation in embedded clusters. In addition, dynamical friction from the gas can effectively reduce the time scale of the dynamical mass segregation. In consequence, the probability of temporary mass segregation is increased.     

Diffusion and Mixing in Main-Sequence Stars

The element settling which occurs inside stars, also called `microscopic diffusion', due to the combined effect of gravity, thermal gradient, radiative acceleration and concentration gradient, leads to abundance variations which cannot be neglected in the computations of stellar structure. These processes where first introduced to account for abundance anomalies in `peculiar stars', but their importance in the so-called `normal' stars is now fully acknowledged, specially after the evidence of helium settling in the Sun from helioseismology. The reason why abundance variations as large as predicted by microscopic diffusion are not always observed is due to the influence of macroscopic motions, like rotation-induced mixing, or mass loss, which increase the settling time scales. In the present review, I discuss the theories of element settling and rotation-induced mixing and the importance of their coupling. I also give some comments about the links between diffusion processes and asteroseismology.     

Study of the nearest open clusters and the associated moving clusters by numerical simulations

In our previous papers, we showed that at the final phases of the dynamical evolution of an open cluster, an extended population of stars elongated along its Galactic orbit, the stellar tail of the cluster, is formed. The tail stars that escaped from the cluster at different times move in a common orbit with low relative velocities. Experiencing a weak interaction with Galactic field stars, these objects, the relics of open clusters, can exist for a fairly long time. In this paper, we investigate the structures of such stellar tails in the nearest open clusters: Hyades, Pleiades, Praesepe, Alpha Persei, Coma, IC 2391, and IC 2602. To this end, we performed several numerical simulations of the dynamical evolution of these clusters in the tidal field of the Galaxy. Our computations of the dynamical evolution were based on known cluster age estimates and real Galactic orbits. The initial conditions were chosen in such a way that the parameters of the simulated clusters corresponded to their observed parameters. As a result, we obtained models of the stellar tails for the nearest open clusters and estimated such parameters of the tails as their sizes, densities, locations relative to the solar neighborhood, and others.     

Structure and evolution of single WR stars

New computations of massive stars follow the evolution up to advanced stages and include:

-A large and flexible nuclear network consisting of 174 nuclear species that are linked by 1742 nuclear reactions.

-Semiconvection, overshooting and mass loss.

-Modern rates for both strong and weak interaction processes as well as the latest rates for the neutrino processes.

-Improved grid distribution and a large number of grid points.

The nuclear network and the diffusion equation are solved for each time step during the whole evolution. In this way the accuracy of nuclear yields and chemical abundances are mainly limited by uncertainties in the diffusion coefficient found from the convection theories. Several instability mechanisms may affect the mass loss rates of massive stars and thereby the structure and abundances of WR stars. Due to heavy mass loss at the LBV and WR stages, the masses at the pre-SN stage may be less than 5M _⊙. Yields and abundances throughout the stars are discussed together with the amount of all elements expelled.     

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.     

Fragmentation and Structure Formation

I present an overview of the hierarchy of structures existing in the interstellar medium (ISM) and the possible mechanisms that cause the fragmentation of one level into the next, with the formation of stars as its last step. Within this framework, I then give an overview of the contributions to this session. Numerical work addresses, at the largest scales, the shaping and formation of structures in the ISM through turbulence driven by stellar energy injection, and the resulting star formation rate as a function of mean density. At the scales of molecular clouds, results comparing observational and numerical data on the density and velocity structure of turbulence-produced cores, as well as their mass spectra, are summarized, together with existing theories of core and star formation controlled by the turbulence. Observationally, an attempt to discriminate between the standard and turbulent models of star formation is presented, finding inconclusive results, but suggesting that both turbulence and the magnetic field are dynamically important in molecular clouds and their cores. Finally, various determinations of the magnetic field strength and geometry are also presented.     

