1.3.1 Model 1-001

We see that whil LOSC and GYRE behaves very similarly, there is a signficiant difference with GraCo, in particular for \(\ell = 0\) modes. Having verified, that outer boundary conditios are well \(\delta P\) for all the computations, we conclude that, as found in ESTA/CoRoT exercises, a O(2) integration scheme produces too large differences even for 4K models.

1.3.2 Model 1-002

For model 1-002, results are equivalent to those of 1-001, except for the general behaviour of frequency differences, which are smoother (no ridges are present). In order to ensure good compatibility, i.e. \(\Delta f < 0.01\) for the whole p-mode domain (as shown in LOSC-GYRE comparisons), we recalculate the frequencies but using the same integration scheme in all the codes.

1.4.1 Model 1-001

1.4.2 Model 1-002

1.5.1 Model 1-001

Even at second order the behavior of GraCo’s \(\ell=0\) modes is quite different and have nothing to do (apparently with the outer boundary condition, which is the same as the other codes) but the implementation of the radial modes computation itself. On the other hand the largest differences for \(\ell=1,2,3\) are of the order of \(0.06\,\mu\mathrm{Hz}\) (for the highest radial order) and around \(0.04\,\mu\mathrm{Hz}\) around \(\nu_{\mathrm{max}}\). This, in return, is the average difference for the whole range betwee GYRE and LOSC.

1.5.2 Model 1-002

As for the other IS, this second model behaves (overall) better than 1-001, with similar numerical results

1.6.1 Model 1-001

As expected the differences of large separations with GraCo is larger for radial modes (insets depicts the differences only for non-radial modes). As for the frequencies, such differences grow with \(n\). However, for the large separation, such differences are smaller than those found for the individual frequencies.

1.6.2 Model 1-002

The comparison confirms the results obtained for the individual frequency comparisons. Except for the radial modes, for which differences in the large separation reach \(0.015 \mu\mathrm{Hz}\) for the highest orders, the separations for the non-radial modes span between \(10^{-5}\) up to \(10^{-3}\mu\mathrm{Hz}\).