Coefficients of Hough function

[fffeynman]

Hi, Rich
Is it possible to add the coefficients of Hough function as a combination of spherical harmonics
to the mode or summary file? It is interesting to use them to calculate mode visibility for g modes.
Thanks!

best regards,
Zhao

[rhtownsend]

Hi, Rich
Is it possible to add the coefficients of Hough function as a combination of spherical harmonics
to the mode or summary file? It is interesting to use them to calculate mode visibility for g modes.
Thanks!

best regards,
Zhao

Hi Zhao --

GYRE doesn't have direct access to the coefficients, as it only needs the Hough eigenvalues (lambda) to solve the pulsation equations within the traditional approximation (and it uses pre-calculated tables to evaluate these eigenvalues).

However, it should be relatively straightforward to write a wrapper around the astro_hough module (see src/extern/astro/astro_hough.fpp) which does what you want. Feel free to email me if you would like some help with this.

Best wishes,

Rich

[mankovich]

Hi Rich (and fellow GYREators),

Can I ask you to elaborate a little bit on what the tables contain? Am I right in thinking that the tables contain coefficients to Chebyshev polynomials fit to solutions for the Hough eigenvalues obtained numerically?

(For a little context, I started digging around when I noticed that the traditional approximation only works for l≤3 as a result of the coverage of gyre/data/trad_table.h5. I suppose to calculate the eigenvalues on the fly as part of a GYRE calculation would be significantly more complexity than it's worth!)

Cheers,

chris

[rhtownsend]

Hi Rich (and fellow GYREators),

Can I ask you to elaborate a little bit on what the tables contain? Am I right in thinking that the tables contain coefficients to Chebyshev polynomials fit to solutions for the Hough eigenvalues obtained numerically?

(For a little context, I started digging around when I noticed that the traditional approximation only works for l≤3 as a result of the coverage of gyre/data/trad_table.h5. I suppose to calculate the eigenvalues on the fly as part of a GYRE calculation would be significantly more complexity than it's worth!)

Cheers,

chris

Hi Chris --

Sort of! The Chebyshev fits are to lambda/(l(l+1)) for |nu| < 1, where lambda is the Hough eigenvalue.

For |nu| > 1, the fits are to the ratio lambda/lambda_asymp, where lambda_asymp is the asymptotic eigenvalue found in Townsend (2003).

In the latest version of GYRE (5.0, currently pre-release), I extend the fits up to higher l,m (10, I think). Also, I use an improved routine for calculating the eigenvalues, and an improved asymptotic formula for lambda_asymp.

You're right that fits are used for efficiency reasons -- in differentially rotating stars lambda must be evaluated at each grid point, which can be very time consuming if we're doing it on-the-fly.

cheers,

Rich

[mankovich]

Thanks Rich, that's most helpful. Cheers!