TIDAL DISSIPATION COMPARED TO SEISMIC DISSIPATION: IN SMALL BODIES, EARTHS, AND SUPEREARTHS
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 (selfgravitation 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 selfgravitation 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 selfgravitation and rheology becomes more complex, though for sufficiently large superEarths 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 (superEarths). 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 zerofrequencymore »
 Authors:

 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 0004637X
 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 SUPEREARTHS. United States: N. p., 2012.
Web. doi:10.1088/0004637X/746/2/150.
Efroimsky, Michael. TIDAL DISSIPATION COMPARED TO SEISMIC DISSIPATION: IN SMALL BODIES, EARTHS, AND SUPEREARTHS. United States. doi:10.1088/0004637X/746/2/150.
Efroimsky, Michael. Mon .
"TIDAL DISSIPATION COMPARED TO SEISMIC DISSIPATION: IN SMALL BODIES, EARTHS, AND SUPEREARTHS". United States. doi:10.1088/0004637X/746/2/150.
@article{osti_22011681,
title = {TIDAL DISSIPATION COMPARED TO SEISMIC DISSIPATION: IN SMALL BODIES, EARTHS, AND SUPEREARTHS},
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 (selfgravitation 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 selfgravitation 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 selfgravitation and rheology becomes more complex, though for sufficiently large superEarths 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 (superEarths). 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 zerofrequency 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 = {10.1088/0004637X/746/2/150},
journal = {Astrophysical Journal},
issn = {0004637X},
number = 2,
volume = 746,
place = {United States},
year = {2012},
month = {2}
}