Download Are planetary systems flat?

Are planetary systems flat?
collaborators:
Subo Dong (IAS)
Dan Fabrycky (UC Santa Cruz)
Boaz Katz (IAS)
Aristotle Socrates (IAS)
Thursday, April 26, 2012
Why do astronomers think that planetary
systems are flat?
Thursday, April 26, 2012
Why do astronomers think that planetary
systems are flat?
•
the solar system is flat (maximum inclination 7 deg)
•
the inner satellite systems of Jupiter, Saturn, Uranus are flat
Thursday, April 26, 2012
Why do astronomers think that planetary
systems are flat?
Thursday, April 26, 2012
Why do astronomers think that planetary
systems are flat?
• many other astrophysical systems are flat
Thursday, April 26, 2012
Why do astronomers think that planetary
systems are flat?
•disks minimize energy at constant angular momentum
Laplace, Exposition du système du monde (1796):
– it is astonishing to see all the planets move around the Sun from west to east,
and almost in the same plane; all the satellites move around their planets in the
same direction and nearly in the same plane as the planets; finally, the Sun, the
planets, and all the satellites that have been observed rotate in the direction
and nearly in the plane of their orbits...another equally remarkable phenomenon
is the small eccentricity of the orbits of the planets and the satellites...we are
forced to acknowledge the effect of some regular cause since chance alone could
not give a nearly circular form to the orbits of all the planets
Thursday, April 26, 2012
Kepler
Thursday, April 26, 2012
•
launch March 6 2009
•
0.95 meter mirror, 100
megapixel camera, 12 degree
diameter field of view
•
monitor ~105 stars continuously
over ~6 yr mission
•
20 parts per million
photometric precision
1769
Transit of Venus
next June 6, 2012, sunrise
to 06:55 in Zurich
Thursday, April 26, 2012
Thursday, April 26, 2012
Thursday, April 26, 2012
fractional brightness dip: Jupiter 0.01 = 1%
Earth 0.0001=0.01%
1%
Thursday, April 26, 2012
transit: planet moves in front of the
star; U-shape because of limb
darkening in star
occultation: planet moves behind the
star; square shape
Thursday, April 26, 2012
transit: planet moves in front of the
star; U-shape because of limb
darkening in star
occultation: planet moves behind the
star; square shape
Thursday, April 26, 2012
transit: planet moves in front of the
star; U-shape because of limb
darkening in star
occultation: planet moves behind the
star; square shape
currently 230 planets by this method
from the ground and ~2000 candidates
from Kepler
Thursday, April 26, 2012
van Kerkwijk et al. (2010)
• orbital period P = 5.2 days
• two curious features:
• sinusoidal brightness variations at fundamental and first harmonic
• transit (U shape) is shallower than occultation (square well)
Thursday, April 26, 2012
van Kerkwijk et al. (2010)
• orbital period P = 5.2 days
• two curious features:
• sinusoidal brightness variations at fundamental and first harmonic
• transit (U shape) is shallower than occultation (square well)
• both can be explained if the companion is a white dwarf rather than a planet:
• occultation is deeper because the white dwarf is hotter than the primary
(T=13,000 K vs. 9,400 K)
• first harmonic due to tidal distortion of the primary by the white dwarf
• fundamental due to Doppler boosting (gives velocity curve to 1 km/s)
• white dwarf has mass 0.22±0.03 M⊙; radius 0.043±0.004 R⊙
Thursday, April 26, 2012
Why do astronomers think that planetary
systems are flat?
•
mutual inclination of planets around PSR B1257+12 is < 13 degrees
•
modeling of radial velocities, astrometry, and dynamics implies that mutual
inclination of GJ 876b and c is
•
< 2 degrees (Correia et al. 2010)
•
3-9 degrees (Bean & Seifahrt 2009)
•
5-15 degrees (Baluev 2011)
•
dynamical modeling of transit timing variations in Kepler-9 system implies
that mutual inclination is < 10 degrees (Holman et al. 2010)
•
absence of transit timing variations in Kepler-11 implies inclination of
Kepler-11e < 2 degrees (Lissauer et al. 2011)
Thursday, April 26, 2012
Why do astronomers think that planetary
systems are flat?
