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

[Warrick Ball]

Andrea,

Thanks for the reply!

I've made another pass through the code, and I think I misunderstood it 
the first time.  It now looks like the convective boundaries are specified 
by set_mlt_boundary_info() in star/private/mix_info.f:342.  This is a 
relatively simple loop that passes through the model and compares the 
mixing_types of neighbouring points.  When the mixing_types differ, it 
decides whether or not to use the Ledoux or Schwarzschild gradient, then 
finally does the interpolation to determine at which point the relevant 
criterion is satisfied.

So that's where the interpolation is made.  But how to fix it...?  The 
"double mesh-point" solution is more than I have time to try right now...

Cheers,
Warrick


On Tue, 6 May 2014, Andrea Miglio wrote:

> Hi Warrick,
> there is indeed a problem in how the Ledoux criterion is implemented in MESA, and this of course propagates into any treatments of semiconvection.
>
> Actually, as the paper points out and you've summarised, the problem (at least how we see it) lies in the definition of convective boundaries themselves which can have quite dramatic consequences on the size and evolution of convective cores.
>
> Diego Bossini here in Birmingham is running tests to understand on how convective boundaries are determined in MESA (focusing on models in the core He-burining phase): it would be just great if you/ Bill /others are willing to invest time on these issues!
>
> cheers, and thanks for bringing this up: MESA and the MESA forum are a great opportunity to openly discuss issues that everybody has to deal with in stellar evolution codes...
>
> Andrea
>
>
> Il giorno 06/mag/2014, alle ore 10:17, Warrick Ball <wball at astro.physik.uni-goettingen.de> ha scritto:
>
>> 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<profile27.data.gz><convective_criteria.png>------------------------------------------------------------------------------
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>


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