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Matteo Cantiello deleted file In_the_presence_of.tex about 11 years ago

Commit id: 0c322cc5168aa452e850d705f39f3569bbf2ea62

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In the presence of strong wind mass-loss, another consideration related to the He convective zone becomes important, due to the fact that it comprises only a tiny amount of mass. Convection can set in only if the turnover time $\tau_{\rm turn}\simeq \hp/\varv_c$ is shorter than the time scale for which convection is predicted to prevail at a fixed Lagrangian mass shell inside the convection zone, $\tau_{\rm conv}$, which is $\tau_{\rm conv} \simeq \Delta M_{\rm conv}/\dot M$. We find a critical mass-loss rate $\dot{M} \sim 10^{-6} \mso \rm{yr}^{-1}$, above which convection has no time to develop in the helium region, since the wind is removing an amount of mass equivalent to the mass of the convection zone before a convective eddy can turn over (see Tab.~\ref{clumps}). For a metallicity $Z$=0.02, stars above 40 $\mso$ cannot develop the He convection zone, and in a 20 $\mso$ such a layer is convective only for 10 - 100 turnovers before convection moves to a lower mass coordinate. None of these concerns is significant for the iron convection zone (FeCZ hereafter), where convection is always fully developed. Moreover the convective velocities for the FeCZ are always found to be much higher than those in the helium convection zones. We disregard the occurrence of the helium convection zones unless it is explicitly mentioned.