[mesa-users] Misuse of Ledoux criterion in mesa MLT

[Bill Paxton]

Hi Arlette,

I think we have reached a natural stopping point.  Let me try to summarize the situation as I understand it.

You and the authors of Gabriel et al 2014 do not think it is physically possible to have a separate semiconvective zone adjacent to a convective zone.   You've made that clear in your emails; they make it clear in their statement that the only correct use of the Ledoux criterion is in radiative regions to check for instability caused by composition gradients (i.e. to check if there is what in mesa would be called a "thermohaline mixing" region).  Some other authors seem to disagree since they've written papers about semiconvection and published results showing it in stellar evolution results.

I'm perfectly happy to let that debate go forward without me!   MESA doesn't take sides on that sort of argument.  And that's the main point of my hopefully final email in this thread.

MESA is a tool for exploring different options such as whether or not to include semiconvection in a stellar model.  The fact that there is a figure in the MESA paper showing semiconvection does not mean that we require the use of semiconvection; on the contrary, we make it easy for users to turn it off just by changing a single control parameter.   

It isn't a bug in MESA that users can turn on semiconvection, it is a feature!  And if a MESA user wants to explore your belief that it is necessary to eliminate semiconvective regions and pick convective boundaries according to the Schwarzschild criterion, no problem --- just make one small edit to the inlist file and MESA will do it.

Bottom line: if there is a misuse of the Ledoux criterion in MESA it is the result of a user choice rather than a bug in MESA itself.  

In there is a fault, it is in the setting of controls, not in the code that implements the possible choices.

Or as Shakespeare put it in Julius Caesar (I,ii,140):

	"The fault, dear Brutus, is not in our stars".


As a minor issue, there have been comments both in emails and in the Gabriel et al paper about implementation details such as introducing double mesh points at convective boundaries.   Those comments seem to be based on a picture of stellar evolution codes created in the 1960s; there is such a gap between the comments and how a 21st century code such as MESA actually works that it is difficult to respond other than to say "Huh?".   In particular, MESA doesn't assume perfect mixing, and as a result it doesn't scan inward or outward to search for boundaries of convection zones to be fully mixed.  Also, MESA doesn't use a finite difference scheme in which it would make sense to talk about introducing double points; instead as I've explained it uses a finite volume scheme -- this is covered in detail in the MESA instrument papers.   And of course since MESA is open source, you and the Gabriel el al authors are welcome to take a look inside and then let us know if you find problems.   You don't need to guess what it is doing or (falsely) assume it is doing the same thing as some other code you happen to be familiar with.

Finally, I want to thank you for this exchange.  It has pointed out a problem in MESA that I will fix in the next release.  I failed to provide for an option to allow for only one or the other of semiconvection or thermohaline mixing -- it was both or neither according to whether the flag "use_Ledoux_criterion" was true or false.  That will be fixed by replacing the single flag by two, one to enable semiconvection and another to enable thermohaline mixing.  Then it will be possible to try the combination that seems to be the choice of you and the Gabriel et al authors: turn semiconvection off but allow thermohaline mixing.

Best wishes,
Bill











On Jun 19, 2014, at 1:17 AM, Arlette Grotsch wrote:

> Hi Bill,
> 
> I comment the first part of your mail, which is the most important in order to understand what is going on. My comments are based on MLT theory.
> 
> 
>> 
>> In your 1st answer, you say your convective region is "pure", no semiconvection.  According to the definitions I think we've agreed to use, that means it is unstable both for Schw and Ledoux (in contrast to semiconvection which is unstable for Schw but not for Ledoux).  So far just definitions, but i'll spell it out in excessive detail as is my usual style.  For cases involving semiconvection, the boundary of the convection zone is where it changes from Ledoux unstable (convective) to Ledoux stable (semiconvective).  Both convective and semiconvective are Schw unstable, so there is no change in that criterion at the boundary.  It looks like this (again using grad_L = grad_ad + B, where B is the composition gradient term).
>> 
>> 		Convective			<boundary>	Semiconvective		
>> 	Schw unstable (grad_rad > grad_ad)	   |		Schw unstable (grad_rad > grad_ad)
>> 	Ledoux unstable (grad_rad > grad_L)	   |		Ledoux stable (grad_rad < grad_L)
> 
> Important: At the boundary —>                             grad_rad = grad_ad  | grad_rad > grad_ad
>                                                                                     L_rad = L               | L_rad = L
> Since the mixing is assumed to be perfect in the convective region,        |
> grad_mu = 0 and grad_L = grad_ad. 
> 
> This comes directly out of the MLT theory, as we discuss in Gabriel et al. (attached file). See our Fig. 6 (left panel) where convective boundary is located at the jump.
>                                                      
>>         
>> Hurray!  Now we clear about the convective boundary in the presence of semiconvection.  We expect a change in sign of (grad_L - grad_rad), but we require (grad_rad > grad_ad) to be positive on both sides.
> 
>>  
> We require grad_rad - grad_ad to be positive on the semi convective side and zero on the convective side. So the function grad_rad - grad_ad jumps from zero to a positive value at the boundary if there is a discontinuity in the chemical composition (this happens when the convective core is growing). The function grad_rad - grad_L jumps from zero to a positive value at the boundary if there is a gradient of chemical composition (when the convective core shrinks).
> 
>> Of course if there is no semiconvection, then it would look like the following with both Schw and Ledoux switching together from unstable to stable at the boundary.
>> 
>> 		Convective			<boundary>	Radiative		
>> 	Schw unstable (grad_rad > grad_ad)	   |		Schw stable (grad_rad < grad_ad)
>> 	Ledoux unstable (grad_rad > grad_L)	   |		Ledoux stable (grad_rad < grad_L)
>> 
> Important: At the boundary —>                             grad_rad = grad_ad  | grad_rad < or = grad_ad
>                                                                                     L_rad = L               | L_rad = L
> Since the mixing is assumed to be perfect in the convective region,        |
> grad_mu = 0 and grad_L = grad_ad. 
> 
> If the check on (grad_rad - grad_ad (or grad_L)) is made layer by layer, it will be impossible in cases of discontinuities in mu or grad_mu to have zero on the convective side of the boundary.
> 
> Do we agree on this?
> 
> Cheers,
> Arlette
> 
> 
> 

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