Observed interstellar magnetized supershells and stellar-wind theories

Early theories of stellar winds from an association of OB stars predicted the formation of a common superbubble enclosed by athin, dense supershell, through the combined effort of the winds from the stars at the center. These early theories were adequate for explaining the primary observational features (defined as: shell age, outer radius, shell speed, shell mass, shell energy), but they were not adequate to explain the secondary features (defined as: shell thickness, shell magnetic field, shell gas density). A recently published theory for a stellar-wind-bubble and supershell, predicting a range ofthick supershells, can now be compared with the secondary observational features.Using the observed parameters from all large (> 100 pc) interstellar magnetized supershells near the sun (< 1 kpc away), I assemble for comparison with stellar-wind theories: (a) the primary observational features of these shells — I find: large shell age, large outer radius, low shell speed, large shell mass, large shell energy; and (b) some of their secondary observational features — I find: thick shell, low shell magnetic field strengh, low shell gas density.     

Changes of the profiles of spectral lines due to mass transfer in close binaries

In this paper, the model of the ring envelope round the primary component and the stream of the gaseous mass flowing from the secondary component to the primary is constructed on the basis of theoretical computations concerning the exchange of the mass between the components of the binary. The paper studies the influence of the gaseous mass on the profiles of spectral lines before and after occultation; the influence of the stream on the profile in case the secondary is near elongation, is also investigated. The line profiles obtained by numerical computations show that their changes caused by outflowing mass should be well detectable from spectrograms taken at particular phase of the binary. Changes in the lines may influence the measurement of radial velocities. The method for distinguishing the influence of the stream from the influence of the ring is described.     

Mass-loss predictions for Subdwarf B stars

We present the results of Monte Carlo mass-loss computations for hot low-mass stars, specifically for subdwarf B (sdB) stars. It is shown that the mass-loss rates on the Horizontal Branch (HB) computed from radiative line-driven wind models are not high enough to create sdB stars. We argue, however, that mass loss plays a role in the chemical abundance patterns observed both in field sdB stars, as well as in cluster HB stars. The derived mass loss recipe for these (extremely) hot HB stars may also be applied to other groups of hot low-mass stars, such as post-HB (AGB-manqué, UV-bright) stars, over a range in effective temperatures between ?10 000 and 50 000 K. Finally, we present preliminary spectral synthesis on the more luminous sdB stars for which emission cores in Hα have been detected (Heber, U., et al.: 2003, in:Stellar Atmosphere Modeling, ASP Conference Proceedings, p. 251). We find that these line profiles can indeed be interpreted as the presence of a stellar wind with mass loss on the order of 10^?11?M _⊙ yr ^?1.     

Evolution of magnetic fields in stars across the upper main sequence: II. Observed distribution of the magnetic field geometry

We re‐discuss the evolutionary state of upper main sequence magnetic stars using a sample of Ap and Bp stars with accurate Hipparcos parallaxes and definitely determined longitudinal magnetic fields. We confirm our previous results obtained from the study of Ap and Bp stars with accurate measurements of the mean magnetic field modulus and mean quadratic magnetic fields that magnetic stars of mass M < 3 M_⊙ are concentrated towards the centre of the main‐sequence band. In contrast, stars with masses M > 3 M_⊙ seem to be concentrated closer to the ZAMS. The study of a few known members of nearby open clusters with accurate Hipparcos parallaxes confirms these conclusions. Stronger magnetic fields tend to be found in hotter, younger and more massive stars, as well as in stars with shorter rotation periods. The longest rotation periods are found only in stars which spent already more than 40% of their main sequence life, in the mass domain between 1.8 and 3 M_⊙ and with log g values ranging from 3.80 to 4.13. No evidence is found for any loss of angular momentum during the main‐sequence life. The magnetic flux remains constant over the stellar life time on the main sequence. An excess of stars with large obliquities β is detected in both higher and lower mass stars. It is quite possible that the angle β becomes close to 0. in slower rotating stars of mass M > 3 M_⊙ too, analog to the behaviour of angles β in slowly rotating stars of M < 3 M_⊙. The obliquity angle distribution as inferred from the distribution of r ‐values appears random at the time magnetic stars become observable on the H‐R diagram. After quite a short time spent on the main sequence, the obliquity angle β tends to reach values close to either 90. or 0. for M < 3 M_⊙. The evolution of the obliquity angle β seems to be somewhat different for low and high mass stars. While we find a strong hint for an increase of β with the elapsed time on the main sequence for stars with M > 3 M_⊙, no similar trend is found for stars with M < 3 M_⊙. However, the predominance of high values of β at advanced ages in these stars is notable. As the physics governing the processes taking place in magnetised atmospheres remains poorly understood, magnetic field properties have to be considered in the framework of dynamo or fossil field theories. (© 2007 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)     

