A metal-rich O star of has and a wind of terminal speed

PHYSICS · Multi-part · Fermi University Physics · Astrophysics & Cosmology · Stellar structure, energy generation and evolution · Stellar structure, energy generation and evolution

Stars from the Inside, Ch Stellar evolution: from the Hayashi track to the iron core, and the ages of clusters

Problem

A metal-rich O star of 60 M⊙60\,M_\odot has L=105.8 L⊙L = 10^{5.8}\,L_\odot and a wind of terminal speed v∞=3000 km s−1v_\infty = 3000\ \mathrm{km\,s^{-1}}. Its main-sequence life lasts about 3.5 Myr3.5\ \mathrm{Myr} (a model value, because tMS∝M−2.5t_{\rm MS}\propto M^{-2.5} is poor at this mass), and the hydrogen-rich envelope outside its eventual helium core holds about 35 M⊙35\,M_\odot. ((a)) Find the single-scattering limit M˙max⁡=L/(cv∞)\dot M_{\max} = L/(cv_\infty) in M⊙ yr−1M_\odot\,\mathrm{yr^{-1}}. ((b)) Its measured mass-loss rate is twice that limit. Taking the rate as constant over the main sequence, how much mass does the wind remove, and does it strip most of the envelope? ((c)) A metal-poor star of the same mass and luminosity has a wind three times weaker. What fraction of its envelope does it lose over the same life?

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