[mesa-users] arxiv:1405.0128: "On the proper use of the Schwarzschild and Ledoux criteria"

[Warrick Ball]

Hi all,

I noticed this paper on arXiv yesterday, and was wondering what the 
community's take is.


http://arxiv.org/abs/1405.0128

TITLE:  On the proper use of the Schwarzschild and Ledoux criteria in 
stellar evolution computations


In short, the authors claim that the boundaries of convective zones are 
only correctly specified if they are determined by extrapolating from 
inside the convective zone.  They detail how the computation goes awry 
(though I need to go through that part again) and also specify that a 
model can be checked by looking at whether grad_r - grad_a = 0 on the 
convective side of a convective boundary.  They focus on results from MESA 
Paper II (see Figs. 13-15) and Silva Aguirre et al. (2011).

I've attached a plot from the semiconvection test suite, with 
alpha_semiconvection = 0, to compare to Fig. 6 in the paper.  (I apologize 
for the quality.  It's a quick hack to look at what's going on.)  The red, 
green and blue curves show the radiative, adiabatic, and Ledoux 
temperature gradients.  The magenta and cyan curves show the hydrogen and 
helium abundances, so I could see where the extent of the fully mixed 
region.  The MESA model (profile27.data) seems to correspond to the 
"incorrectly" computed model on the right of their Fig. 6.  That is, at 
the boundary of the fully convective region, grad_r != grad_a.  I can 
intuitively see why this is suspect.  If the fully convective region is 
fully mixed, then the Ledoux gradient (grad_L) should be zero anyway, 
until you reach the edge of the convection zone.  So the boundary of this 
zone should have grad_r = grad_a.  Past this point, there can be the 
composition gradient that separates the Schwarzschild and Ledoux criteria.

So, should I be worried about using semiconvection in MESA?  I tried to 
dig around in the MLT routines for MESA, but I eventually went cross-eyed 
looking at the subroutines locate_convection_boundaries(), 
locate_mixing_boundaries(), and two subroutines they contain, 
end_of_convective_region() and end_of_mixing_region(), all located in
star/private/mix_info.f (which calls subroutines in mlt_info.f, which 
itself calls from the MLT module).  I imagine this is the appropriate area 
to see how the convective boundaries are determined.  I'd be happy to see 
if I can implement the proposed "fix" and see how it changes things, if 
someone can steer me a bit better in the right direction.

All input welcome!

Cheers,
Warrick




------------
Warrick Ball
Postdoc, Institut für Astrophysik Göttingen
wball at astro.physik.uni-goettingen.de
+49 (0) 551 39 5069
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