## 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 $\sim 20 M_\oplus$

## DDA 2015 – Dynamical Analysis of the 6:1 Resonance of the Brown Dwarfs Orbiting the K Giant Star ν Ophiuchi

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: Dynamical Constraints from Exoplanet Observaons II

Man Hoi Lee (University of Hong Kong)

#### Abstract

The K giant star ν Oph has two brown dwarf companions (with minimum masses of about 22 and 25 times the mass of Jupiter), whose orbital periods are about 530 and 3200 days and close to 6:1 in ratio. We present a dynamical analysis of this system, using 150 precise radial velocities obtained at the Lick Observatory in combination with data already available in the literature. We investigate a large set of orbital fits by applying systematic $\chi^2$ grid-search techniques coupled with self-consistent dynamical fitting. We find that the brown dwarfs are indeed locked in an aligned 6:1 resonant configuration, with all six mean-motion resonance angles librating around 0°, but the inclination of the orbits is poorly constrained. As with resonant planet pairs, the brown dwarfs in this system were most likely captured into resonance through disk-induced convergent migration. Thus the ν Oph system shows that brown dwarfs can form like planets in disks around stars.

#### Notes

• Lick G & K giants RV survey
• 373 bright G & K giant stars
• 0.6-m Coude
• ~1999-2012
• RV precision ~5 m/s
• $\nu$Oph
• K0III HB star, 2.73 $M_\odot$
• brown dwarf companion, P = 530 d
• 150 Lick RV measurements
• Fitting codes: Tan et al. 2013
• Grid search to minimize $\chi^2$
• SyMBA 10 Myr integrations
• Best fit:
• $M_1 = 22 M_J$, $P_1 = 530$ d, $a_1 = 1.79$ AU, $e_1 = 0.124$
• $M_2 = 25 M_J$, $P_2 = xxx$ d, $a_2 = 6.02$ AU, $e_2 = 0.1xx$
• 6:1 MMR at $3\sigma$
• Stability: all fits stable (numerically) to 10 Myr
• No constraints on inclination
• Origin
• Resonant capture via migration
• Type II (Ward 1997)
• $\left|\dfrac{\dot{a}}{a}\right| = \dfrac{3\nu}{2a^2}$
• Conclusions
• 2 brown dwarf companions
• minimum mass $22 M_J$ and $25 M_J$
• 6:1 MMR
• 6:1MMR couldindicate formation & migration in a disk
• But resonant capture requires slow migration and nonzero eccentricities