The role of rotation on Petersen Diagrams. II The influence of near-degeneracy

TL;DR

This study investigates how near-degeneracy affects rotational Petersen diagrams, revealing significant impacts on frequency calculations and stellar parameter estimations at moderate rotational velocities.

Contribution

It provides a detailed analysis of near-degeneracy effects on RPD, including mode contamination, amplitude, and frequency shifts, enhancing understanding of stellar oscillations with rotation.

Findings

Near-degeneracy causes large frequency wriggles at >15-20 km/s rotation.

Uncertainties in metallicity estimates can reach 0.50 dex due to these effects.

Mass determination uncertainties can reach up to 0.5 solar masses.

Abstract

In the present work, the effect of near-degeneracy on rotational Petersen diagrams (RPD) is analysed. Seismic models are computed considering rotation effects on both equilibrium models and adiabatic oscillation frequencies (including second-order near-degeneracy effects). Contamination of coupled modes and coupling strength on the first radial modes are studied in detail. Analysis of relative intrinsic amplitudes of near-degenerate modes reveals that the identity of the fundamental radial mode and its coupled quadrupole pair are almost unaltered once near-degeneracy effects are considered. However, for the first overtone, a mixed radial/quadrupole identity is always predicted. The effect of near-degeneracy on the oscillation frequencies becomes critical for rotational velocities larger than 15-20 km/s, for which large wriggles in the evolution of the period ratios are obtained (up $10^{-2}$). Such wriggles imply uncertainties, in terms of metallicity determinations using RPD, reaching up to 0.50 dex, which can be critical for Pop. I HADS (High Amplitude \dss). In terms of mass determinations, uncertainties reaching up to 0.5 M_sun are predicted. The location of such wriggles is found to be independent of metallicity and rotational velocity, and governed mainly by the avoided-crossing phenomenon.