Asymptotic theory of gravity modes in rotating stars

Abstract

Context. The seismology of early-type stars is limited by our incomplete understanding of gravito-inertial modes. Aims. We develop a short-wavelength asymptotic analysis for gravito-inertial modes in rotating stars. Methods. The Wentzel-Kramers-Brillouin approximation was applied to the equations governing adiabatic small perturbations about a model of a uniformly rotating barotropic star. Results. A general eikonal equation, including the effect of the centrifugal deformation, is derived. The dynamics of axisymmetric gravito-inertial rays is solved numerically for polytropic stellar models of increasing rotation and analysed by describing the structure of the phase space. Three different types of phase-space structures are distinguished. The first type results from the continuous evolution of structures of the non-rotating integrable phase space. It is predominant in the low-frequency region of the phase space. The second type of structures are island chains associated with stable periodic rays. The third type of structures are large chaotic regions that can be related to the envelope minimum of the Brunt-Väisälä frequency. Conclusions. Gravito-inertial modes are expected to follow this classification, in which the frequency spectrum is a superposition of sub-spectra associated with these different types of phase-space structures. The detailed confrontation between the predictions of this ray-based asymptotic theory and numerically computed modes will be presented in a companion paper.

Atmospheric tides in Earth-like planets

“…N, but is less appropriate if |σ| " 2Ω, as discussed in Mathis (2009). Its validity domain, not well defined, remains essentially limited to the regime of super-inertial waves (Prat et al 2016). It is represented in Fig.…”

Sub-Inertial Gravity Modes in the B8v Star Kic 7760680 Reveal Moderate Core Overshooting and Low Vertical Diffusive Mixing

“…The pulsation description of rotating stars is at least a twodimensional problem (e.g., Prat et al 2016). However, it is possible to reduce this dimensionality into two separate onedimensional (1D) problems for the radial (Lee & Saio 1986) and angular dependence (Lee & Saio 1997;Townsend 2003b) of eigensolutions.…”

Seismic diagnosis from gravity modes strongly affected by rotation

“…As shown in [17], low-frequency gravito-inertial waves are trapped near the equatorial plane, but can propagate near the centre, which is not accounted for by the traditional approximation. In the limit of very low frequencies (ω f ), the trapping implies that…”

“…Such an asymptotic theory has been built for acoustic waves ( [15]) and has led to the prediction of regularities in corresponding spectra of fast-rotating stars ( [16]). For gravito-inertial waves, a first study ( [17]) has allowed us to constrain the structure of the phase space. In particular, we have shown that it is dominated by nearly integrable structures at low frequencies.…”

“…Most of the information we have about the internal rotation of stars comes from modes that are weakly affected by rotation, for example by using rotational splittings. In contrast, we present here a method, based on the asymptotic theory of Prat et al (2016), which allows us to analyse the signature of rotation where its effect is the most important, that is in low-frequency gravity modes that are strongly affected by rotation. For such modes, we predict two spectral patterns that could be confronted to observed spectra and those computed using fully two-dimensional oscillation codes.…”