[mesa-users] Misuse of Ledoux criterion in mesa MLT
Bill Paxton
paxton at kitp.ucsb.edu
Mon Jun 16 15:40:33 EDT 2014
hi chris,
thanks for your input. before i reply to it, i want to wait for a response for Arlette. one confusing conversation at a time is all i can manage. ;D
but you might want to clarify what your "y" is and why you expect the convective zone to have y ~ 0.
-B
On Jun 16, 2014, at 12:27 PM, Chris Mankovich wrote:
> I think the crux of it is that although the local criteria are correct, there is no guarantee that your topmost convective zone is convectively neutral, i.e. y ~ 0. Indeed if y is discontinuous, then the tentative topmost convective zone you find by seeking a sign change in y is necessarily still superadiabatic (or super-Ledoux) and fluid elements are still accelerated upward of that point.
>
> Chris
>
>
> On Mon, Jun 16, 2014 at 10:37 AM, Bill Paxton <paxton at kitp.ucsb.edu> wrote:
> Hi Arlette,
>
>
> On Jun 16, 2014, at 1:56 AM, Arlette Grotsch wrote:
>
>> Hi Bill,
>>
>> Thanks for your mail! I shall try to make my point clearer!
>>
>> The criterions and combinations you describe are correct, no doubt about that. Our point refers to the determination of convective boundaries.
>
>
> i still don't understand. how is the determination of convective boundaries different than determining at each point whether it is convective or not? That's what I described in my email -- in mesa MLT each location is categorized as convective, semiconvective, radiative, or thermohaline. You say it that classification is correct, no doubt about it, but then you seem to imply it is incorrect in your next sentence by saying it gives bogus convective boundaries. Huh? Is the categorization in mesa using local values for gradients correct or not? If correct, that fixes the convective boundary as coming between locations with different classifications -- but perhaps you have something else in mind that is NOT part of local MLT as a way of (re)defining boundaries? But you say you are doing local MLT -- so I continue to be confused.
>
>
> Here's my main question for this email: is your analysis assuming a finite difference scheme? that might be the source of the confusion. mesa doesn't use that. we use a finite volume scheme -- cells and boundaries. that can make a huge difference for this.
>
> some older stellar evolution codes used a finite difference scheme where everything is defined at points without explicitly differentiating between cells and boundaries. i can certainly see how that might lead to a mess. but mesa doesn't do that.
>
> in mesa, abundances are defined in cells along with intensive variables T, Rho, P.... The extensive variables (R, L, M, v...) are defined at the boundaries between cells. mixing happens at boundaries. MLT applies to boundaries to calculate diffusion coefficients for mixing between the adjacent cells. if there is a stabilizing jump in abundances between adjacent cells (B >> 0 in the terms of my previous email), then there will be a huge grad_L at the boundary between them, and that will make MLT classify the boundary as semiconvective instead of convective (assuming that the boundary is Schw unstable). the large composition jump will thus lead to a boundary with negligible mixing (very small diffusion coefficients). the jump in composition will NOT be eroded by mixing across the boundary. so it doesn't seem to lead to the problems you mention. but perhaps i'm still just not understanding. please explain.
>
> if your answer is that "it doesn't matter whether finite difference or finite volume", then please try again to explain where the error lies in the mesa MLT where cell boundaries are classified on the basis of local information about gradients of cell values and composition jumps are not eroded.
>
>
> thanks,
> Bill
>
>
>
>
>>
>> Imagine the convective boundary as having an inner side (convective side) and an outer side (radiative side). Let’s now define the function y_1 = grad_rad - grad_ad and y_2 = grad_rad - grad_Ledoux. Depending on the criterion you adopt, y_1 or y_2 must be equal to 0 on the convective side, not on the radiative side.
>>
>> The problem is of course the possible presence of a discontinuity in y at the boundary.
>>
>> When is there a discontinuity in y?
>> 1. y_1 is discontinuous when mu is discontinuous at the boundary. This happens when the convective core grows, i.e. mostly in 2 cases:
>> (1) MS low mass stars with a growing convective core
>> (2) core helium burning stars
>>
>> 2. y_2 is discontinuous when grad_mu is discontinuous, i.e. in all MS stars during the whole MS phase (except at the very beginning).
>>
>> If y_1 or y_2 is 0 on the radiative side, a discontinuity means that the convective neutrality is not encountered at the last convective point and the model is not coherent.
>>
>> Let’s discuss the problem of the Ledoux criterion applied to compute the evolution of a low mass star (M > 1.2Msun). Imagine that the boundary of a convective core is searched for through (for instance) a change of sign of y_2. If the boundary estimated at the start of the iteration process is too small, the presence of a discontinuity will necessarily prevent any increase of the convective core mass. Indeed all smaller values will be accepted by the iteration process and the result is a rapidly vanishing convective core.
