## DDA 2015 – Recent Formation of Saturnian Moons: Constraints from Their Cratering Records

This is one of a series of notes taken during the 2015 meeting of the AAS Division on Dynamical Astronomy, 3-7 May, at CalTech. An index to this series (all the papers presented at the meeting) is here.

### Session: Moon Formation and Dynamics I

Henry C. (Luke) Dones (SWRI)

#### Abstract

Charnoz et al. (2010) proposed that Saturn’s small “ring moons” out to Janus and Epimetheus consist of ring material that viscously spread beyond the Roche limit and coagulated into moonlets. The moonlets evolve outward due to the torques they exert at resonances in the rings. More massive moonlets migrate faster; orbits can cross and bodies can merge, resulting in a steep trend of mass vs. distance from the planet. Canup (2010) theorized that Saturn’s rings are primordial and originated when a differentiated, Titan-like moon migrated inward when the planet was still surrounded by a gas disk. The satellite’s icy shell could have been tidally stripped, and would have given rise to today’s rings and the mid-sized moons out to Tethys. Charnoz et al. (2011) investigated the formation of satellites out to Rhea from a spreading massive ring, and Crida and Charnoz (2012) extended this scenario to other planets. Once the mid-sized moons recede far from the rings, tidal interaction with the planet determines the rate at which the satellites migrate. Charnoz et al. (2011) found that Mimas would have formed about 1 billion years more recently than Rhea. The cratering records of these moons (Kirchoff and Schenk 2010; Robbins et al. 2015) provide a test of this scenario. If the mid-sized moons are primordial, most of their craters were created through hypervelocity impacts by ecliptic comets from the Kuiper Belt/Scattered Disk (Zahnle et al. 2003; Dones et al. 2009). In the Charnoz et al. scenario, the oldest craters on the moons would result from low-speed accretionary impacts. We thank the Cassini Data Analysis program for support.

References
Canup, R. M. (2010). Nature 468, 943
Charnoz, S.; Salmon, J., Crida, A. (2010). Nature 465, 752
Charnoz, S., et al. (2011). Icarus 216, 535
Crida, A.; Charnoz, S. (2012). Science 338, 1196
Dones, L., et al. (2009). In Saturn from Cassini-Huygens, p. 613
Kirchoff, M. R.; Schenk, P. (2010). Icarus 206, 485
Robbins, S. J.; Bierhaus, E. B.; Dones, L. (2015). Lunar and Planetary Science Conference 46, abstract 1654
(http://www.hou.usra.edu/meetings/lpsc2015/eposter/1654.pdf)
Zahnle, K.; Schenk, P.; Levison, H.; Dones, L. (2003). Icarus 163, 263

#### Notes

• Can cratering records constrain moon ages?
• see http://space.jpl.nasa.gov
• small inner moons (and Mimas) interact strongly with rings — the so-called “ring moons”
• migrated from outer edge of rings ~100 Myr
• regular moons (Mimas-Iapetus) are (assumed?) primordial
• transition is abrupt where tidal forces prevent formation
• formation of moons from spreading rings:Charnoz et al. 2010,Canup 2010,Charnoz et al. 2011,Crida &Charnoz 2012
• outside Roche limit, formation
• Lainey et al. 2012: dissipation stronger than thought
• decreases timescale considerably
• Impact rates
• $R_{moon} = R_J \dfrac{R_S}{R_J} \dfrac{R_{moon}}{R_S}$
• Crater scaling: diameter vs. velocity
• impacts/$10^9$ yr: Mimas 8.5, Rhea 48
• Mimas & Rhea counts: Robbins et al. 2015 (LPSC)
• plot: #craters larger than D vs. D
• Mimas: saturated up to $D \sim 20-45$ km
• Rhea: saturated up to $D \sim 25$ km
• Summary
• Mimas: Craters are near saturation for diameters < 20 km
• Rhea: saturation < 25 km
• Ages may be underestimated

## DDA 2015 – The Evidence for Slow Migration of Neptune from the Inclination Distribution of Kuiper Belt Objects

This is one of a series of notes taken during the 2015 meeting of the AAS Division on Dynamical Astronomy, 3-7 May, at CalTech. An index to this series (all the papers presented at the meeting) is here.

David Nesvorny (SWRI)

#### Abstract

Much of the dynamical structure of the Kuiper Belt can be explained if Neptune migrated over several AU, and/or if Neptune was scattered to an eccentric orbit during planetary instability. An outstanding problem with the existing formation models is that the distribution of orbital inclinations predicted by them is narrower than the one inferred from observations. Here we perform numerical simulations of the Kuiper belt formation starting from an initial state with Neptune at $20\lt a^{N,0} \lt 30$ AU and a dynamically cold outer disk extending from beyond $a^{N,0}$ to 30 AU. Neptune’s orbit is migrated into the disk on an e-folding timescale $1 \le \tau \le 100$ Myr. A small fraction ($\sim10^{-3}$) of disk planetesimals become implanted into the Kuiper belt in the simulations. By analyzing the orbital distribution of the implanted bodies in different cases we find that the inclination constraint implies that $\tau \ge 10$ Myr and $a^{N,0} \le 26$ AU.The models with $\tau \lt 10$ Myr do not satisfy the inclination constraint, because there is not enough time for various dynamical processes to raise inclinations. The slow migration of Neptune is consistent with other Kuiper belt constraints, and with the recently developed models of planetary instability/migration. Neptune’s eccentricity and inclination are never large in these models ($e^N \lt 0.1$, $i^N \lt 2$ deg), as required to avoid excessive orbital excitation in the $\gt 40$ AU region, where the Cold Classicals presumably formed.

#### Notes

• Early SS evolution
• giant planets emerged from dispersing protopl disk on compact orbits (inside massive belt)
• planetesimal driven migration?
• dynamical instability?
• giant planets now spread from 5 to 30 AU
• Kuiper Belt is the best clue to evolution of Neptune’s orbit
• KB structure is complex (plot: $e$ vs $a$)
• between 3:2 and 2:1 MMRs: a mess, but hot and cold populations
• where did hot population come from (including high-$i$ 3:2 objects)?
• model: too many Plutinos compared to observations
• New model
• 4 outer planets
• ICs:
• Neptune starting points: 22, 24, 26, 28 AU
• Neptune migration e-folding timescales 1, 3, 10, 30, 100 Myr
• 1e6 particles, Rayleigh initial distribution
• swift_rmvs3 integrator
• 500 cores of Pleiades supercomputer
• 20 jobs total, most stopped 1 Gyr, interesting ones to 4 Gyr
• $\rightarrow$ result matches observed distribution
• 24 AU, 30 Myr
• but too manyPlutinos(?)
• observational bias?
• cf Petit et al. 2012
• CFEPS detection simulator
• agreement (of hot population) is actually pretty good
• Gomes capture mechanism:Gomes 2003
• 2:1 MMR secular structure is complex
• Conclusions:
• Neptune migrated into a massive cometary disk at $\lt 30$ AU
• Neptune’s migration hadto be slow
• need time to increase inclinations
• Model also explains other KB properties
• Initial disk had to be $\sim 20 M_\oplus$