On the effect of overshooting as predicted by the modelling of the pre-main-sequence evolution of a 2 M⊙ star

We discuss the effects of convective overshooting in the pre-main-sequence (PMS) evolution of intermediate-mass stars, by analysing in detail the early evolution towards the main sequence of a  2 M_⊙  stellar model. These effects can be extremely important in the end of the PMS, when the abundances in CNO elements approach the equilibrium in the centre. We provide a possible physical explanation on why a moderate amount of overshooting produces, as the star approaches the zero-age main-sequence, an extra loop in the evolutionary tracks on the Hertzsprung–Russell diagram.
An interesting feature is that there is a very well defined amount of overshooting (for a given stellar mass and chemical composition) beyond which a loop is produced. For smaller amounts of overshooting such a loop does not take place and the evolutionary tracks are similar to those found in the literature. The amount of overshooting needed to produce the loop decreases with stellar mass.
We discuss the underlining physical reasons for the behaviour predicted by the evolution models and argue that it provides a crucial observational test for convective overshooting in the core of intermediate-mass stars.     

Accretion in stellar clusters and the initial mass function

We present a simple physical mechanism that can account for the observed stellar mass spectrum for masses M ∗≳0.5 M_⊙ . The model depends solely on the competitive accretion that occurs in stellar clusters where each star's accretion rate depends on the local gas density and the square of the accretion radius. In a stellar cluster, there are two different regimes depending on whether the gas or the stars dominate the gravitational potential. When the cluster is dominated by cold gas, the accretion radius is given by a tidal-lobe radius. This occurs as the cluster collapses towards a ρ  ∝  R ⁻² distribution. Accretion in this regime results in a mass spectrum with an asymptotic limit of γ =−3/2 (where Salpeter is γ =−2.35) . Once the stars dominate the potential and are virialized, which occurs first in the cluster core, the accretion radius is the Bondi–Hoyle radius. The resultant mass spectrum has an asymptotic limit of γ =−2 with slightly steeper slopes ( γ ≈−2.5) if the stars are already mass-segregated. Simulations of accretion on to clusters containing 1000 stars show that, as expected, the low-mass stars accumulate the majority of their masses during the gas-dominated phase whereas the high-mass stars accumulate the majority of their masses during the stellar-dominated phase. This results in a mass spectrum with a relatively shallow γ ≈3/2 power law for low-mass stars and a steeper power law for high-mass stars −2.5≲ γ ≤−2 . This competitive accretion model also results in a mass-segregated cluster.     

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.     

中等质量恒星在赫罗图中由E-AGB星进入TP-AGB星的分界点

通过对3～10 M_☉恒星在赫罗图上演化轨迹的研究,分析恒星内部氦壳层燃烧峰值处能量、密度、温度、氦壳层表面光度与恒星表面光度比及恒星半径的变化,给出了中等质量恒星由早期AGB星演化至热脉冲AGB星阶段在赫罗图上的分界点,与119颗碳星的观测结果吻合得相当好.同时提出:在恒星演化至该分界点之后,其星风物质损失公式可能需要引入一个与表面光度无关的量以主导超星风的形成.在此基础上,通过对考虑湍流压效应下5 M_☉恒星的结构和演化及星风物质损失率的分析,发现湍流压在热脉冲AGB星阶段对星风物质损失影响较大,从而使得热脉冲AGB星的湍流压不可忽略,进而提出了影响热脉冲AGB星星风物质损失的可能的物理因素.     

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.     

The distance to the Orion Nebula cluster

The distance to the Orion Nebula cluster (ONC) is estimated using the rotational properties of its low-mass pre-main-sequence (PMS) stars. Rotation periods, projected equatorial velocities and distance-dependent radius estimates are used to form an observational sin  i distribution (where i is the axial inclination), which is modelled to obtain the distance estimate. A distance of  440 ± 34 pc  is found from a sample of 74 PMS stars with spectral types between G6 and M2, but this falls to  392 ± 32 pc  when PMS stars with accretion discs are excluded on the basis of their near-infrared excess. Since the radii of accreting stars are more uncertain and probably systematically underestimated, then this closer distance is preferred. The quoted uncertainties include statistical errors and uncertainties due to a number of systematic effects including binarity and inclination bias. This method is geometric and independent of stellar evolution models, though does rely on the assumption of random axial orientations and the Cohen & Kuhi effective temperature scale for PMS stars. The new distance is consistent with, although lower and more precise, than most previous ONC distance estimates. A closer ONC distance implies smaller luminosities and an increased age based on the positions of PMS stars in the Hertzsprung–Russell diagram.     

