▪ Abstract In this article we first review the main physical effects to be considered in the building of evolutionary models of rotating stars on the Upper Main-Sequence (MS). The internal rotation...

The Evolution of Rotating Stars

The existing grids of star models without rotation allow us to already explain a number of properties of massive and WR stars (cf Maeder and Conti,1994) In particular, the sequences of star clusters are well reproduced, as well as the relations of filiation between the various kinds of massive stars: O-type stars, blue-and red-supergiants, Wolf-Rayet (WR) stars The observed abundances of CNO elements in WN stars and of He, C, O and Ne in WC stars are nicely accounted for, as well as the luminosities of WR stars, the number ratios WR/O and WC/WN in galaxies of various metallicities The consequences of mass loss for the chemical yields are quite important and allow us in particular to understand the evolution of the CNO elements during the galactic history

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Stellar Evolution with Rotation

Parallax data from the Hipparcos mission allow the direct distance to open clusters to be compared with the distance inferred from main-sequence (MS) fitting. There are surprising differences between the two distance measurements, indicating either the need for changes in the cluster compositions or reddening, underlying problems with the technique of MS fitting, or systematic errors in the Hipparcos parallaxes at the 1 mas level. We examine the different possibilities, focusing on MS fitting in both metallicity-sensitive B-V and metallicity-insensitive V-I for five well-studied systems (the Hyades, Pleiades, α Per, Praesepe, and Coma Ber). The Hipparcos distances to the Hyades and α Per are within 1 σ of the MS-fitting distance in B-V and V-I, while the Hipparcos distances to Coma Ber and the Pleiades are in disagreement with the MS-fitting distance at more than the 3 σ level. There are two Hipparcos measurements of the distance to Praesepe; one is in good agreement with the MS-fitting distance and the other disagrees at the 2 σ level. The distance estimates from the different colors are in conflict with one another for Coma but in agreement for the Pleiades. Changes in the relative cluster metal abundances, age related effects, helium, and reddening are shown to be unlikely to explain the puzzling behavior of the Pleiades. We present evidence for spatially dependent systematic errors at the 1 mas level in the parallaxes of Pleiades stars. The implications of this result are discussed.

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The Problem of Hipparcos Distances to Open Clusters. I. Constraints from Multicolor Main-Sequence Fitting*

Aims. We test predictions of evolution models on mixing of CNO-cycled products in massive stars from a fundamental perspective. Relative changes within the theoretical C:N:O abundance ratios and the buildup of helium are compared with observational results.Methods. A sample of well-studied Galactic massive stars is presented. High-quality optical spectra are carefully analysed using improved NLTE line-formation and comprehensive analysis strategies. The results are put in the context of the existing literature data.Results. A tight trend in the observed N/C vs. N/O ratios and the buildup of helium is found from the self-consistent analysis of main-sequence to supergiant stars for the first time. The catalytic nature of the CNO-cycles is confirmed quantitatively, though further investigations are required to derive a fully consistent picture. Our observational results support the case of strong mixing, as predicted e.g. by evolution models that consider magnetic fields or by models that have gone through the first dredge-up in the case of many supergiants.

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Mixing of CNO-cycled matter in massive stars

