Inter-comparison of the g-, f- and p-modes calculated using different oscillation codes for a given stellar model

TL;DR

This study compares oscillation codes for stellar models to ensure consistent frequency calculations, highlighting the importance of numerical schemes, mesh resolution, and physical parameters like the gravitational constant for accurate asteroseismology.

Contribution

It provides a comprehensive inter-comparison of nine seismic codes, identifying key factors affecting frequency differences and proposing optimization strategies.

Findings

Second-order schemes with Richardson extrapolation match fourth-order results.

Mesh resolution and placement significantly influence frequency accuracy.

Inconsistent gravitational constant values cause notable frequency discrepancies.

Abstract

In order to make astroseismology a powerful tool to explore stellar interiors, different numerical codes should give the same oscillation frequencies for the same input physics. This work is devoted to test, compare and, if needed, optimize the seismic codes used to calculate the eigenfrequencies to be finally compared with observations. The oscillation codes of nine research groups in the field have been used in this study. The same physics has been imposed for all the codes in order to isolate the non-physical dependence of any possible difference. Two equilibrium models with different grids, 2172 and 4042 mesh points, have been used, and the latter model includes an explicit modelling of semiconvection just outside the convective core. Comparing the results for these two models illustrates the effect of the number of mesh points and their distribution in particularly critical parts of the model, such as the steep composition gradient outside the convective core. A comprehensive study of the frequency differences found for the different codes is given as well. These differences are mainly due to the use of different numerical integration schemes. The use of a second-order integration scheme plus a Richardson extrapolation provides similar results to a fourth-order integration scheme. The proper numerical description of the Brunt-Vaisala frequency in the equilibrium model is also critical for some modes. An unexpected result of this study is the high sensitivity of the frequency differences to the inconsistent use of values of the gravitational constant (G) in the oscillation codes, within the range of the experimentally determined ones, which differ from the value used to compute the equilibrium model.