Helium burning stars with masses between 10 Mo and 40 Mo are evolved up to core helium exhaustion including mass loss by stellar wind at rates between 10-5 Mo/yr and 10-4 Mo/yr appropriate for WR stars. Different M formalisms were used. It should however be noted that the results presented here are only marginally dependent on this formalism. The initial models contain a small hydrogen shell. The atmospherical hydrogen abundance Xatm = 0.2-0.3. These models correspond to primary remnants (with hydrogen ZAMS masses between 30 M0 and 100 M0) after a case B mode of mass transfer in close binaries, or to stars after a red giant phase of huge mass loss comparable to late case B remnants after Roche lobe overflow. Evolutionary details can be found elsewhere (Vanbeveren, D., Ph.D. Thesis, Vrije Universiteit Brussel) and will not be discussed here. I want to focus on two applications

Evolutionary computations are presented for massive stars between 20 Mo and 100 Mo with chemical abundances holding for the Small Magellanic Cloud, i.e. X = .76 and Z = .003. Mass loss by stellar wind is taken into account during core hydrogen burning. After core hydrogen burning some models are considered as members of close binary systems and are followed during their Roche lobe overflow stage according an early case B of mass transfer. During the core helium burning stage of the RL0F remnants mass loss rates comparable to WR stars are included in order to study the formation and the evolution of WR stars. Comparison with similar galactic computations (Vanbeveren, Packet, 1978) is made.

We have calculated evolutionary models of massive stars in the range 15-120 Mʘ from the zero-age sequence up to the end of the carbon burning stage (Maeder, 1981). Three sets of models with different mass loss rates Ṁ have been computed; the adopted parametrisation of Ṁ is fitted on the observations and thus the expression for Ṁ differs according to the location of the stars in the HRD.

In this short note we concentrate on the location of the He-burning stars in the HRD. The helium burning phase, which lasts 8 to 10% of the MS phase, is spent mainly as red supergiants (RSG) and as WR stars (note that for low mass loss, the time spent as A-G supergiants becomes longer).

Stothers and Chin (1972) examined numerically thermal instability of H burning shells in very massive stars. They reported the discovery of the thermal pulses in the shell on a stage of the contracting core just after the core exhaustion. Their results, however, are inconsequential because the pulses are very feeble and the mechanism of such feeble pulses is not well known at the shell burning phases. In this note, we summarize our analytical method and the results on the possibility of such feeble pulses in H burning shells, of which detailed procedure is described in another paper(Tanaka et al., 1980).

The theoretical (Mb versus Log Te) HR diagram for the brightest galactic OB stars shows an upper boundary for the luminosity, which is characterized by a decreasing luminosity with decreasing effective temperature (Humphreys and Davidson, 1979). The existence of this limit was interpreted by Chiosi et al. (1978) as due to the effect of mass loss by stellar wind on the evolution of most massive stars in core H-burning phase. In fact, evolutionary models calculated at constant mass cover a wider and wider range in effective temperature as the initial mass increases during the main sequence phase. On the contrary, sufficiently high mass-loss rates make the evolutionary sequences of most massive stars (M 60⩾Mʘ) shrink toward the zero age main sequence whenever, due to mass loss, CNO processed material is brought to the surface (Chiosi et al., 1978; de Loore et al., 1978; Maeder, 1980).

1. Introduction

It is essential to consider the effect of mass loss to understand the distribution of supergiant stars in the HR diagram. This research concerns the evolution of massive stars with X=0.700 and Z=0.001 during the phases up to central Heexhaustion with the inclusion of mass loss. Such low value of Z has been chosen in order to allow a comparison with the supergiant stars of SMC. The rate of mass loss is formulated as in Chiosi, Nasi and Sreenivasan (1978). More specifically, in the range of high effective temperatures, we adopt the mass-loss rate relationship for radiation pressure driven wind of Castor, Abbott and Klein (1975), whereas in the range of low effective temperatures we assume the mass loss rate to be driven by the acoustic flux mechanism of Fusi Pecci and Renzini (1975).