We present an atlas of H ,H ei 4471 and Mg ii 4481 line proles obtained in a 10 year observation period of 116 Be stars, which enabled many of them to be observed at quite dierent emission epochs. From the best t of the observed He i 4471 line proles with non-LTE, uniform (Te; logg) and full limb-darkened model line proles, we determined the V sini of the program stars. To account, to some degree, for the line formation peculiarities related to the rapid rotation-induced non-uniform distributions of temperature and gravity on the stellar surface, the t was achieved by considering (Te; logg) as free parameters. This method produced V sini estimations that correlate with the rotational velocities determined by Slettebak (1982) within a dispersion 30 km s 1 and without any systematic deviation. They can be considered as given in the new Slettebak's et al. (1975) system. Only 13 program stars have discrepant V sini values. In some objects, this discrepancy could be attributed to binary eects. Using the newly determined V sini parameters, we found that the ratio of true rotational velocities V=Vc of the program Be stars has a very low dispersion around the mean value. Assuming then that all the stars are rigid rotators with the same ratio V (!)=Vc, we looked for the value of ! that better represents the distribution of V sini=Vc for randomly oriented rotational axes. We obtained ! =0 :795. This value enabled us to determine the probable inclination angle of the stellar rotation axis of the program stars. In the observed line proles of H ,H ei 4471, Mg ii 4481 and Fe ii 4351 we measured several parameters related to the absorption and/or emission components, such as: equivalent width, residual emission and/or absorption intensity, FWHM, emission peak separations, etc. The parameters related to the H line emission proles were used to investigate the structure of the nearby environment of the central star. From the characteristics of the correlations between these quantities and the inferred inclination angle, we concluded that in most of cases the H line emission forming regions may not be strongly flattened. Using a simple representation of the radiation flux emitted by the star+envelope system, we derived rst order estimates of physical parameters characterizing the H line emission formation region. Thus, we obtained that the total extent of the H region is Rf' 2:5 1:0 R and that the density distribution in these layers can be mimicked with a power law R ,w here =2 :5 +2:2 0:6 . The same approach enabled us to estimate the optical depth of the H line emission formation region. From its dependence with the aspect angle, we concluded that these regions are caracterized by a modest flattening and that the (equator)=(pole) density contrast of the circumstellar envelope near the star should be two orders of magnitude lower than predicted by models based on a priori disc-shaped circumstellar envelopes. We found that the separation between the emission peaks, p, and the full width at half maximum, 1=2 ,o f the H line emission are not only sensitive to kinematic eects, but to line optical depth as well. This nding agrees with previous theoretical predictions and conrms that Huang's (1972) relation overestimates the extent of the H line emission formation region.

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High and intermediate-resolution spectroscopy of Be stars - An atlas of H$\gamma$, He I 4471 and Mg II 4481 lines

The helium and nitrogen enrichment of the atmospheres of early B-type stars during the main sequence (MS) evolutionary phase is re-analysed. It is confirmed that the effect depends on both the aget and the stellar massM. For example, the helium abundanceHe/H increases by 0.04 (60–70% of initial value) for stars withM=8–13M
⊙ and by 0.025 (about 30%) for stars withM=6M
⊙. The nitrogen abundance rises by three times forM=14M
⊙ and by, two times forM=10M
⊙. According to the latest theoretical computations, the observed appearance of CNO-cycled material in surface layers of the stars can be a result of the rotationally induced mixing, in particular, of the turbulent diffusion. Carbon is in deficiency in B stars, but unexpectedly does not show any correlation with the stellar age. However it is shown that the total C+N abundance derived for early B stars conflicts with the theory. Basing on modern data the helium enrichment is first examined in O-type MS stars, as well as in components of binaries. As compared with early B stars, the He abundance for more massive O stars and for components of binaries show a different relation with the relative aget/t

 MS
 . Namely during short time betweent/t

 MS
 ≈0.5 and 0.7 a sharp jump is observed up toHe/H=0.2 and more. In particular, such a jump is typical for fast rotating O stars (v sini≥200 km s−1),. Therefore the effect of mixing depends on massM, relative aget/t

 MS
 , rotational velocityv and duplicity. The mass problem (the discrepancy betweenM

 ev
 andM

 sp
 ) is also analysed, because some authors consider it as a possible evidence of early mixing, too. It is shown that the accurate data for components of binaries lead to the conclusion that the discrepancy is less than 30%. Such a difference can be removed at the expense of theM

 ev
 lowering, if the displacement of evolutionary tracks, owing to the rotationally induced mixing is taken into consideration.

L. S. Lyubimkov

Papers

Observational manifestations of early mixing in B- and O-type stars