Download A Pretty Nice Model

A Pretty
Nice Model
Grace Telford
Brett Morris
Outline
•  Nice Model v1.0
–  Levison et al. 2005, Morbidelli et al. 2005, Gomes
et al. 2005
•  Issues with v1.0 and their solutions
–  Morbidelli et al. 2007
•  Nice Model v2.0
–  Levison et al. 2011
•  Follow ups and extensions to v2.0
Elusive Questions in 2005
•  Explain the bulk orbital properties of the planets
•  Did the planets form in the disk where they are
observed today?
•  What was the Late Heavy Bombardment that we
have evidence for in the inner Solar System?
–  Why did it happen so “late”?
•  Why are the orbits of Jupiter’s Trojans excited?
The Nice Model (2005)
Jupiter
Saturn
Uranus
Neptune
Basic idea: Jupiter & Saturn crossed 1:2 Mean Motion
Resonance (MMR) and caused the solar system to rearrange
Ice I
Before MMR
crossing
JS
Ice II
Ice I
After MMR
crossing
JS
Ice II
Gomes et al. 2005
Simulations
•  Planets in compact configuration; PS/PJ < 2
•  Varied ice giant semi-major axes, Mdisk, Ndisk
•  30-50 ME planetesimal disk just outside ice
giant orbits
–  Hot and cold
•  Dynamical evolution simulated with N-body
codes
•  43 systems
Typical evolution
•  Jupiter moves inward, other giants move
out
•  Jupiter and Saturn cross 1:2 MMR after
several hundred Myr
•  Compact system à chaotic orbits
•  Ice giants scatter outward into disk
•  Giants migrate rapidly until disk depleted
Resonance Crossing
Since Uranus and Neptune may swap orbits,
they are referred to as “Ice I” and “Ice II”
Tsiganis et al. 2005
Outcomes
•  Saturn < 3 AU from Ice I à Ice I ejected
(14 runs)
•  Of “successful” runs:
–  Class A: no encounters between ice and gas
giants (15 runs)
–  Class B: encounters between Saturn and one
or both ice giants (14 runs)
Class B runs, where
Saturn has a close
encounter with an ice
giant, best reproduce
the orbits of the outer
planets
Black open circles: class B
Grey open circles: class A
Tsiganis et al. 2005
Notes on Nice Model Simulations
•  Separation between Jupiter and Saturn
dependent on initial mass of planetesimal
disk
•  Eccentricities depend on “hotness” of disk
•  Can only excite all orbits when Jupiter and
Saturn 1:2 MMR crossed
v1.0 Successes
•  Reasonable probability of reproducing
current giant planet orbits
•  8 simulations tested survivability of satellites
–  All satellites survive 50% of time
•  Some disk particles trapped in orbits like
those of Neptune’s Trojans
•  Companion papers: LHB, Jupiter’s Trojans
Late Heavy Bombardment
•  Spike in cratering rate ~700 Myr after
planets formed
•  Nice Model of rapid giant planet migration
naturally accounts for:
–  Flux of planetesimals
–  “Late” timing of the event (we’ll show this in
v2.0)
Late Heavy Bombardment
•  Both planetesimal
disk and asteroid
belt perturbed
•  In-scattered material
may be important for
volatile delivery to
the Earth
•  The Oort Cloud
forms naturally from
the outwardscattered disk
•  Planetary
interactions
probably did not
cause significant
migration before
solar nebula
dissipated
•  A disk that has
lifetime longer
than that of
nebula leads to
LHB ~1 Gyr after
planet formation
Gomes et al. 2005
•  Simulate
scattered
planetesimals
that impact the
moon
•  Total amount of
material
consistent with
estimates from
observations
•  This happens in
all 8 simulations
Gomes et al. 2005
Ice I
Ice II
S
J
Jupiter’s Trojans
•  Previously thought that
Trojans formed with
Jupiter in current
locations
•  Issue:
–  Distribution of inclinations
observed is broader than
you would expect for coevolution
Nice model to the rescue!
