| Issue |
A&A
Volume 580, August 2015
|
|
|---|---|---|
| Article Number | A20 | |
| Number of page(s) | 24 | |
| Section | Stellar structure and evolution | |
| DOI | https://doi.org/10.1051/0004-6361/201525945 | |
| Published online | 22 July 2015 | |
Online material
Appendix A: Interior structure of a 85 M⊙ stellar model
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Fig. A.1
Density structure of the stellar model. The black solid line marks the base of the inflated envelope, i.e. where β = 0.15. The intersection of the dotted lines with the red line on either side mark the points where β = 0.15 ± 0.045. |
| Open with DEXTER | |
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Fig. A.2
Run of Γ in the interior of the stellar model. |
| Open with DEXTER | |
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Fig. A.3
Rosseland mean opacity κ in the interior of the stellar model. |
| Open with DEXTER | |
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Fig. A.4
Run of β( = Pgas/Ptot) in the interior of the stellar model. |
| Open with DEXTER | |
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Fig. A.5
Fraction of flux carried by radiation (Lrad/Ltot) in the interior of the stellar model. |
| Open with DEXTER | |
Appendix B: Effect of efficient convection on inflation
Knowing that convective flux is proportional to the mixing length, we show here (Fig. B.1) that by increasing the mixing length parameter α in an inflated 300 M⊙ model near the ZAMS, the inflation gradually goes away and what we are left with is an almost non-inflated star, whose radius is well-approximated by core radius rcore of the inflated model.
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Fig. B.1
Density profile of a 300 M⊙ model with different values of the mixing length parameter α (see Sect. 2). The black dotted line marks the location of rcore, i.e. the base of the inflated envelope where β = 0.15. |
| Open with DEXTER | |
Appendix C: Convective velocity profile in a WR model
In Fig. C.1, the convective velocity is shown as a function of radius in a massive (147 M⊙) WR-type (YS = 0.89) stellar model.
The variation of isothermal and adiabatic sound speeds are also plotted for comparison. The convective velocities exceed the local isothermal sound speed in the envelope where conditions are non-adiabatic, i.e. the thermal adjustment time is short. In these models, turbulent pressure becomes important (which is not taken into account in our models) as well as standard MLT fails to be a good approximation for modelling convection.
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Fig. C.1
Convective velocity, isothermal sound speed, and adiabatic sound speed profiles in a 147 M⊙ WNL type star with Ys = 89%. |
| Open with DEXTER | |
Appendix D: Representative models
The profiles of different relevant physical quantities are shown for a few selected stellar models at five distinct effective temperatures corresponding to the three peaks in Γmax and the two troughs in between the peaks (cf. Fig. 2).
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Fig. D.1
Detailed structure examples for stellar models with an effective temperature near 50 000 K, for three different luminosities (cf. Fig. 2). The dashed line marks the point at which β falls below 0.15, i.e. the beginning of the inflated envelope. The square symbol marks the temperature TFe at which κ is maximum because of the iron opacity bump. The hatched regions show the convective zones. |
| Open with DEXTER | |
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Fig. D.2
Detailed structure examples for stellar models with an effective temperature near 25 000 K, for three different luminosities (cf. Fig. 2). The dashed line marks the point at which β falls below 0.15, i.e. the beginning of the inflated envelope. The square and the cross mark the temperatures TFe and TFe at which κ is maximum because of the iron and the helium opacity bumps respectively. The hatched regions show the convective zones. |
| Open with DEXTER | |
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Fig. D.3
Detailed structure examples for stellar models with an effective temperature near 5000 K, for two different luminosities (cf. Fig. 2). The dashed line marks the point at which β falls below 0.15, i.e. the beginning of the inflated envelope. The square, cross and the circle mark the temperatures TFe, THe, and TH at which κ is maximum because of the iron, helium, and hydrogen opacity bumps respectively. The hatched regions show the convective zones. |
| Open with DEXTER | |
 |
Fig. D.4
Detailed structure examples for stellar models with an effective temperature near 32 000 K, for three different luminosities (cf. Fig. 2). The dashed line marks the point at which β falls below 0.15, i.e. the beginning of the inflated envelope. The square symbol marks the temperature TFe at which κ is maximum because of the iron opacity bump. The hatched regions show the convective zones. |
| Open with DEXTER | |
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Fig. D.5
Detailed structure examples for stellar models with an effective temperature near 10 000 K, for three different luminosities (cf. Fig. 2). The dashed line marks the point at which β falls below 0.15, i.e. the beginning of the inflated envelope. The square, cross and the circle mark the temperatures TFe, THe, and TH at which κ is maximum because of the iron, helium, and hydrogen opacity bumps respectively. The hatched regions show the convective zones. |
| Open with DEXTER | |
© ESO, 2015
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