[mesa-users] Too much mesh points

Ehsan Moravveji e.moravveji at gmail.com
Tue Aug 9 09:53:46 EDT 2016


> On 08 Aug 2016, at 17:35, David Arnett <wdarnett at gmail.com> wrote:
> 
> Hi Ehsan,
> 
> I think your plot agrees with my point: steep composition boundaries (or any steep boundaries) change the propagation and reflection of waves, whether the steepness is real or computational. I wonder whether we can use Kepler (and company) data to constrain how steep (or shallow) such boundaries are. We have hydro predictions for the late stages already, but Kepler only has data for H and He burning. We can extend the hydro predictions to these stages, but it takes hard work;-(
Kepler has provided hundreds of beautiful light curves for main sequence stars, earlier than mid-F-type, which pulsate predominantly in g-modes; there are no supergiants. Even if there were any, the pulsation periods would be comparable to the mission duration, and essentially useless for seismic purposes.
The Kepler g-mode pulsators (SPB and gamma Dor) provide the best tests for any theory of convection, because the inner turning point of such waves is the interface between the fully mixed core and the radiative envelope; thus, such waves have a great “feel” of the steepness of the boundary, and the required mixing in that neighbourhood. 

> 
> However, back to your figure: does the base model you feed to GYRE have steep boundaries?
To answer your question, I have attached several Brunt-Vaisala profiles, corresponding to all models I showed yesterday. I have put an exponential overshoot with f=0.005. So, the boundary (N^2) is slightly smoothed. Clearly the shape of the N2 profile in the mu-gradient region depends on the number of mesh, and is pretty noisy.

A critical feature in this figure is that the width of the mu-gradient zone depends explicitly on how the meshing is treated (please compare, e.g., the black and red lines). By “improving" the mesh, different profiles converge better to a form the N2 composition peak (at the cost of additional noise therein). 
These subtle differences immediately translate into the depths of period spacing dips that I compared in my last email. So, before comparing observed and model period spacings, one must ensure that the meshing around the mu-gradient zone sufficiently constrains the width of this region.

> Did you interpolate smoothly or did you "fit with step functions"? Do a spline fit on the lowest zoning, interpolate to finer zoning, and compare that. We need to know how the results depend upon the interpolation/zoning algorithm.  It should be easy (relatively easy) for you to do this now. We might learn something we need to know. Let me know what you find!
I propose we take the rest of this discussion offline, and get back to the public with some highlights.

Regards,
Ehsan.



> 
> My dumb prediction (please show me wrong): A smooth interpolation will not change much when zones are added, but  "step function" rezoning will.
> 
> Thanks for your clear reply,
> Dave 
> 
> On Mon, Aug 8, 2016 at 4:02 AM, Ehsan Moravveji <e.moravveji at gmail.com <mailto:e.moravveji at gmail.com>> wrote:
> Dear Dave,
> 
> Thanks for your insightful remarks; it is always great to hear your words.
> Indeed, nothing fills up the void of "missing physics” in massive star evolution, but the physics itself; to be developed, implemented and tested against observations.
> Thus, I never plea to increasing number of mesh points, to compensate for our lack of knowledge of stellar interiors.
> 
> The reason for tuning the number of mesh is that I pipe MESA output into GYRE, for later seismic modelling of beta Cephei and SPB stars.
> Back in 2008, and in preparation for seismic interpretation of CoRoT data, an interesting exercise was done among several pulsation code developers, and it is published in Moya et al. (2008, Ap&SS) <http://adsabs.harvard.edu/abs/2008Ap&SS.316..231M>. I quote from their abstract:
> 
> “… Two equilibrium models with different grids, 2172 and 4042 mesh points, have been used, .... Comparing the results for these two models illustrates the effect of the number of mesh points and their distribution in particularly critical parts of the model, such as the steep composition gradient outside the convective core. ...”
> 
> So, to prepare for modelling Kepler data (which exceeds CoRoT in precision), we have to ensure that such numerical issues are better taken care of. That is the only reason that I put several mesh adjustment weights around "regions of interest”, which is actually one of MESA’s niches.
> 
> If you’re still reading his email with interest, then, I have attached a figure I made quite some time ago, showing the influence of meshing in MESA on the period spacing of g-modes in SPB models (3 Msun). All used models have identical physics (same inlist, same age). The only difference is in the meshing: in the first 6 top panels, I only change the mesh_delta_coeff (delta) between 1 and 0.02, giving 863 to 47000 mesh points. A visual inspection quickly tells how the dips in the period spacing (Delta P) are modified. In the latter two (bottom) panels, I use MESA’s mesh refinements with a modest mesh_delta_coeff value. Then, the Delta P for the last model with 4100 mesh looks “similar” to some of high-resolution models (in the observed SPB period range of 1 to 3 days). Then, I stop adding more mesh.
> 
> The Kepler SPB stars (with tens of observable g-modes easily probing the near-core environment) are only one among many other applications, where going beyond MLT is urgently needed. We’re desperately waiting for it … 
> Fortunately, asteroseismology can quantitatively test boundary mixing. 
> 
> Thanks again Dave for your motivating email.
> 
> Regards,
> Ehsan.
> 
> 
> 
> 
> 
>> On 07 Aug 2016, at 17:46, David Arnett <wdarnett at gmail.com <mailto:wdarnett at gmail.com>> wrote:
>> 
>> Hi Ehsan,
>> 
>> You are asking for more resolution than the physics in MESA can provide. MESA is great, but it is only as good as the accepted science we give Bill to implement. Mixing-length theory (MLT) fails at convective boundaries (it is singular there, and as 3D simulations have shown a boundary layer develops, for braking). None of this is in MLT, so we have to use various patches to get over this embarrassment. Finer zoning does not capture missing physics. I suspect that the default mesh would contain as much correct information as the 3,000 mesh points you seek.  
>> 
>> If you wish to do convective boundaries better, you must go beyond MLT.
>> 
>> -- 
>> 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
> 
> 
> 
> 
> 
> 
> -- 
> 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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