arXiv subjects

Antony Trinh

Publications and source records attributed to Antony Trinh.

7 recordsLinked to original sources

arXiv2024

Librations and obliquity of the largest moons of Uranus

Following the discovery of several ocean worlds in the solar system, and the selection of Uranus as the highest priority objective by the Planetary Science and Astrobiology Decadal Survey 2023-2032, the five largest moons of Uranus (Miranda, Ariel, Umbriel, Titania and Oberon) have been receiving renewed attention as they may also harbor a subsurface ocean. We assess how rotation measurements could help confirm the internal differentiation of the bodies and detect internal oceans if any. Because of the time-varying gravitational torque of Uranus on the flattened shape of its synchronous satellites, the latter librate with respect to their mean rotation and precess with a non zero obliquity. For a range of interior models with a rocky core surrounded by a hydrosphere, either solid or divided into an outer ice shell with a liquid ocean underneath, we compute their diurnal libration amplitude and obliquity.

astro-ph.EP↗

arXiv2023

Electric interface condition for sliding and viscous contacts

First principles of electromagnetism impose that the tangential electric field must be continuous at the interface between two media. The definition of the electric field depends on the frame of reference leading to an ambiguity in the mathematical expression of the continuity condition when the two sides of the interface do not share the same rest frame. We briefly review the arguments supporting each choice of interface condition and illustrate how the most theoretically consistant choice leads to a paradox in induction experiments. We then present a model of sliding contact between two solids and between a fluid and a solid, and show how this paradox can be lifted by taking into account the shear induced by the differential motion in a thin intermediate viscous layer at the interface, thereby also lifting the ambiguity in the electric interface condition. We present some guidelines regarding the appropriate interface condition to employ in magnetohydrodynamics applications, in particular for numerical simulations where sliding contact is used as an approximation to the viscous interface between a conducting solid and a fluid of very low viscosity such as in planetary interior simulations.

physics.class-ph↗

arXiv2020

Powering the Galilean Satellites with Moon-Moon Tides

There is compelling evidence for subsurface water oceans among the three outer Galilean satellites, and evidence for an internal magma ocean in the innermost moon, Io. Tidal forces from Jupiter periodically deform these bodies, causing heating and deformation that, if measured, can probe their interior structures. In addition to Jupiter-raised tides, each moon also raises tides on the others. We investigate moon-moon tides for the first time in the Galilean moons, and show that they can cause significant heating through the excitation of high-frequency resonant tidal waves in their subsurface oceans. The heating occurs both in the crust and ocean, and can exceed that of other tidal sources and radiogenic decay if the ocean is inviscid enough. The resulting tidal deformation can be used to constrain subsurface ocean thickness. Our understanding of the thermal-orbital evolution and habitability of the Jovian system may be fundamentally altered as a result.

astro-ph.EP↗

arXiv2020

Inertial modes of a freely rotating ellipsoidal planet and their relation to nutations

We compute the inertial modes of a freely rotating two-layer planetary model with an ellipsoidal inviscid fluid core and a perfectly rigid mantle. We present a method to derive analytical formulae for the frequencies of the Free Core Nutation (FCN) and Chandler Wobble (CW) which are valid to all orders of the dynamical flattening of the core and mantle, and we show how the FCN and CW are the direct generalisation of the purely fluid Spin-Over mode (SO) and of the Eulerian Wobble (EW) to the case where the mantle can oscillate freely around a state of steady rotation. Through a numerical computation for an axisymmetric (oblate spheroidal) planet, we demonstrate that all other inertial modes of the steadily rotating fluid core are also free modes of the freely rotating two-layer planet.

astro-ph.EP↗

arXiv2019

The formation of the Martian moons

Almost all the planets of our solar system have moons. Each planetary system has however unique characteristics. The Martian system has not one single big moon like the Earth, not tens of moons of various sizes like for the giant planets, but two small moons: Phobos and Deimos. How did form such a system? This question is still being investigated on the basis of the Earth-based and space-borne observations of the Martian moons and of the more modern theories proposed to account for the formation of other moon systems. The most recent scenario of formation of the Martian moons relies on a giant impact occurring at early Mars history and having also formed the so-called hemispheric crustal dichotomy. This scenario accounts for the current orbits of both moons unlike the scenario of capture of small size asteroids. It also predicts a composition of disk material as a mixture of Mars and impactor materials that is in agreement with remote sensing observations of both moon surfaces, which suggests a composition different from Mars. The composition of the Martian moons is however unclear, given the ambiguity on the interpretation of the remote sensing observations. The study of the formation of the Martian moon system has improved our understanding of moon formation of terrestrial planets: The giant collision scenario can have various outcomes and not only a big moon as for the Earth. This scenario finds a natural place in our current vision of the early solar system when conditions were favorable for giant collisions to occur. The next step in exploration of Martian moon is a sample return mission to test the giant collision scenario for their origin, and to provide tests of models of early solar system dynamics since Mars may retain material exchanged between the inner and outer solar system.

astro-ph.EP↗

arXiv2019

The coupling between inertial and rotational eigenmodes in planets with liquid cores

The Earth is a rapidly rotating body. The centrifugal pull makes its shape resemble a flattened ellipsoid and Coriolis forces support waves in its fluid core, known as inertial waves. These waves can lead to global oscillations, or modes, of the fluid. Periodic variations of the Earth's rotation axis (nutations) can lead to an exchange of angular momentum between the mantle and the fluid core and excite these inertial modes. In addition to viscous torques that exist regardless of the shape of the boundaries, the small flattening of the core-mantle boundary (CMB) allows inertial modes to exert pressure torques on the mantle. These torques effectively couple the rigid-body dynamics of the Earth with the fluid dynamics of the fluid core. Here we present the first high resolution numerical model that solves simultaneously the rigid body dynamics of the mantle and the Navier-Stokes equation for the liquid core. This method takes naturally into account dissipative processes in the fluid that are ignored in current nutation models. We find that the Free Core Nutation (FCN) mode, mostly a toroidal fluid flow if the mantle has a large moment of inertia, enters into resonance with nearby modes if the mantle's moment of inertia is reduced. These mode interactions seem to be completely analogous to the ones discovered by Schmitt (2006) in a uniformly rotating ellipsoid with varying flattening.

astro-ph.EP↗

arXiv2016

Enceladus's and Dione's floating ice shells supported by minimum stress isostasy

Enceladus's gravity and shape have been explained in terms of a thick isostatic ice shell floating on a global ocean, in contradiction of the thin shell implied by librations. Here we propose a new isostatic model minimizing crustal deviatoric stress, and demonstrate that gravity and shape data predict a $\rm{38\pm4\,km}$-thick ocean beneath a $\rm{23\pm4\,km}$-thick shell agreeing with -- but independent of -- libration data. Isostatic and tidal stresses are comparable in magnitude. South polar crust is only $7\pm4\rm\,km$ thick, facilitating the opening of water conduits and enhancing tidal dissipation through stress concentration. Enceladus's resonant companion, Dione, is in a similar state of minimum stress isostasy. Its gravity and shape can be explained in terms of a $\rm{99\pm23\,km}$-thick isostatic shell overlying a $\rm{65\pm30\,km}$-thick global ocean, thus providing the first clear evidence for a present-day ocean within Dione.

physics.geo-ph↗