Recent advances in modeling stellar interiors

Advances in stellar interior modeling are being driven by new data from large-scale surveys and high-precision photometric and spectroscopic observations. Here we focus on single stars in normal evolutionary phases; we will not discuss the many advances in modeling star formation, interacting binaries, supernovae, or neutron stars. We review briefly: (1) updates to input physics of stellar models; (2) progress in two and three-dimensional evolution and hydrodynamic models; (3) insights from oscillation data used to infer stellar interior structure and validate model predictions (asteroseismology). We close by highlighting a few outstanding problems, e.g., the driving mechanisms for hybrid γ Dor/δ Sct star pulsations, the cause of giant eruptions seen in luminous blue variables such as η Car and P Cyg, and the solar abundance problem.     

The Eddington Mission

The Eddington mission was given full approval by the European Space Agency on the 23rd May 2002, with launch scheduled for 2007/8. Its science objectives are stellar evolution and asteroseismology, and planet finding. In its current design it consists of 4 × 60 cm folded Schmidt telescopes, each with 6^o × 6^o field of view and its own CCD array camera. Eddington will spend 2 years primarily devoted to asteroseismology with 1–3 months on different target fields monitoring up to 50,000 stars per field, and 3 years continuously on a single field monitoring upwards of 100,000 stars for planet searching. The asteroseismic goal is to be able to detect oscillations frequencies of stars with a precision 0.1–0.3 μHz, to probe their interior structure and the study the physical processes that govern their evolution. This revised version was published online in August 2006 with corrections to the Cover Date.     

Using the seismology of non-magnetic chemically peculiar stars as a probe of dynamical processes in stellar interiors

Chemical composition is a good tracer of the hydrodynamical processes that occur in stars as they often lead to mixing and particle transport. By comparing abundances predicted by models and those observed in stars we can infer some constraints on those mixing processes. As pulsations in the stars are often very sensitive to chemical composition, we can use asteroseismology to probe the internal chemical composition of stars where no direct observations are possible. In this paper I focus on main sequence stars Am, λ Bootis, and HgMn stars and discuss what we can learn of mixing processes in these stars from seismology.     

CLÉS, Code Liégeois d’Évolution Stellaire

CLÉS is an evolution code recently developed to produce stellar models meeting the specific requirements of studies in asteroseismology. It offers the users a lot of choices in the input physics they want in their models and its versatility allows them to tailor the code to their needs and implement easily new features. We describe the features implemented in the current version of the code and the techniques used to solve the equations of stellar structure and evolution. A brief account is given of the use of the program and of a solar calibration realized with it.     

Evolutionary and pulsational properties of white dwarf stars

White dwarf stars are the final evolutionary stage of the vast majority of stars, including our Sun. Since the coolest white dwarfs are very old objects, the present population of white dwarfs contains a wealth of information on the evolution of stars from birth to death, and on the star formation rate throughout the history of our Galaxy. Thus, the study of white dwarfs has potential applications in different fields of astrophysics. In particular, white dwarfs can be used as independent reliable cosmic clocks, and can also provide valuable information about the fundamental parameters of a wide variety of stellar populations, such as our Galaxy and open and globular clusters. In addition, the high densities and temperatures characterizing white dwarfs allow these stars to be used as cosmic laboratories for studying physical processes under extreme conditions that cannot be achieved in terrestrial laboratories. Last but not least, since many white dwarf stars undergo pulsational instabilities, the study of their properties constitutes a powerful tool for applications beyond stellar astrophysics. In particular, white dwarfs can be used to constrain fundamental properties of elementary particles such as axions and neutrinos and to study problems related to the variation of fundamental constants. These potential applications of white dwarfs have led to renewed interest in the calculation of very detailed evolutionary and pulsational models for these stars. In this work, we review the essentials of the physics of white dwarf stars. We enumerate the reasons that make these stars excellent chronometers, and we describe why white dwarfs provide tools for a wide variety of applications. Special emphasis is placed on the physical processes that lead to the formation of white dwarfs as well as on the different energy sources and processes responsible for chemical abundance changes that occur along their evolution. Moreover, in the course of their lives, white dwarfs cross different pulsational instability strips. The existence of these instability strips provides astronomers with a unique opportunity to peer into their internal structure that would otherwise remain hidden from observers. We will show that this allows one to measure stellar masses with unprecedented precision and to infer their envelope thicknesses, to probe the core chemical stratification, and to detect rotation rates and magnetic fields. Consequently, in this work, we also review the pulsational properties of white dwarfs and the most recent applications of white dwarf asteroseismology.     