•
mutual inclination of planets around PSR B1257+12 is < 13 degrees
•
modeling of radial velocities, astrometry, and dynamics implies that mutual
inclination of GJ 876b and c is
•
< 2 degrees (Correia et al. 2010)
•
3-9 degrees (Bean & Seifahrt 2009)
•
5-15 degrees (Baluev 2011)
•
dynamical modeling of transit timing variations in Kepler-9 system implies
that mutual inclination is < 10 degrees (Holman et al. 2010)
•
absence of transit timing variations in Kepler-11 implies inclination of
Kepler-11e < 2 degrees (Lissauer et al. 2011)
Thursday, April 26, 2012
✘
Why do astronomers think that planetary
systems are flat?
•
mutual inclination of planets around PSR B1257+12 is < 13 degrees
•
modeling of radial velocities, astrometry, and dynamics implies that mutual
inclination of GJ 876b and c is
•
< 2 degrees (Correia et al. 2010)
•
3-9 degrees (Bean & Seifahrt 2009)
•
5-15 degrees (Baluev 2011)
•
dynamical modeling of transit timing variations in Kepler-9 system implies
that mutual inclination is < 10 degrees (Holman et al. 2010)
•
absence of transit timing variations in Kepler-11 implies inclination of
Kepler-11e < 2 degrees (Lissauer et al. 2011)
Thursday, April 26, 2012
✘
✘
Why do astronomers think that planetary
systems are flat?
•
mutual inclination of planets around PSR B1257+12 is < 13 degrees
•
modeling of radial velocities, astrometry, and dynamics implies that mutual
inclination of GJ 876b and c is
•
< 2 degrees (Correia et al. 2010)
•
3-9 degrees (Bean & Seifahrt 2009)
•
5-15 degrees (Baluev 2011)
•
dynamical modeling of transit timing variations in Kepler-9 system implies
that mutual inclination is < 10 degrees (Holman et al. 2010)
•
absence of transit timing variations in Kepler-11 implies inclination of
Kepler-11e < 2 degrees (Lissauer et al. 2011)
Thursday, April 26, 2012
✘
✘
✘
✘
Why might we believe that planetary systems are
not flat?
•
in most disks, rms
eccentricity is
correlated with rms
inclination (e.g.,
asteroids have <i> ≈ <e>)
•
rms eccentricities in
extrasolar planetary
systems are much
larger than in the solar
system
•
<e>
0.25 implies <i>
15o
Thursday, April 26, 2012
Why might we believe that planetary systems are
not flat?
• in most disks, rms eccentricity is correlated with rms inclination, and rms
eccentricities in extrasolar planetary systems are much larger than in the
solar system
• mutual inclination of upsilon And c and d is 30±1 degrees (McArthur et al.
2010)
• extrasolar planetary systems look quite
different from the solar system (e.g., hot
Jupiters) so there is no reason to expect
that they formed in the same way
• if planet formation were similar to star formation (collapse of dense cores
in a cloud) we would expect an isotropic distribution
– distribution of eccentricities of extrasolar planets is quite similar to
distribution of eccentricities of binary stars (Black 1997)
Thursday, April 26, 2012
Thursday, April 26, 2012
Jupiter
Thursday, April 26, 2012
hot Jupiters
Jupiter
Thursday, April 26, 2012
Why might we believe that planetary systems are
not flat?
• in most disks, rms eccentricity is correlated with rms inclination, and rms
eccentricities in extrasolar planetary systems are much larger than in the
solar system
• mutual inclination of upsilon And c and d is 30±1 degrees (McArthur et al.
2010)
• extrasolar planetary systems look quite
different from the solar system (e.g., hot
Jupiters) so there is no reason to expect
that they formed in the same way
• if planet formation were similar to star formation (collapse of dense cores
in a cloud) we would expect an isotropic distribution
– distribution of eccentricities of extrasolar planets is quite similar to
distribution of eccentricities of binary stars (Black 1997)
Thursday, April 26, 2012
Ribas & Miralda-Escudé
(2007)
Thursday, April 26, 2012
Why might we believe that planetary systems are
not flat?
• in most disks, rms eccentricity is correlated with rms inclination,
and rms eccentricities in extrasolar planetary systems are much
larger than in the solar system
• mutual inclination of υ And c and d is 30±1 degrees (McArthur et al.
