Mode Mixing and Rotational Splittings: I. Near-Degeneracy Effects Revisited

Abstract

Rotation is typically assumed to induce strictly symmetric rotational splitting into the rotational multiplets of pure p- and g-modes. However, for evolved stars exhibiting mixed modes, avoided crossings between different multiplet components are known to yield asymmetric rotational splitting, particularly for near-degenerate mixed-mode pairs, where notional pure p-modes are fortuitiously in resonance with pure g-modes. These near-degeneracy effects have been described in subgiants, but their consequences for the characterisation of internal rotation in red giants has not previously been investigated in detail, in part owing to theoretical intractability. We employ new developments in the analytic theory of mixed-mode coupling to study these near-resonance phenomena. In the vicinity of the most p-dominated mixed modes, the near-degenerate intrinsic asymmetry from pure rotational splitting increases dramatically over the course of stellar evolution, and depends strongly on the mode mixing fraction $\zeta$. We also find that a linear treatment of rotation remains viable for describing the underlying p- and g-modes, even when it does not for the resulting mixed modes undergoing these avoided crossings. We explore observational consequences for potential measurements of asymmetric mixed-mode splitting, which has been proposed as a magnetic-field diagnostic. Finally, we propose improved measurement techniques for rotational characterisation, exploiting the linearity of rotational effects on the underlying p/g modes, while still accounting for these mixed-mode coupling effects.

21 pages, 13 figures. Accepted to ApJ

References in corpus (18)

• Array Programming with NumPy
• Modules for Experiments in Stellar Astrophysics (MESA)
• Modules for Experiments in Stellar Astrophysics (MESA): Pulsating Variable Stars, Rotation, Convective Boundaries, and Energy Conservation
• Slowing the Spins of Stellar Cores
• Surface rotation and photometric activity for Kepler targets. II. G and F main-sequence stars, and cool subgiant stars
• The stability of poloidal magnetic fields in rotating stars
• Asteroseismology of evolved stars to constrain the internal transport of angular momentum II. Test of a revised prescription for transport by the Tayler instability
• Magnetic signatures on mixed-mode frequencies. I. An axisymmetric fossil field inside the core of red giants
• Near-degeneracy effects on the frequencies of rotationally-split mixed modes in red giants
• Semi-analytic Expressions for the Isolation and Coupling of Mixed Modes
• Origin and evolution of magnetic fields in PMS stars : influence of rotation and structural changes
• Latitudinal differential rotation in the solar analogues 16 Cyg A and B
• A Diagnostic for Localizing Red Giant Differential Rotation
• Topology and obliquity of core magnetic fields in shaping seismic properties of slowly rotating evolved stars
• Asteroseismology of evolved stars to constrain the internal transport of angular momentum. IV. Internal rotation of Kepler 56 from an MCMC analysis of the rotational splittings
• Mixed Modes and Asteroseismic Surface Effects: I. Analytic Treatment
• Asteroseismic Inference of the Central Structure in a Subgiant Star
• Mixed Modes and Asteroseismic Surface Effects: II. Subgiant Systematics

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