[mesa-users] Calculating oscillation modes of higher degree

[Richard Townsend]

> On Nov 25, 2014, at 3:32 PM, Bill Paxton <paxton at kitp.ucsb.edu> wrote:
> 
> Hi Wiebke,
> 
> On Nov 25, 2014, at 11:31 AM, Wiebke Herzberg wrote:
> 
>> Is it indeed a problem with the hydrostatic equilibrium that hampers the mode calculation? 
> 
> 
> 
> Pieter Degroote has repeatedly told me that the hydrostatic equilibrium solutions in mesa/star were not a problem.
> This quote is from a 2013 email from Pieter to me on the topic of numerical issues including hydrostatic equilibrium in mesa/star models for asteroseisomology:
> 
> On Feb 25, 2013, at 5:48 AM, Pieter Degroote wrote:
> 
>> In real applications, people still interpolate the model themselves to have a higher mesh density in the center (for gravity modes) or envelope (for pressure modes). So they will interpolate the model anyway, breaking numerical hydrostatic equilibrium anyway unless this is forced. Joergen actually prefers to  reintegrate the models to satisfy (his definition of) equilibrium (but in the process changing their mass or radius slightly)
> 
> 
> 
> I don't understand what Rich had in mind when he suggested that hydrostatic balance in the model might be the problem.  Perhaps he can elaborate on that -- and provide us with a good solution too!   I certainly hope so.   And perhaps there are also other users who can also comment on this issue.  I'd be interested to hear more.
> 

There’s certainly an issue with certain MESA models — as written out in GYRE format, or one of the other formats — not completely satisfying the stellar structure equations (hydrostatic eqm., mass conservation). I’ve been pointing this issue out for a year now, but maybe my comments haven’t reached the ears they needed to! 

The result of not satisfying the structure equations is that non-consecutive or non-monotonic mode indices (n) arise, even though these are expressly forbidden for radial (l=0) and dipole (l=1) oscillations (the situation is less certain for higher-order modes, but in practice mode orders seem to remain consecutive and monotonic). 

It’s possible to modify the model to try to re-enforce the structure equations — this is the ‘regularize’ option in recent releases of GYRE. But a better approach would be to establish the true origin of the problem (is is the interpolation from cell-centered to face-centered variables?) and sort things out there.

I’d appreciate any help I can get on fixing this — I’ve been worrying about it for some time now.

cheers,

Rich

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