[mesa-users] Overshooting

Wed Jun 3 01:00:27 EDT 2015

Dear All,
the He-core burning is a notoriously difficult phase with regard to mixing, as we all know. The growing He-core and the
low opacity of He conspire to a layer above the proper convection that has been referred to as semi-convection, and it is home to secular instabilities in addition to dynamical timescale convective instabilities.

Merryfield (1995) http://adsabs.harvard.edu/abs/1995ApJ...444..318M investigated this situation 20 years ago based on hydro simulations, actually here in Victoria working as post-doc with Don VandenBerg. Since then and before many have looked into this situation, and the work of Norbert Langer in the 1980’s comes to mind as well. I attach some plots from my own thesis (1998) in which the effect of exponential overshooting is documented for core He-burning convection. Admittedly I constrained myself to small values that were considered reasonable at the time, based on comparison with observations of main-sequence stars. The erratic behaviours seen in core He-burning without overshooting (sometime refereed to as “breathing pulses”) do not go away, but for small values of f overshooting they do not become worse either. But I would entirely agree that convection plus this or any overshooting model can not be the right physics answer to the situation of core He-burning. Secular instabilities are involved.

The intention of the overshooting algorithm as implemented in MESA has always been to be used as a near-boundary approximation of convective boundary mixing (CBM) with relatively small f values. The assumption that necessitates this is the choice of reference length scale for the exponential decay, which is the pressure scale height at the Schwarzschild boundary. Back in the days I remember discussing this with Bernd Freytag and Hans-Gunther Ludwig extensively, and this was adopted in view of simplicity. However, this can give obviously unintended results, especially if a large f value is used and/or the pressure scale height is changing quite a bit in the overshooting layer.

The fact that the f value is different at different types of convective boundaries should not be too  surprising as there is no physics in this model that could capture the various ingredients that would induce more or less extensive convective boundary mixing. The only aspect of CBM that this model accounts for is a gradual decrease of the mixing efficiency through and beyond the Schwarzschild boundary, here in the form of an exponential decay. I would retain though that the exponential overshooting model is superior to an instantaneous overshooting for reasonable values of f adopted in numerous works by many authors over the past years. This notion seems to be supported by recent work by Ehsan and collaborators that he kindly pointed out to me, see their recent paper (Moravveji+ ’15, eprint arXiv:1505.06902, A&A accepted). I agree with Dave that hydrodynamic simulations are now capable to refine the convective boundary mixing model, and like Dave and his collaborators we are in the process of doing just that.

One thing, though that I should mention as a potential weakness of the overshooting implementation is the fact that as a non-local model (the diffusion coefficient in the tail of the overshooting region depends on the D0 and pressure scale many grid zones away at the Schwarzschild boundary) the diffusion coefficient with overshooting is not part of the Henyey joint-operator iteration and there is potentially an inconsistency between the D profile the model has adopted and the final solution the numerical scheme arrives at. This is something Bill and I have talked about several times, but as far as I know we do not yet have a solution for this.

A final note on nomenclature. I have now adopted the terminology "convective boundary mixing" (CBM) instead of overshooting. The reasoning here is that overshooting in the classical sense, i.e. coherent convective systems crossing the Schwarzschild boundary and then turning around, is not the physical mechanism we observe in all convection zone boundaries. Notably, in the deep interior where the convection is very efficient and adiabatic convective boundaries are very stiff. In Woodward etal (2015, ApJ) we have documented convective boundary mixing even in a case that is formally stable against the Kelvin-Helmholtz instability according to the 1D stratification. Still, convective boundary layers have on average a finite thickness that hydrodynamic simulations can now resolve. At other convective boundaries in the deep stellar interior other hydrodynamic instabilities  may dominate, yet many of these cases would not resemble our classical notion of overshooting or even penetration.

Well, before I continue here and write a paper, ….
All the best, Falk.

[cid:44FA8940-01AE-40C4-AE5F-27C5AFE9B8E2 at phys.uvic.ca]

[cid:239BD8F2-E958-4329-88D7-418DDF79ABB4 at phys.uvic.ca]

[cid:F2DBDA4A-22F9-41A7-A823-1A9D856D3CE1 at phys.uvic.ca]
[cid:3B404F5A-F7A3-4C4A-A493-D95C8A23E939 at phys.uvic.ca]

--
Falk Herwig
Dept of Physics & Astronomy, U of Victoria
fherwig at uvic.ca<mailto:fherwig at uvic.ca>, tel: +1 (250) 721-7743

On Jun 2, 2015, at 11:39 AM, David Arnett <wdarnett at gmail.com<mailto:wdarnett at gmail.com>> wrote:

The present implementation of overshooting in MESA causes large errors in some cases;
see  (Schindler et al 2015 ApJ accepted). We are working on a fix.
2014arXiv1410.8204S <http://cdsads.u-strasbg.fr/cgi-bin/nph-data_query?bibcode=2014arXiv1410.8204S&db_key=PRE&link_type=ABSTRACT&high=555a90a0bb02864>

<http://cdsads.u-strasbg.fr/cgi-bin/nph-data_query?bibcode=2014arXiv1410.8204S&db_key=PRE&link_type=ABSTRACT&high=555a90a0bb02864>
David Arnett
Regents Professor
Steward Observatory
University of Arizona

Facts are stubborn, but statistics are more pliable.  Mark Twain
Facts do not cease to exist because they are ignored.  Aldous Huxley
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