KOI-730 as a System of Four Planets in a Chain of Resonances

Daniel Fabrycky UC Santa Cruz

Matthew Holman, Joshua Carter, Jason Rowe, Darin Ragozzine, William Borucki,David Koch, and the Kepler Team

Planets in Resonance

• Resonances are common among RV-discovered gas giants (~1 period commensurability in 3 multi systems: Wright et al. 2011, a 4:2:1 chain in GJ 876: Rivera et al. 2010)

• Kepler has found Neptune-size pairs especially abundant near resonances (Lissauer et al. 2011)

• Theories suggest the Solar System giants may have started in a resonant chain (Morbidelli et al. 2007, Thommes et al. 2008)

KOI-730: Three Pairs of First-Order Resonances

3:4:6:8

P/PP=1.33411(8) 4:3

P/P=1.50157(5) 3:2

P/P=1.33341(3) 4:3

candidate period (d) Rp (RE)

730.04 7.3831 1.8

730.02 9.8499 2.1

730.01 14.7903 2.8

730.02 19.7216 2.4

Laplace-type resonances

• Involves 3 planets at once• Io, Europa, & Gaynmede obey λI-3λE+2λG=180°

TTVs??

Theory:• Match P, T0

• coplanar• mass: Mp = Rp

2.06

• e = 0

Observed:transit timesthrough Q8

P=7.3831 ddP/dE= -1±1 s

P=9.8499 ddP/dE= 0±3 s

P=19.7216 ddP/dE= -12±12 s

P=14.7903 ddP/dE= 15±2 s relax

Lee & Peale 02GJ 876 b/c

Disk Migration Theory

Rules-of-thumb for resonance capture:• Converging and slow• Low eccentricity favors first-order resonances• High eccentricity favors high-order resonances

Capture into Resonance

first-order resonances Laplace-type resonances moderate eccentricities increased stability

• A candidate system of 4 low-mass planets on compact, resonant orbits

• It informs migration models: limits the speed, direction, and damping properties

• It’s the missing link to RV exoplanet systems, the Kepler multis, and maybe even the Solar System giants

KOI-730:

Coorbital no more

KOI-730.03’s period was revised from 9.861 days to twice that: 19.722 days. This took it out of 1:1 resonance with KOI-730.02. This was apparent even in the Q1-Q2 data and is confirmed by the data through Q8.

• Stellar properties (determined by photometry, accounting for a blended companion, and fit to isochrones):

Kp15.3 mag