•  During migration,
scattered planetesimals
captured into transient
Trojan orbits
•  Once planets reach
stable configuration, any
bodies that happen to be
in those orbits would
remain there
Gomes et al. 2005
•  Bottom plot:
fraction of
Trojans at each
time that survive
for 2x105 yrs
•  All original
Trojans before
MMR crossing
are emptied
Morbidelli et al. 2005
Captured Trojans
•  Two simulation sets, different migration speeds
•  Find that 4x10-6 – 3x10-5 ME of particles trapped in
Trojan region when orbits stabilize
–  Consistent with observed mass: 1.1x10-5 ME
•  Many simulated Nice Model Trojans were on high
e orbits at some point, with 68% coming within 2
AU of Sun
–  Observations show Trojans may be depleted of
volatiles
Grey dots:
Observed
Black circles:
Simulated
Morbidelli et al. 2005
Nice Model Explains Many
Observational Constraints
•  Only model that naturally explains:
–  Orbital properties of planets
–  Late Heavy Bombardment
–  Jupiter’s and Neptune’s Trojan asteroids
•  BUT it isn’t perfect…
Issue #1
•  Original model doesn’t account for
interactions within the disk
–  Likely contained ~1000 Pluto mass
planetesimals – computational challenge
–  Viscous stirring would excite eccentricities,
more effectively causing interactions with
planets
–  Could be harder to delay onset of LHB for
~700 Myr
Issue #2
•  Ad hoc choice of initial giant planet orbits
–  No reliable predictions available at the time
–  Assumed circular orbits with PSaturn/PJupiter < 2
–  Initial conditions fine-tuned to produce 1:2
MMR crossing around time of LHB
•  To be consistent, disk edge must be between
14.5-15.5 AU à fine tuning
Solution
•  Morbidelli et al. (2007)
studied evolution of 4
giant planets in gas
disk
–  Found that planets
naturally evolve to
quadruple MMR state
–  Identified 4
configurations stable
for > 1 Gyr after gas
dissipated
Morbidelli et al. 2007
Nice Model v2.0 (2011)
•  New initial orbital configurations informed by
gas disk models (Morbidelli et al. 2007)
–  Planets become locked in quadruple MMR
–  Inner ice giant has a larger eccentricity than other
giants:
eIce I~0.05 vs. eothers~0.01
•  This drives the energy exchange between planetesimal
disk and planets
•  Eliminates fine-tuning problems with
planetesimal disk inner edge
•  Discover new energy exchange mechanism
for triggering instability
Morbidelli et al. 2007
Simulations
•  50 ME planetesimal disk with ~1500
particles
–  Surface density goes as 1/r
–  Vary disk inner edge rin à does it affect LHB
timing?
•  N-body integration with SyMBA
–  Include viscous stirring - gravitational
interactions between disk particles
Nice v2.0
Simulation shows slow transfer of energy between the
planetesimal disk and giant planets – what’s the cause?
Levison et al. 2011
What’s driving
Saturates Np ~ 500
Levison et al. 2011
dE
dt planets
?
Set Np = 1000, planets crossing MMRs with
planetesimal disk would cause jumps.
No jumps seen à MMRs not responsible for
energy exchange between planets and disk
What’s driving
•  MMRs are not
responsible – so what
else is changing…?
•  Eccentricity of Ice I
increases whether or
not Ice II is in the
simulation
dE
dt planets
?
What’s driving
dE
dt planets
?
•  Previously though that close encounters between
Ice II and the disk would dominate energy
exchange
Levison et al. 2011
What’s driving
dE
dt planets
?
•  Previously though that close encounters between
Ice II and the disk would dominate energy
exchange
“Thus, in order for Ice I to play a decisive role,
the dynamical mechanism responsible for the
coupling must be a strong function of the
eccentricity. Given the results thus far, we can
infer that the observed energy exchange is
related to secular interactions between the
planets and the disk.”
Levison et al. 2011
What’s driving
dE
dt planets
?
•  Secular interactions between disk and high-e
inner ice giant
– 
dE
dt planets
proportional to MIce I*Mdisk
–  Ice I would migrate inward but MMRs halt a, increase
e instead
–  For some systems e is damped by giant planets
–  If e increases faster than damping, secular
interactions grow and e continues to increase
–  Ice I e grows large enough to throw 25% of multiresonant systems unstable in <1 Gyr
What’s driving
dE
dt planets
?
