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

[Chris Mankovich]

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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