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
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
P/P=1.33411(8)
4:3
P/P=1.50157(5)
3:2
P/P=1.33341(3)
4:3
3:4:6:8
Laplace-type resonances
• Involves 3 planets at once
• Io, Europa, & Gaynmede obey λI-3λE+2λG=180°
TTVs??
P=7.3831 d
dP/dE= -1±1
s
P=9.8499 d
dP/dE= 0±3
s
Observed:
transit times
through Q8
P=14.7903 d
dP/dE= 15±2
s
P=19.7216 d
dP/dE= -12±12 s
Theory:
• Match P, T0
• coplanar
• mass:
Mp = Rp2.06
•e=0
relax
Disk Migration Theory
Lee & Peale 02
GJ 876 b/c
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
KOI-730:
• 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
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 KOI730.02. 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):
Kp
15.3 mag