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

## Coefficients of Hough function

- rhtownsend
- Site Admin
**Posts:**313**Joined:**Sun Mar 31, 2013 4:22 pm

### Re: Coefficients of Hough function

Hi Zhao --fffeynman wrote: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

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

### Re: Coefficients of Hough function

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

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
- Site Admin
**Posts:**313**Joined:**Sun Mar 31, 2013 4:22 pm

### Re: Coefficients of Hough function

Hi Chris --mankovich wrote: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

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

### Re: Coefficients of Hough function

Thanks Rich, that's most helpful. Cheers!