Theoretical basal Ca II fluxes for late-type stars: results from magnetic wave models with time-dependent ionization and multi-level radiation treatments

In the current study we present ab initio numerical computations of the generation and propagation of longitudinal waves in magnetic flux tubes embedded in the atmospheres of late-type stars. The interaction between convective turbulence and the magnetic structure is computed and the obtained longitudinal wave energy flux is used in a self-consistent manner to excite the small-scale magnetic flux tubes. In the current study we reduce the number of assumptions made in our previous studies by considering the full magnetic wave energy fluxes and spectra as well as time-dependent ionization (TDI) of hydrogen, employing multi-level Ca II atomic models, and taking into account departures from local thermodynamic equilibrium. Our models employ the recently confirmed value of the mixing-length parameter \(\alpha=1.8\). Regions with strong magnetic fields (magnetic filling factors of up to 50%) are also considered in the current study.The computed Ca II emission fluxes show a strong dependence on the magnetic filling factors, and the effect of time-dependent ionization (TDI) turns out to be very important in the atmospheres of late-type stars heated by acoustic and magnetic waves. The emitted Ca II fluxes with TDI included into the model are decreased by factors that range from 1.4 to 5.5 for G0V and M0V stars, respectively, compared to models that do not consider TDI.The results of our computations are compared with observations. Excellent agreement between the observed and predicted basal flux is obtained. The predicted trend of Ca II emission flux with magnetic filling factor and stellar surface temperature also agrees well with the observations but the calculated maximum fluxes for stars of different spectral types are about two times lower than observations. Though the longitudinal MHD waves considered here are important for chromosphere heating in high activity stars, additional heating mechanism(s) are apparently present.     

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.     

On the lifetimes of galactic clusters

From the observed age distribution of galactic clusters within 1 kpc we deduce that the typical total lifetime of a galactic cluster is about 2×10⁸ yr. The individual lifetimes vary between 10⁸ and 10¹⁰ yr. The observed lifetimes are compared with the evaporation times which are found from numerical experiments with star cluster models. These models contain up to 250 stars with a realistic mass spectrum. The effect of the galactic tidal field is taken into account and enhances the rate of escape significantly. Escapers are identified by using the Jacobian integral. We give the evaporation time in years as a function of the median radius for different values of the total mass of a cluster. The agreement between the resulting theoretical lifetimes and the observed values is sufficiently good. We estimate that the tidal field of passing interstellar clouds should be in most cases less efficient in dissolving a galactic cluster than the internal evaporation process combined with the effect of the general galactic field.     

Central energy equipartition in multimass models of globular clusters

In the construction of multimass King–Michie models of globular clusters, an approximated central energy equipartition between stars of different mass is usually imposed by scaling the velocity parameter of each mass class inversely with the stellar mass, as if the distribution function were isothermal. In this paper, this 'isothermal approximation' has been checked and its consequences on the model parameters studied by a comparison with models including central energy equipartition correctly. It is found that, under the isothermal approximation, the 'temperatures' of a pair of components can differ to a non-negligible amount for low concentration distributions. It is also found that, in general, this approximation leads to a significantly reduced mass segregation in comparison with that given under the exact energy equipartition at the centre. As a representative example, an isotropic three-component model fitting a given projected surface brightness and line-of-sight velocity dispersion profiles is discussed. In this example, the isothermal approximation gives a cluster envelope much more concentrated (central dimensionless potential   W = 3.3  ) than under the true equipartition  ( W = 5.9 × 10⁻²)  , as well as a higher mass function logarithmic slope. As a consequence, the inferred total mass (and then the global mass-to-light ratio) is a factor of 1.4 times lower than the correct value and the amount of mass in heavy dark remnants is 3.3 times smaller. Under energy equipartition, the fate of stars having a mass below a certain limit is to escape from the system. This limit is derived as a function of the mass and W of the component of giant and turn-off stars.     

