Evolutionary track

We have determined the positions of our stars in H-R diagrams for the appropriate Fe and [a/Fe] abundances, using Teff obtained by Method 1 and the absolute magnitudes, Mv, derived from Hipparcos parallaxes. The good agreement between the gravities obtained from the evolutionary tracks ([4]) and those from Method 1 suggests that non-LTE effects are unlikely in Method 1. 

The observations were performed at ESO using the 1.52m telescope and FEROS. The obtained spectra have high nominal resolving power (R 48000), and S/N 500 at maximum and a coverage from 4000 A to 9200 A. Many spectra were acquired for all sample stars. The atmospheric parameters (Teff, log g, [Fe/H] and microturbulence velocities) have been obtained through an iterative and totally self-consistent procedure from Fe lines of the observed spectrum. The initial values of Teg were obtained from a (B-V) vs Teg calibration and log were determined from Hipparcos parallaxes and evolutionary tracks. The [O/Fe] abundances were derived by fitting synthetic spectra to the observed one. 

Fig. 1. Evolutionary tracks (labelled in Mq) and isochrones (in Myr) for low-mass stars taken from two models [8,31]. The epochs of photospheric Li depletion (and hence Li-burning in the core of a fully convective star or at the convection zone base otherwise) and the development of a radiative core are indicated. The numbers to the right of the tracks indicate the fraction of photospheric Li remaining at the point where the radiative core develops and at the end of Li burning.

Fig. 2 (left panel) shows that by adopting the a calibration by Ludwig et al. (1999), we obtain evolutionary tracks very similar to those obtained by means of the Full Spectrum Turbulence (FST) model (Canuto, Goldman Mazzitelli 1996), which is also known to be a high efficiency model. 

Fig. 2. (Left panel) evolutionary tracks using FST in the logTefj vs. log g plane (solid line non gray models with rph = 10 by Montalban et al.,2004) and 2D calibrated MLT (dashed line).(Right panel) Lithium evolution for the solar mass with different assumptions about convection and model atmospheres. The dotted line at bottom represents today s solar lithium abundance. MLT models with AH97 model atmospheres down to Tph = 10 and 100 are shown dotted for cum = 1 and dash-dotted for cpr, = 1.9. The Montalban et al. (2004) MLT models with Heiter et al. (2002) atmospheres down to Tph = 10 (lower) and 100 (upper) are dashed The continuous lines show the non gray FST models for rph = 10 and 100, and, in between, the long dashed model employing the 2D calibrated MLT.

Fig. 3.37. Rough locations of chemically evolved and peculiar stars in the HR diagram. Full lines show the ZAMS with stellar masses indicated and evolutionary tracks for 0.8, 3 and 15 Af , the helium main sequence (0.5 to 1.5 A/ ),...

PN nucleus, horizontal-branch and white-dwarf regions. The dotted line shows a schematic main sequence and evolutionary track for Population II, while various dashed lines show roughly the Cepheid instability strip, the transition to surface convection zones and the helium-shell flashing locus for Population I. After Pagel (1977). Copyright by the IAU. Reproduced with kind permission from Kluwer Academic Publishers. 

Fig. 5.7. Evolutionary tracks for Z = 0.02 (near solar metallicity) stars with different masses in the HR diagram. (Luminosities are in solar units.) Points labelled 1 define the ZAMS and points labelled 2 the terminal main sequence (TAMS), the point where central hydrogen is exhausted. The Schonberg-Chandrasekhar limit may be reached either before or after this (for M > 1.4 Af0). Points marked 3 show the onset of shell hydrogen-burning. Few stars are found in the Hertzsprung gap between point 4 and point 5 , where the surface convection zone has grown deep enough to bring nuclear processed material to the surface in the first dredge-up. Adapted from Iben (1967).

Fig. 5.15. Evolutionary tracks of stars with mass 1, 5 and 25 Mq in the HR diagram. Adapted from Iben (1985, 1991).

Fig. 5.19. Evolutionary track in the HR diagram of an AGB model of total mass 0.6 Mq, initial composition (Y, Z) = (0.25, 0.001 Z /20). Heavy dots marked 2 to 11 indicate the start of a series of thermal pulses (see Fig. 5.20), which lead to excursions along the steep diagonal lines. Numbers along the horizontal and descending track indicate times in years relative to the moment when an ionized planetary nebula appears and (in parentheses) the mass of the envelope in units of Mq. R = 0.0285 indicates a line of constant radius (R in solar units) corresponding to the white-dwarf sequence. Shaded areas represent earlier evolutionary stages for stars with initial masses 3,5 and 7 Mq and the steep broken line marks the high-temperature boundary of the instability strip in which stars pulsate in their fundamental mode. The y-axis gives log L/Lq. Adapted from Iben and Renzini (1983).

The star continues to burn hydrogen in a thin shell until the bluest point on its evolutionary track, at which point H-buming is switched off and both the H-rich envelope and the He-rich layer contract rapidly. At this point, in most cases, it is... 

For a whole range of stellar masses between 1 and 100 times the mass of the Sun, evolutionary tracks are traced out in the temperature-luminosity plane, also known as the Hertzsprung-Russell diagram, so frequently referred to by astronomers. 

The evolutionary track followed by the center and the temperature profiles against density are shown by the solid lines in Figure 2. The numerals attached to the lines denote the time before the onset of the flash in units of 10 yr. The center does not reach the NCO ignition curve before the 3a reaction ignites at the site of the maximum temperature. The NCO reaction does not change the existing evolutionary models, as was pointed out by Spulak (1980), except that a considerable amount of 80 is produced in the central region. 

