The stellar initial mass function (IMF) is a very important question in modern astrophysics. Globular clusters (GCs) are good samples for studying the IMF, but the Galactic GCs can provide only one time-scale evolutionary stage. The Large Magellanic Cloud (LMC) is an ideal environment for studying the IMF because it contains compact clusters at different evolutionary stages. By studying the IMF at different evolutionary stages, we can see how the mass function evolves with time.

There is a difference of a few Kelvins in the effective temperature between a model used only two-point interpolation of opacity and a model used piecewise linear interpolation of opacity. However the frequency difference between the models is of the order of several microHertz at a certain stage, which is almost 10 times worse than the observational precision of p-modes of solar-like stars. Therefore, the two-point interpolation of opacity is unsuitable in modelling of solar-like stars with element diffusion.

From the two-fluid plasma theory, we derived a kind of current in differentially moved plasma. The current is from the different viscosities between electrons and ions. The higher temperature and lighter mass of the electrons make the viscosity of electrons much stronger than ions. In this way, the electrons will have smaller velocity than ions in the differentially moved layer and contribute a net current in the plasma. The value of the current depends on the temperature and density of electrons in the plasma and the differential velocity ∇2v.

We investigate the formation of neutral and singly ionized scandium lines in the solar photospheres. Extensive statistical equilibrium calculations were carried out for a model atom, which comprises 92 terms for Sc I and 79 for Sc II. Synthetic line profiles calculated from the level populations according to the NLTE departure coefficients were compared with the observed solar spectral atlas. Abundance determinations using the ODF model lead to a solar Sc abundance of between log ϵ⊙ = 3.07 and 3.13, depending on the choice of f values.

We positionally cross-identified FIRST (the Faint Images of the Radio Sky at Twenty centimeters) catalogue with 2MASS (the Two Micron All Sky Survey) pointed-source database and collected the data from radio band and near infrared band. Then the data were cross-matched with the Véron-Cetty & Véron 2006 catalog and the Tycho-2 catalog, respectively. Therefore the known samples of quasars and stars are obtained. We applied principal component analysis (PCA) on the known sample. The overall sample may be projected in the principal component space. From the space, we can easily locate the area that radio stars occupy, and select out radio star candidates. With the follow-up observation of these candidates, the properties of radio stars may be studied.

We present the properties of a large sample (12,282) of nearly face-on low surface brightness disk galaxies selected from the main galaxy sample of SDSS-DR4. Those properties includes B-band central surface brightness μ0(B), scale lengths h, distances D, integrated magnitudes, colors and some resulted relations. This sample has μ0(B) from 22 to 24.5 mag arcsec−2 with a median value of 22.44 mag arcsec−2. They are quite bright with MB taking values from −18 to −23 mag with a median value of −20.08 mag. The disk scale lengths h are from 2 kpc to 19 kpc. There exist clear correlations between log h and MB, log h and log D. Both the optical-optical and optical-NIR color-color relations show most of them have a mix of young and old stellar populations.

Turbulent convection models (TCM) provide a better way to study convection in stars than the MLT. Improving numerical method, we adopted larger diffusion parameters and smaller dissipation parameters in order to further correct the p-mode oscillation frequencies of TCM models. The density gradient reversing is discussed.

Observations of solar and stellar oscillations are providing detailed information about stellar interiors. In the case of the Sun the set of observed frequencies is sufficiently detailed and accurate that the properties of the solar interior, such as sound speed, density and internal rotation, can be inferred with substantial precision and resolution. This allows detailed tests of solar modelling, with interesting and to some extent controversial results. Observations of solar-like oscillations in distant stars have started only recently, owing their very small amplitudes. However, developments in ground-based equipment and observations from space are revolutionizing this field, promising greatly increased insight into the structure and evolution of the stars.