2010)
• extrasolar planetary systems look quite different from the solar
system (e.g., hot Jupiters) so there is no reason to expect that
they formed in the same way
• if planet formation were similar to star formation (collapse of
dense cores in a cloud) we would expect an isotropic distribution
• current theoretical models of planet formation in a disk face
serious obstacles
Thursday, April 26, 2012
Why might we believe that planetary systems are
not flat?
• rms eccentricities in extrasolar planetary systems are much larger
than in the solar system
• mutual inclination of υ And c and d
• extrasolar planetary systems are different from the solar system
• if planet formation were similar to star formation (collapse of
dense cores in a cloud) we would expect an isotropic distribution
• current theoretical models of planet formation in a disk face
serious obstacles
• stellar spin axis and planet orbital axis are often mis-aligned (by 7
degrees for the Sun and much more for some other systems)
Thursday, April 26, 2012
(from J. Winn)
Thursday, April 26, 2012
λ
obliquity = angle between spin angular
momentum of star and orbital angular
momentum of planet
Rossiter-McLaughlin measures
projected obliquity (λ) = angle between
projection of spin angular momentum of
star and orbital angular momentum of
planet on the sky plane
(from J. Winn)
Thursday, April 26, 2012
Thursday, April 26, 2012
HAT-P-30b
20
0
−20
v sin i [km s−1]
RV [m s−1]
HAT P-7b
λ = 183±9°
Winn et al. (2009)
HAT P-30b
λ = 74 ± 9°
Winn et al. (2009)
4.0
40
−40
O−C [m s−1]
7
10
0
3.5
HAT P-14b
λ = 189 ± 5°
Winn et al.
(2011)
3.0
2.5
−10
−2
0
2
Time from midtransit [hr]
50
60
70 80
! [deg]
90
100
Fig. 4.— Rossiter-McLaughlin effect for HAT-P-30 Left.—Apparent radial velocity variation on the night of 2011 Feb 21, spanning
Thursday,
April
2012
a
transit. The
top 26,
panel
shows the observed RVs. The bottom panel shows the residuals between the data and the best-fitting model.
projected obliquity λ (degrees)
Brown et al. (2012)
effective temperature (K)
Thursday, April 26, 2012
projected obliquity λ (degrees)
Brown et al. (2012)
observations imply that either:
(a) the planetary system is flat, but the
stellar spin is tilted relative to the
planetary orbital plane, or
(b) planetary system is not flat, but the
stellar spin is aligned with the mean
planetary orbital angular momentum
effective temperature (K)
Thursday, April 26, 2012
(a) the planetary system is flat, but the stellar
spin is tilted relative to the planetary orbital plane
• collision with a giant planet:
• spin angular momentum of the Sun = 2 X 1048 gm cm2/s
• angular momentum of Jupiter-mass object on a parabolic orbit with
perihelion of 0.5R⊙ = 6 X 1048 gm cm2/s
Thursday, April 26, 2012
(a) the planetary system is flat, but the stellar
spin is tilted relative to the planetary orbital plane
• collision with a giant planet
• tilt the plane of the planetary orbits by external torques
• planets stay coplanar so long as tilting time longer than precession times
due to their mutual gravitational interactions (104 to 3 X 105 yr)
• stellar spin does not follow the tilt if tilting time is shorter than
precession time of stellar spin due to planets (~3 X 1010 yr)
fffff
Thursday, April 26, 2012
(b) planetary system is not flat, but the stellar
spin is aligned with the mean planetary orbital
angular momentum
•form planets in collapsing clouds around the
host star, as in binary stars
• form planets in a disk, and excite their
inclinations later. For example:
• migration and resonance capture
Thursday, April 26, 2012
Pluto’s peculiar orbit
Pluto has:
• the highest eccentricity of any “planet” (e = 0.250 )
• the highest inclination of any “planet” ( i = 17o )
• perihelion distance q = a(1 – e) = 29.6 AU that is smaller than Neptune’s
semi-major axis ( a = 30.1 AU )
How do they avoid colliding?
