Period spacing of gravity modes strongly affected by rotation. Going beyond the traditional approximation

Abstract

Context. As of today, asteroseismology mainly allows us to probe the internal rotation of stars when modes are only weakly affected by rotation using perturbative methods. Such methods cannot be applied to rapidly rotating stars, which exhibit complex oscillation spectra. In this context, the so-called traditional approximation, which neglects the terms associated with the latitudinal component of the rotation vector, describes modes that are strongly affected by rotation. This approximation is sometimes used for interpreting asteroseismic data, however, its domain of validity is not established yet. Aims. We aim at deriving analytical prescriptions for period spacings of low-frequency gravity modes strongly affected by rotation through the full Coriolis acceleration, which can be used to probe stellar internal structure and rotation. Methods. We approximated the asymptotic theory of gravito-inertial waves in uniformly rotating stars using ray theory described in a previous paper in the low-frequency regime, where waves are trapped near the equatorial plane. We put the equations of ray dynamics into a separable form and used the EBK quantisation method to compute modes frequencies from rays. Results. Two spectral patterns that depend on stratification and rotation are predicted within this new approximation: one for axisymmetric modes and one for non-axisymmetric modes. Conclusions. The detection of the predicted patterns in observed oscillation spectra would give constraints on internal rotation and chemical stratification of rapidly rotating stars exhibiting gravity modes, such as $\gamma$ Doradus, SPB, or Be stars. The obtained results have a mathematical form that is similar to that of the traditional approximation, but the new approximation takes the full Coriolis, which allows for propagation near the centre, and centrifugal accelerations into account.

9 pages, 6 figures, accepted for publication in A&A

References in corpus (10)

• Asteroseismic measurement of surface-to-core rotation in a main sequence A star, KIC 11145123
• The interior rotation of a sample of gamma Doradus stars from ensemble modelling of their gravity mode period spacings
• Asteroseismic measurement of slow, nearly-uniform surface-to-core rotation in the main sequence F star KIC 9244992
• Acoustic oscillations of rapidly rotating polytropic stars. II. Effects of the Coriolis and centrifugal accelerations
• A new asteroseismic diagnostic for internal rotation in $\gamma$ Doradus stars
• Gravito-inertial and pressure modes detected in the B3 IV CoRoT target HD 43317
• Gravity modes in rapidly rotating stars. Limits of perturbative methods
• Impact of rotation on stochastic excitation of gravity and gravito-inertial waves in stars
• Inversion of stellar fundamental parameters from Espadons and Narval high-resolution spectra
• Regular Oscillation Sub-spectrum of Rapidly Rotating Stars

Cited by in corpus (6)

• Effect of a strong magnetic field on gravity-mode period spacings in red giant stars
• Convection and Overshoot in models of gamma Doradus and delta Scuti stars
• The traditional approximation of rotation for rapidly rotating stars and planets. II. Deformation and differential rotation
• Constraining the near-core rotation of the gamma Doradus star 43 Cygni using BRITE-Constellation data
• Modelling $\delta$ Scuti pulsations: A new grid of p, g, and f modes across pre-main-sequence to post-main-sequence evolution
• Co-existence of Internal Gravity Waves and Tayler-Spruit Magnetic Fields in the Radiative Core of Low-mass Stars