•  Secular interactions between disk and high-e
inner ice giant
– 
dE
dt planets
proportional to MIce I*Mdisk
–  Ice I would migrate inward but MMRs halt a, increase
e instead
–  For some systems e is damped by giant planets
–  If e increases faster than damping, secular
interactions grow and e continues to increase
–  Ice I e grows large enough to throw 25% of multiresonant systems unstable in <1 Gyr
•  Surprise! Dynamical lifetime NOT monotonic with rin
–  75% of systems never leave multi-resonant state
•  Unstable system median lifetime ~730 Myr – LHB
timing is a natural consequence
Levison et al. 2011
Can Nice II explain SS Architecture?
•  Gas disk sets initial orbits (generic!)
•  Eccentricity of Ice I mediates energy
exchange with disk (generic!)
•  25% of disks go unstable
–  Instability time commensurate with LHB
(generic!)
•  Not strongly dependent on rin (generic!)
</Nice II standard canon>
<Follow Ups And Extensions>
Other Initial Configurations
•  Ejected 5th outer planet?
–  Could get ejected during
scattering
•  Microlensing
Observations in
Astrophysics, Sumi et al.
2013
–  “We report the discovery
of a population of
unbound or distant
Jupiter-mass objects,
which are almost twice
as common as mainsequence stars”
Planet mass objects: tE < 2 days
Sumi et al. 2013
Five Planet Simulations
•  N-body simulations
–  4 and 5 planet
configurations
–  Initially multi-resonant
orbits
–  New ice giant mass
between 1/3 –
3MUranus
Nesvorny 2011
Results: 5 Planets = Maybe
•  5 planet configurations
better reproduce SS
–  4 planet initial
configurations
•  ~10% end up with 4
planets
•  3% of runs produce
systems matching current
SS
–  5 planet initial
configurations
•  37% end up with 4 planets
•  23% match observational
constraints
Nesvorny 2011
Triangle:
real planet
Dots:
sim. planets
What about the terrestrial planets?
•  Can inner planets survive such a violent
instability?
•  How would dynamics of inner planets be
changed?
•  Brasser et al. (2013) attempt to constrain
primordial terrestrial planet orbits using
Nice model
Results
•  Nice-like simulations significantly alter the
angular momentum deficit (AMD) of terrestrial
planets
–  When you hear AMD, think “difference from
coplanarity and from e = 0”
•  To reproduce observed AMD, need to have
little migration in Jupiter/Saturn after MMR
crossing
–  More probable when starting with 5 giant planets
Primordial Terrestrial Planet Orbits
•  To reproduce terrestrial orbits with probability
~ 20%, primordial AMD < 70% current value
(orbits start more circular, lower inclinations)
•  Inner 3 planets were excited more than Mars
by giant planet migration
–  Currently AMD roughly equally split
–  Original inner three orbits were circular and
coplanar
–  Mars’ current orbit ≈ original orbit
•  Terrestrial orbits best reproduced with 5 outer
planets
Do Planets Really Cross MMRs?
Kepler Architectures - Lissauer et al. 2011
Some planets have been found near MMRs
Lissauer et al. 2011
If you look at the period ratios of
planets in Kepler multi-planet
systems, there are small piles of
planets near first-order MMRs…
…strongest peaks near 1:2 MMR
and 2:3 MMR in Kepler data, 1:2
MMR strong in RV data
Lissauer et al. 2011
Kepler Architectures
“Most multiple planet candidates are neither
in nor very near mean-motion orbital
resonances. Nonetheless, such resonances
and near resonances are clearly more
numerous than would be the case if period
ratios were random.”
Lissauer et al. 2011
Final Summary:
Did the Nice Model Happen?
•  Model nicely explains
many observational
constraints of our SS
•  Major limiting probability
may be that systems
become unstable within 1
Gyr in only ~25% of
simulations
•  The probability to exactly
reproduce our SS is
pretty low – but not
impossible