Tidal Angular Momentum in Close Binary Systems in presence of Wind Driven Non-conservative Mass Transfer with Uniform Mass Accretion Rate

A very well-known property of close binary stars is that they usually rotate slowly than a similar type single star. Massive stars in close binary systems are supposed to experience an exchange of mass and angular momentum via mass transfer and tidal interaction, and thus the evolution of binary stars becomes more complex than that of individual stars. In recent times, it has become clear that a large number of massive stars interact with binary companions before they die. The observation also reveals that in close pairs the rotation tends to be synchronized with the orbital motion and the companions are naturally tempted to invoke tidal friction. We here introduce the effect of tidal angular momentum in the model of wind driven non-conservative mass transfer taking mass accretion rate as uniform with respect to time. To model the angular momentum evolution of a low mass main sequence companion star can be a challenging task. So, to make the present study more interesting, we have considered initial masses of the donor and gainer stars at the proximity of bottom-line main sequence stars and they are taken with lower angular momentum. We have produced a graphical profile of the rate of change of tidal angular momentum and the variation of tidal angular momentum with respect to time under the present consideration.     

疏散星团的质量分层

对疏散星团质量分层的有关问题做了简要的评述,包括空间质量分层和速度质量分层的表现形式和探测途径,质量分层形成机制的研究现状.最后概要介绍了2MASS测光资料对探讨疏散星团质量分层效应的作用.     

Numerical simulations of the Hyades dynamics and the nature of the moving Hyades cluster

We present our numerical simulations of the dynamical evolution of the Hyades open cluster. The simulations were performed usinga modified NBODY6 algorithm that included tidal forces and a realistic orbit of the cluster in a gravitational field described by the Miyamoto-Nagai potential. Our goal was to study the nature of movingclu sters. We show that the stars that were earlier cluster members could be later identified within a sphere of 50 pc in diameter around the Sun. The number of such stars for the chosen initial mass and virial radius of the cluster does not exceed ten. The maximum space velocity of these stars relative to the core of the current cluster does not exceed 3 km s^?1. Our numerical simulations confirm the assumption that some of the moving clusters near the Sun could consist of stars that have escaped from open clusters in the course of their dynamical evolution.     

The origin of the lead-rich stars in the Galactic halo: investigation of model parameters for the s-process

Several stars at the low-metallicity extreme of the Galactic halo show large spreads of lead and associated 'heavy' s-process elements ([Pb/hs]). Theoretically, an s-process pattern should be obtained from an AGB star with a fixed metallicity and initial mass. For the third dredge-up and the s-process model, several important properties depend primarily on the core mass of AGB stars. Zijlstra reported that the initial-to-final mass relation steepens at low metallicity, due to low mass-loss efficiency. This might affect the model parameters of the AGB stars, e.g. the overlap factor and the neutron irradiation time, in particular at low metallicity. The calculated results do indeed show that the overlap factor and the neutron irradiation time are significantly small at low metallicities, especially for  3.0 M_⊙ AGB  stars. The scatter of [Pb/hs] found in low metallicities can therefore be explained naturally when varying the initial mass of the low-mass AGB stars.     

The formation of a bound star cluster: from the Orion nebula cluster to the Pleiades

Direct N -body calculations are presented of the formation of Galactic clusters using GasEx , which is a variant of the code Nbody6 . The calculations focus on the possible evolution of the Orion nebula cluster (ONC) by assuming that the embedded OB stars explosively drove out 2/3 of its mass in the form of gas about 0.4 Myr ago. A bound cluster forms readily and survives for 150 Myr despite additional mass loss from the large number of massive stars, and the Galactic tidal field. This is the very first time that cluster formation is obtained under such realistic conditions. The cluster contains about 1/3 of the initial 10⁴ stars, and resembles the Pleiades cluster to a remarkable degree, implying that an ONC-like cluster may have been a precursor of the Pleiades. This scenario predicts the present expansion velocity of the ONC, which will be measurable by upcoming astrometric space missions. These missions should also detect the original Pleiades members as an associated expanding young Galactic-field subpopulation. The results arrived at here suggest that Galactic clusters form as the nuclei of expanding OB associations.
The results have wide implications, also for the formation of globular clusters and the Galactic-field and halo stellar populations. In view of this, the distribution of binary orbital periods and the mass function within and outside the model ONC and Pleiades is quantified, finding consistency with observational constraints. Advanced mass segregation is evident in one of the ONC models. The calculations show that the primordial binary population of both clusters could have been much the same as is observed in the Taurus–Auriga star-forming region. The computations also demonstrate that the binary proportion of brown dwarfs is depleted significantly for all periods, whereas massive stars attain a high binary fraction.