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Matteo Cantiello edited For_convection_to_develop.tex
about 11 years ago
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is coupled to the internal energy of the gas or not. Since the helium convection zone
occurs very close to the surface in our models, these
additional uncertainties could be relevant.
Ideally, the properties of the helium convection zone could be studied
through multi-dimensional hydrodynamic calculations. However,
the large thermal diffusivity poses a
formidable computational challenge since it makes the
problem numerically stiff: the diffusive timescale is much shorter than the dynamical one, which leads
to very short time steps if an explicit solver is used (unfortunately, most codes used for compressible
convection are explicit). Any simulation would have only limited value unless it includes a
sufficiently realistic treatment of the coupling between plasma and radiation.
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.