Signatures of Core-Envelope Rotational Misalignment in the Mixed-Mode Asteroseismology of Kepler-56

TL;DR

This paper develops a theoretical framework to detect and interpret rotational misalignment between a star's core and envelope using mixed-mode asteroseismology, applied to Kepler-56, revealing differential rotation axes.

Contribution

It introduces perturbative expressions for asteroseismic signatures of core-envelope misalignment and applies them to Kepler-56, uncovering differential rotation axes in the star.

Findings

Kepler-56's core and envelope rotate around different axes

The core's rotational axis is misaligned with planetary orbits

The envelope's rotational axis may be aligned with planetary orbits

Abstract

Existing asteroseismic rotational measurements assume that stars rotate around a single axis. However, tidal torques from misaligned companions, or their possible engulfment, may bring the rotational axis of a star's envelope out of alignment with its core, breaking azimuthal symmetry. I derive perturbative expressions for asteroseismic signatures of such hitherto unexamined rotational configurations, under the ``shellular approximation'' of constant rotation rates on radially stratified mass shells. In the aligned case, the distribution of power between multiplet components is determined by the inclination of the rotational axis; radial differential misalignment causes this to vary from multiplet to multiplet. I examine in particular detail the phenomenology of gravitoacoustic mixed modes as seen in evolved sub- and red giants, where near-resonance avoided crossings may break geometrical degeneracies. Upon applying the revised asteroseismic observational methodology that results from this theoretical discussion to revisit Kepler-56 -- a red giant with a misaligned planetary system -- I find that its core and envelope rotate around different rotational axes. While the rotational axis of its core is indeed misaligned from the orbit normal of its transiting planets (consistently with earlier studies), its envelope's rotational axis is close to lying in the sky plane, and may well be aligned with them. More detailed asteroseismic modelling, and spectroscopic follow-up, will be required to fully elucidate the full spin-orbit geometry of the Kepler-56 system, and potentially discriminate between hypotheses for how it formed.