We report on an ongoing investigation into a seismic calibration of solar models designed for estimating the main-sequence age and a measure of the chemical abundances of the Sun. Only modes of low degree are employed, so that with appropriate modification the procedure could be applied to other stars. We have found that, as has been anticipated, a separation of the contributions to the seismic frequencies arising from the relatively smooth, glitch-free, background structure of the star and from glitches produced by helium ionization and the abrupt gradient change at the base of the convection zone renders the procedure more robust than earlier calibrations that fitted only raw frequencies to glitch-free asymptotics. As in the past, we use asymptotic analysis to design seismic signatures that are, to the best of our ability, contaminated as little as possible by those uncertain properties of the star that are not directly associated with age and chemical composition. The calibration itself, however, employs only numerically computed eigenfrequencies. It is based on a linear perturbation from a reference model. Two reference models have been used, one somewhat younger, the other somewhat older than the Sun. The two calibrations, which use BiSON data, are more-or-less consistent, and yield a main-sequence age t⊙ = 4.68 ± 0.02 Gy, coupled with a formal initial heavy-element abundance Z = 0.0169 ± 0.0005. The error analysis has not yet been completed, so the estimated precision must be taken with a pinch of salt.

The pre-white dwarf pulsators of PG 1159 type, or GW Virginis variable stars, are in a phase of rapid evolution towards the white dwarf cooling sequence. The rate of change of their nonradial g-mode frequencies can be measured on a reasonably short time scale. From a theoretical point of view, it was expected that one could derive the rate of cooling of the stellar core from such measurements. At the cool end of the GW Virginis instability strip, it is predicted that the neutrinos flux dominates the cooling. PG 0122+200 which defines the red edge of the instability strip is in principle a good candidate to check this prediction. It has been followed-up through multisite photometric campaigns for about fifteen years. We report here the first determination of the rate of change of its 7 largest amplitude frequencies. We find that the amplitudes of the frequency variations are one to two orders of magnitude larger than predicted by theoretical models based on the assumption that these variations are uniquely caused by cooling. The time scales of the variations are much shorter than the ones expected from a neutrino dominated core cooling. These results point to the existence of other mechanisms responsible for the frequency variability. We discuss the role of nonlinearities as one possible mechanism.

Low-mass stars exhibit, at all stages of their evolution, the signatures of complex physical processes that require challenging modeling beyond standard stellar theory. In this review, we recall the most striking observational evidences that probe the interaction and interdependence of various transport processes of chemicals and angular momentum in these objects. We then focus on the impact of atomic diffusion, large scale mixing due to rotation, and internal gravity waves on stellar properties on the main sequence and slightly beyond.

We present 3-D hydrodynamical simulations of the extended turbulent convective envelope of a low-mass red giant star. These simulations, computed with the ASH code, aim at understanding the redistribution of angular momentum and heat in extended turbulent convection zones of these giant stars. We focus our study on the effects of turbulence and of the rotation rate on the convective patterns and on the distribution of angular momentum within the inner 50% of the convective envelope of such stars.

Mixing length parameter of the mixing length theory is a free parameter and used to calibrate radii of late-type stars. From the Hyades cluster and the α Centauri system, we find that the parameter depends on the stellar mass and some other properties of stars. Considering some other systems, we describe how the parameter depends on stellar parameters.

Observations tend to select mass loss rates near the critical rate, Ṁcrit = M/L. There are two reasons for this. In some situations, such as near the tip of the AGB, the mass loss rate is very sensitive to stellar parameters. In this case, stars with Ṁ ≪ Ṁcrit have dust-free, hard-to-measure mass loss rates while stars with Ṁ ≫ Ṁcrit do not survive very long and thus make up a small fraction of any sample. Selection effects dominate the fitting of empirical formulae; observations of mass loss rates tell us more about which stars are losing mass than about how a star loses mass. In other situations, such as for some of the stars along the RGB, a steady state situation occurs where the loss of mass leads to a decrease in mass loss rate while the evolutionary changes lead to an increase; the result is a steady state with Ṁ = Ṁcrit. To determine the envelope mass and composition at the end of a phase of intensive mass loss requires stellar evolution models capable of responding on a time scale ~ tKH and thus, a new generation of stellar modeling codes.

Planetary nebulae are formed by an interacting winds process where the remnant of the AGB wind is compressed and accelerated by a later-developed fast wind from the central star. One-dimensional dynamical models have successfully explained the multi-shell (bubble, shell, crown, haloes) structures and the kinematics of planetary nebulae. However, the origin of the diverse asymmetric morphology of planetary nebulae is still not understood. Recent observations in the visible, infrared, and the submillimeter have suggested that the AGB mass loss becomes aspherical in the very late stages, forming an expanding torus around the star. A fast, highly collimated wind then emerges in the polar directions and carves out a cavity in the AGB envelope to form a bipolar nebula. Newly discovered structures such as concentric arcs, 2-D rings, multiple lobes, and point-symmetric structures suggest that both the slow and fast winds may have temporal and directional variations, and precession can play a role in the shaping of planetary nebulae. In this paper, we review the latest observations of planetary nebulae and proto-planetary nebulae and discuss the various physical mechanisms (rotation, binary, magnetic field, etc) that could lead to the observed morphologies.

