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Title: TIDAL DISSIPATION COMPARED TO SEISMIC DISSIPATION: IN SMALL BODIES, EARTHS, AND SUPER-EARTHS

Abstract

While the seismic quality factor and phase lag are defined solely by the bulk properties of the mantle, their tidal counterparts are determined by both the bulk properties and the size effect (self-gravitation of a body as a whole). For a qualitative estimate, we model the body with a homogeneous sphere, and express the tidal phase lag through the lag in a sample of material. Although simplistic, our model is sufficient to understand that the lags are not identical. The difference emerges because self-gravitation pulls the tidal bulge down. At low frequencies, this reduces strain and the damping rate, making tidal damping less efficient in larger objects. At higher frequencies, competition between self-gravitation and rheology becomes more complex, though for sufficiently large super-Earths the same rule applies: the larger the planet, the weaker the tidal dissipation in it. Being negligible for small terrestrial planets and moons, the difference between the seismic and tidal lagging (and likewise between the seismic and tidal damping) becomes very considerable for large exoplanets (super-Earths). In those, it is much lower than what one might expect from using a seismic quality factor. The tidal damping rate deviates from the seismic damping rate, especially in the zero-frequencymore » limit, and this difference takes place for bodies of any size. So the equal in magnitude but opposite in sign tidal torques, exerted on one another by the primary and the secondary, have their orbital averages going smoothly through zero as the secondary crosses the synchronous orbit. We describe the mantle rheology with the Andrade model, allowing it to lean toward the Maxwell model at the lowest frequencies. To implement this additional flexibility, we reformulate the Andrade model by endowing it with a free parameter {zeta} which is the ratio of the anelastic timescale to the viscoelastic Maxwell time of the mantle. Some uncertainty in this parameter's frequency dependence does not influence our principal conclusions.« less

Authors:
 [1]
  1. U.S. Naval Observatory, Washington, DC 20392 (United States)
Publication Date:
OSTI Identifier:
22011681
Resource Type:
Journal Article
Journal Name:
Astrophysical Journal
Additional Journal Information:
Journal Volume: 746; Journal Issue: 2; Other Information: Country of input: International Atomic Energy Agency (IAEA); Journal ID: ISSN 0004-637X
Country of Publication:
United States
Language:
English
Subject:
79 ASTROPHYSICS, COSMOLOGY AND ASTRONOMY; FREQUENCY DEPENDENCE; GRAVITATION; MOON; ORBITS; PLANETS; SOLAR SYSTEM EVOLUTION; STARS

Citation Formats

Efroimsky, Michael. TIDAL DISSIPATION COMPARED TO SEISMIC DISSIPATION: IN SMALL BODIES, EARTHS, AND SUPER-EARTHS. United States: N. p., 2012. Web. doi:10.1088/0004-637X/746/2/150.
Efroimsky, Michael. TIDAL DISSIPATION COMPARED TO SEISMIC DISSIPATION: IN SMALL BODIES, EARTHS, AND SUPER-EARTHS. United States. doi:10.1088/0004-637X/746/2/150.
Efroimsky, Michael. Mon . "TIDAL DISSIPATION COMPARED TO SEISMIC DISSIPATION: IN SMALL BODIES, EARTHS, AND SUPER-EARTHS". United States. doi:10.1088/0004-637X/746/2/150.
@article{osti_22011681,
title = {TIDAL DISSIPATION COMPARED TO SEISMIC DISSIPATION: IN SMALL BODIES, EARTHS, AND SUPER-EARTHS},
author = {Efroimsky, Michael},
abstractNote = {While the seismic quality factor and phase lag are defined solely by the bulk properties of the mantle, their tidal counterparts are determined by both the bulk properties and the size effect (self-gravitation of a body as a whole). For a qualitative estimate, we model the body with a homogeneous sphere, and express the tidal phase lag through the lag in a sample of material. Although simplistic, our model is sufficient to understand that the lags are not identical. The difference emerges because self-gravitation pulls the tidal bulge down. At low frequencies, this reduces strain and the damping rate, making tidal damping less efficient in larger objects. At higher frequencies, competition between self-gravitation and rheology becomes more complex, though for sufficiently large super-Earths the same rule applies: the larger the planet, the weaker the tidal dissipation in it. Being negligible for small terrestrial planets and moons, the difference between the seismic and tidal lagging (and likewise between the seismic and tidal damping) becomes very considerable for large exoplanets (super-Earths). In those, it is much lower than what one might expect from using a seismic quality factor. The tidal damping rate deviates from the seismic damping rate, especially in the zero-frequency limit, and this difference takes place for bodies of any size. So the equal in magnitude but opposite in sign tidal torques, exerted on one another by the primary and the secondary, have their orbital averages going smoothly through zero as the secondary crosses the synchronous orbit. We describe the mantle rheology with the Andrade model, allowing it to lean toward the Maxwell model at the lowest frequencies. To implement this additional flexibility, we reformulate the Andrade model by endowing it with a free parameter {zeta} which is the ratio of the anelastic timescale to the viscoelastic Maxwell time of the mantle. Some uncertainty in this parameter's frequency dependence does not influence our principal conclusions.},
doi = {10.1088/0004-637X/746/2/150},
journal = {Astrophysical Journal},
issn = {0004-637X},
number = 2,
volume = 746,
place = {United States},
year = {2012},
month = {2}
}