Comparing GYRE polytropic calculations with MU88

[dariusb]

Hi,

I've been trying to use GYRE to compute the pulsation modes in a polytrope.
I found that I could not match GYRE results with the results of Mullan and Ulrich (Ap. J. 331, 1013-1028 (1988); paper attached here).

I quote the results of the adiabatic calculation for polytrope of n_poly = 3, l = 2 with Gamma (ad. exponent) = 5/3 here.
I've attached the input files, and the HDF5 files containing the solutions to the Lane-Emden equation that I obtained from Poly-Web (with n=10,000).
(I also compared the calculations of Poly-Web with simple ode45 calculations in Matlab and found that the two agree well.)

I'm comparing GYRE results with Table 5 in the MU88 paper.
The eigenfrequencies there are quoted in microHz. So, to obtain the dimensionless frequency values, I divided MU98 results with their standard frequency of 99.778 microHz.

Here are the results of the comparison:

Code: Select all

n_p  GYRE (dimensionless) MU88 (dimensionless) diff
  12  17.798566070357630  18.009240513940949   0.210674443583319
  13  19.053638741113261  19.258553989857482   0.204915248744221
  14  20.307647148745161  20.506865240834653   0.199218092089492
  15  21.560666941618109  21.754304556114572   0.193637614496463
  16  22.812768928028021  23.000962135941787   0.188193207913766
  17  24.064019119958981  24.246928180560843   0.182909060601862
  18  25.314478781948690  25.492292890216280   0.177814108267590
  19  26.564204667608522  26.737086331656275   0.172881664047754
  20  27.813249240906021  27.981388682875984   0.168139441969963
  21  29.061661104514009  29.225240032872978   0.163578928358969

I'm using GYRE 2.3 and MESASDK (April 2013) on Mac OS 10.9 (Mavericks) with 4 cores.
I tried changing the boundary conditions and the integrators to no avail.

Also, I've only used GYRE for a week so I could be making really ridiculous mistakes in my calculations here.
Please let me know if you need any further information that could be helpful. Thank you in advance.

Best Regards,
—Darius

[rhtownsend]

Hi Darius --

It looks like you're making sensible choices with the input parameters to GYRE. In fact, the issue is with the Mullan & Ulrich (1988) frequencies -- they are calculated within the Cowling approximation, where the perturbation to the gravitational potential is neglected. GYRE doesn't use the Cowling approximation, and therefore gives slightly different results (with the differences getting smaller as the mode order becomes higher).

Fortunately, all is not lost -- instead of comparing against Mullan & Ulrich, try looking at the results in Christensen-Dalsgaard & Mullan (1994). This latter paper also doesn't use the Cowling approximation, so you should be able to do a like-for-like comparison.

Best wishes,

Rich

[dariusb]

Hi Rich,

Thanks a lot for pointing that out to me. I incorrectly thought that the 'reduce_order = .TRUE.' option means that GYRE is performing Cowling approximation.

Here's my comparison with Christensen-Dalsgaard and Mullan (MNRAS 270, 921-935). They agree beautifully!

Code: Select all

n_p  GYRE(dimensionless)  C-D&M94(dimensionless) diff
  12  17.798566070357630  17.798565819845635   0.000000250511995
  13  19.053638741113261  19.053637942802016   0.000000798311245
  14  20.307647148745161  20.307646527637665   0.000000621107496
  15  21.560666941618109  21.560666682976919   0.000000258641190
  16  22.812768928028021  22.812768510202510   0.000000417825511
  17  24.064019119958981  24.064018104903855   0.000001015055126
  18  25.314478781948690  25.314477556877083   0.000001225071607
  19  26.564204667608522  26.564202947228370   0.000001720380151
  20  27.813249240906021  27.813247352718921   0.000001888187100
  21  29.061661104514009  29.061658842868319   0.000002261645690

Thank you again.
—Darius

[rhtownsend]

OK, that's good!

But I wonder whether we should be expecting better agreement. Any thoughts?

[dariusb]

Hi Rich,

C-D&M94 quotes their numbers up to 8th significant figure for the standard frequency and (most of) the eigenfrequencies.
So, with only rudimentary comparisons, I think that GYRE results and C-D&M's results should agree at least to the 7th significant figure.

I tried some quick calculations using MAGNUS_GL4 and MAGNUS_GL6 for n_poly = 3, l = 2, n = 50,000:

Code: Select all

n_pg  C-D&M (dim-less)  MAGNUS_GL4 (dim-less)  MAGNUS_GL6 (dim-less)
40    52.704371         52.70437674195573       52.70437661953667
1      3.9068732         3.906873716291662       3.906873716291651
-1     2.2168836         2.216883693995618       2.216883693995617
-55    0.12187254        0.1218725539390301      0.1218725539390620

that agree pretty well to the 7th significant figure.
I do notice that if I used n = 10,000, instead of 50,000, sometimes the frequencies only agree up to 6th significant figure.
I don't know if increasing n even further would improve the agreement.

What are your thoughts on this?
—Darius