arXiv subjects

Melaine Saillenfest

Publications and source records attributed to Melaine Saillenfest.

24 records · Page 2Linked to original sources

arXiv2018

Strong tidal energy dissipation in Saturn at Titan's frequency as an explanation for Iapetus orbit

Natural satellite systems present a large variety of orbital configurations in the solar system. While some are clearly the result of known processes, others still have largely unexplained eccentricity and inclination values. Iapetus has a still unexplained 3% orbital eccentricity and its orbital plane is tilted with respect to its local Laplace plane. On the other hand, astrometric measurements of saturnian moons have revealed high tidal migration rates, corresponding to a quality factor Q of Saturn of around 1600 for the mid-sized icy moons. We show how a past crossing of the 5:1 mean motion resonance between Titan and Iapetus may be a plausible scenario to explain Iapetus' orbit. We have carried out numerical simulations of the resonance crossing using an N-Body code as well as using averaged equations of motion. A large span of migration rates were explored for Titan and Iapetus was started on its local Laplace plane with a circular orbit. The resonance crossing can trigger a chaotic evolution of the eccentricity and the inclination of Iapetus. The outcome of the resonance is highly dependent on the migration rate. For a quality factor Q of over around 2000, the chaotic evolution of Iapetus in the resonance leads in most cases to its ejection, while simulations with a quality factor between 100 and 2000 show a departure from the resonance with post-resonant eccentricities spanning from 0 up to 15%, and free inclinations capable of reaching 11 degrees. Usually high inclinations come with high eccentricities but some simulations show elements compatible with Iapetus' current orbit. A quality factor between 100 and 2000 at the frequency of Titan would bring Titan and Iapetus into a 5:1 resonance, which would perturb Iapetus' eccentricity and inclination to values observed today. Such rapid tidal migration would have avoided Iapetus' ejection around 40 to 800 million years ago.

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arXiv2018

Solar wind dynamics around a comet: The paradigmatic inverse-square-law model

Aims. Observations of solar protons near comet 67P/Churyumov-Gerasimenko (67P) by the Rosetta spacecraft can be modelled by the planar motion in an effective magnetic field proportional to 1/r^2. We aim to provide a thorough study of such dynamics, with a clear description of the behaviour of an incoming flux of particles. We will be able, then, to calibrate the free parameters of the model to Rosetta observations. Methods. Basic tools of dynamical analysis are used. They lead to a definition of the relevant parameters for the system and a classification of the possible types of trajectories. Using the so-obtained formalism, the structures formed by a flux of particles coming from infinity can be studied. Results. All the trajectories are parametrised by two characteristic radii, rE and rC, derived from first integrals. There are three different types of motion possible divided by a separatrix corresponding to rE = rC. An analytical expression of the trajectories, defined by an integral, is developed. Using this formalism, the application to a flux of particles coming from infinity (modelling the incident solar wind) gives one free parameter only, the radius rE, which scales the problem. A circular cavity of radius 0.28 rE is created, as well as an overdensity curve (analogous to a caustic in optics). At each observation time, rE can be calibrated to Rosetta plasma measurements, giving a qualitative understanding of the solar particle dynamics (incoming direction, cavity and density map). We also deduce that, in order to properly capture the essence of the dynamics, numerical simulations of the solar wind around a comet must use simulation boxes much larger than rE and grids much finer than rE.

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arXiv2017

Non-resonant secular dynamics of trans-Neptunian objects perturbed by a distant super-Earth

We use a secular model to describe the non-resonant dynamics of trans-Neptunian objects in the presence of an external ten-earth-mass perturber. The secular dynamics is analogous to an "eccentric Kozai mechanism" but with both an inner component (the four giant planets) and an outer one (the eccentric distant perturber). By the means of Poincaré sections, the cases of a non-inclined or inclined outer planet are successively studied, making the connection with previous works. In the inclined case, the problem is reduced to two degrees of freedom by assuming a non-precessing argument of perihelion for the perturbing body. The size of the perturbation is typically ruled by the semi-major axis of the small body: we show that the classic integrable picture is still valid below about 70 AU, but it is progressively destroyed when we get closer to the external perturber. In particular, for a>150 AU, large-amplitude orbital flips become possible, and for a>200 AU, the Kozai libration islands are totally submerged by the chaotic sea. Numerous resonance relations are highlighted. The most large and persistent ones are associated to apsidal alignments or anti-alignments with the orbit of the distant perturber.

