Accuracy of the numerical computation of solar g-modes

TL;DR

This paper evaluates the numerical accuracy of solar g-mode frequency computations, demonstrating that current models and methods achieve an accuracy sufficient for matching observational data within 0.01 μHz.

Contribution

It assesses the numerical precision of different pulsation codes and confirms that existing methods meet the accuracy requirements for solar g-mode analysis.

Findings

Numerical accuracy of about 0.01 μHz achieved with current models.

Richardson extrapolation improves frequency precision.

Comparison of different codes confirms reliability of results.

Abstract

From the recent work of the Evolution and Seismic Tools Activity (ESTA, Monteiro et al. 2006; Lebreton et al. 2008), whose Task 2 is devoted to compare pulsational frequencies computed using most of the pulsational codes available in the asteroseismic community, the dependence of the theoretical frequencies with non-physical choices is now quite well fixed. To ensure that the accuracy of the computed frequencies is of the same order of magnitude or better than the observational errors, some requirements in the equilibrium models and the numerical resolutions of the pulsational equations must be followed. In particular, we have verified the numerical accuracy obtained with the Saclay seismic model, which is used to study the solar g-mode region (60 to 140$\mu$Hz). We have compared the results coming from the Aarhus adiabatic pulsation code (ADIPLS), with the frequencies computed with the Granada Code (GraCo) taking into account several possible choices. We have concluded that the present equilibrium models and the use of the Richardson extrapolation ensure an accuracy of the order of $0.01 \mu Hz$ in the determination of the frequencies, which is quite enough for our purposes.