Oscillation Frequencies of Moderately Rotating Delta Scuti Stars: Asymmetric Mode Splittings Due to Non-spherical Distortion

TL;DR

This study investigates the asymmetric rotational mode splittings in Delta Scuti stars caused by non-spherical distortion, combining theoretical modeling with observational implications for different rotation rates.

Contribution

It provides a detailed analysis of second-order rotational effects and mode coupling on mode splitting asymmetries in Delta Scuti stars, enhancing understanding of stellar oscillation complexities.

Findings

Positive asymmetry observed in mode splittings aligns with second-order rotational distortion effects.

Near-degeneracy mode coupling can significantly alter splitting asymmetry in faster rotators.

Predicted correlations between asymmetry, amplitude, and frequency aid future observational detection.

Abstract

We find that the observed pressure-mode rotational splittings of slowly/moderately rotating Delta Scuti stars and Beta Cephei stars mostly have a positive asymmetry. That is, the left frequency spacing is larger than the right spacing in the dipole mode splitting triplets and the $l=2$ mode splitting multiplets (considering $m=1, 0, -1$ modes only). This is in agreement with the second-order perturbative effect of the rotational non-spherical distortion: both the prograde and retrograde modes have their frequencies shifted towards lower values relative to the $m=0$ modes. We thus study the rotational perturbation both in the first and second order, as well as the near-degeneracy mode coupling effect in MESA models representing Delta Scuti stars. For faster rotators, the near-degeneracy mode coupling between the nearest radial and quadrupole modes can significantly shift the $m=0$ modes, reduce the splitting asymmetry, and even change its sign. We find the theoretical splitting asymmetry from the second-order non-spherical distortion is larger than observed asymmetry. To facilitate future detections, we predict correlations between splitting asymmetry, splitting amplitude, and pulsation frequency. We also discuss additional factors that can influence splitting asymmetry, including embedded magnetic fields, resonant mode coupling, and binarity.