Thursday, April 26, 2012
Pluto’s peculiar orbit
Orbital period of Pluto =
247.7 y
Orbital period of Neptune =
164.8 y
247.7/164.8 = 1.50 = 3/2
Resonance ensures that when
Pluto is at perihelion it is
approximately 90o away from
Neptune
(Cohen & Hubbard 1965)
Thursday, April 26, 2012
Pluto’s peculiar orbit
PPluto/PNeptune
Pluto’s semi-major axis
Pluto’s eccentricity
Pluto’s inclination
time
•early in the history of the solar system
there was debris left over between the
planets
•ejection of this debris by Neptune caused
its orbit to migrate outwards
•if Pluto were initially in a low-eccentricity,
low-inclination orbit outside Neptune it is
inevitably captured into 3:2 resonance with
Neptune
•once Pluto is captured its eccentricity and
inclination grow as Neptune continues to
migrate outwards
•other objects may be captured in the
resonance as well
Malhotra (1993)
Thursday, April 26, 2012
objects in 2:3 resonance
Kuiper belt objects
comets
Thursday, April 26, 2012
t
Period ratios in
Kepler’s multi-planet
systems
biggest
second biggest
third biggest
fourth biggest
Fabrycky et al. (2012)
Thursday, April 26, 2012
Period ratios in Kepler’s multi-planet systems
Fabrycky et al. (2012)
Thursday, April 26, 2012
planetary system is not flat, but the stellar
spin is aligned with the mean planetary orbital
angular momentum
•form planets in collapsing clouds around the host star, as in
binary stars
• form planets in a disk, and excite their inclinations later.
For example:
• migration and resonance capture
• Kozai-Lidov oscillations
Thursday, April 26, 2012
Kozai-Lidov oscillations
• Kozai (1962); Lidov (1962)
• arise most simply in restricted three-body problem (two massive bodies
on a Kepler orbit + a test particle, e.g., binary star + planet orbiting one
member of the binary)
•in Kepler potential Φ = -GM/r, eccentric orbits have a fixed orientation
Thursday, April 26, 2012
Kozai-Lidov oscillations
• now subject the Kepler orbit to a weak, time-independent external
force F
• because the orbit orientation is fixed even weak external forces
act for a long time in a fixed direction relative to the orbit and
therefore change the angular momentum or eccentricity
• if F ~ ε then timescale for evolution ~ 1/ε" but nature of evolution
is independent of ε
F
Thursday, April 26, 2012
Kozai-Lidov oscillations
planet
Consider a planet orbiting one member of a
binary star system:
pericenter
• can average over both planetary and binary star
orbits
• both energy and z-component of angular
momentum of planet are conserved
• thus the orbit-averaged problem has only one
degree of freedom (e.g., eccentricity e and angle
in orbit plane from the equator to the
pericenter, ω), so potential Φ=Φ(e,ω)
• motion is along level surfaces of Φ(e,ω)
Thursday, April 26, 2012
binary star orbital plane
Kozai-Lidov oscillations
• initially circular orbits remain circular if
and only if the initial inclination is < 39o =
cos-1(3/5)1/2
circular
• for larger initial inclinations the phase
plane contains a separatrix
• circular orbits cannot remain circular, and
are excited to high inclination and
eccentricity
•circular orbits are chaotic
radial
Thursday, April 26, 2012
Kozai-Lidov oscillations
• as initial inclination approaches 90
,
maximum eccentricity approaches unity
°
circular
collision or tidal dissipation
• mass and separation of companion affect
period of Kozai-Lidov oscillations, but not
the amplitude
radial
Thursday, April 26, 2012
eccentricity
oscillations of a
planet in a binary
star system
M3=0.9M⊙
M3=0.08 M⊙
•
aplanet = 2.5 AU
•
companion has
inclination 75°, semimajor axis 750 AU,
mass 0.08 M⊙ (solid) or
0.9 M⊙ (dotted)
(Takeda & Rasio 2005)
Thursday, April 26, 2012
Kozai-Lidov oscillations
circular
•
may excite inclinations of planets in
some binary star systems, but
probably not all planet inclinations:
• not all systems have stellar companions
• oscillations are suppressed by additional
coplanar planets
• oscillations can be suppressed by general
relativity (!)