>>
>> In core helium burning stars, the situation is similar, whatever the criterion (Sch or Ledoux). Because of the chemical discontinuity, the boundary will remain blocked at the initial value and the convective core does not grow. The inner value of y grows and grows as helium is burned.
>>
>> In all these cases, y is not zero on the convective side, which illustrates the fact that the model is not coherent.
>>
>> The solution should consist in searching the zero of y through an extrapolation process from the convective (only) points. When doing this, convective cores in low mass stars are identical when computed with Ledoux or Schwarzschild.
>>
>> The best way to deal with convective boundaries would be to insert a double mesh point, which can easily reflect the convective and radiative sides of this boundary.
>>
>> Does this help?
>> Arlette
>>
>>
>>
>>
>>
>>
>>
>>>
>>> Schwarzschild stable: grad_rad <= grad_ad
>>> Ledoux stable: grad_rad <= grad_Ledoux (i.e., grad_ad + B replaces grad_ad in this criterion)
>>>
>>> There are 4 combinations of stable and unstable for the 2 criteria, and all are covered in the mesa MLT.
>>> Here are the names we use for the cases:
>>>
>>> "radiative": both Schwarzschild and Ledoux stable
>>> "convective": both Schwarzschild and Ledoux unstable
>>> "semiconvective": Schwarzschild unstable, but Ledoux stable
>>> grad_ad < grad_rad <= grad_ad + B (requires B > 0, i.e., stabilizing composition)
>>> "thermohaline": Ledoux unstable, but Schwarzschild stable
>>> grad_ad + B < grad_rad <= grad_ad (requires B < 0, i.e., destabilizing composition)
>>>
>>> The 4 case are treated separately in the mesa MLT for computing mixing diffusion coefficients and thermal transport at the location.
>>>
>>> When we turn off Ledoux in mesa, we set B = 0. In that situation, only radiative and convective cases apply. When Ledoux is on, some cases that were convective with B = 0 can become semiconvective (but only if B > 0), and some cases that were radiative can become thermohaline (but only if B < 0).
>>>
>>> Okay --- now, referencing that explanation could you perhaps point out the mistaken application of the Ledoux criterion in the mesa MLT? If there's a bug in mesa, I'll try to fix it!
>>>
>>> Thanks,
>>> Bill
>>>
>>>
>>>
>>>
>>>
>>> On Jun 15, 2014, at 12:20 AM, Arlette Grotsch wrote:
>>>
>>>> Hi Richard,
>>>>
>>>> When the Ledoux criterion is used (and applied on the radiative side), the convective core disappears only for low mass stars with an otherwise growing convective core. For a higher mass, like the 5M you show in your graph, the extent is smaller but it does not disappear. The problem can bee also seen on your graph: with the Ledoux criterion applied on the radiative side, the convective core cannot grow, even at the very beginning of MS, when the mu-gradient is very small, due to the strong stabilizing effect of the mu-gradient.
>>>>
>>>> Once more, this is an illustration of the fact that the criterion, Schwarzschild's or Ledoux's, should be applied on the convective side of the boundary.
>>>>
>>>> I hope this helps. Best wishes,
>>>> Arlette
>>>>
>>>>
>>>>> Le 15 juin 2014 à 05:55, Richard Townsend <townsend at astro.wisc.edu> a écrit :
>>>>>
>>>>> Hi Andrea & others —
>>>>>
>>>>> In fact, it turns out that the problem was a user error on my part; because I had not correctly set the ‘max_num_profile_models’ inlist parameter to a negative value, MESA was overwriting early-stage profile files with late stage (post-MS) ones. Hence, what I thought were MS models were in fact post-MS models, and therefore (quite correctly) had a radiative core.
>>>>>
>>>>> For the record, with this problem fixed, I went back and ran models with/without Ledoux. The attached plot shows the convective core mass as a function of core hydrogen mass fraction (i.e., the same plot shown by Andrea in his email, but for a 5 Msun model). The Ledoux core is certainly smaller than the Schwarzschild core, but nevertheless at no point during the MS evolution does it disappear.
>>>>>
>>>>> Thanks to all who responded to me, and apologies for the confusion!
>>>>>
>>>>> Best wishes,
>>>>>
>>>>> Rich
>>>>>
>>>>> <core_sizes.pdf>
>>>>>
>>>>>
>>>>>
>>>>>> On Jun 13, 2014, at 5:05 PM, Andrea Miglio <miglioa at bison.ph.bham.ac.uk> wrote:
>>>>>>
>>>>>> Hi Rich and Bill,
>>>>>>>> I’m playing around with evolving a 5 Msun model across the ZAMS. To my surprise, I find that core convection disappears (leading to a positive Brunt N2) when I set the use_Ledoux flag to .true.
