Download The role of migration and planet-planet scattering in shaping

The role of migration and planet-planet
scattering in shaping planetary systems
F. Marzari,
Dept. Physics,
Padova Univ.
Small semimajor axes
Large eccentricities
Spin-orbit misalignment
Standard model of
planet formation
based on Solar
system exploration:
low eccentricities &
inclinations, large
semimajor axes for
giant planets.....
The standard model
Protostar +Disk
Planetesimal formation by
dust coagulation with
contribution from
turbulence, instability ….
Plugins
Formation of Terrestrial
planets and core of giant
planets (subsequent gas
infall) by planetesimal
accumulation
Gas dissipation – final
planetary system
Planet migration
 P-P scattering

P-P scattering
 Residual planetesimal scattering
 Tidal interaction with the star

Turbulence ->
stochastic migration
Kley & Crida (2008)
Isothermal,
adiabatic, or
fully radiative
energy equation
Type I migration:
Small planets (150 ME)
HS drag
Saturn-Jupiter and
more massive
planets: Type II, III
migration
Planetary migration
by interaction with
the disk: a very
complex problem
Masset & Papaloizou (2003)
TYPE I MIGRATION
The inner wake exerts a positive
torque on the planet accelerating
it and causing an outward
migration
The outer wake exerts a negative
torque slowing down the planet
and leading to inward migration
The sum of the two torques, the
differential Lindblad torque, is
negative and causes inward
migration.
Wakes (2 arms) are
given by superposition
of sound waves,
excited at Lindblad
resonances, in a
differentially rotating
disk.
p
F
~p ~F
(m+ k ) n −(m±1) n −k ω̇ ∓ω̇ =0
Horseshoe torque
The inner and outer disc
are responsible for the
Lindblad torque.
In the horseshoe region,
gas particles make Uturns → exchange
angular momentum with
the planet
→ Corotation torque.
Paardekooper et al.
(2010, 2011)
Because of horshoe drag
Type I migration can be
reversed for radiative
disks (Kley & Crida, 2008)
due to the horseshoe
torque.
Up to 40 Earth masses the
torque is positive. This is
important for Jupiter size
planets where the core is about
10-30 ME Before gas infall they
migrate outwards and after the
gas infall (very rapid, 1 kyr)
they undergo type II migration
potentially skipping the critical
fast inward migration phase.
Coleman & Nelson (2014)
Low mass planets: the
horseshoe period long compared
to viscous/radiative diffusion
timescale: weak corotation
torque. Inward migration
Intermediate masses: two
timescales comparable, strong
corotation torque, outward
migration
Large masses: saturation of
corotation torque. The
viscous/radiative diffusion
timescales long compared to
horseshoe period, phase mixing,
no torque.
Nelson (2005). Large scale MHD-driven turbulence can
cause a stochastic migration of planets overcoming the
Lindblad torques. Dead zones?
1 ME
10 ME
Type II migration: Jupiter size planets
Gap opening criterium: TOS > T
4
2
Τ OS ≈a Ω Σ
Mp
2
( )( )
Mz
a
Δ
3
Δ=max( H , R Hill )
∂
Ω
Τ ν =−2 πr νΣ
∂r
( )
3
Crida et al. (2006)
The gas is pushed away by the resonance perturbations which
overcome viscosity.
d a 3ν
∼
dt 2a
2
If
π a Σ⩾M p
e p <h
Orbital migration is important not only for changing the architecture
of planetary systems but it also influences the growth of a planet in
particular during the gas infall from the disk: shorter formation
timescales are obtained.
Even
Alibert et al. (2005):
if.....
migration is included
Movshovitz et al. (2010):
during growth
detailed grain physics, no
migration.
What about Jupiter and Saturn? Why
didn't they migrate very close to the
sun? Coupled migration while
trapped in resonance!
Masset & Snellgrove (2001):
Jupiter and Saturn trapped
in a 3:2 resonance migrates
outwards.
Jupiter excites inner
Lindblad resonances,
Saturn the outer ones.
2
3
M
a
J
Τ OS ≈a 4J Ω2 Σ(
) ( J)
Δ
M star
A positive torque is obtained
when TJ > TS
M S 2 (1 / 3)
<( )
MJ 3
The grand tack scenario.
