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.     

Sensitivity in the models of massive stars

Two related problems are discussed in this article: The width of the Main-Sequence of massive stars and sensitivity peatures introduced into the evolutionary tracks of massive stars by mass loss and core-overshooting. It is suggested that core-overshooting may not necessarily be implied by the observations of the width of the Main-Sequence band. It is also noted that models evolved with both mass loss and/or core-overshooting reveal the presence of a large and unexplained expansion of the stellar models under certain conditions. This sensitivity feature would seem to be a fundamental feature inherent to the structure of massive stars.     

Parametrization of single and binary stars

Stellar masses and ages are not directly observable parameters, and the methods used to determine them are based on the calibrating relations. In particular, the mass–luminosity relation, based on the masses of less than 200 well-studied binaries, is virtually the only way to estimate the mass of single stars. Thus, the development of methods for estimating stellar masses with accuracy comparable to direct methods is a problem of vital importance.
Here, we describe a method for estimating stellar masses and ages, which is based on the geometric similarity of evolutionary tracks for the stars at the same evolutionary stage in the Hertzsprung–Russell (HR) diagram. To examine the proposed approach, it has been applied to various test data sets. Application of the method, using synthetic stellar spectra Basel Stellar Library (of theoretical spectra; BaSeL), demonstrates that it allows determination of masses and ages of stars with a predictable distribution of uncertainties.
This statistical approach allows us to demonstrate the viability of the method using it on the set of double-lined eclipsing binaries with intermediate-mass and low-mass components which allows us to compare calculated characteristics with observational ones. As a result, the uncertainties of the stellar masses estimated with the proposed method are comparable with the accuracy of ones obtained from direct observations. This allows us to recommend the method for mass estimates of masses of single stars by the localization in the HR diagram.
As for the ages, the estimates for intermediate-mass stars are more reliable, while those obtained for low-mass stars are very uncertain, due both to slower movement of these stars in the HR diagram with age at stages close to the main sequence and to certain disagreements between theoretical models for this mass range.     

Cosmological origin of the lowest metallicity halo stars

We explore the predictions of the standard hierarchical clustering scenario of galaxy formation, regarding the numbers and metallicities of PopIII stars that are likely to be found within our Galaxy today. By PopIII we refer to stars formed at large redshift ( z >4), with low metallicities ([ Z /Z_⊙]<−2.5) and in small systems (total mass ≲ 2×10⁸ M_⊙) that are extremely sensitive to stellar feedback, and which through a prescribed merging history end up becoming part of the Milky Way today. An analytic, extended Press–Schechter formalism is used to obtain the mass functions of haloes which will host PopIII stars at a given redshift, and which will end up in Milky Way sized systems today. Each of these is modelled as a mini-galaxy, with a detailed treatment of the dark halo structure, angular momentum distribution, final gas temperature and disc instabilities, all of which determine the fraction of the baryons that are subject to star formation. The use of new primordial metallicity stellar evolutionary models allows us to trace the history of the stars formed, and give accurate estimates of their expected numbers today and their location in L /L_⊙ versus T /K Hertzsprung–Russell (HR) diagrams. A first comparison with observational data suggests that the initial mass function (IMF) of the first stars was increasingly high-mass weighted towards high redshifts, levelling off at z ≳9 at a characteristic stellar mass scale m _s=10–15 M_⊙.     

Evidence of recent changes in the local Galactic IMF of stars and substars

This paper calculates the stellar–substellar initial mass function (IMF) based on data from low-luminosity stars and substars. We find the mass spectrum for the stars and substars less than 10 million years in age, and we estimate the low-mass part of the stellar–substellar IMF for 10 million years ago.     

