Evection resonance in Saturn's coorbital moons Dr. Cristian Giuppone1, Lic Ximena Saad Olivera2, Dr. Fernando Roig2 (1) Universidad Nacional de Córdoba, OAC - IATE, Córdoba, Ar (2) Observatorio Nacional, Rio de Janeiro, Brasil OPS III - Diversis Mundi - Santiago - Chile Evection resonance in Saturn's coorbital moons MOTIVATION: recent studies in Jovian planets links the evection resonance and the architecture and evolution of their satellites. Evection resonance in Saturn's coorbital moons MOTIVATION: recent studies in Jovian planets links the evection resonance and the architecture and evolution of their satellites. GOAL: understand the evection resonance in the frame of coorbital motion of Satellites, through numerical evidence of its importance. Evection resonance ● The evection resonance is produced when the orbit pericenter of a satellite (ϖ) precess with the same period that the Sun movement as a perturber (λO) (Brouwer and Clemence, 1961) The evection angle → Ψ=λO – ϖ Satellite Sun Saturn ψ = 0° Evection resonance ● The evection resonance is produced when the orbit pericenter of a satellite (ϖ) precess with the same period that the Sun movement as a perturber (λO) (Brouwer and Clemence, 1961) The evection angle → Ψ=λO – ϖ Satellite Sun Saturn ψ = 0° Evection resonance ● Interior resonance: ● Produced by the oblateness of the planet. ● -3 Located at a ~ 10 RP (a~10 au), and several armonics are present. ● Importance: tides produce outward migration of inner moons. The moons can cross the resonance and may change substantially their orbital elements (e.g. Nesvorny et al 2003, Cuk et al. 2016) Evection resonance ● Interior resonance: ● Produced by the oblateness of the planet. ● -3 Located at a ~ 10 RP (a~10 au), and several armonics are present. ● Importance: tides produce outward migration of inner moons. The moons can cross the resonance and may change substantially their orbital elements (e.g. Nesvorny et al 2003, Cuk et al. 2016) a (RP) e a (au) Evection resonance ● Interior resonance: ● Exterior resonance: ● Produced by the oblateness of the planet. ● Produced by external massive perturber (the Sun). ● -3 Located at a ~ 10 RP (a~10 au), and ● Located at a ~ 0.5 RH (a ~ 0.2 au) several armonics are present. and high eccentricity. ● Importance: tides produce outward migration of inner moons. The moons can ● Importance: the outhermost stable cross the resonance and may change resonance in satellites (Yokoyama et substantially their orbital elements (e.g. al 2008, Frouard et al. 2010). Nesvorny et al 2003, Cuk et al. 2016) a (RP) e a (au) Evection resonance ● Interior resonance: ● Exterior resonance: ● Produced by the oblateness of the planet. ● Produced by external massive perturber (the Sun). ● -3 Located at a ~ 10 RP (a~10 au), and ● Located at a ~ 0.5 RH (a ~ 0.2 au) several armonics are present. and high eccentricity. ● Importance: tides produce outward migration of inner moons. The moons can ● Importance: the outhermost stable cross the resonance and may change resonance in satellites (Yokoyama et substantially their orbital elements (e.g. al 2008, Frouard et al. 2010). Nesvorny et al 2003, Cuk et al. 2016) a (RP) a (RP) Chaotic layer e a (au) Orbital elements distribution JE Interior resonance Tethys Dione in Saturnin satellites Rhea Titan Hyperion Iapetus Exterior resonance Orbital elements distribution in Saturn satellites regular satellites Hyperion e Iapetus c n Titan a n o s Rhea e r r Dione o i r e t x Tethys Irregular satellites E Interior resonance ● Irregular Satellites: inclined and eccentric orbits. Supposed to be captured. ● Regular Satellites: e~0 in the equatorial plane → formed in a circum-planetary disk irc un the equatorial plane → formed from the spreading of a Ring (Crida & Charnoz, 2014) Orbital elements distribution in Saturn satellites regular satellites Hyperion e Iapetus c n JE Titan a n o s Rhea e r r Dione o i r e t x Tethys Irregular satellites E Interior resonance ● Irregular Satellites: inclined and eccentric orbits. Supposed to be captured. ● Regular Satellites: e~0 in the equatorial plane → formed in a circum-planetary disk irc un the equatorial plane → formed from the spreading of a Ring (Crida & Charnoz, 2014) Telesto (L4) and Calypso (L5) of Saturn-Tethys Helene (L4) and Polydeceus (L5) of Saturn-Dione Evection resonance & Trojans in Saturn Is the evection resonance present for satellites in coorbital motion? Ψ=λO – ϖ Evection resonance & Trojans in Saturn Is the evection resonance present for satellites in coorbital motion? Ψ=λO – ϖ Choosing an adequate system of coordinates and variables ● m1 and m2 coordinates are referred to m0 ● m3 coordinates referred to the barycenter of subsystem m0,m1,m2 ● N-body equations, BS integrator. Evection resonance & Trojans in Saturn Is the