Recent model by Walsh et
.
al. Nature
2011, assumes
that Jupiter migrated to 1.5
AU before reversing the
drift direction. This would
explains the low mass of
Mars and the compositional
mixing in the main asteroid
belt.
A model of coupled giant planet migration must account for the disk
evolution driven by viscous torques and wind dispersal (EUV
photoevaporation, Dullemond et al. 2007, Clarke 2011...)
∂
1 ∂
Σ+
(r Σ u r )=−Σ̇ pe
∂t
r ∂r
Q ν + Q irr −Q cool =0
Σ (t , r ) , h(t , r )
Continuity equation
+
thermal balance
The disk evolves with
time due to viscosity (→
mass accretion on the
star) and
photoevaporation. The
local gas density
decreases with time and
when the planets
(Jupiter and Saturn for
example) begin to
migrate outwards they
may not go far out. In the
GT model Jupiter and
Saturn may not have
enough time to return to
their present position.
Ad example, 1D models predict a superficial density around 100
g/cm2 or lower at 1 AU by the time Jupiter migrates to 1.5 AU.
Only in a minority of disk models
(less than 2%) the planets are
able to move back to 5 AU or
beyond, possible site of their
formation
IN ADDITION: In evolved
disks with low density, the
2:1 occurs first and the
planets move inwards.
D'Angelo & Marzari (2012)
Mass growth of the two planets may lead to violation of the conditions
for outward migration
 ~ 50 gr/cm2 (at 1 AU)
 ~ 800 gr/cm2
Time (104 yr)
 ~ 1600 gr/cm2
 ~ 5000 gr/cm2
Gas is accreted within 0.1 RH (under the hypothesis of disk-limited accretion rate).
Conditions for
extended
migration of
planets in
resonance
.
The interior planet's mass must
exceed that of the exterior planet during
all migration. If the mass growth
changes the ratio, the outward
migration is interrupted and possibly
reversed.
The gas density has not to be too low
at the time of trapping otherwise the
planets are captured in the 2:1
resonance. This sets a lower limit on
the gas density at the capture.
The outward migration must be fast
before the dispersal of the disk.
The planets must not have crossing
orbits
CPD: CircumPlanetary Disk
Size: Defined either by truncation or
by the rotation profile. (sw=specific
angular momentum)
Gas trajectories in the
proximity of the planet
orbit. Close to the
planet there is a vertical
inflow on the CPD
Mass:
Minimum
Mass, gas
starved,
numerical
models …..
Planet growth:
Gas from the disk falls on the CPD while
crossing the gap
The planet accrete gas from the CPD
For the second step the presence of viscosity in the CPD is
relevant for the mass accretion rate dMp/dt
Potential sources of
viscosity:
MRI (inner regions)
Gravitational instability (outer regions)
Spiral waves induced by the sun tidal
force (outer regions).
Different scenarios for the CPD:
Inviscid CPD: according to Szulagyi et al. (2014) the disk is MRI
inactive. Inferred accretion rate from other mechanisms of the order of
2.5 x 10-6 MJ/yr for the planet. It does not explain why there are planets
with 2 and more Jupiter masses among extrasolar planets.
Viscous CPD:
Gressel et al. (2013) performed resistive MHD
simulations with adiabatic equation of state. They find
that the CPD should be MRI active at least in the outer
region with ionization due to XRs and CRs. Accretion
rate of the order of 2.5 x 10-5 MJ/yr
Keith & Wardle (2014): self-consistent model of CPD
where MRI mostly caused by thermal ionization can
drive accretion out to ∼ 200 RJ , beyond which
gravitoturbulence dominates. Large values of are
observerd within 30 RJ.
Turner et al. (2014) suggests that CPD have
magnetically-active surface layers leading to accretion
onto the planet and decoupled interior dead zones.
Images of the planet+CPD
surroundings for increasing
resolution. The vector
indicates the direction of the
gas flux. The gas falls onto
the planet from high latitudes
while the gas in the CPD is not
moving radially due to the low
viscosity.
1 MJ is not a
threshold value for
the mass of giant
planets
The growth
process must
allow for the
formation of more
massive planets
The Jumping Jupiter model
How do planets achieve large e and small q?
