About the dynamics of the evection resonance

Frouard, Julien; Fouchard, Marc; Vienne, A.

doi:10.1051/0004-6361/200913048

Cited by 24 publications

(32 citation statements)

References 16 publications

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“…In addition, the inner orbit precession frequency can be close to, but still longer than the outer orbital period in some cases (such as in the Earth-Moon system), in which case evection terms may become important. In case of comparable inner orbit precession frequency and outer orbital period, the evection resonance can come into play (e.g., Frouard et al 2010;Grishin et al 2017). Another example is the occurrence of mean-motion resonance in 2+2 systems (Breiter & Vokrouhlický 2018).…”

Section: Breakdown Of the Averaging Approximationmentioning

confidence: 99%

Shrinking orbits in hierarchical quadruple star systems

Hamers

2018

Monthly Notices of the Royal Astronomical Society

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The distribution of the inner orbital periods of solar-type main-sequence (MS) triple star systems is known to be peaked at a few days, and this has been attributed to tidal evolution combined with eccentricity excitation due to Lidov-Kozai oscillations. Solar-type MS quadruple star systems also show peaks in their inner orbital period distributions at a few days. Here, we investigate the natural question whether tidal evolution combined with secular evolution can explain the observed inner orbital period distributions in quadruple stars. We carry out population synthesis simulations of solar-type MS quadruple star systems in both the 2+2 (two binaries orbiting each other's barycentre) and 3+1 (triple orbited by a fourth star) configurations. We take into account secular gravitational and tidal evolution, and the effects of passing stars. We assume that no short-period systems are formed initially, and truncate the initial orbital period distributions below 10 d accordingly. We find that, due to secular and tidal evolution, the inner orbital period distributions develop tails at short periods. Although qualitatively consistent with the observations, we find that our simulated orbital period distributions only quantitatively agree with the observations for the 3+1 systems. The observed 2+2 systems, on the other hand, show an enhancement of systems around 10 d, which is not reproduced in the simulations. This suggests that the inner orbital periods of 2+2 systems are not predominantly shaped by tidal and secular evolution, but by other processes, most likely occurring during the stellar formation and early evolution.

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Section: Breakdown Of the Averaging Approximationmentioning

confidence: 99%

Shrinking orbits in hierarchical quadruple star systems

Hamers

2018

Monthly Notices of the Royal Astronomical Society

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“…Special care has been taken in the study of (i) the secular resonance ν =˙ −˙ (Saha & Tremaine 1993;Whipple & Shelus 1993;Beaugé & Nesvorný 2007;Nesvorný et al 2003;Yokoyama et al 2003;Ćuk & Burns 2004;Correa Otto et al 2009), which is one of the most important secular resonances acting on the satellites; (ii) the Lidov-Kozaï resonance for distant satellites (Beaugé et al 2006;Beaugé & Nesvorný 2007;Carruba et al 2002;Ćuk & Burns 2004;Nesvorný et al 2003); and (iii) the evection resonancė − n (Yokoyama et al 2008;Frouard et al 2010;Nesvorný et al 2003). In most of these works, the important need for the development of high-order perturbation methods or numerical ones is clearly stressed.…”

Section: Introductionmentioning

confidence: 99%

The long-term dynamics of the Jovian irregular satellites

Frouard

Vienne

Fouchard

2011

A&A

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Context. The dynamical region of the Jovian irregular satellites presents an interesting web of resonances that are not yet fully understood. Of particular interest is the influence of the resonances on the stochasticity of the individual orbits of the satellites, as well as on the long-term chaotic diffusion of the different families of satellites. Aims. We make a systematic numerical study of the satellite region to determine the important resonances for the dynamics, to search for the chaotic zones, and to determine their influences on the dynamics of the satellites. We also compare these numerical results to previous analytical works. Methods. Using extensive numerical integrations of the satellites along with an indicator of chaos (MEGNO), we show global and detailed views of the retrograde and prograde regions for various dynamical models of increasing complexity and indicate the appearance of the different types of resonances and the implied chaos. Results. Along with secular and mean motion resonances that shape the dynamical regions of the satellites, we report a number of resonances involving the Great Inequality, and which are present in the system thanks to the wide range of the values of frequencies of the pericenter available for the satellites. The chaotic diffusion of the satellites is also studied and shows the long-term stability of the Ananke and Carme families, in contrast to the Pasiphae family.

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“…We note that when m 3 = 0, all the A ki and C k functions are zero and the expansion reduces to the same expansion as reported by Robutel & Pousse (2013), with the addition of the oblateness terms D i . On the other hand, when m 2 = 0, all the B k and C k functions are zero, and the expansion reduces to the classical expansion of the lunar theory, again with the addition of the oblateness terms (Frouard et al 2010).…”

Section: Analytical Model For Trojan Satellitesmentioning

confidence: 99%

“…Therefore, regions with large variations in δe i are more sensitive to perturbations and are very likely chaotic. Frouard et al (2010) used a similar indicator in their study of the evection resonance in Jupiter satellites, defined as (e τa max −e τ b max )/e τa max , where the total integration time, τ , was divided into two consecutive samples τ a and τ b . Nevertheless, we realized that this indicator is quite sensitive to the value of τ and may artificially create some structures that are not related with actual resonances.…”

Section: Numerical Studymentioning

confidence: 99%

Modeling the evection resonance for Trojan satellites: application to the Saturn system

Giuppone

Roig

Saad-Olivera

2018

A&A

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Context. The stability of satellites in the solar system is affected by the so-called evection resonance. The moons of Saturn, in particular, exhibit a complex dynamical architecture in which co-orbital configurations occur, especially close to the planet where this resonance is present. Aims. We address the dynamics of the evection resonance, with particular focus on the Saturn system, and compare the known behavior of the resonance for a single moon to that of a pair of moons in co-orbital trojan configuration. Methods. We developed an analytic expansion of the averaged Hamiltonian of a trojan pair of bodies, including the perturbation from a distant massive body. The analysis of the corresponding equilibrium points was restricted to the asymmetric apsidal corotation solution of the co-orbital dynamics. We also performed numerical N-body simulations to construct dynamical maps of the stability of the evection resonance in the Saturn system, and to study the effects of this resonance under the migration of trojan moons caused by tidal dissipation.Results. The structure of the phase space of the evection resonance for trojan satellites is similar to that of a single satellite, differing in that the libration centers are displaced from their standard positions by an angle that depends on the periastron difference 2 − 1 and on the mass ratio m2/m1 of the trojan pair. In the Saturn system, the inner evection resonance, located at ∼ 8 RS, may capture a pair of trojan moons by tidal migration; the stability of the captured system depends on the assumed values of the dissipation factor Q of the moons. On the other hand, the outer evection resonance, located at > 0.4 R Hill , cannot exist at all for trojan moons, because trojan configurations are strongly unstable at distances from Saturn longer than ∼ 0.15 R Hill .

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About the dynamics of the evection resonance

Cited by 24 publications

References 16 publications

Shrinking orbits in hierarchical quadruple star systems

Shrinking orbits in hierarchical quadruple star systems

The long-term dynamics of the Jovian irregular satellites

Modeling the evection resonance for Trojan satellites: application to the Saturn system

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