The influence of multiple stars on the high-mass stellar initial mass function and age dating of young massive star clusters

The study of young stellar populations has revealed that most stars are in binary or higher order multiple systems. In this study, the influence on the stellar initial mass function (IMF) of large quantities of unresolved multiple massive stars is investigated by taking into account the stellar evolution and photometrically determined system masses. The models, where initial masses are derived from the luminosity and colour of unresolved multiple systems, show that even under extreme circumstances (100 per cent binaries or higher order multiples), the difference between the power-law index of the mass function (MF) of all stars and the observed MF is small (≲0.1). Thus, if the observed IMF has the Salpeter index  α= 2.35  , then the true stellar IMF has an index not flatter than  α= 2.25  . Additionally, unresolved multiple systems may hide between 15 and 60 per cent of the underlying true mass of a star cluster. While already a known result, it is important to point out that the presence of a large number of unresolved binaries amongst pre-main-sequence stars induces a significant spread in the measured ages of these stars even if there is none. Also, lower mass stars in a single-age binary-rich cluster appear older than the massive stars by about 0.6 Myr.     

On the formation of massive stars

We present a model for the formation of massive ( M ≳10 M⊙) stars through accretion-induced collisions in the cores of embedded dense stellar clusters. This model circumvents the problem of accreting on to a star whose luminosity is sufficient to reverse the infall of gas. Instead, the central core of the cluster accretes from the surrounding gas, thereby decreasing its radius until collisions between individual components become sufficient. These components are, in general, intermediate-mass stars that have formed through accretion on to low-mass protostars. Once a sufficiently massive star has formed to expel the remaining gas, the cluster expands in accordance with this loss of mass, halting further collisions. This process implies a critical stellar density for the formation of massive stars, and a high rate of binaries formed by tidal capture.     

The key role of massive stars in Oort cloud comet dynamics

The effects of a sample of 1300 individual stellar encounters spanning a wide range of parameter values (mass, velocity and encounter distance) are investigated. Power law fits for the number of injected comets demonstrate the long range effect of massive stars, whereas light stars affect comets mainly along their tracks. Similarly, we show that the efficiency of a star to fill the phase space region of the Oort cloud where the Galactic tides are able to inject comets into the observable region - the so-called “tidally active zone” (TAZ) - is also strongly dependent on the stellar mass. Power laws similar to those for direct injection are obtained for the efficiency of stars to fill the TAZ. This filling of the tidally active zone is crucial for the long term flux of comets from the Oort cloud. Based on long-term Monte Carlo simulations using a constant Galactic tide and a constant flux of stellar encounters, but neglecting the detailed effects of planetary perturbations, we show that this flux essentially results from a two step mechanism: (i) the stellar injection of comets into the TAZ; and (ii) the tidal injection of TAZ comets into the loss cone. We find that single massive stars are able to induce “comet drizzles” - corresponding to an increase of the cometary flux of about 40% - which may last for more than 100 Myr by filling the TAZ to a higher degree than normal. It appears that the stars involved in this process are the same that cause comet showers.     

Probability distribution of terrestrial planets in habitable zones around host stars

With more and more exoplanets being detected, it is paid closer attention to whether there are lives outside solar system. We try to obtain habitable zones and the probability distribution of terrestrial planets in habitable zones around host stars. Using Eggleton’s code, we calculate the evolution of stars with masses less than 4.00 M _⊙. We also use the fitting formulae of stellar luminosity and radius, the boundary flux of habitable zones, the distribution of semimajor axis and mass of planets and the initial mass function of stars. We obtain the luminosity and radius of stars with masses from 0.08 to 4.00 M _⊙, and calculate the habitable zones of host stars, affected by stellar effective temperature. We achieve the probability distribution of terrestrial planets in habitable zones around host stars. We also calculate that the number of terrestrial planets in habitable zones of host stars is 45.5 billion, and the number of terrestrial planets in habitable zones around K type stars is the most, in the Milky Way.     

Presupernova structure of massive stars

Issues concerning the structure and evolution of core collapse progenitor stars, and stellar evolution in general, are discussed with an emphasis on interior evolution. We discuss some recent results that address quantifying the uncertainties inherent in modern stellar evolution calculations, and we describe a research effort aimed at investigating the transport and mixing processes associated with stellar turbulence, which is arguably the greatest source of uncertainty in supernova progenitor structure, besides mass loss, at the time of core collapse. We highlight the important role played by precision observations of stellar parameters in constraining theoretical models, as well as the physical insight that can be garnered from three-dimensional hydrodynamic simulation.     