New spectroscopic observations in the LMC/SMC combined with published data on Galactic WR stars lead to a correlation between mass ratio, MWR/MO, and WR subclass. As a consequence of this and their high mass loss rates, WR stars probably evolve from cool to hot ionization class in a way which depends on the metallicity.

If the Wolf-Rayet stars are produced by the evolution of massive stars with mass loss (Paczynski 1967, Conti 1976) from 0 stars to WN stars and thereafter to WC stars, then we may expect to observe a correlation of decreasing mean masses in the same sense as the evolution.Information about the masses of TO stars are obtained from studies of binary systems with WR components. Table 1 presents the today available data for the WN type stars.

As yet there have been few detailed analyses of Wolf-Rayet (WR) emission line spectra. Such analyses must certainly take account of line transfer in a spherically extended, expanding medium, a problem not yet completely addressed in the complexity of WR envelopes. However, visual examination of optical spectra suggests real differences in line strengths among the Balmer and Pickering series lines in WN stars. If hydrogen is present, the Balmer lines will be stronger than the adjacent Pickering lines of ionized helium; if hydrogen is weak or absent, then there will be a smooth transition in intensities along the Pickering series with no additional contribution from the Balmer lines at alternatively blending wavelengths (Underhill 1967).

The re-examination of the spatial distribution of 158 Wolf-Rayet stars in the Galaxy may help to define different breeds of Wolf-Rayet stars and put constraints on possible evolutionary scenarios.

The effects of mass loss on the evolution of low-mass stars (actual mass smaller than 1.4 Mʘ) are reviewed. The case of globular cluster stars is discussed in some detail, and it is shown that evolutionary theory sets quite precise limits to the mass-loss rate in population II red giants. The effects of mass loss on the final evolutionary stages of stars producing white dwarfs is also discussed. In particular, the interaction of the wind from the hot central star with the surrounding planetary nebula is considered. Finally, the problem of the origin of hydrogen-deficient stars is briefly discussed.

The relation between initial and final masses is discussed under consideration of changing theoretical concepts and new empirical data on masses of white dwarfs and nuclei of planetary nebulae. It is concluded that presently adopted schemes of evolution need revision, and that no universal relation exists.

The strongest evidence for large amounts of mass loss during stellar evolution has been provided by the existence of white dwarfs – with masses typically of 0.6 m (m = M/Mʘ), much below the galactic turn-off masses – and by the phenomenon of planetary nebula production before a star descends into the white dwarf region.

The evolution of a 1.2Mʘ star along the asymptotic branch with continuous mass loss is presented, showing that this mass loss leads to the formation of a PN with a typical central star in its center.

A former investigation (Harpaz and Kovetz, 1980) has shown that mechanisms for PN creation based on sudden violent processes are not likely to work in the envelope of a red giant star. On the other hand, significant mass loss from red giants was observed as a general phenomenon.

We have followed the evolution of a 1.2Mʘ star along the asymptotic branch, including in the evolutionary calculations a mass loss according to Reimers’ empirical formula. It was found that towards the end of this stage, the mass loss rate was about 2.7xl0-6Mʘ/y, which is consistent with the formation of a typical PN within 30,000 years. When the mass content of the hydrogen rich envelope dropped to 1.5x10-3Mʘ, the star began to contract rapidly, forming a typical central star of 0.6Mʘ