evection resonance present for satellites in coorbital motion? Ψ=λO – ϖ Choosing an adequate system of coordinates and variables ● m1 and m2 coordinates are referred to m0 ● m3 coordinates referred to the barycenter of subsystem m0,m1,m2 ● N-body equations, BS integrator. Saturn m m 2 Sun 0 Two evection angles 60° Ψ1=λO – ϖ1 Ψ2=λO – ϖ2 m3 m1 Evection resonance & Trojans in Saturn Is the evection resonance present for satellites in coorbital motion? Ψ=λO – ϖ Choosing an adequate system of coordinates and variables ● m1 and m2 coordinates are referred to m0 ● m3 coordinates referred to the barycenter of subsystem m0,m1,m2 ● N-body equations, BS integrator. Coorbital resonance at L4 (or L5) TROJAN configuration: o o (σ, Δϖ ) = (λ2-λ1,ϖ2-ϖ1)=(60 , 60 ) Initial conditions near to periodic coorbital orbits n1~ n2 and e1~ e2 (Giuppone et al 2011) Saturn m m 2 Sun 0 Two evection angles 60° Ψ1=λO – ϖ1 Ψ2=λO – ϖ2 m3 m1 Evection resonance & Trojans in Saturn – INTERIOR - Numerical Analysis Single Satellite Sun Saturn ψ = 0° aΔ (ReP) Δe Evection resonance & Trojans in Saturn – INTERIOR - Numerical Analysis ψ = 0°, ψ = -60°, λ = 0° Single 2 1 3 Δϖ = ϖ2-ϖ1=60° σ = λ2-λ1=60° Satellite Sun Sun m2 Saturn ψ = 0° m 1 60° a (R ) a (RP) P 2 e = 1 e Δe Δe a1=a2 (au) The resonance is present almost at same location than when single satellite is considered Evection resonance & Trojans in Saturn – Exterior - Numerical Analysis a (R ) P Δe White:unstable in ~ 5 104 y o m2/m1=1, ψ2=0 2 e = 1 e a1=a2 (au) Evection resonance & Trojans in Saturn – Exterior - Numerical Analysis a (R ) P Δe White:unstable in ~ 5 104 y o m2/m1=1, ψ2=0 2 e = 1 e a1=a2 (au) ● Trojan configurations can not exist beyond 0.08 au because Solar perturbation provokes that Δϖ librates, breaking the resonant protection. Evection resonance & Trojans in Saturn – Exterior - Numerical Analysis a (R ) P Δe White:unstable in ~ 5 104 y o m2/m1=1, ψ2=0 2 e = 1 e a1=a2 (au) ● Can we have a trojan pair of satellites in the region of exterior evection resonance? Evection resonance & Trojans in Saturn – Exterior - Numerical Analysis o Instead of setting Ψ2=0 , we choose to change the orientation of trojan-pair orbits with respect to o the Sun (initially at λO=0 ). Short integrations (T=100 y), guessing initial eccentricity similar to exterior resonance in single systems (ei=0.4). Sun Saturn m2 m0 m3 60° m1 m2 ° Sun 0 6 n r 1 tu m a S 0 m m3 Evection resonance & Trojans in Saturn – Exterior - Numerical Analysis o Instead of setting Ψ2=0 , we choose to change the orientation of trojan-pair orbits with respect to o the Sun (initially at λO=0 ). Δψ2 Δψ2 Ψ1=λO – ϖ1 Ψ2=λO – ϖ2= – ϖ2 Ψ1 librates a1=a2 (au) Evection resonance & Trojans in Saturn – Exterior - Numerical Analysis o Instead of setting Ψ2=0 , we choose to change the orientation of trojan-pair orbits with respect to o the Sun (initially at λO=0 ). Δψ2 Δψ2 Δψ1 Ψ1=λO – ϖ1 Ψ2=λO – ϖ2= – ϖ2 Ψ1 librates Ψ2 librates a1=a2 (au) a1=a2 (au) No regions where both evection angles librates Evection resonance & Trojans in Saturn – Exterior - Numerical Analysis ● o o Condition 1. Ψ1 librates, Ψ2 circulates. ϖ2=75 (Ψ2 = 285 ) σ ● Ψ2 e2→ chaotic nature ● Survival time ~ 106 y. Ψ1 Evection resonance & Trojans in Saturn – Exterior - Numerical Analysis ● o o Condition 1. Ψ1 librates, Ψ2 circulates. ϖ2=75 (Ψ2 = 285 ) σ ● Ψ2 e2→ chaotic nature ● Survival time ~ 106 y. Ψ1 ● o o Condition 2. Ψ1 circulates, Ψ2 librates. ϖ2=0 (Ψ2 = 0 ) Ψ ● 1 σ e1→ chaotic nature ● Survival time ~ 103 y. Ψ2 Evection resonance & Trojans in Saturn – Tidal Evolution Evection resonance & Trojans in Saturn – Tidal Evolution There is evidence that many trojan systems can form in regions closer to the planet than the position of the interior evection (Crida et al 2017) Interior Evection resonance seems to be important in the past evolution of regular moons of Saturn (Cuk et al 2016). Evection resonance & Trojans in Saturn – Tidal Evolution There is evidence that many trojan systems can form in regions closer to the planet than the position of the interior evection (Crida et al 2017). Interior Evection resonance seems to be important in the past evolution of regular moons of Saturn (Cuk et al 2016). We can include an additional perturbative term, that mimics Tidal evolution of trojan pairs Evection resonance & Trojans in Saturn – Tidal Evolution There is evidence that many trojan systems can form in regions closer to the planet than the position of the interior evection (Crida et al 2017). Interior Evection resonance seems to be important in the past evolution of regular moons of Saturn (Cuk et al 2016). We can include an additional perturbative term, that mimics Tidal evolution of trojan pairs. We run experiments with different folding times, starting with the same I.C.s (~ Dione + Helene) .