Estimates of the radii,masses, and luminosities of LAMOST stars

Based on the spectral observations of the LAMOST (DR2) survey, the radii, masses, and luminosities of 700 481 stars were estimated. These stars belong to spectral types A, F, G, and K, and have metallicities between ?0.845 and 0.0. To determine the properties of the stars, we used up-to-date models of the stellar interior structure, computed with account for the stellar evolution rate and the initial mass function. The use of evolutionary estimates for two types of stars—with and without rotation—allowed us to account for the uncertainty associated with the lack of data on the rotation velocity of the stars under consideration. The obtained stellar radii, together with the photometric estimates of interstellar extinction and angular diameters can be used to study the dependence of interstellar extinction on distance as well as to estimate the stellar distances.     

The fractions of post-binary-interaction stars and evolved blue straggler stars on the red giant branch of globular clusters

The red giant branch(RGB) of globular clusters(GCs) is home to some exotic stars,which may provide clues on the formation of multiple stellar populations in GCs.It is well known that binary interactions are responsible for many exotic stars.Thus,it is important to understand what fraction of stars on the RGB of GCs is the result of binary interactions.In this paper,we performed a binary population synthesis study to track the number of post-binary-interaction(post-BI) stars that appear on the RGB,with particular emphasis on the evolved blue straggler stars(E-BSSs).Assuming an initial binary fraction of nearly 50%,we find that about half of the objects on the RGB(called giants) underwent the binary interactions,and that E-BSSs account for around 10% of the giants in our standard simulation.We also compare the properties of post-BI giants that evolved from different channels.We find that the initial orbital period and mass ratio distributions significantly affect the fraction of post-BI giants.Our results imply that the non-standard stars from binary interactions provide a non-negligible contribution to the RGB stars in GCs,which should be considered in future investigations of the origin of multiple stellar populations.     

Massive stars

We describe the present state of massive star research seen from the viewpoint of stellar evolution, with special emphasis on close binaries. Statistics of massive close binaries are reasonably complete for the Solar neighbourhood. We defend the thesis that within our knowledge, many scientific results where the effects of binaries are not included, have an academic value, but may be far from reality. In chapter I, we summarize general observations of massive stars where we focus on the HR diagram, stellar wind mass loss rates, the stellar surface chemistry, rotation, circumstellar environments, supernovae. Close binaries can not be studied separately from single stars and vice versa. First, the evolution of single stars is discussed (chapter I). We refer to new calculations with updated stellar wind mass loss rate formalisms and conclusions are proposed resulting from a comparison with representative observations. Massive binaries are considered in chapter II. Basic processes are briefly described, i.e. the Roche lobe overflow and mass transfer, the common envelope process, the spiral-in process in binaries with extreme mass ratio, the effects of mass accretion and the merging process, the implications of the (asymmetric) supernova explosion of one of the components on the orbital parameters of the binary. Evolutionary computations of interacting close binaries are discussed and general conclusions are drawn. The enormous amount of observational data of massive binaries is summarized. We separately consider the non-evolved and evolved systems. The latter class includes the semi-detached and contact binaries, the WR binaries, the X-ray binaries, the runaways, the single and binary pulsars. A general comparison between theoretical evolution and observations is combined with a discussion of specially interesting binaries: the evolved binaries HD 163181, HD 12323, HD 14633, HD 193516, HD 25638, HD 209481, Per and Sgr; the WR+OB binary V444 Cyg; the high mass X-ray binaries Vela X-1, Wray 977, Cyg X-1; the low mass X-ray binaries Her X-1 and those with a black hole candidate; the runaway Pup, the WR+compact companion candidates Cyg X-3, HD 50896 and HD 197406. We finally propose an overall evolutionary model of massive close binaries as a function of primary mass, mass ratio and orbital period. Chapter III deals with massive star population synthesis with a realistic population of binaries. We discuss the massive close binary frequency, mass ratio and period distribution, the observations that allow to constrain possible asymmetries during the supernova explosion of a massive star. We focuss on the comparison between observed star numbers (as a function of metallicity) and theoretically predicted numbers of stellar populations in regions of continuous star formation and in starburst regions. Special attention is given to the O-type star/WR star/red supergiant star population, the pulsar and binary pulsar population, the supernova rates. Received 17 July 1998     