Asteroseismology: Past, present and future

Asteroseismology studies stars with a wide variety of interior and surface conditions. For two decades asteroseismic techniques have been applied to many pulsating stars across the HR diagram. Asteroseismology is now a booming field of research with stunning new discoveries; I highlight a personal selection of these in this review, many of which are discussed in more detail elsewhere in these proceedings. For many years the Nainital-Cape Survey for northern roAp stars has been running at ARIES, so I emphasise new spectroscopic results for roAp stars and point out the outstanding prospects for the planned ARIES 3-m telescope at Devastai. High precision spectroscopy has revolutionised the asteroseismic study of some types of stars — particularly solar-like oscillators and roAp stars — while photometry is still the best way to study the frequency spectra that are the basic data of asteroseismology. New telescopes, new photometers and space missions are revolutionising asteroseismic photometry. In addition to the ground-based potential of asteroseismic spectroscopy, India has the knowledge and capability for space-based asteroseismic photometry. The future for asteroseismology is bright indeed, especially for Indian astronomers.     

Lessons for asteroseismology from white dwarf stars

The interpretation of pulsation data for sun-like stars is currently facing challenges quite similar to those faced by white dwarf modelers ten years ago. The observational requirements for uninterrupted long-term monitoring are beginning to be satisfied by successful multi-site campaigns and dedicated satellite missions. But exploration of the most important physical parameters in theoretical models has been fairly limited, making it difficult to establish a detailed best-fit model for a particular set of oscillation frequencies. I review the past development and the current state of white dwarf asteroseismology, with an emphasis on what this can tell us about the road to success for asteroseismology of other types of stars.     

Sounding stellar cycles with Kepler – I. Strategy for selecting targets

The long-term monitoring and high photometric precision of the Kepler satellite will provide a unique opportunity to sound the stellar cycles of many solar-type stars using asteroseismology. This can be achieved by studying periodic changes in the amplitudes and frequencies of the oscillation modes observed in these stars. By comparing these measurements with conventional ground-based chromospheric activity indices, we can improve our understanding of the relationship between chromospheric changes and those taking place deep in the interior throughout the stellar activity cycle. In addition, asteroseismic measurements of the convection zone depth and differential rotation may help us determine whether stellar cycles are driven at the top or at the base of the convection zone. In this paper, we analyse the precision that will be possible using Kepler to measure stellar cycles, convection zone depths and differential rotation. Based on this analysis, we describe a strategy for selecting specific targets to be observed by the Kepler Asteroseismic Investigation for the full length of the mission, to optimize their suitability for probing stellar cycles in a wide variety of solar-type stars.     

Asteroseismic Determination of sdB Stars Fundamental Parameters

Recent observational efforts and theoretical breakthroughs have encouraged the development of detailed asteroseismic analyses of rapidly oscillating sdB stars (the so-called EC14026 stars). This led to the first seismic determinations of the fundamental parameters that define the structure of EHB stars. We briefly review the current status of these analyses, discussing some of the properties of acoustic modes in EHB models that affect the asteroseismology of these stars. We then recall the basic ideas behind the method we developed in an attempt to objectively extract, from models, asteroseismic solutions suitable to any given sdB pulsator. A preliminary application of this method to the pulsating sdB star Feige 48 is also presented.     