>>>>>>>
>>>>>>> Just like what happens for the 3 Msun case in Fig 15 of the 2nd mesa paper, assuming you are running with no semiconvection.
>>>>>>>
>>>>>>>
>>>>>>>> Can someone explain what’s going on here, please!
>>>>>>>
>>>>>>> I look forward to hearing the explanation myself!
>>>>>>
>>>>>> I suspect the problem is always the same: the Ledoux criterion applied from the 'radiative side' leads (incorrectly) to smaller, eventually vanishing, convective cores.
>>>>>> I've attached a recent email thread where this issue was discussed in some detail.
>>>>>>
>>>>>> hope this helps,
>>>>>>
>>>>>> cheers,
>>>>>>
>>>>>> Andrea
>>>>>>
>>>>>>
>>>>>>
>>>>>>>> Da: Arlette Grotsch <Arlette.Noels at ulg.ac.be>
>>>>>>>> Oggetto: Re: Consistently extending the core boundary
>>>>>>>> Data: 09 giugno 2014 14:32:46 GMT+1
>>>>>>>> A: Andrea Miglio <miglioa at bison.ph.bham.ac.uk>
>>>>>>>> Cc: Ehsan Moravveji <Ehsan.Moravveji at ster.kuleuven.be>, David Arnett <wdarnett at gmail.com>, Conny Aerts <Conny.Aerts at ster.kuleuven.be>, Bill Paxton <paxton at kitp.ucsb.edu>, Warrick Ball <wball at astro.physik.uni-goettingen.de>, Diego Bossini <dbossini at bison.ph.bham.ac.uk>, Thoul Anne <anne.thoul at ulg.ac.be>, Pieter Degroote <Pieter.Degroote at ster.kuleuven.be>
>>>>>>>>
>>>>>>>> Dear all,
>>>>>>>>
>>>>>>>> Just an example of how the core behaves in a low mass star with the Ldx criterion applied on the convective side and on the radiative side, and with the Schwarzschild criterion. You can see the near identical behavior of the core evolution when the criterions are applied on the convective sides. The big advantage is of course a more coherent Brunt-Väisälä frequency.
>>>>>>>>
>>>>>>>> This means that using Ledoux or Schwarzschild criterion is the same for a convective cores, which is obvious since the mixing is assumed to be perfect so the criteria are identical. The problem of the Ledoux criterion arises when a radiative layer (not adjacent to a convective zone) becomes convective. The criterion should be Ledoux in that case. If grad rad is intermediate between grad ad and grad Ldx, the layer is not convective since convection is the result of the non-linear development of the linear instability of dynamically unstable gravity modes. Only some high degree g+ modes are likely found unstable, leading to semi-convection.
>>>>>>>>
>>>>>>>> I recommend the very interesting recent paper by Georgy, C. et al. 2014, MNRAS 439, L6, which gives arguments in favor of Ledoux.
>>>>>>>>
>>>>>>>> I am fully aware that the « real » situation is closer to 3D simulations than to our poor LMLT, but, half a loaf is better than no loaf😉 for the time being.
>>>>>>>>
>>>>>>>> Cheers,
>>>>>>>> Arlette
>>>>>> <mcSch.pdf>
>>>>>>>
>>>>>>>>
>>>>>>>>
>>>>>>>>
>>>>>>>>
>>>>>>>> Da: Arlette Grotsch <Arlette.Noels at ulg.ac.be>
>>>>>>> Oggetto: Re: Consistently extending the core boundary
>>>>>>> Data: 09 giugno 2014 13:56:33 GMT+1
>>>>>>> A: Andrea Miglio <miglioa at bison.ph.bham.ac.uk>
>>>>>>> Cc: Ehsan Moravveji <Ehsan.Moravveji at ster.kuleuven.be>, David Arnett <wdarnett at gmail.com>, Conny Aerts <Conny.Aerts at ster.kuleuven.be>, Bill Paxton <paxton at kitp.ucsb.edu>, Warrick Ball <wball at astro.physik.uni-goettingen.de>, Diego Bossini <dbossini at bison.ph.bham.ac.uk>, Thoul Anne <anne.thoul at ulg.ac.be>, Pieter Degroote <Pieter.Degroote at ster.kuleuven.be>
>>>>>>>
>>>>>>> Dear all,
>>>>>>>
>>>>>>> I of course fully agree with Andrea. Our paper is not at all presenting a new way of treating convective zones and convective boundaries. With the simple LMLT implemented in most codes (including our own CLES code), the boundary is searched for through an interpolation process of the function grad rad - grad ad (or grad Ledoux) in order to locate its zero, even when the function presents a discontinuity, which is the case with Schwarzschild when μ is discontinuous and is the case with Ledoux when gradient μ is discontinuous.
