Jupiter's Small Inner Moons As Clues to Satellite Formation

Jupiter’s small inner moons as clues to satellite formation

Douglas P. Hamilton and Amanda L. Proctor, and Kevin P. Rauch Astronomy Dept., U. Maryland, College Park, MD 20742

Astronomy Dept., U. Arizona, Tucson, AZ 85721

The orbits of regular planetary satellites, moons that formed in situ from primordial circumplan- tary disks of gas and dust, are characterized by their nearly coplanar and almost circular orbits. Among Jupiter’s satellites, however, tiny Thebe (and to a lesser extent its neighbor Amalthea) stand out because of their anomalously large or- bital tilts and eccentricities. We show here that if Thebe and Amalthea were initially formed with coplanar circular orbits, they gain their current non-zero inclinations and eccentricities when mean motion resonances swept over their positions during the tidal expansion of Io’s orbit. Our model naturally explains the inclinations of the two moonlets, constrains Io’s formation distance to be between 4.02 and 4.92 Jupiter radii, and puts strong new limits on Jupiter’s tidal dissipation parame- ter. Over the age of the Solar System, the orbits of Jupiter’s massive Galilean satellites have expanded signiﬁcantly due to forces from the tidal bulges that they raise on Jupiter. This outward motion is believed to naturally lead to the development of the Laplace resonance that currently exists between Io, Europa, and Ganymede. Res- onant interactions with Europa force Io’s orbit to be slightly out of round, thereby allowing tides raised by Jupiter on Io to orbit power that satellite’s volcanoes (1). Although dramatic, Io is not the only signature of tidal expansion still visible in the jovian system. Thebe, a small satellite Jupiter has one of the largest inclinations in the Solar System. Tidal migration models for planetary satellites suﬀer from We show that resonances from Io swept over the small interior satellites Thebe and Amalthea. We propose that the anomalously large inclinations of the inner moonlets Amalthea (I = 0.33◦) and Thebe

1 Table 1: Properties of the Regular Jovian Satellites

Object amoon eccentricity inclination Radii (RJ ) degrees km Metis 1.79 (0) (0) 20 Adrastea 1.80 (0) (0) 10 Amalthea 2.54 0.002 0.036 100 Thebe 3.10 0.02 1.094 50 Io 5.90 0.004 0.04 1821 Europa 9.38 0.01 0.47 1565 Ganymede 14.97 0.00 0.21 2634 Callisto 26.34 0.01 0.28 2403 Caption.

(I = 1.09◦) result from kicks imparted by Io’s strong mean motion resonances as those resonances scan across the location of the moonlets. Both the eccentricities and inclinations of the moonlets are excited during resonant passages. But while the eccentricities decay rapidly due to the large satellite tides raised by the planet, the inclinations are basically preserved since they decay very slowly due to the tiny planetary tides raised by the satellite. For similar reasons, tides do not move the moonlets significantly outward. Our numerical simulations show that two of Io’s 3:1 resonances can impart an inclination of ∼ 0.3◦ to Amalthea when Io passes through a distance of aIo ≈ 5.27RJ (Jo- vian radii). The passage of Io’s 4:2 resonances across Amalthea, at aIo ≈ 4.02RJ , would kick the moonlet’s inclination by 0.6◦, which is significantly larger than the observed value. Io’s 4:2, 5:3, and 3:2 resonances cross Thebe when Io is at 4.92, 4.35, and 4.06 Jupiter radii, respectively. We find that either the 4:2 resonance act- ing alone, or in combination with the other resonances, causes Thebe’s inclination to rise to about 1 degree. Our theory naturally explains the high inclinations of these two small satellites and limits Io’s formation distance from Jupiter to between 4.02 and 4.92 Jovian Radii. References:

1. Goldreich, P. & Soter, S. Icarus 5, 375-389 (1966).

2. Peale, S.J., Cassen, P., & Reynolds, R.T. Science 203, 892-894–733 (1979).

3. Burns, J.A., Showalter, M.R., Hamilton, D.P., Nichol- son, P.D., de Pater, I., Ockert-Bell, M.E., & Thomas, P.C.

2 Amalthea Resonances. Top panel: Io’s 4:2 resonance is too strong. The 3:1 resonace, however, is just the right strength.

Science 284 1146-1150.

3 Thebe Resonances. A sequence of three are required.

Past history of Io.