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arXiv2017

The long-term evolution of known resonant trans-Neptunian objects

Aims. Numerous trans-Neptunian objects are known to be in mean-motion resonance with Neptune. We aim to describe their long-term orbital evolution (both past and future) by means of a one-degree-of-freedom secular model. In this paper, we focus only on objects with a semi-major axis larger than 50 astronomical units (au). Methods. For each resonant object considered, a 500 000-year numerical integration is performed. The output is digitally filtered to get the parameters of the resonant secular model. Their long-term (Giga-year) orbital evolution is then represented by the level curves of the secular Hamiltonian. Results. For the majority of objects considered, the mean-motion resonance has little impact on the long-term trajectories (the secular dynamics is similar to a non-resonant one). However, a subset of objects is strongly affected by the resonance, producing moderately-high-amplitude oscillations of the perihelion distance and/or libration of the argument of perihelion around a fixed centre. Moreover, the high perihelion distance of the object 2015 FJ345 is plainly explained by long-term resonant dynamics, allowing us to also deduce its orbital elements at the time of capture in resonance (at least 15 million years ago). The same type of past evolution is expected for 2014 FZ71.

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arXiv2016

Long term dynamics beyond Neptune: secular models to study the regular motions

Two semi-analytical one-degree-of-freedom secular models are presented for the motion of small bodies beyond Neptune. A special attention is given to trajectories entirely exterior to the planetary orbits. The first one is the well-known non-resonant model of Kozai (1962) adapted to the transneptunian region. Contrary to previous papers, the dynamics is fully characterized with respect to the fixed parameters. A maximum perihelion excursion possible of 16.4 AU is determined. The second model handles the occurrence of a mean-motion resonance with one of the planets. In that case, the one-degree-of-freedom integrable approximation is obtained by postulating the adiabatic invariance, and is much more general and accurate than previous secular models found in the literature. It brings out in a plain way the possibility of perihelion oscillations with a very high amplitude. Such a model could thus be used in future studies to deeper explore that kind of motion. For complex resonant orbits (especially of type 1:k), a segmented secular description is necessary since the trajectories are only "integrable by parts". The two models are applied to the Solar System but the notations are kept general so that it could be used for any quasi-circular and coplanar planetary system.

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arXiv2016

Study and application of the resonant secular dynamics beyond Neptune

We use a secular representation to describe the long-term dynamics of transneptunian objects in mean-motion resonance with Neptune. The model applied is thoroughly described in Saillenfest et al. (2016). The parameter space is systematically explored, showing that the secular trajectories depend little on the resonance order. High-amplitude oscillations of the perihelion distance are reported and localised in the space of the orbital parameters. In particular, we show that a large perihelion distance is not a sufficient criterion to declare that an object is detached from the planets. Such a mechanism, though, is found unable to explain the orbits of Sedna or 2012VP113, which are insufficiently inclined (considering their high perihelion distance) to be possibly driven by such a resonant dynamics. The secular representation highlights the existence of a high-perihelion accumulation zone due to resonances of type 1:k with Neptune. That region is found to be located roughly at semi-major axes in [100;300] AU, perihelion distances in [50;70] AU and inclinations [30;50]°. In addition to the flux of objects directly coming from the Scattered Disc, numerical simulations show that the Oort Cloud is also a substantial source for such objects. Naturally, as that mechanism relies on fragile captures in high-order resonances, our conclusions break down in the case of a significant external perturber. The detection of such a reservoir could thus be an observational constraint to probe the external Solar System.

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