On the Origin of the Long-Lived Asteroidsin the 2:1 Mean-Motion Resonance

with Jupiter

O. Chrenko1, M. Broz1, D. Nesvorny2

1 Astronomical Institute, Faculty of Mathematics and Physics,Charles University in Prague

2 Southwest Research Institute, Boulder, Colorado

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Data in figure by Knezevic & Milani (2003)

Motivation and update

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reso

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ecc

entr

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resonant semi-major axis ar [AU]

island A

island B

Kozai

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ν5

2/1 separatrix 0

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stable B:I < 5°

stable A:I > 5°

124 dynamically stable asteroids (lifetime > 1Gyr) and106 marginally stable asteroids (0.07Gyr < lifetime ≤ 1Gyr)

◮ resonant elements computed according to Roig et al. (2002)◮ primordial origin or resonant capture? the presentation is

focused on the latter

(some) previous papers on the origin: Moons et al. (1998), Ferraz-Mello et al. (1998),Roig et al. (2002), Broz et al. (2005), Broz & Vokrouhlicky (2008) 2 / 8

Migration scenarios and methods

◮ orbital evolution of planets prescribed according to scenariosby Nesvorny & Morbidelli (2013), Morbidelli et al. (2010)

fifth giant planet scenariojumping Jupiter scenario with four giant planets

◮ planets: interpolation in cartesian coordinates (x , y , z) alongKeplerian ellipses; input data sampling ∆t = 1 yr

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a, q

, Q [A

U]

time t [Myr]

Jupiter

Saturn

Uranus

Neptune

5th planet

◮ test particles: symplectic SWIFT-RMVS algorithm(Levison & Duncan 1994) with 0.25 yr timestep

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Capture in the fifth-giant-planet scenario

◮ initial population of 5000 test particles with isotropic (a, e, I )distribution in the outer main belt; I ∈ (0◦, 15◦)

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2:1 center

t = 2 Myr

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t = 6.26 MyrJump!

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t = 10 Myr

◮ capture is significant, but which asteroids are long-lived?4 / 8

Dynamical map present configuration of planets

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island A

island B

secondaryresonances

separatrix

◮ δ ≡ the difference between the initial and final resonantelement over 10 Myr timespan

◮ distance d ≡

√

(

δarar

)2+ (δer)

2 + (δ sin Ir)2

◮ 24000 test particles per simulation5 / 8

Dynamical map post-migration configuration of planets

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◮ the post-migration map is used to extract the long-livedasteroids at the end of our simulations(i.e. similar structure, stable islands exist)

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Result: Captured long-lived asteroids

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◮ initial population rescaled to outer main belt values– captured population increased by factor 10 to 13

◮ long-term depletion rate applied– 93% to 95% decay over 4 Gyr; by Skoulidou et al. (CPS-IAU, 2014)

◮ 158 to 219 test particles in B (vs 180 observed) - match◮ 37 to 51 test particles in A (vs 11 observed) - mismatch

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Conclusions (and confusions)

◮ capture works in the fifth-giant-planet scenario with1.5% efficiency in the island A and with 5% efficiency in B

◮ moreover, 3% of the primordial population survives the jump!

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◮ how to explain the observed steep SFD (cumulative slope −4.3)?

◮ is primordial population really primordial?

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