星族等时综合模型的现状

总结了星族综合模型的两个要素：处于根本地位的恒星演化计算，以及把理论赫罗图转化为可观测量的光谱定标。当前恒星模型中的不确定性来自于输入的物理参数；原子数据，对流理论，辐射区的混合和和质量丢失。光谱定标不准是因为尚没有准确的温度测定，准确的分光光度测量，而且光谱库中缺少一些类型的恒星。     

Observations of pulsating Ap stars in South Africa

The rapidly oscillating Ap (roAp) stars currently represent the only main sequence stars other than the Sun which exhibit non-radial acoustic pulsations of high overtone. This makes them excellent subjects for asteroseismology, an approach which promises to yield accurate knowledge of the interior structures of stars. Of the 27 known roAp stars, 24 were discovered in Sutherland despite extensive searches conducted elsewhere. This paper reviews the discovery of the roAp phenomenon and describes the factors that contribute to the high discovery rate for these stars at Sutherland. Two long-term observational projects in progress at Sutherland are discussed,viz. the Cape roAp Star Survey and long-term monitoring of frequency variations in roAp stars.     

A Review to the Studies of Lithium-Rich Giants

Lithium (Li) is one of the most important light elements that was primordially synthesized in the Big Bang Nucleosynthesis (BBN). It is also an element that confused astrophysicists for decades, as its observed abundance often contradicts with the theoretical prediction in many different types of celestial objects. Li-rich giant stars are such objects. Their atmospheres contain anomaly high Li abundance than that expected by the standard stellar evolution model. Although the first Li-rich giant star was discovered almost 40 years ago, their origin is still being debated. With the launch of massive spectroscopic survey program such as the Large Sky Area Multi-Object Fiber Spectroscopy Telescope (LAMOST) survey, the extending of available asteroseismology data from space satellites (such as Kepler), and the developments of data-driven techniques, breakthroughs have been archived in the field of Li-rich studies. In this paper, we review the progress that was made during the past four decades, and present our up-to-date understanding to Li-rich giant stars.     

Stellar adiabatic mass loss model and applications

Roche-lobe overflow and common envelope evolution are very important in binary evolution, which is believed to be the main evolutionary channel to hot subdwarf stars. The details of these processes are difficult to model, but adiabatic expansion provides an excellent approximation to the structure of a donor star undergoing dynamical time scale mass transfer. We can use this model to study the responses of stars of various masses and evolutionary stages as potential donor stars, with the urgent goal of obtaining more accurate stability criteria for dynamical mass transfer in binary population synthesis studies. As examples, we describe here several models with the initial masses equal to 1 M _⊙ and 10 M _⊙, and identify potential limitations to the use of our results for giant-branch stars.     

Wolf-Rayet stars

This paper reviews the current status of knowledge regarding the basic physical and chemical properties of Wolf-Rayet stars; their overall mass loss and stellar wind characteristics and current ideas about their evolutionary status. WR stars are believed to be the evolved descendents of massive O-type stars, in which extensive mass loss reveals successive stages of nuclear processed material: WN stars the products of interior CNO-cycle hydrogen burning, and WC and WO stars the products of interior helium burning. Recent stellar evolution models, particularly those incorporating internal mixing, predict results which are in good accord with the different chemical compositions observationally inferred for WN, WC and WO stars. WR stars exhibit the highest levels of mass loss amongst earlytype stars: mass loss rates, typically, lie in the range [1–10]×10⁻⁵ M _⊙yr⁻¹. Radiation pressure-driven winds incorporating multi-scattering in high ionisation-stratified winds may cause these levels, but additional mechanisms may also be needed.     

Spectral analyses of WR-type central stars of planetary nebulae

So far, the evolution of post-AGB stars is not fully understood. In particular the formation of hydrogen-deficient and hydrogen-free Central Stars of Planetary Nebulae (CSPN) is unsettled. New evolution models, which allow for the consistent treatment of the physics of late thermalpulses, promise new insights to the formation of these stars. In this paper we summarize the results of non-LTE analyses of CSPN with wind. By comparing these results with the predictions of the new evolutionmodels, open questions concerning the evolution of the stars might be answered. In addition we discuss the driving mechanism of the winds of Wolf-Rayet CSPN. New models, which account for millions of iron lines, support the assumptions that these winds are driven by radiation.     