• also excites eccentricity and high
eccentricity is not well-correlated with
presence of a companion star
Thursday, April 26, 2012
radial
Kozai-Lidov oscillations
binary
single
Thursday, April 26, 2012
Kozai-Lidov oscillations and the formation of
hot Jupiters
Giant planets at small semi-major axes cannot be formed in situ. There
are two mechanisms for placing giant planets in orbits of size < 0.1 AU:
1. migration due to gravitational torques from the protoplanetary disk
2. “high-eccentricity migration” is a multi-step process:
• planet-planet scattering at 5-10 AU kicks a planet into an eccentric,
inclined orbit (e.g., Rasio & Ford 1996)
• torques from other planets drive KL oscillations
• KL oscillations drive the pericenter of the orbit to < 0.05 AU where tidal
friction from the host star drains energy and eccentricity from the orbit
• eventually the planet settles on a circular orbit near the star
Thursday, April 26, 2012
theory (Kozai-Lidov oscillations)
Fabrycky & Tremaine 2007
observations (from R-M
effect) Brown et al. 2012
misaligned
projected obliquity
Thursday, April 26, 2012
theory (Kozai-Lidov oscillations)
Fabrycky & Tremaine 2007
observations (from R-M
effect) Brown et al. 2012
misaligned
• high-eccentricity migration models predicted large
obliquities seen in Rossiter-McLaughlin observations
• predict that a population of “super-eccentric”
planets (e > 0.9) is present in the Kepler planet sample
(Socrates et al. 2011
)
projected
obliquity
Thursday, April 26, 2012
first Kepler data release (Borucki et al. 2011)
•
•
•
155,000 stars
•
comparison of numbers of multi-planet systems between Kepler and
radial-velocity surveys should constrain inclination distribution
(Dong & Tremaine 2011)
1235 planetary candidates, ~90-95% real (Morton & Johnson 2011)
115 two-planet systems, 45 three-planet systems, 8 four-planet
systems, one 5-planet and one 6-planet system
Good news:
•
Kepler provides a large, homogeneous database with well-defined selection
criteria
Bad news:
•
radial-velocity surveys are heterogeneous and have poorly defined
selection effects
•
Kepler and RV surveys cover different range of mass and semi-major axis
Thursday, April 26, 2012
radial velocities
transits
Thursday, April 26, 2012
radial velocities
there are reliable, modelindependent ways to correct
the exoplanet multiplicity
distribution for different survey
properties
transits
Thursday, April 26, 2012
Kepler survey gives:
n0 = 123,700 n1 = 737 n2 = 104 n3 = 37 n4 = 7 n5 = 1 n6 = 1 n7,8,9,… = 0
All RV surveys give
n0 = ?? n1 = 162 n2 = 24 n3 = 7 n4 = 1 n5 = 1 n6,7,8,… = 0,
Note that n0 is not known!
Fit using free parameters:
•
N1, N2, N3, …, NK - number of k-planet systems in parent population
•
<sin2 i>½ - rms inclination in multi-planet systems
Thursday, April 26, 2012
Kepler survey gives:
n0 = 123,700 n1 = 737 n2 = 104 n3 = 37 n4 = 7 n5 = 1 n6 = 1 n7,8,9,… = 0
All RV surveys give
n0 = ?? n1 = 162 n2 = 24 n3 = 7 n4 = 1 n5 = 1 n6,7,8,… = 0,
Note that n0 is not known!
Fit using free parameters:
•
N1, N2, N3, …, NK - number of k-planet systems in parent population
•
<sin2 i>½ - rms inclination in multi-planet systems
Thursday, April 26, 2012
flat
Thursday, April 26, 2012
isotropic
Estimating the effective number of target stars in RV
surveys:
1) Cumming et al. (2008) derive percentage of FGK stars with a planet having
M > MJupiter and P < 1 yr, p = 0.019 ± 0.007. All major RV surveys should be
complete in this range, and our sample has 46 such planets. Thus ntotal = 46/p =
2400 ± 900
2) Convert Kepler planet radii to mass using empirical mass-radius relation,
then compute number of target stars needed to produce observed number of
RV planets as a function of maximum period and minimum velocity semiamplitude
Thursday, April 26, 2012
ntot=3000±1000
Thursday, April 26, 2012
Dong & Tremaine (2011)
Thursday, April 26, 2012
<sin2i>1/2 < 0.1
or <i> < 6o
Dong & Tremaine (2011)
Thursday, April 26, 2012
•
if two planets have circular, coplanar orbits around the same star orbit
the same star their impact parameters b and semi-major axes a are
related by
b2/b1 = a2/a1
•
b
by Kepler’s law semi-major axis and orbital period are related by
Rs
a2/a1 = (P2/P1)2/3
•
transit duration is 2(Rs2-b2)1/2/v where v ∝ P-1/3
➨ transit durations in multi-planet systems constrain the inclination
distribution (Fabrycky et al. 2012) -- find rms inclination between 1o and
2.5o
•
advantage: doesn’t require comparison of Kepler and RV samples