Stellar winds from hot low-mass stars

Stellar winds appear as a persistent feature of hot stars, irrespective of their wide range of different luminosities, masses, and chemical composition. Among the massive stars, the Wolf–Rayet types show considerably stronger mass loss than the O stars. Among hot low-mass stars, stellar winds are seen at central stars of planetary nebulae, where again the hydrogen-deficient stars show much stronger winds than those central stars with “normal” composition. We also studied mass-loss from a few extreme helium stars and sdOs. Their mass-loss rate roughly follows the same proportionality with luminosity to the power 1.5 as the massive O stars. This relation roughly marks a lower limit for the mass loss from hot stars of all kinds, and provides evidence that radiation pressure on spectral lines is the basic mechanism at work. For certain classes of stars the mass-loss rates lie significantly above this relation, for reasons that are not yet fully understood. Mass loss from low-mass stars may affect their evolution, by reducing the envelope mass, and can easily prevent diffusion from establishing atmospheric abundance patterns. In close binary systems, their winds can feed the accretion onto a companion.     

First stars. II. Evolution with mass loss

The first stars are assumed to be predominantly massive. Although, due to the low initial abundances of heavy elements the line-driven stellar winds are supposed to be inefficient in the first stars, these stars may loose a significant amount of their initial mass by other mechanisms.     

X-ray spectroscopy of stars

Non-degenerate stars of essentially all spectral classes are soft X-ray sources. Their X-ray spectra have been important in constraining physical processes that heat plasma in stellar environments to temperatures exceeding one million degrees. Low-mass stars on the cooler part of the main sequence and their pre-main sequence predecessors define the dominant stellar population in the galaxy by number. Their X-ray spectra are reminiscent, in the broadest sense, of X-ray spectra from the solar corona. The Sun itself as a typical example of a main-sequence cool star has been a pivotal testbed for physical models to be applied to cool stars. X-ray emission from cool stars is indeed ascribed to magnetically trapped hot gas analogous to the solar coronal plasma, although plasma parameters such as temperature, density, and element abundances vary widely. Coronal structure, its thermal stratification and geometric extent can also be interpreted based on various spectral diagnostics. New features have been identified in pre-main sequence stars; some of these may be related to accretion shocks on the stellar surface, fluorescence on circumstellar disks due to X-ray irradiation, or shock heating in stellar outflows. Massive, hot stars clearly dominate the interaction with the galactic interstellar medium: they are the main sources of ionizing radiation, mechanical energy and chemical enrichment in galaxies. High-energy emission permits to probe some of the most important processes at work in these stars, and put constraints on their most peculiar feature: the stellar wind. Medium and high- resolution spectroscopy have shed new light on these objects as well. Here, we review recent advances in our understanding of cool and hot stars through the study of X-ray spectra, in particular high-resolution spectra now available from XMM-Newton and Chandra. We address issues related to coronal structure, flares, the composition of coronal plasma, X-ray production in accretion streams and outflows, X-rays from single OB-type stars, massive binaries, magnetic hot objects and evolved WR stars.     

Circumstellar dust and variability of carbon stars

A sample of 35 variable carbon stars has been considered. The stellar temperatures, radii, absolute luminosities, masses, and mass loss rates have been estimated. Then the spherical circumstellar dust shells around the analysed stars are discussed and the differences in the infrared properties between semi-regular, irregular, and long-period variables are indicated.     

