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Published February 1, 2022 | Accepted Version + Published
Journal Article Open

Dynamical Tidal Love Numbers of Rapidly Rotating Planets and Stars

Abstract

Tidal interactions play an important role in many astrophysical systems, but uncertainties regarding the tides of rapidly rotating, centrifugally distorted stars and gaseous planets remain. We have developed a precise method for computing the dynamical, nondissipative tidal response of rotating planets and stars, based on summation over contributions from normal modes driven by the tidal potential. We calculate the normal modes of isentropic polytropes rotating at up to ≃90% of their critical breakup rotation rates, and tabulate fits to mode frequencies and tidal overlap coefficients that can be used to compute the frequency-dependent, nondissipative tidal response (via potential Love numbers k_(ℓm)). Although fundamental modes (f-modes) possess dominant tidal overlap coefficients at (nearly) all rotation rates, we find that the strong coupling of retrograde inertial modes (i-modes) to tesseral (ℓ > ∣m∣) components of the tidal potential produces resonances that may be relevant to gas giants like Jupiter and Saturn. The coupling of f-modes in rapid rotators to multiple components of both the driving tidal potential and the induced gravitational field also affect the tesseral response, leading to significant deviations from treatments of rotation that neglect centrifugal distortion and high-order corrections. For very rapid rotation rates (≳70% of breakup), mixing between prograde f-modes and i-modes significantly enhances the sectoral (ℓ = ∣m∣) tidal overlap of the latter. The tidal response of very rapidly rotating, centrifugally distorted planets or stars can also be modified by resonant sectoral f-modes that are secularly unstable via the Chandrasekhar–Friedman–Schutz mechanism.

Additional Information

© 2022. The Author(s). Published by the American Astronomical Society. Original content from this work may be used under the terms of the Creative Commons Attribution 4.0 licence. Any further distribution of this work must maintain attribution to the author(s) and the title of the work, journal citation and DOI. Received 2021 October 21; revised 2021 November 25; accepted 2021 November 29; published 2022 February 1. We thank the anonymous referee who reviewed this manuscript, and provided thorough and constructive comments that significantly improved the quality of the paper. J.W.D. gratefully acknowledges support from the Natural Sciences and Engineering Research Council of Canada (NSERC), funding reference #CITA 490888-16, and from the Sloan Foundation through grant FG-2018-10515.

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Published - Janosz_W._Dewberry_and_Dong_Lai_2022_ApJ_925_124.pdf

Accepted Version - 2110.12129.pdf

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Additional details

Created:
August 22, 2023
Modified:
October 23, 2023