•
disadvantage: only works if the rms inclinations are small compared to
Rs/a ~ 0.05 or 3o
Thursday, April 26, 2012
Summary
•
for the first time we have a strong constraint on the inclinations in a large sample
of extrasolar planets
•
typical multi-planet systems in the Kepler sample of planets are flat, with mean
inclination < 6o and probably <3o
•
nevertheless
– RV planets have <e> ~ 0.25 so if <i>=<e> we expect much larger <i> ~ 15o
• eccentricities have declined ~20% as observations improve in number and quality
• in some formation models <i> is as small as 0.5<e>
• <e> seems to decline as planet mass shrinks
– there is strong observational evidence that many exoplanet systems have large
misalignments between the host star and planet angular momenta
•
these are clues to resolving one of the basic questions of exoplanet formation: do
giant planets at small radii get there via
– disk migration
– high-eccentricity migration
– some other process
Thursday, April 26, 2012
Summary
•
for the first time we have a strong constraint on the inclinations in a large sample
of extrasolar planets
•
typical multi-planet systems in the Kepler sample of planets are flat, with mean
inclination < 6o and probably <3o
•
nevertheless
– RV planets have <e> ~ 0.25 so if <i>=<e> we expect much larger <i> ~ 15o
• eccentricities have declined ~20% as observations improve in number and quality
• in some formation models <i> is as small as 0.5<e>
• <e> seems to decline as planet mass shrinks
– there is strong observational evidence that many exoplanet systems have large
misalignments between the host star and planet angular momenta
•
these are clues to resolving one of the basic questions of exoplanet formation: do
giant planets at small radii get there via
– disk migration
– high-eccentricity migration
– some other process
Thursday, April 26, 2012
Summary
•
for the first time we have a strong constraint on the inclinations in a large sample
of extrasolar planets
•
typical multi-planet systems in the Kepler sample of planets are flat, with mean
inclination < 6o and probably <3o
•
nevertheless
– RV planets have <e> ~ 0.25 so if <i>=<e> we expect much larger <i> ~ 15o
• eccentricities have declined ~20% as observations improve in number and quality
• in some formation models <i> is as small as 0.5<e>
• <e> seems to decline as planet mass shrinks
– there is strong observational evidence that many exoplanet systems have large
misalignments between the host star and planet angular momenta
•
these are clues to resolving one of the basic questions of exoplanet formation: do
giant planets at small radii get there via
– disk migration
– high-eccentricity migration
– some other process
Thursday, April 26, 2012
Summary
•
for the first time we have a strong constraint on the inclinations in a large sample
of extrasolar planets
•
typical multi-planet systems in the Kepler sample of planets are flat, with mean
inclination < 6o and probably <3o
•
nevertheless
– RV planets have <e> ~ 0.25 so if <i>=<e> we expect much larger <i> ~ 15o
• eccentricities have declined ~20% as observations improve in number and quality
• in some formation models <i> is as small as 0.5<e>
• <e> seems to decline as planet mass shrinks
– there is strong observational evidence that many exoplanet systems have large
misalignments between the host star and planet angular momenta
•
these are clues to resolving one of the basic questions of exoplanet formation: do
giant planets at small radii get there via
– disk migration
– high-eccentricity migration
– some other process
Thursday, April 26, 2012
Summary
•
for the first time we have a strong constraint on the inclinations in a large sample
of extrasolar planets
•
typical multi-planet systems in the Kepler sample of planets are flat, with mean
inclination < 6o and probably <3o
•
nevertheless
– RV planets have <e> ~ 0.25 so if <i>=<e> we expect much larger <i> ~ 15o
• eccentricities have declined ~20% as observations improve in number and quality
• in some formation models <i> is as small as 0.5<e>
• <e> seems to decline as planet mass shrinks
– there is strong observational evidence that many exoplanet systems have large
misalignments between the host star and planet angular momenta
•
these are clues to resolving one of the basic questions of exoplanet formation: do
giant planets at small radii get there via
– disk migration
– high-eccentricity migration
– some other process
Thursday, April 26, 2012