arXiv subjects

Stéfan Renner

Publications and source records attributed to Stéfan Renner.

3 recordsLinked to original sources

arXiv2019

The rings of Neptune

In 1984, three telescopes in South America recorded an occultation of a star near Neptune. It was attributed to the existence of a partial ring or ring arc. The existence of ring arcs around Neptune was confirmed during subsequent years via other occultation experiments and by the Voyager 2 spacecraft. The Voyager observations established that the Neptunian arcs are concentrations of particles embedded within Neptune's narrow Adams ring, the outermost of six tenuous rings discovered by Voyager and discussed here. Four ring arcs were identified: the trailing arc Fraternité, a double-component arc Egalité, dubbed Egalité 1 and 2, Liberté, and the leading arc Courage. The arcs varied in extent from $\sim$ 1$^\circ$ to $\sim$ 10$^\circ$, and together were confined to a longitude range of 40$^\circ$, with typical radial widths of $\sim$ 15 km and optical depth of order 0.1. The properties of the dusty component of Neptune's rings are also discussed in this chapter. Although the arcs should have been destroyed in a few months time through differential Keplerian motion, they appeared to persist at least throughout the Voyager era, and well beyond. However, observations from Earth (both with the Hubble Space Telescope and ground-based adaptive optics) show an evolution in the last three decades, with the disappearance of both Courage and Liberté by 2009. This chapter reviews the constraints provided on the mean motion of the arcs and Galatea, the satellite possibly responsible for the arc confinement. This in turn constrains the various models that have been proposed to explain the arc longevity.

astro-ph.EP↗

arXiv2016

Derivation of Capture Probabilities for the Corotation Eccentric Mean Motion Resonances

We study in this paper the capture of a massless particle into an isolated, first order Corotation Eccentric Resonance (CER), in the framework of the Planar, Eccentric and Restricted Three-Body problem near a m+1:m mean motion commensurability (m integer). While capture into Lindblad Eccentric Resonances (where the perturber's orbit is circular) has been investigated years ago, capture into CER (where the perturber's orbit is elliptic) has not yet been investigated in detail. Here, we derive the generic equations of motion near a CER in the general case where both the perturber and the test particle migrate. We derive the probability of capture in that context, and we examine more closely two particular cases: (i) if only the perturber is migrating, capture is possible only if the migration is outward from the primary. Notably, the probability of capture is independent of the way the perturber migrates outward; (ii) if only the test particle is migrating, then capture is possible only if the algebraic value of its migration rate is a decreasing function of orbital radius. In this case, the probability of capture is proportional to the radial gradient of migration. These results differ from the capture into Lindblad Eccentric Resonance (LER), where it is necessary that the orbits of the perturber and the test particle converge for capture to be possible. Possible applications for planetary satellites are discussed.

astro-ph.EP↗

arXiv2013

Coupling between corotation and Lindblad resonances in the elliptic planar three-body problem

We investigate the dynamics of two satellites with masses $μ_s$ and $μ'_s$ orbiting a massive central planet in a common plane, near a first order mean motion resonance $m$+1:$m$ ($m$ integer). We consider only the resonant terms of first order in eccentricity in the disturbing potential of the satellites, plus the secular terms causing the orbital apsidal precessions. We obtain a two-degree of freedom system, associated with the two critical resonant angles $ϕ= (m+1)λ' -mλ- \varpi$ and $ϕ'= (m+1)λ' -mλ- \varpi'$, where $λ$ and $\varpi$ are the mean longitude and longitude of periapsis of $μ_s$, respectively, and where the primed quantities apply to $μ'_s$. We consider the special case where $μ_s \rightarrow 0$ (restricted problem). The symmetry between the two angles $ϕ$ and $ϕ'$ is then broken, leading to two different kinds of resonances, classically referred to as Corotation Eccentric resonance (CER) and Lindblad Eccentric Resonance (LER), respectively. We write the four reduced equations of motion near the CER and LER, that form what we call the CoraLin model. This model depends upon only two dimensionless parameters that control the dynamics of the system: the distance $D$ between the CER and LER, and a forcing parameter $ε_L$ that includes both the mass and the orbital eccentricity of the disturbing satellite. Three regimes are found: for $D=0$ the system is integrable, for $D$ of order unity, it exhibits prominent chaotic regions, while for $D$ large compared to 2, the behavior of the system is regular and can be qualitatively described using simple adiabatic invariant arguments. We apply this model to three recently discovered small Saturnian satellites dynamically linked to Mimas through first order mean motion resonances : Aegaeon, Methone and Anthe.

astro-ph.EP↗