1) Planet-Planet scattering: at the end of the chaotic phase a planet
is ejected, one is injected on a highly eccentric orbit that will be
tidally circularized to the pericenter, one is sent on an outer orbit
1)
2)
3)
L=¿
Weidenschilling & Marzari
(1996), Rasio and Ford (1996),
Ida & Lin (1997).......
Stability limit for 3 planets
Stability limit for 2 planets
Δ c ∼2 √ 3 R H
m +m
RH = 1 2
3Ms
(
(1/ 3)
) (
a1 +a 2
2
M P =M Neptune
M P =M Saturn
M P =M Jupiter
Marzari (2014)
)
a i+ 1=a i + K R H
Energy conservation
[
G M s m1 m2 m3
E =−
+ +
2
a 1 a 2 a3
G M s mi
a i≈
2E
]
Eccentricity and inclination excitation. Outcome of many
simulations with 3 initial planets within the instability limit by
Chatterjee et al. (2008).
Tidal interaction
with the central
star (Nagasawa et
al 2008)
Pure N-body P-P
scattering
Interaction with the
gas of the
circumstellar disk
(Marzari et al. 2010)
Interaction with a
leftover planetesimal
disk (Raymond et al.
2009)
Tidal migration of eccentric orbits
Maximum e declines with
distance from the star: tidal
circularization. Energy is
dissipated but the angular
momentum J is preserved.
m p ms
2
J=
G (M s + M p) √ a (1−e p )
√
m p + ms
a f =a (1−e 2)=q (1+ e p )≈2 q
Inclined hot
Jupiters due to
instability+tide
+Kozai with
outer planet(s)
from Nagasawa
et al. (2008).
Example of 'Jumping
Jupiters' in presence of the
protostellar disk. The density
of the disk is MMSN/2. Code
used is FARGO (RK5
modified to have variable
stepsize). One planet (1 MJ)
merges with another one (0.7
MJ) after a sequence of close
encounters.
Eccentricity evolution after
P-P scattering: damping or
excitation because of
corotation resonance
saturation?
Marzari et al. (2010),
Lega et al. (2013)
Planetesimal disks
and P-P scattering:
Lower eccentricities and
inclinations for outer low-mass
planets after P-P scattering
(Raymond 2009, 2010)
Possible formation of mini Oort
clouds by scattered planetesimals
(Raymond & Armitage 2013)
Lower fraction of debris disks
co-existing with the final planet
system (Marzari 2014)
Green dots are systems which
might retain a debris disk.
Synthetic population
models: combine all
processes to explain the
present population of
exoplanets.
Ida et al. 2013
Benz et al. 2014
Comparison with
observed population
(with and without
observative bias)
There are many weird
planets out there, and theory
must explain them all!
Single steps of planet growth and evolution are well studied: it
is their combination that is still difficult to model and follow for
an extended time
1 ME
●Population synthesis models
1 ME
3 ME
10 ME
15 ME
1 Ms
1 MJ
2 MJ
●Type II, Type III migration
●P-P scattering
●Resonance capture
●Residual planetesimal scattering
●Gas accretion onto the planet
Kozai mechanism; invoked for the first time to explain the
large eccentricity of the planet in the binary system 16 Cyn B.
L=√ GM (1−e ) cos (i )
2
√
3
arcos ( )≈39.2 o
5
One of the planets (HD80606b)
has a highly eccentric (e = 0.93)
and tight (a = 0.46 AU) orbit. The
presence of a stellar companion
of the host star can cause Kozai
oscillations in the planet's
eccentricity. Combined with tidal
dissipation, this can move the
planet inward well after it has
formed. Such a migration
mechanism can account for the
orbit of HD80606b, but only if the
initial planet orbit was highly
inclined relative to the binary
orbit.
300 g/cm
D'Angelo & Lubow (2008)
first attempt to include
planet growth in a
hydrodynamical simulation.
2
100
g/cm2
3 ME
Superficial
density at
the planet
location
Finding planets inclined respect to the star
equator (WASP-14, Johnson et al, 2009) is a
strong indication that happened AFTER. Why?
Jumping Jupiters can lead to inclined planetary
orbits but.......................
Marzari and Nelson (2009).
.....the interaction with the
gaseous disk drives the
planet quickly back within
the disk (103 yrs).