The idea that planetary nebulae (PN) originated from outer layers of red giants goes back to Shlovskii (1956). This hypothesis was supported by Abell and Goldreich (1966) who argued convincingly that red giants are the most likely progenitors of PN. Although this is generally accepted today, the details of the transition from red giants to PN remain in controversy. It was pointed out by Paczyński (1971 a) that PN progenitors must have similar luminosities to central stars of PN, and therefore are likely to be late-type supergiants undergoing double-shell burning. The advent of infrared astronomy led to the discovery that most, if not all, late-type giants and supergiants are losing mass at rates of 10-6 - 10-5 Mʘyr-1 (Gehrz and Woolf 1971). Such mass loss rates greatly exceed the nuclear burning rate (6 x 10-8 - 5 x 10-7 Mʘyr-1 for stars with core masses between 0.6 and 1.2 Mʘ) and must be the dominant factor in the late evolution of intermediate mass stars. The observation of white dwarfs in open clusters implies that up to 6 Mʘ can be lost during the red-giant phase (Romanishin and Angel 1980). Since the observed masses of PN are no more than a few tenths of a solar mass, the existence of massive circumstellar envelopes formed by steady mass loss must have an effect on the formation of PN.

Mira variables are found at the tip of the asymptotic giant branch, with L≈3000-5000Lʘ and TeH3000K. (Feast 1981; Willson 1981a). They are fundamental mode pulsators (Willson 1979, 1981a). A typical Mira has P~350 days, R~200-300Rʘ, M~1-2Mʘ (Willson 1979; 1981a). From the atmospheric velocities of the Miras plus a fundamental mode period-massradius relation one finds present masses for the Miras which are not very different from their progenitor masses (Willson 1981a). This suggests that pre-Mira mass loss is moderate -- ≲20% of the mass is lost before pulsation starts. In fact one expects only moderate mass loss before the Mira stage;

The total amount of mass lost during the first giant phase of Population II red giants is derived from Horizontal Branch properties: it is found to be proportional to the metal content.

In this paper we present a fully hydrodynamical treatment of the stationary isothermal accretion problem onto a moving gravitating point mass. The derivation is purely analytical. We find that the accretion rate is more than a factor of 50 higher than the accretion rate derived from the partially non-hydrodynamical treatment by Hoyle and Lyttleton (1939) or Bondi and Hoyle (1944). This result may have some bearing on the evolutionary tracks of young pre-Main Sequence stars still embedded in their parent protocluster cloud. We discuss the work by Federova (1979) who investigated the pre-Main Sequence evolution of degenerate low mass ‘stars’ with strong accretion of protocluster cloud material. We suggest that the stars which lie below the Main Sequence in young clusters could strongly accrete matter at the pre-Main Sequence stage.

There are two major effects of mass loss from stars of intermediate mass. First, the ultimate fate of such stars--whether they become supernovae of the type that leave no condensed remnant or whether they become white dwarfs--is extremely sensitive to the rate at which they lose mass during the last portion of their nuclear-burning lives. Second, the contribution of intermediate-mass stars to the enrichment of the interstellar medium in helium, carbon, nitrogen, s-process isotopes, and possibly also in iron-peak elements and r-process isotopes is similarly sensitive to mass-loss rates during this last, quiet phase of nuclear burning.

Photometry (uvbyβ) of five cepheids with B-type companions has been utilized to derive the spectral types and apparent magnitudes of the companions. By utilizing the period-luminosity relation it is possible to estimate the absolute magnitudes of the companions since the differences in magnitude between the companions and cepheids are known. The spectral types and absolute magnitudes of the B-type components indicate they are all evolved from the zero-age main sequence. By utilizing the ages of the B stars we can derive the ages of the cepheids under the assumptions that both stars of a binary were formed at the same time and the cepheids are more evolved than their B components. A period-age relation of the form log tage = 8.60 - 0.83 log P is found. Minimum masses of the cepheids can also be estimated from the data. No evidence of large mass loss is evident in the intermediate-band photometry of cepheids.

To understand the evolution of giant stars, it is important to pin down the masses for Cepheids. The 7– to 10–day “bump” Cepheids imply lower than evolutionary mass (60%). Recent theoretical work, though, indicates that for Cepheids with periods of 15 to 16 days, the best understanding of the light curves results from using evolutionary masses.