Third Order Effect of Rotation on Stellar Oscillations of a $\beta$-Cephei Star

TL;DR

This paper investigates the third-order rotational effects on stellar oscillation frequencies in a $eta$-Cephei star, using perturbation theory to quantify frequency shifts up to third order for different modes.

Contribution

It applies third-order perturbation formalism to model the rotational effects on oscillation frequencies of a specific $eta$-Cephei star, providing detailed numerical estimates.

Findings

Third-order corrections can reach up to 0.6% of the oscillation frequency.

Rotation significantly affects oscillation modes at high angular velocities.

Frequency shifts vary with mode and radial order.

Abstract

Here the effect of rotation up to third order in the angular velocity of a star on the p, f and g modes is investigated. To do this, the third-order perturbation formalism presented by Soufi et al. (1998) and revised by Karami (2008), was used. I quantify by numerical calculations the effect of rotation on the oscillation frequencies of a uniformly rotating $\beta$-Cephei star with 12 $M_\odot$. For an equatorial velocity of 90 $\rm km s^{-1}$, it is found that the second- and third-order corrections for $(l,m)=(5,-4)$, for instance, are of order of 0.07% of the frequency for radial order $n=-3$ and reaches up to 0.6% for $n=-20$.