Fig. 1. Evolutionary tracks of accreting helium white dwarfs.

The quantities determined directly by the spectroscopic analysis as performed for hot stars are effective temperature Tef f surface gravity g and element abundances. Of course, this is not sufficient to place a star in the HR diagram. This is possible only with further knowledge of either luminosity, radius, mass or distance of the star. However, uncertainties in these quantities (which are usually much larger than the uncertainties in Te and g) directly translate into the HR diagram. On the other hand, theoretical evolutionary tracks can be easily expressed in terms of Teff and g without loss of precision. It is therefore good practice to discuss the results of spectroscopic analyses directly in a (log Te -log g) diagram as we shall do in this paper. 

Figure 2 Comparison between observations and evolutionary tracks applicable for sdB, sdOB and classical sdO stars. HB is the horizontal branch with core mass Mcore = 0.475 MQ, on which some values of q = Mcore/M 0j.aj are indicated. CC denotes the track of Caloi and Castellani (1985), the tracks G1 and G2 are from Gingold (1976). Post-AGB tracks applicable for CSPN are from Schonberner (1983 SI M = 0.546 MQ, S2 M = 0.565 Mq). The hatched strip marks the area in which Groth et al. (1985) have found photospheric convection. Stellar symbols are the same as in Fig. 1. 

Figure 3 Comparison between observations and evolutionary tracks applicable for extremely helium-rich stars. The helium main sequence (HeMS) is labelled with stellar masses, HL is the Hayashi limit. The hatched line indicates the Eddington limit for pure helium composition. Evolutionary tracks are from Paczynski (1971 dashed lines labelled with M/MQ), Schonberner (1977, M = 0.7 MQ, full drawn line) and Law (1982 M = 1 Mq, dotted line). Stellar symbols are the same as in Fig. 1. 

Figure 1. Lines of constant mass and varying chemical composition for the computed Wolf-Rayet models of 3, 5, 7, 10, 15, 20, SO, 40, and 60Mq in the HR diagram (solid lines). The pure helium stars are connected through a dashed line, while the extreme helium poor stars are connected through a dotted line. Also the HRD positions after applying a correction for the partly optically thick stellar wind on the effective temperature are shown. Furthermore, the theoretical zero age main sequence (ZAMS) is indicated, together with schematic evolutionary tracks for stars of 15, 30, and IOOMq. The crosses and circles correspond to HRD positions of observed WNE and WC stars, respectively, according to Smith and Willis (198S, Astron. Astrophys. Suppl. 54,229).

Figure 2 Stars and evolutionary tracks near the Humphreys-Davidson limit. From Humphreys (1987).

Figure 3 The upper part of the HR diagram with evolutionary tracks calculated by Maeder and Meynet (1987). The branch of dots in the red part is the proposed Red Supergiant Branch. Lower to the right (at log Teff 3.4) is the uppermost part of the Asymptotic Giant Branch. The hatched area near log Teff = 3.75 is the upper part of the Cepheid branch. 

Fig. 8 displays the relation of log M vs. log L along the evolutionary tracks in each galaxy. It is clearly seen that for each track of similar initial mass the relation MGaj > > MgMC holds. However,... 

Fig. 11 Wind models along evolutionary tracks representing different luminosity classes.

The second observational correlation results from the detailed photo-spheric quantitative spectroscopy by Mdndez et al. (1987), which allows to determine the position of CSPN in the log g, log Te -plane with high precision. By transformation of evolutionary tracks into this plane stellar masses M/MQ and radii R/R0 can be read off directly. The log g, log Te diagram of CSPN can also be used to investigate how the strength of stellar winds depends on the stellar parameters. This is done in Fig. 14, which reveals clearly that the more massive objects closer to the Eddington limit have observable wind features. 

Fig. 15 Same as Fig. 13 for CSPN with normal H abundance, but including wind calculations along evolutionary tracks. 

If we compare the HRD position of the progenitor to evolutionary tracks (keeping in mind that the luminosity is nearly constant after helium ignition) we see that the progenitor had a mass between 15 and 20 M0 (Fig.l). Depending on the inclusion of overshooting in the model computations, the mass at explosion may vary from 12.5 Mg (overshooting) to 17.5 M0... 

In general, the decrease in opacity obtained with the lower abundances characteristic of the LMC tends to help to confine the evolutionary tracks to the blue side of the H-R Diagram. However, most models are computed with the an abundance set taken as solar divided by, say, four. In practice, the LMC abundance distribution is not this simple.Dopita (1986) and Russell, Bessell and Dopita have shown that, in the LMC, the underabundance of various elements with respect to solar is dependent upon their atomic number. For example, Cand N are depleted by about 0.8 dex, O and Ne by about 0.5 dex, Ca by anbout 0.3 dex and the heavy elements from Ti through Fe to Ba by about 0.2 dex. This pattern is similar to that produced in models of deflagration supemovae, and may indicate that these have been relatively more important in enriching the interstellar medium in the LMC. 

Figure 1 Evolutionary tracks in the HR diagram of the initially 20 M star. Cases A, B, and C correspond to models with no mass loss (A), with no artificial enhancement of helium in the hydrogen-rich envelope (C), and with enhancement of helium up to Y = 0.4 (B).

Fig.l Evolutionary tracks in the HR diagram for a model with an intial mass of 20... 

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