Theoretical p Mode Oscillation Frequencies for the Rapidly Rotating Delta Scuti Star Alpha Ophiuchi

TL;DR

This paper develops a 2D stellar model for Alpha Ophiuchi, computes oscillation frequencies including nonaxisymmetric modes, and compares them to observations, revealing complex frequency patterns due to rapid rotation.

Contribution

It introduces detailed 2D rotating stellar models and computes both axisymmetric and nonaxisymmetric oscillation frequencies for Alpha Ophiuchi, advancing understanding of rapidly rotating stars.

Findings

Computed frequencies agree within 0.26% with different Legendre polynomial assumptions.

Significant departures from single Legendre polynomial eigenfunctions.

Frequency differences between positive and negative m modes are proportional to rotation rate.

Abstract

A rotating, two dimensional stellar model is evolved to match the approximate conditions of Alpha Oph. Both axisymmetric and nonaxisymmetric oscillation frequencies are computed for 2D rotating models which approximate the properties of Alpha Oph. These computed frequencies are compared to the observed frequencies. Oscillation calculations are made assuming the eigenfunction can be fit with six Legendre polynomials, but comparison calculations with eight Legendre polynomials show the frequencies agree to within about 0.26% on average. The surface horizontal shape of the eigenfunctions for the two sets of assumed number of Legendre polynomials agrees less well, but all calculations show significant departures from that of a single Legendre polynomial. It is still possible to determine the large separation, although the small separation is more complicated to estimate. With the addition of the nonaxisymmetric modes with |m| less than or equal 4, the frequency space becomes sufficiently dense that it is difficult to comment on the adequacy of the fit of the computed to the observed frequencies. While the nonaxisymmetric frequency mode splitting is no longer uniform, the frequency difference between the frequencies for positive and negative values of the same m remains 2m times the rotation rate.