Spectral classification of stars based on LAMOST spectra

In this work, we select spectra of stars with high signal-to-noise ratio from LAMOST data and map their MK classes to the spectral features. The equivalent widths of prominent spectral lines, which play a similar role as multi-color photometry, form a clean stellar locus well ordered by MK classes. The advantage of the stellar locus in line indices is that it gives a natural and continuous classification of stars consistent with either broadly used MK classes or stellar astrophysical parameters. We also employ an SVM-based classification algorithm to assign MK classes to LAMOST stellar spectra. We find that the completenesses of the classifications are up to 90% for A and G type stars, but they are down to about 50% for OB and K type stars. About 40% of the OB and K type stars are mis-classified as A and G type stars,respectively. This is likely due to the difference in the spectral features between late B type and early A type stars or between late G and early K type stars being very weak. The relatively poor performance of the automatic MK classification with SVM suggests that the direct use of line indices to classify stars is likely a more preferable choice.     

Dark stars at the Galactic Centre – the main sequence

In regions of very high dark matter density such as the Galactic Centre, the capture and annihilation of WIMP dark matter by stars has the potential to significantly alter their evolution. We describe the dark stellar evolution code D ark S tars , and present a series of detailed grids of WIMP-influenced stellar models for main-sequence stars. We describe the changes in stellar structure and main-sequence evolution which occur as a function of the rate of energy injection by WIMPs, for masses of  0.3–2.0 M_⊙  and metallicities   Z = 0.0003–0.02  . We show what rates of energy injection can be obtained using realistic orbital parameters for stars at the Galactic Centre, including detailed consideration of the velocity and density profiles of dark matter. Capture and annihilation rates are strongly boosted when stars follow elliptical rather than circular orbits. If there is a spike of dark matter induced by the supermassive black hole at the Galactic Centre, single solar mass stars following orbits with periods as long as 50 yr and eccentricities as low as 0.9 could be significantly affected. Binary systems with similar periods about the Galactic Centre could be affected on even less eccentric orbits. The most striking observational effect of this scenario would be the existence of a binary consisting of a low-mass protostar and a higher mass evolved star. The observation of low-mass stars and/or binaries on such orbits would either provide a detection of WIMP dark matter, or place stringent limits on the combination of the WIMP mass, spin-dependent nuclear-scattering cross-section, halo density and velocity distribution near the Galactic Centre. In some cases, the derived limits on the WIMP mass and spin-dependent nuclear-scattering cross-section would be of comparable sensitivity to current direct-detection experiments.     

Mass loss of stars on the asymptotic giant branch

As low- and intermediate-mass stars reach the asymptotic giant branch (AGB), they have developed into intriguing and complex objects that are major players in the cosmic gas/dust cycle. At this stage, their appearance and evolution are strongly affected by a range of dynamical processes. Large-scale convective flows bring newly-formed chemical elements to the stellar surface and, together with pulsations, they trigger shock waves in the extended stellar atmosphere. There, massive outflows of gas and dust have their origin, which enrich the interstellar medium and, eventually, lead to a transformation of the cool luminous giants into white dwarfs. Dust grains forming in the upper atmospheric layers play a critical role in the wind acceleration process, by scattering and absorbing stellar photons and transferring their outward-directed momentum to the surrounding gas through collisions. Recent progress in high-angular-resolution instrumentation, from the visual to the radio regime, is leading to valuable new insights into the complex dynamical atmospheres of AGB stars and their wind-forming regions. Observations are revealing asymmetries and inhomogeneities in the photospheric and dust-forming layers which vary on time-scales of months, as well as more long-lived large-scale structures in the circumstellar envelopes. High-angular-resolution observations indicate at what distances from the stars dust condensation occurs, and they give information on the chemical composition and sizes of dust grains in the close vicinity of cool giants. These are essential constraints for building realistic models of wind acceleration and developing a predictive theory of mass loss for AGB stars, which is a crucial ingredient of stellar and galactic chemical evolution models. At present, it is still not fully possible to model all these phenomena from first principles, and to predict the mass-loss rate based on fundamental stellar parameters only. However, much progress has been made in recent years, which is described in this review. We complement this by discussing how observations of emission from circumstellar molecules and dust can be used to estimate the characteristics of the mass loss along the AGB, and in different environments. We also briefly touch upon the issue of binarity.