Matching the frequency spectrum of pre-main sequence stars by means of standard and rotating models

We applied the aton evolutionary code to the computation of detailed grids of standard (non-rotating) and rotating pre-main sequence (PMS) models and computed their adiabatic oscillation spectra, with the aim of exploring the seismic properties of young stars. As, until now, only a few frequencies have been determined for ∼40 PMS stars, the way of approaching the interpretation of the oscillations is not unique. We adopt a method similar to the matching mode method by Guenther and Brown making use, when necessary, also of our rotating evolutionary code to compute the models for PMS stars. The method is described by a preliminary application to the frequency spectrum of two PMS stars (85 and 278) in the young open cluster NGC 6530. For the Star 85, we confirm with self-consistent rotating models, previous interpretation of the data, attributing three close frequencies to the mode   n = 4, l = 1  and   m = 0  , +1 and −1. For the Star 278, we find a different fit for the frequencies, corresponding to a model within the original error box of the star, and dispute the possibility that this star has a T _eff much cooler that the red boundary of the radial instability strip.     

Evolutionary stellar population synthesis at high spectral resolution: optical wavelengths

We present the single stellar population (SSP) synthesis results of our new synthetic stellar atmosphere models library with a spectral sampling of 0.3 Å, covering the wavelength range from 3000 to 7000 Å for a wide range of metallicities (twice solar, solar, half solar and 1/10 solar). The stellar library is composed of 1650 spectra computed with the latest improvements in stellar atmospheres. In particular, it incorporates non-local thermodynamic equilibrium (LTE) line-blanketed models for hot  ( T _eff≥ 27 500 K)  , and LTE line-blanketed models (Phoenix) for cool  (3000 ≤ T _eff≤ 4500 K)  stars. Because of the high spectral resolution of this library, evolutionary synthesis models can be used to predict the strength of numerous weak absorption lines and the evolution of the profiles of the strongest lines over a wide range of ages. The SSP results have been calculated for ages from 1 Myr to 17 Gyr using the stellar evolutionary tracks provided by the Geneva and Padova groups. For young stellar populations, our results have a very detailed coverage of high-temperature stars with similar results for the Padova and Geneva isochrones. For intermediate and old stellar populations, our results, once degraded to a lower resolution, are similar to the ones obtained by other groups (limitations imposed by the stellar evolutionary physics notwidthstanding). The limitations and advantages of our models for the analysis of integrated populations are described. The full set of the stellar library and the evolutionary models are available for retrieval at the websites http://www.iaa.csic.es/~rosa and http://www.iaa.csic.es/~mcs/sed@ , or on request from the first two authors.     

The Galactic hybrid Wolf–Rayet WN 7o/CE + O7V((f)) binary system WR 145

A spectroscopic study of the binary Wolf–Rayet (WR)+O system WR 145 is performed, in order to determine the radial velocity orbits of the individual stars, the angle of orbital inclination and the stellar masses. The emission and absorption components are separated from the original spectra, allowing us to confirm the spectral classification WN 7o/CE of the hybrid WR component and to derive a spectral classification O7V((f)) for the O star. A study of the wind-collision properties is performed. Fitting the radial velocity and full width at half-maximum of the excess emission with Lührs' model results in an inclination angle of   i = 63°  , leading to estimates of the stellar masses:   M _WR= 18 M_⊙  and   M _O= 31 M_⊙  . Both of these masses are compatible with those of other stars of similar types.     

The Demarcation Point from E-AGB Stars to TP-AGB Stars in HR Diagram for Medium-mass Stars

Via a study of the evolutionary tracks of 3∼10 M stars on the Hertzsprung-Russell diagram, the variations of the energy, density, temperature at the peak of helium-shell burning, ratio of surface luminosity of helium shell to stellar surface luminosity as well as the stellar radius are analyzed. Then the demarcation point of medium-mass stars in the evolution from early AGB stars to thermally pulsing AGB stars on the HR diagram is determined, and for 119 carbon stars our analysis agrees rather well with observation. At the same time the following is suggested. After arriving at this demarcation point in stellar evolution, in the formula of the loss of stellar wind material it is probably needed to introduce a quantity which is not concerned with the surface luminosity, but it dominates the formation of super stellar wind. On this basis and via the analysis of the structure and evolution of 5 M stars as well as the rate of mass loss of stellar wind, it is found that the effect of turbulent pressure on the mass loss of stellar wind in the stage of thermally pulsing AGB stars is rather great, hence the turbulent pressure of thermally pulsing AGB stars cannot be overlooked. Furthermore, the physical factors which possibly affect the matter loss of the stellar winds of thermally pulsing AGB stars are suggested.     

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.     

