Free Access
Volume 524, December 2010
Article Number A98
Number of page(s) 21
Section Stellar structure and evolution
Published online 25 November 2010

Online material

Appendix A: Stellar evolution

The evolution of stars used in this work is based on the stellar evolution models for solar and non-solar metallicity, rotating with 300 km s-1 and non-rotating by Meynet & Maeder (2003) and Meynet & Maeder (2005) and each two models with LMC and SMC metallicity (15 and 20 M) by Bertelli et al. (2009). Model tracks are only provided for stars with 9, 12, 15, 20, 25, 40, 60, 85 and 120 M for solar metallicity and even fewer for non-solar metallicity. As the lifetime of the stars and their respective evolutionary stages are dependent on the mass of the star, it is not possible to linearly interpolate between the track of a 40 and a 60 M star in order to get, for example, a 50 M star. Therefore, a special interpolation routine is employed here. The model tracks immediately above and below the target mass are normalized to their individual lifetimes (the point when the star becomes a neutron star or a black hole). Then the two normalized tracks are interpolated linearly to the target mass. The resulting track is then multiplied with the lifetime for the targeted star. This lifetime is linearly interpolated from the lifetime of the two input models.

Figure A.1 shows the stellar evolution of a 85 M and a 120 M star with time from Meynet & Maeder (2003) for several stellar parameters (luminosity, radius, mass, Teff) together with an interpolated track of a 100 M star.

thumbnail Fig. A.1

Panel A: mass evolution over 4 Myr for a 85 M (solid line) and a 120 M star (dotted line) from literature data (Meynet & Maeder 2003). The dashed line shows a 100 M star interpolated from the two models. Panel B: luminosity evolution over 4 Myr for the same three stars as in the panel A. Panel C: radius evolution over 4 Myr for the same three stars as in panel A. Panel D: effective temperature evolution over 4 Myr for the same three stars as in panel A.

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Appendix B: Spectral-type-stellar evolution tables

The following Table 9 shows the different spectral types that stellar evolution models reach during their lifetime. It uses solar metallicity (Meynet & Maeder 2003) and non-solar metallicities (Meynet & Maeder 2005) and rotating (vrot,initial = 300 km s-1) and non-rotating tracks between 20 and 120 M. In this table are also shown evolutionary phases that go beyond the O spectral type used in the current work. Below we describe how these additional phases are classified. As the surface abundances for

several species (H, He, C, N, O, Ne and Al) are also given in the models, it is possible to assign the beginning of the hydrogen-rich Wolf-Rayet phase (WNL) as soon the surface hydrogen abundance is below 60% (Hamann et al. 2006) and the helium-rich Wolf-Rayet phase (WNE) is given when the surface abundance of hydrogen is below 10-4. Later on, stars are designated as carbon-rich Wolf-Rayet stars (WC) when helium starts to be depleted on the surface and the carbon abundance rises above 10-4. Exceptions from this scheme are made when the stars enter the Luminous Blue Variable (LBV), Yellow Hyper-Giant (YHG), Yellow Giant (YG), Blue Supergiant (BSG) or Red Supergiant (RSG) phases. The hot end of the LBVs is defined by log 10(LLBV   hot) = 2.2056·log 10(Teff) − 3.7737 and on the cool edge by TLBV   cool = 7500 K with a lower limit of log 10(L/L) = 5.3 (Smith et al. 2004). YHGs lie between 4500 to 7500 K and log 10(L/L) ≥ 5.3 (Smith et al. 2004). Models that evolve between 4500 to 7500 K, but have log 10(L/L)  < 5.3, are named YGs. The BSGs are stars that are too cold for the O9.5 III or the O9.5 I types, but that are still below the LBV limit and hotter than YHGs. And finally, RSGs are stars colder than 4500 K and log 10(L) ≥ 3.55log 10(L/L) (Levesque 2010).

The evolutionary sequence for solar metallicity roughly agrees with the currently used observational sequence by e.g. Crowther (2007):

  • Minitial > 75   M: O  →  WNL  →  LBV  →  WNE  →  WC  →  SNIc,

  • Minitial = 40–75 M: O  →  LBV  →  WNE  →  WC  →  SNIc,

  • Minitial = 25–40 M: O  →  LBV/RSG  →  WNE  →  SNIb.

Where SNIb and SNIc are supernovae type Ib and Ic, although it has recently been suggested that LBVs could explode early (Kotak & Vink 2006; Gal-Yam & Leonard 2009), which would significantly alter the later evolutionary phases of these types of schemes.

Table 9

Spectral type evolution of stellar models.

© ESO, 2010

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