The role of rotation on Petersen diagrams

II. The influence of near-degeneracy

¹ Instituto de Astrofísica de Andalucía (CSIC), CP3004 Granada, Spain e-mail: jcsuarez@iaa.es
² Observatoire de Paris, LESIA, UMR 8109, Meudon, France

Received: 13 April 2007
Accepted: 7 August 2007

Abstract

Aims.In the present work, the effect of near-degeneracy on rotational Petersen diagrams (RPD) is analysed.

Methods.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.

Results.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^-1, 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 δ Scuti stars). In terms of mass determinations, uncertainties reaching up to 0.5  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.

Conclusions.Near-degeneracy affects significantly the period ratios even for relatively low rotational velocities, and that can be critical when accurate determinations of mass and metallicity are required. Nevertheless, analysis of near-degeneracy effects provides some clues for the identification of the fundamental radial mode, the first overtone, and their corresponding quadrupole coupled pairs. This can be especially useful when additional information on mode identification and/or metallicity is available, for example from multicolour photometry and/or spectroscopy, not only for accurate diagnostics on metallicity and mass, but also because it is possible to constrain, to some extent, the rotational velocity of the star (and thereby its inclination angle).