Tidal effects in differentiated viscoelastic bodies: a numerical approach

Walterová, Michaela; Běhounková, M.

doi:10.1007/s10569-017-9772-x

Cited by 10 publications

(6 citation statements)

References 42 publications

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“…The Maxwell model does not capture the anelastic behavior of ices and silicates, which can become especially important when the forcing period is much smaller than the Maxwell time η / μ (Efroimsky, 2012 ). It is for this reason that recent studies have considered the Andrade rheological model (Andrade & Trouton, 1910 ) for ices (e.g., Castillo‐Rogez et al., 2011 ; Gevorgyan et al., 2020 ; Rambaux et al., 2010 ; Rhoden & Walker, 2022 ; Shoji et al., 2013 ) and silicates (e.g., Bierson & Nimmo, 2016 ; Efroimsky, 2012 ; Renaud & Henning, 2018 ; Rovira‐Navarro et al., 2021 ; Walterová & Běhounková, 2017 ). In Appendix F we discuss how more complex rheology models can be incorporated into our theory and demonstrate this using the Andrade model.…”

Section: Methodsmentioning

confidence: 99%

The Tides of Enceladus' Porous Core

et al. 2022

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The inferred density of Enceladus' core, together with evidence of hydrothermal activity within the moon, suggests that the core is porous. Tidal dissipation in an unconsolidated core has been proposed as the main source of Enceladus' geological activity. However, the tidal response of its core has generally been modeled assuming it behaves viscoelastically rather than poroviscoelastically. In this work, we analyze the poroviscoelastic response to better constrain the distribution of tidal dissipation within Enceladus. A poroviscoelastic body has a different tidal response than a viscoelastic one; pressure within the pores alters the stress field and induces a Darcian porous flow. This flow represents an additional pathway for energy dissipation. Using Biot's theory of poroviscoelasticity, we develop a new framework to obtain the tidal response of a spherically symmetric, self‐gravitating moon with porous layers and apply it to Enceladus. We show that the boundary conditions at the interface of the core and overlying ocean play a key role in the tidal response. The ocean hinders the development of a large‐amplitude Darcian flow, making negligible the Darcian contribution to the dissipation budget. We therefore infer that Enceladus' core can be the source of its geological activity only if it has a low rigidity and a very low viscosity. A future mission to Enceladus could test this hypothesis by measuring the phase lags of tidally induced changes of gravitational potential and surface displacements.

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Section: Methodsmentioning

confidence: 99%

The Tides of Enceladus' Porous Core

et al. 2022

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“…Most of these different studies are considering a homogeneous body (except for Henning & Hurford 2014;Tobie et al 2019) and most of them are assuming a Maxwell rheology (except for Noyelles et al 2014;Tobie et al 2019). Note that Walterová & Běhounková (2017) revisited the work of Correia et al (2014) using a multilayer model for the planets and investigated the tidal dissipation and tidal torques for the Maxwell and the Andrade rheology. They showed that considering a multi-layer structure does not significantly impact the rotational states of the planets.…”

Section: Introductionmentioning

confidence: 99%

Solid tidal friction in multi-layer planets: Application to Earth, Venus, a Super Earth and the TRAPPIST-1 planets

Bolmont

Breton

Tobie

et al. 2020

A&A

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With the discovery of TRAPPIST-1 and its seven planets residing within 0.06 au, it is becoming increasingly necessary to carry out correct treatments of tidal interactions. The eccentricity, rotation, and obliquity of the planets of TRAPPIST-1 do indeed result from the tidal evolution over the lifetime of the system. Tidal interactions can also lead to tidal heating in the interior of the planets (as for Io), which may then be responsible for volcanism or surface deformation. In the majority of studies aimed at estimating the rotation of close-in planets or their tidal heating, the planets are considered as homogeneous bodies and their rheology is often taken to be a Maxwell rheology. Here, we investigate the impact of taking into account a multi-layer structure and an Andrade rheology in the way planets dissipate tidal energy as a function of the excitation frequency. We use an internal structure model, which provides the radial profile of structural and rheological quantities (such as density, shear modulus, and viscosity) to compute the tidal response of multi-layered bodies. We then compare the outcome to the dissipation of a homogeneous planet (which only take a uniform value for shear modulus and viscosity). We find that for purely rocky bodies, it is possible to approximate the response of a multi-layer planet by that of a homogeneous planet. However, using average profiles of shear modulus and viscosity to compute the homogeneous planet response leads to an overestimation of the averaged dissipation. We provide fitted values of shear modulus and viscosity that are capable of reproducing the response of various types of rocky planets. However, we find that if the planet has an icy layer, its tidal response can no longer be approximated by a homogeneous body because of the very different properties of the icy layers (in particular, their viscosity), which leads to a second dissipation peak at higher frequencies. We also compute the tidal heating profiles for the outer TRAPPIST-1 planets (e to h).

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“…For all these reasons, the model of tidal evolution of a binary planet should be sufficiently complex and should account for the internal structure and rheology (e.g. Boué et al 2016;Walterová & Běhounková 2017).…”

Section: Tidal Evolutionmentioning

confidence: 99%

Binary Planet Formation by Gas-assisted Encounters of Planetary Embryos

Chrenko

Brož

Nesvorný

2018

ApJ

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We present radiation hydrodynamic simulations in which binary planets form by close encounters in a system of several super-Earth embryos. The embryos are embedded in a protoplanetary disk consisting of gas and pebbles and evolve in a region where the disk structure supports convergent migration due to Type I torques. As the embryos accrete pebbles, they become heated and thus affected by the thermal torque (Benítez-Llambay et al. 2015) and the hot-trail effect (Chrenko et al. 2017) which excites orbital eccentricities. Motivated by findings of Eklund & Masset (2017), we assume the hot-trail effect operates also vertically and reduces the efficiency of inclination damping. Non-zero inclinations allow the embryos to become closely packed and also vertically stirred within the convergence zone. Subsequently, close encounters of two embryos assisted by the disk gravity can form transient binary planets which quickly dissolve. Binary planets with a longer lifetime ∼10 4 yr form in 3-body interactions of a transient pair with one of the remaining embryos. The separation of binary components generally decreases in subsequent encounters and due to pebble accretion until the binary merges, forming a giant planet core. We provide an order-of-magnitude estimate of the expected occurrence rate of binary planets, yielding one binary planet per ≃2-5 × 10 4 planetary systems. Therefore, although rare, the binary planets may exist in exoplanetary systems and they should be systematically searched for.

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Tidal effects in differentiated viscoelastic bodies: a numerical approach

Cited by 10 publications

References 42 publications

The Tides of Enceladus' Porous Core

The Tides of Enceladus' Porous Core

Solid tidal friction in multi-layer planets: Application to Earth, Venus, a Super Earth and the TRAPPIST-1 planets

Binary Planet Formation by Gas-assisted Encounters of Planetary Embryos

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