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.

arXiv comment9 pages, 6 figures, accepted for publication in A&A

References in corpus (26)

• Fast core rotation in red-giant stars revealed by gravity-dominated mixed modes
• Spin down of the core rotation in red giants
• Seismic evidence for a rapidly rotating core in a lower-giant-branch star observed with Kepler
• Seismic constraints on the radial dependence of the internal rotation profiles of six Kepler subgiants and young red giants
• Rotation and magnetism of Kepler pulsating solar-like stars. Towards asteroseismically calibrated age-rotation relations
• Asteroseismic measurement of surface-to-core rotation in a main sequence A star, KIC 11145123
• The VLT-FLAMES Tarantula Survey XII. Rotational velocities of the single O-type stars
• 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
• Seismic evidence for a weak radial differential rotation in intermediate-mass core helium burning stars
• Sub-Inertial Gravity Modes in the B8V Star KIC 7760680 Reveal Moderate Core Overshooting and Low Vertical Diffusive Mixing
• 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
• The Rotation Of The Deep Solar Layers
• Nearly-uniform internal rotation of solar-like main-sequence stars revealed by space-based asteroseismology and spectroscopic measurements
• Gravito-inertial and pressure modes detected in the B3 IV CoRoT target HD 43317
• Self-consistent 2D models of fast rotating early-type star
• Asymptotic analysis of high-frequency acoustic modes in rapidly rotating stars
• The internal rotation profile of the B-type star KIC10526294 from frequency inversion of its dipole gravity modes and statistical model comparison
• Gravity modes in rapidly rotating stars. Limits of perturbative methods
• Impact of rotation on stochastic excitation of gravity and gravito-inertial waves in stars
• Asymptotic theory of gravity modes in rotating stars. I. Ray dynamics
• Gravito-inertial waves in a differentially rotating spherical shell
• Inversion of stellar fundamental parameters from Espadons and Narval high-resolution spectra
• Regular Oscillation Sub-spectrum of Rapidly Rotating Stars
• Regular modes in rotating stars

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