Composite spectra Paper 15: HD 216572, a triple system containing a short-period, double-lined secondary

We analyse 81 optical spectra of the composite-spectrum binary HD 216572, and show that the primary is a cool giant of type G8 III while the secondary is a double-lined binary consisting of two nearly identical B9 dwarfs in a 1.18-d orbit. The inner system undergoes partial eclipses, whose photometry we model to derive the physical parameters of both secondary stars. The outer system does not eclipse. We isolate the combined spectrum of the secondary by spectral subtraction, and from 48 separate radial-velocity measurements of both secondary components we obtain a triple-lined orbit solution from which we determine the individual masses of all three stars and the inclinations of both the inner and the outer orbits. The period of the outer system is 55 d, which is surprisingly short for a giant star, and our detection of small but non-negligible amounts of variable chromospheric emission in the Ca  ii K line is not unlike that detected in other systems with comparably short periods. The secondary components are in a circular orbit and are rotating at about  95 ± 10 km s⁻¹  ; although their surface-to-surface separation is only  4 R_⊙  the stars are not noticeably distorted geometrically by such close proximity. All three stars appear to be in synchronous rotation in their respective orbits. We derive fairly accurate Hertzsprung–Russell diagram positions for all three stars and compare them to evolutionary tracks calculated for the respective stellar masses, but cannot reconcile the age of the cool giant with that of the B stars.     

On the mass of dense star clusters in starburst galaxies from spectrophotometry

The mass of unresolved young star clusters derived from spectrophotometric data may well be off by a factor of 2 or more once the migration of massive stars driven by mass segregation is accounted for. We quantify this effect for a large set of cluster parameters, including variations in the stellar initial mass function (IMF), the intrinsic cluster mass, and mean mass density. Gas-dynamical models coupled with the Cambridge stellar evolution tracks allow us to derive a scheme to recover the real cluster mass given measured half-light radius, one-dimensional velocity dispersion and age. We monitor the evolution with time of the ratio of real to apparent mass through the parameter η. When we compute η for rich star clusters, we find non-monotonic evolution in time when the IMF stretches beyond a critical cut-off mass of  25.5 M_⊙  . We also monitor the rise of colour gradients between the inner and outer volume of clusters: we find trends in time of the stellar IMF power indices overlapping well with those derived for the Large Magellanic Cloud cluster NGC 1818 at an age of 30 Myr. We argue that the core region of massive Antennae clusters should have suffered from much segregation despite their low ages. We apply these results to a cluster mass function, and find that the peak of the mass distribution would appear to observers shifted to lower masses by as much as 0.2 dex. The star formation rate derived for the cluster population is then underestimated by from 20 to 50 per cent.     

Δ Y/Δ Z from fine structure in the main sequence based on Hipparcos parallaxes

The slope Δ Y /Δ Z is a quantity of interest in relation to stellar evolution, the initial mass function and the determination of the primordial helium abundance. In this paper we estimate Δ Y /Δ Z from fine structure in the main sequence of nearby stars from Hipparcos data for stars with Z  ≤ Z⊙. We find a value of about 3, which is consistent with what has been found in extragalactic H  II regions and with stellar models for suitable upper limits to the initial masses of supernovae according to the initial mass function slope adopted.     

Towards the main sequence: detailed analysis of weak line and post-T Tauri stars

A detailed study was performed for a sample of low-mass pre-main-sequence (PMS) stars, previously identified as weak-line T Tauri stars, which are compared to members of the Tucanae and Horologium Associations. Aiming to verify if there is any pattern of abundances when comparing the young stars at different phases, we selected objects in the range from 1 to 100 Myr, which covers most of PMS evolution. High-resolution optical spectra were acquired at European Southern Observatory and Observatório do Pico dos Dias . The stellar fundamental parameters effective temperature and gravity were calculated by excitation and ionization equilibria of iron absorption lines. Chemical abundances were obtained via equivalent width calculations and spectral synthesis for 44 per cent of the sample, which shows metallicities within 0.5 dex solar. A classification was developed based on equivalent width of Li  i 6708 Å and Hα lines and spectral types of the studied stars. This classification allowed a separation of the sample into categories that correspond to different evolutive stages in the PMS. The position of these stars in the Hertzsprung–Russell diagram was also inspected in order to estimate their ages and masses. Among the studied objects, it was verified that our sample actually contains seven weak-line T Tauri stars, three are Classical T Tauri, 12 are Fe/Ge PMS stars and 21 are post-T Tauri or young main-sequence stars. An estimation of circumstellar luminosity was obtained using a disc model to reproduce the observed spectral energy distribution. Most of the stars show low levels of circumstellar emission, corresponding to less than 30 per cent of the total emission.     