>>>>>>>
>>>>>>> We show that this leads to smaller convective cores in massive stars and vanishing convective cores in low mass stars when Ledoux is applied. Some problems also arise with Schwarzschild's criterion especially during core helium burning but H burning can be affected as well.
>>>>>>>
>>>>>>> If the estimated convective core mass is too small at a given iteration, the interpolation through a discontinuity will inevitably block the boundary and an expansion of the core can only be found when the initial estimation is too large.
>>>>>>>
>>>>>>> The remedy is an extrapolation from the layers inside the core which leads to grad rad = grad ad or grad Ldx on the convective side of the boundary. We also advocate the use of a double mesh point at each boundaries and chemical discontinuities, which is a great help for stability analyses.
>>>>>>>
>>>>>>> I shall be very happy to discuss these points in Geneva. I shall briefly present some of the related problems in my talk, especially those coming from an intermediate convection zone, for which, apart for showing the problems, I do not have any satisfying solutions😥.
>>>>>>>
>>>>>>> All the best,
>>>>>>> Arlette
>>>>>>
>>>>>>>>> Le 9 juin 2014 à 13:48, Andrea Miglio <miglioa at bison.ph.bham.ac.uk> a écrit :
>>>>>>>>>
>>>>>>>>> Dear all,
>>>>>>>>> sorry to get into the discussion quite late.
>>>>>>>>>
>>>>>>>>> The Gabriel et al paper is not advocating for a new method to determine convective boundaries, but just re-stating a point which was known decades ago but then got somehow lost. The risk we are facing is that, thanks to these wonderful asteroseismic constraints, we may end up claiming we are testing convection while what we are doing is merely fitting observations with models in which a simple - yet tricky to implement - theory is not implemented correctly.
>>>>>>>>>
>>>>>>>>> This is e.g. the case when computing models with the current implementation of the Ledoux criterion in MESA, which leads to very small convective cores and which also impacts on the efficiency of any additional process that depends on the definition of a convective boundary (e.g. semiconvection). Another example (which we are focussing on in Birmingham) are the properties of convective cores during the core-He burning phase.
>>>>>>>>> Diego Bossini here is working on the tricky (for any code) definition of the convective core in core-Helium burning stars and, although he made some progress, he is now focussing on getting a paper out: this is why he has been very quiet lately (apologies in particular to Warrick and Eshan for the little feedback from Birmingham)
>>>>>>>>>
>>>>>>>>> This message (and the paper) is by no means a criticism to MESA itself: the vast majority of the codes neglects this aspect. I am sure 3D hydro simulations will show us the way, but a precise implementation of the Schwarzschild criterion I would say is a pre-requisite for trying to introduce a more accurate description inspired by 3D hydro simulations.
>>>>>>>>>
>>>>>>>>> ok, after all this blathering, and having unfortunately too little time to get my hands dirty with the code in the next few weeks, what I suggest is that we set aside some time in Geneva and discuss the details. Arlette will also be in there and I am sure she would be happy to get involved in the discussion (I’ve added her in cc).
>>>>>>>>>
>>>>>>>>> thanks,
>>>>>>>>>
>>>>>>>>> regards,
>>>>>>>>>
>>>>>>>>> Andrea
>>>>>>
>>>>>>
>>>>>>> Il giorno 13/giu/2014, alle ore 22:31, Bill Paxton <paxton at kitp.ucsb.edu> ha scritto:
>>>>>>>
>>>>>>>
>>>>>>>> On Jun 13, 2014, at 2:14 PM, Richard Townsend wrote:
>>>>>>>>
>>>>>>>> Hi folks —
>>>>>>>>
>>>>>>>> I’m playing around with evolving a 5 Msun model across the ZAMS. To my surprise, I find that core convection disappears (leading to a positive Brunt N2) when I set the use_Ledoux flag to .true.
>>>>>>>
>>>>>>> Just like what happens for the 3 Msun case in Fig 15 of the 2nd mesa paper, assuming you are running with no semiconvection.
>>>>>>>
>>>>>>>
>>>>>>>> Can someone explain what’s going on here, please!
>>>>>>>
>>>>>>> I look forward to hearing the explanation myself!
>>>>>>>
>>>>>>>
>>>>>>>>
>>>>>>>> Also, things look more or less OK when I set use_Ledoux = .false. — but the Brunt is a bit noisy in the mu-gradient zone. What’s considered the best approach to smoothing this noise?
>>>>>>>
>>>>>>>
>>>>>>>
>>>>>>> smoothing is the best approach to smoothing. try increasing the value for
>>>>>>>
>>>>>>> num_cells_for_smooth_brunt_B = 2
>>>>>>> ! number of cells on either side to use in weighted smoothing of brunt_B
>>>>>>>
>>>>>>>
>>>>>>> -b
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