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Appendix A: Isochrones

The evolution of our rapidly rotating stellar models is influenced significantly by rotation (see Sect. 3.1). Therefore, isochrones of rotating models calculated for the same age differ from isochrones of non-rotating models.

	Fig. A.1 Isochrones of non-rotating stellar evolution models in the mass range 10–500  M⊙ are depicted for ages up to 5.4 Myr. The different line colours explained in the figure key indicate the age of every isochrone. Models in 10  M⊙-steps are highlighted by filled circles.
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Figure A.1 depicts isochrones of non-rotating models for ages up to 5.4 Myr in the HR diagram. Eight different isochrones are shown with age steps of 0.8 Myr. The core hydrogen burning stellar evolution models presented in Sect. 3 are used to generate the isochrones. Because more massive stellar models have shorter lifetimes, older isochrones terminate at the less massive model at the upper end of the track.

For a given initial composition and age, isochrones span an area in the HR diagram when different initial surface rotational velocities are considered simultaneously (Brott et al. 2011a). Isochrones of 16 different ages from 0.2 to 6.2 Myr for rotating stellar models are shown in Figs. A.2 and A.3 for different ages. Switching from inhomogeneous to chemically homogeneous evolution, the isochrone is located at higher effective temperatures and luminosities than for the non-chemically homogeneous evolution.

Fig. A.2 Several isochrones of different ages and rotating stellar evolution models are shown in the HR diagram. The surface rotational velocity at the ZAMS is chosen in steps of 100 km s-1 from non-rotating to 400 km s-1 and additionally 450 km s-1. Three initial surface rotational velocities are highlighted in particular. The isochrones of non-rotating models are shown in red, 400 km s-1 in blue, and 450 km s-1 in orange.

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Fig. A.3 Several isochrones of different ages and rotating stellar evolution models are shown in the HR diagram. The surface rotational velocity at the ZAMS is chosen in steps of 100 km s-1 from non-rotating to 400 km s-1 and additionally 450 km s-1. Three initial surface rotational velocities are highlighted. The isochrones of non-rotating models are shown in red, 400 km s-1 in blue, and 450 km s-1 in orange.

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The more massive a stellar model is, the earlier it reaches the point in the HR diagram where the stellar evolution track starts to evolve blueward. The related turn in the isochrones in Fig. A.2 is first visible for 1.4 Myr (bottom left panel). The minimum effective temperature depends on the surface rotational velocity at the ZAMS, which is reflected by the isochrones of different rotation rates. The 2.2 Myr and 2.6 Myr isochrones show that the more massive a stellar model is, the earlier the Hamann et al. (1995) mass-loss rate is applied to the stellar evolution calculation. The isochrones therefore show a decrease in luminosity for the most massive models.

Figure A.4 depicts a population synthesis of stars with the age and distributions of mass and surface rotational velocity given in Table A.1. The calculation was done using the code Starmaker (Brott et al. 2011b), using the parameters listed in Table A1.

It can be seen that the randomly drawn stellar models with the same age do not lie on one line, but instead spread over a certain area in the HR diagram. The initial mass distribution determines the model density along the line corresponding to the isochrone of non-rotating stellar models of this age. We choose a flat mass distribution for the simulation to have a better view of the behaviour of the most massive stars. The velocity distribution on the other hand shapes the stellar model density as a function of the effective temperature for (roughly) constant luminosity. The colour coding indicates the number of stars within one pixel of 500 K and log  (L/L_⊙) = 0.05.

Figure A.4 shows similar information as discussed in Fig. A.2. Additionally, it gives the probability of observing a star for the conditions given in Table A.1 depending on the surface rotational velocity distribution.

Isochrones for slow rotating stellar evolution models that undergo non-chemically homogeneous evolution do not differ significantly in the HR diagram. The probability of observing a star along these isochrones is highest. The change from non-chemically homogeneous to quasi-chemically homogeneous evolution occurs at a small velocity range related to a significant change of the position in the HR diagram.Therefore, the probability of observing a star between isochrones of slow-rotating and rapidly rotating models is small. Again, isochrones of rapidly rotating stellar evolution models are close in the HR diagram, leading to a higher probability of observation.

	Fig. A.4 starmaker population-synthesis calculation for 1.5 Myr (and other parameters as explained in Table A.1). The luminosity is depicted as a function of the effective temperature. The colour coding explained at the right bar indicates the number of stars within one pixel of 500 K and log (L/L⊙) = 0.05.
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Appendix B: Summary of data

© ESO, 2014