M4–18: the planetary nebula and its WC10 central star

We present a detailed analysis of the planetary nebula M4–18 (G146.7+07.6) and its WC10-type Wolf–Rayet (WR) central star, based on high‐quality optical spectroscopy (WHT/UES, INT/IDS, WIYN/DensPak) and imaging ( HST /WFPC2). From a non-LTE model atmosphere analysis of the stellar spectrum, we derive T _eff=31 kK,     v _∞=160 km s⁻¹ and abundance number ratios of H/He<0.5, C/He=0.60 and O/He=0.10. These parameters are remarkably similar to those of He 2–113 ([WC10]). Assuming an identical stellar mass to that determined by De Marco et al. for He 2–113, we obtain a distance of 6.8 kpc to M4–18 [ E ( B−V )=0.55 mag from nebular and stellar techniques]. This implies that the planetary nebula of M4–18 has a dynamical age of ∼3100 yr, in contrast to ≥270 yr for He 2–113. This is supported by the much higher electron density of the latter. These observations may be reconciled with evolutionary predictions only if [WC]-type stars exhibit a range in stellar masses.
Photoionization modelling of M4–18 is carried out using our stellar WR flux distribution, together with blackbody and Kurucz energy distributions obtained from Zanstra analyses. We conclude that the ionizing energy distribution from the WR model provides the best consistency with the observed nebular properties, although discrepancies remain.     

The Jeans mass and the origin of the knee in the IMF

We use numerical simulations of the fragmentation of a  1000 M_⊙  molecular cloud and the formation of a stellar cluster to study how the initial conditions for star formation affect the resulting initial mass function (IMF). In particular, we are interested in the relation between the thermal Jeans mass in a cloud and the knee of the IMF, i.e. the mass separating the region with a flat IMF slope from that typified by a steeper, Salpeter-like, slope. In three isothermal simulations with   M _Jeans= 1, 2  and  5 M_⊙  , the number of stars formed, at comparable dynamical times, scales roughly with the number of initial Jeans masses in the cloud. The mean stellar mass also increases (though less than linearly) with the initial Jeans mass in the cloud. It is found that the IMF in each case displays a prominent knee, located roughly at the mass scale of the initial Jeans mass. Thus clouds with higher initial Jeans masses produce IMFs which are shallow to higher masses. This implies that a universal IMF requires a physical mechanism that sets the Jeans mass to be near  1 M_⊙  . Simulations including a barotropic equation of state as suggested by Larson, with cooling at low densities followed by gentle heating at higher densities, are able to produce realistic IMFs with the knee located at  ≈1 M_⊙  , even with an initial   M _Jeans= 5 M_⊙  . We therefore suggest that the observed universality of the IMF in the local Universe does not require any fine tuning of the initial conditions in star forming clouds but is instead imprinted by details of the cooling physics of the collapsing gas.     

S 235 B explained: an accreting Herbig Be star surrounded by reflection nebulosity

The intent of this study is to determine the nature of the star and associated nebulosity S 235 B, which are located in a region of active star formation still heavily obscured by the parent molecular cloud. Low-resolution  ( R = 400)  long-slit spectra of the star and nebulosity, and medium-  ( R = 1800)  and high-resolution  ( R = 60 000)  spectra of the central star are presented along with the results of Fabry–Perot interferometric imaging of the entire region. Based on the long-slit and Fabry–Perot observations, the nebulosity appears to be entirely reflective in nature, with the stellar component S 235 B★ providing most of the illuminating flux. The stellar source itself is classified here as a B1V star, with emission-line profiles indicative of an accretion disc. S 235 B★ thus belongs to the relatively rare class of early-type Hebrig Be stars. Based on the intensity of the reflected component, it is concluded that the accretion disc must be viewed nearly edge-on. Estimates of the accretion rate of S 235 B★ from the width of the Hα profile at 10 per cent of maximum intensity, a method which has been used lately for T Tauri stars and Brown Dwarfs, appear to be inconsistent with the mass outflow rate and accretion rate implied from previous infrared observations by Felli et al., suggesting this empirical law does not extend to higher masses.     

The evolutionary status of W Ursae Majoris-type systems

Well-determined physical parameters of 130 W Ursae Majoris (W UMa) systems were collected from the literature. Based on these data, the evolutionary status and dynamical evolution of W UMa systems are investigated. It is found that there is no evolutionary difference between W- and A-type systems in the   M – J   diagram, which is consistent with the results derived from the analysis of observed spectral type and of   M – R   and   M – L   diagrams of W UMa systems.   M – R   and   M – L   diagrams of W- and A-type systems indicate that a large amount of energy should be transferred from the more massive to the less massive component, so that they are not in thermal equilibrium and undergo thermal relaxation oscillation. Moreover, the distribution of angular momentum, together with the distribution of the mass ratio, suggests that the mass ratio of the observed W UMa systems decreases with decreasing total mass. This could be the result of the dynamical evolution of W UMa systems, which suffer angular momentum loss and mass loss as a result of the magnetic stellar wind. Consequently, the tidal instability forces these systems towards lower q values and finally to rapidly rotating single stars.