Christophe Le Poncin-Lafitte

Strong Tidal Dissipation in Saturn and Constraints on Enceladus' Thermal State from Astrometry

Tidal interactions between Saturn and its satellites play a crucial role in both the orbital migration of the satellites and the heating of their interiors. Therefore, constraining the tidal dissipation of Saturn (here the ratio k2/Q) opens the door to the past evolution of the whole system. If Saturn’s tidal ratio can be determined at different frequencies, it may also be possible to constrain the giant planet’s interior structure, which is still uncertain. Here, we try to determine Saturn’s tidal ratio through its current effect on the orbits of the main moons, using astrometric data spanning more than a century. We find an intense tidal dissipation (k2/Q = (2.3 ± 0.7) × 10 −4 ), which is about 10 times higher than the usual value estimated from theoretical arguments. As a consequence, eccentricity equilibrium for Enceladus can now account for the huge heat emitted from Enceladus’ south pole. Moreover, the measured k2/Q is found to be poorly sensitive to the tidal frequency, on the short frequency interval considered. This suggests that Saturn’s dissipation may not be controlled by turbulent friction in the fluid envelope as commonly believed. If correct, the large tidal expansion of the moon orbits due to this strong Saturnian dissipation would be inconsistent with the moon formations 4.5 Byr ago above the synchronous orbit in the Saturnian subnebulae. But it would be compatible with a new model of satellite formation in which the Saturnian satellites formed possibly over a longer timescale at the outer edge of the main rings. In an attempt to take into account possible significant torques exerted by the rings on Mimas, we fitted a constant rate da/dt on Mimas’ semi-major axis as well. We obtained an unexpected large acceleration related to a negative value of da/dt =− (15.7 ± 4.4) × 10 −15 AU day −1 . Such acceleration is about an order of magnitude larger than the tidal deceleration rates observed for the other moons. If not coming from an astrometric artifact associated with the proximity of Saturn’s halo, such orbital decay may have significant implications on the Saturn’s rings.

Accretion of Saturn's mid-sized moons during the viscous spreading of young massive rings: Solving the paradox of silicate-poor rings versus silicate-rich moons

Abstract The origin of Saturn’s inner mid-sized moons (Mimas, Enceladus, Tethys, Dione and Rhea) and Saturn’s rings is debated. Charnoz et al. [Charnoz, S., Salmon J., Crida A., 2010. Nature 465, 752–754] introduced the idea that the smallest inner moons could form from the spreading of the rings’ edge while Salmon et al. [Salmon, J., Charnoz, S., Crida, A., Brahic, A., 2010. Icarus 209, 771–785] showed that the rings could have been initially massive, and so was the ring’s progenitor itself. One may wonder if the mid-sized moons may have formed also from the debris of a massive ring progenitor, as also suggested by Canup [Canup, R., 2010. Nature 468, 943–946]. However, the process driving mid-sized moon accretion from the icy debris disks has not been investigated in details. In particular, Canup’s (2010) model does not seem able to explain the varying silicate contents of the mid-sized moons (from 6% to 57% in mass). Here, we explore the formation of large objects from a massive ice-rich ring (a few times Rhea’s mass) and describe the fundamental properties and implications of this new process. Using a hybrid computer model, we show that accretion within massive icy rings can form all mid-sized moons from Mimas to Rhea. However in order to explain their current locations, intense dissipation within Saturn (with Q p

General post-Minkowskian expansion of time transfer functions

Modeling most of the tests of general relativity requires us to know the function relating light travel time to the coordinate time of reception and to the spatial coordinates of the emitter and the receiver. We call such a function the reception time transfer function. Of course, an emission time transfer function may as well be considered. We present here a recursive procedure enabling us to expand each time transfer function into a perturbative series of ascending powers of the Newtonian gravitational constant G (general post-Minkowskian expansion). Our method is self-sufficient in the sense that neither the integration of null geodesic equations nor the determination of Synges world function is necessary. To illustrate the method, the time transfer function of a three-parameter family of static, spherically symmetric metrics is derived within the post-linear approximation.

World function and time transfer: general post-Minkowskian expansions

In suitably chosen domains of spacetime, the world function may be a powerful tool for modelling the deflection of light and the time/frequency transfer. In this paper, we work out a recursive procedure for expanding the world function into a perturbative series of ascending powers of the Newtonian gravitational constant G. We show rigorously that each perturbation term is given by a line integral taken along the unperturbed geodesic between two points. Once the world function is known, it becomes possible to determine the time transfer functions giving the propagation time of a photon between its emission and its reception. We establish that the direction of a light ray as measured in the 3-space relative to an observer can be derived from these time transfer functions, even if the metric is not stationary. We show how to derive these functions up to any given order in G from the perturbative expansion of the world function. To illustrate the method, we carry out the calculation of the world function and of the time transfer function outside a static, spherically symmetric body up to the order G2, the metric containing three arbitrary parameters β, γ, δ.

Tests of Lorentz Symmetry in the Gravitational Sector

Lorentz symmetry is one of the pillars of both General Relativity and the Standard Model of particle physics. Motivated by ideas about quantum gravity, unification theories and violations of CPT symmetry, a significant effort has been put the last decades into testing Lorentz symmetry. This review focuses on Lorentz symmetry tests performed in the gravitational sector. We briefly review the basics of the pure gravitational sector of the Standard-Model Extension (SME) framework, a formalism developed in order to systematically parametrize hypothetical violations of the Lorentz invariance. Furthermore, we discuss the latest constraints obtained within this formalism including analyses of the following measurements: atomic gravimetry, Lunar Laser Ranging, Very Long Baseline Interferometry, planetary ephemerides, Gravity Probe B, binary pulsars, high energy cosmic rays, … In addition, we propose a combined analysis of all these results. We also discuss possible improvements on current analyses and present some sensitivity analyses for future observations.

A Universal Tool for Determining the Time Delay and the Frequency Shift of Light: Synge's World function

In almost all of the studies devoted to the time delay and the frequency shift of light, the calculations are based on the integration of the null geodesic equations. However, the above-mentioned effects can be calculated without integrating the geodesic equations if one is able to determine the bifunction

Time transfer functions as a way to validate light propagation solutions for space astrometry

\Omega(x_A, x_B)

Tides in Planetary Systems

giving half the squared geodesic distance between two points

Application of time transfer functions to Gaia’s global astrometry: Validation on DPAC simulated Gaia-like observations

x_A

Scaling laws to understand tidal dissipation in fluid planetary layers and stars

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