In this review I am discussing the current state of simulating the internal evolution of AGB stars. Recent work on AGB stars include the effect of rotation, magnetic fields and internal gravity waves, as well as thermohaline mixing induced by the 3He + 3He pp-chain reaction. Hydrodynamic simulations of the interior convection of AGB stars are now becoming available, giving insights to convective boundary mixing, for example for He-shell flash convection. At very low metallicity convective-reactive events are encountered in AGB stars (as well as in massive stars), and the necessity of hydrodynamic simulations to address this difficult phase of stellar evolution is emphasized.

We desribe and discuss hydrodynamic simulations of the core helium flash using an initial model of a 1.25 M⊙ star with a metallicity of 0.02 near at its peak. Past research concerned with the dynamics of the core helium flash is inconclusive. Its results range from a confirmation of the standard picture, where the star remains in hydrostatic equilibrium during the flash (Deupree 1996), to a disruption or a significant mass loss of the star (Edwards 1969; Cole & Deupree 1980). However, the most recent multidimensional hydrodynamic study (Dearborn et al. 2006) suggests a quiescent behavior of the core helium flash and seems to rule out an explosive scenario. Here we present partial results of a new comprehensive study of the core helium flash, which seem to confirm this qualitative behavior and give a better insight into operation of the convection zone powered by helium burning during the flash. The hydrodynamic evolution is followed on a computational grid in spherical coordinates using our new version of the multi-dimensional hydrodynamic code HERAKLES, which is based on a direct Eulerian implementation of the piecewise parabolic method.

Spectral analysis by means of Non-LTE model-atmosphere techniques has arrived at a high level of sophistication: fully line-blanketed model atmospheres which consider opacities of all elements from H to Ni allow the reliable determination of photospheric parameters of hot, compact stars. Such models provide a crucial test of stellar evolutionary theory: recent abundance determinations of trace elements like, e.g., F, Ne, Mg, P, S, Ar, Fe, and Ni are suited to investigate on AGB nucleosynthesis. E.g., the strong Fe depletion found in hydrogen-deficient post-AGB stars is a clear indication of an efficient s-process on the AGB where Fe is transformed into Ni or even heavier trans iron-group elements. We present results of recent spectral analyses based on high-resolution UV observations of hot stars.

New 2D dynamical models for the winds of AGB stars are presented which include hydrodynamics with radiation pressure on dust, equilibrium chemistry, time-dependent dust formation theory, and coupled frequency-dependent Monte Carlo radiative transfer. The simulations reveal a much more complicated picture of the dust formation and wind acceleration as compared to 1D spherical wind models. Triggered by non-spherical pulsations or large-scale convective motions, dust forms event-like in the cooler regions above the stellar surface which are temporarily less illuminated, followed by the radial ejection of dust arcs and clumps. These simulations can possibly explain recent high angular resolution interferometric IR observations of red giants, which show an often non-symmetric and highly time-variable innermost dust formation and wind acceleration zone. The dependence of the mass-loss rates on stellar parameters is less threshold-like as used from 1D models, and therefore, it seems quite possible that the phenomenon of dust-driven winds may occur also in less evolved red giants.

We have calculated a set of low-mass (0.85 M⊙ ≤ M ≤ 3.0 M⊙) zero metallicity and extremely metal-poor (−6.5 ≤ [Fe/H] ≤ −3.0) stellar models, including nucleosynthetic yields for 74 species. As far as we are aware these are the first detailed yields in the mass and metallicity range considered. Due to the difficulty in modelling such stars the yields naturally contain numerous uncertainties, and thus present interesting challenges for future stellar modelling. We briefly present some results in the context of the Galactic Halo star observations, and also discuss qualitatively some of the uncertainties in the modelling. We conclude by suggesting that much work is still necessary in this research area. For example, multidimensional fluid dynamics models are needed to simulate the violent proton ingestion events that occur during the core He flash and early TPAGB, observations and theory of mass loss at low metallicities are needed, the effects of reaction rate uncertainties need to be quantified, and low temperature opacities variable in carbon (and nitrogen) need to be included in the models.