Ages of globular clusters. II

Evolutionary model sequences for (X, Z)=(0.7,4×10^–3) are constructed by using the same input physics and programming code as those of Saioet al. (1977). From these results the ages of globular clusters are estimated under the assumption of constant helium abundance (Y=0.3). The results suggest that there is a correlation between age and metal abundance for the globular clusters and that metal enrichment in the Galaxy slowly proceeded in several billion years from the value of the extreme Population II stars to that of the Population I stars. Comparison with some models of chemical evolution of galaxies is briefly made.     

Millisecond radio pulsars with known masses: Parameter values and equation of state models

The recent fast growth of a population of millisecond pulsars with precisely measured mass provides an excellent opportunity to characterize these compact stars at an unprecedented level. This is because the stellar parameter values can be accurately computed for known mass and spin rate and an assumed equation of state (EoS) model. For each of the 16 such pulsars and for a set of EoS models from nucleonic, hyperonic, strange quark matter and hybrid classes, we numerically compute fast spinning stable stellar parameter values considering the full effect of general relativity. This first detailed catalogue of the computed parameter values of observed millisecond pulsars provides a testbed to probe the physics of compact stars, including their formation, evolution and EoS. We estimate uncertainties on these computed values from the uncertainty of the measured mass, which could be useful to quantitatively constrain EoS models. We note that the largest value of the central density ρ_c in our catalogue is ∼5.8 times the nuclear saturation density ρ_sat, which is much less than the expected maximum value 13ρ_sat. We argue that the ρ_c-values of at most a small fraction of compact stars could be much larger than 5.8ρ_sat. Besides, we find that the constraints on EoS models from accurate radius measurements could be significantly biased for some of our pulsars, if stellar spinning configurations are not used to compute the theoretical radius values.     

The lithium-rotation correlation for WTTS in Taurus–Auriga

Surface lithium abundance and rotation velocity can serve as powerful and mutually complementary diagnostics of interior structure of stars. So far, the processes responsible for the lithium depletion during pre-main sequence evolution are still poorly understood. We investigate whether a correlation exists between equivalent widths of Li (EW(Li)) and rotation period (P_rot) for weak-line T Tauri stars (WTTSs). We find that rapidly rotating stars have lower EW(Li) and the fast burning of Li begins at the phase when star’s P_rot evolves towards 3 days among 0.9M_⊙ to 1.4M_⊙ WTTSs in Taurus–Auriga. Our results support the conclusion by Piau and Turch-Chiéze about a model for lithium depletion with age of the star and by Bouvier et al. in relation to rotation evolution. The turn over of the curve for the correlation between EW(Li) and P_rot is at the phase of zero-age main sequence (ZAMS). The EW(Li) decreases with decreasing P_rot before the star reaches the ZAMS, while it decreases with increasing P_rot (decreasing rotation velocity) for young low-mass main sequence stars. This result could be explained as an age effect of Li depletion and the rapid rotation does not inhibit Li destruction among low-mass PMS stars.     

The effect of turbulent mixing on the g‐mode spectrum of MS stars

Understanding transport processes inside stars is one of the main goals of asteroseismology. Chemical turbulent mixing can affect the internal distribution of μ near the energy generating core, having an effect on the evolutionary tracks similar to that of overshooting. This mixing leads to a smoother chemical composition profile near the edge of the convective core, which is reflected in the behavior of the buoyancy frequency and, therefore, in the frequencies of gravity modes. We describe the effects of convective overshooting and turbulent mixing on the frequencies of gravity modes in B‐type main sequence stars. In particular, the cases of p‐g mixed modes in β Cep stars and high‐order modes in SPBs are considered. (© 2008 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)