Prezentacja programu PowerPoint

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VI. FORMATION OF GIANT GASEOUS PLANETS
FORMATION EARLY EVOLUTION OF PLANETARY SYSTEMS

M. ROZYCZKA NCAC WARSZAWA SPRING
SEMESTER 2008
2
EVOLUTION OF THE PLANETESIMAL SWARM
PLANETESIMAL DISK ISOLATION MASS

Number of embryos per 1 M? for Venus and Earth
and per 10 M? for outer planets
FORMATION EARLY EVOLUTION OF PLANETARY SYSTEMS

M. ROZYCZKA NCAC WARSZAWA SPRING
SEMESTER 2008
3
EVOLUTION OF THE PLANETESIMAL SWARM
PLANETESIMAL DISK ISOLATION MASS

• A more sophisticated calculation of the isolation
  mass. The mass of locally growing oligarch is
  shown
• as a function of radius for MMSN (solid), disk
  with
• 5SMMSN (dotted) and disk
• with 10SMMSN (dashed).
• Note stationary segments of the curves indicate
  regions where isolation mass has already been
  reached.

Cores able to effectively accrete and bind gas
must be 10 times more massive than Earth
FORMATION EARLY EVOLUTION OF PLANETARY SYSTEMS

M. ROZYCZKA NCAC WARSZAWA SPRING
SEMESTER 2008
Thommes, E.W. Duncan, M.J. 2006 Planet
Formation Theory, Observations and Experiments,
eds. H.Klahr W.Brandner Cambridge
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EVOLUTION OF THE PLANETESIMAL SWARM
AFTER-ISOLATION MESS

• During oligarchic growth the dynamical friction
  due to
• planetesimals balances mutual stirring of
  growing embryos.
• As a result, random velocities of ebryos are
  small (i.e. they
• have small e and i).
• However, the total mass of ebryos increases in
  time, and
• the dynamical friction becomes less effective.
  
• Eventually, it is unable to balance the mutual
  stirring
• of embryos.
• Inner disk giant impacts between stirred-up
  embryos.
• Outer disk embryos with M 10M? accrete gas,
  likely
• while still colliding with smaller objects.

FORMATION EARLY EVOLUTION OF PLANETARY SYSTEMS

M. ROZYCZKA NCAC WARSZAWA SPRING
SEMESTER 2008
5
PLANET FORMATION
AFTER-ISOLATION MESS
Embryos evolving in the inner system slowly
colalesce (note the timescale)
AU
Full N-body t0 100 lunar- to Mars-sized
planetary embryos
FORMATION EARLY EVOLUTION OF PLANETARY SYSTEMS

M. ROZYCZKA NCAC WARSZAWA SPRING
SEMESTER 2008
movie Harold Levison http//www.boulder.swri.edu
/hal/talks/tfakess/gif/ss3_an/
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PLANET FORMATION
ASSEMBLING GAS GIANTS
FORMATION EARLY EVOLUTION OF PLANETARY SYSTEMS

M. ROZYCZKA NCAC WARSZAWA SPRING
SEMESTER 2008
figure after Beckwith, S. et al. 1999, Protostars
Planets IV
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PLANET FORMATION
ASSEMBLING GAS GIANTS
CAGC (Core Accretion Envelope Capture)

• planetesimals accrete into a solid core
• growing core slowly accretes gaseous envelope
• runaway gas accretion ocurs
• accretion ends because
• - gap is opened
• - disk is dispersed
• planet contracts and cools

FORMATION EARLY EVOLUTION OF PLANETARY SYSTEMS

M. ROZYCZKA NCAC WARSZAWA SPRING
SEMESTER 2008
8
PLANET FORMATION
ASSEMBLING GAS GIANTS
Stellar evolution code for planet evolution
FORMATION EARLY EVOLUTION OF PLANETARY SYSTEMS

M. ROZYCZKA NCAC WARSZAWA SPRING
SEMESTER 2008
9
PLANET FORMATION
ASSEMBLING GAS GIANTS

• Major assumptions and boundary conditions
• the planet is embedded in a disk with locally
  uniform initial Sg and Ss
• at all times the planet consists of solid core
  and gaseous envelope
• density of the solid core, rc, is uniform and
  independent of time

FORMATION EARLY EVOLUTION OF PLANETARY SYSTEMS

M. ROZYCZKA NCAC WARSZAWA SPRING
SEMESTER 2008
10
PLANET FORMATION
ASSEMBLING GAS GIANTS
but if gas accretion rate

me is the mass of the envelope
FORMATION EARLY EVOLUTION OF PLANETARY SYSTEMS

M. ROZYCZKA NCAC WARSZAWA SPRING
SEMESTER 2008
11
PLANET FORMATION
ASSEMBLING GAS GIANTS
CAGC results four disticnt evolutionary phases
1. The planet consists mostly of solids. Solids
accrete much faster than gas.
2. Solid and gas accretion rate is small and
nearly constant in time. This phase dictates the
overall evolutionary time-scale.
3. Runaway gas accretion, starting when the
solid and gas masses are roughly equal.
4. Accretion stopped (gap opening disk
dispersal), envelope contracts and cools.
FORMATION EARLY EVOLUTION OF PLANETARY SYSTEMS

M. ROZYCZKA NCAC WARSZAWA SPRING
SEMESTER 2008
after Greg Laughlin The Formation of Giant
Planets http//oklo.org/?page_id13
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PLANET FORMATION
ASSEMBLING GAS GIANTS
Example simulation Jupiters orbit Ss
1.5SMMSN intermediatek
FORMATION EARLY EVOLUTION OF PLANETARY SYSTEMS

M. ROZYCZKA NCAC WARSZAWA SPRING
SEMESTER 2008
Hubickyj, O. et al. 2005, Icarus 179,
415 http//www.stsci.edu/institute/itsd/informatio
n/streaming/archive/MaySymposium2005
13
PLANET FORMATION
ASSEMBLING GAS GIANTS
Example simulation Jupiters orbit Ss1.5SMMSN
intermediatek
FORMATION EARLY EVOLUTION OF PLANETARY SYSTEMS

M. ROZYCZKA NCAC WARSZAWA SPRING
SEMESTER 2008
Hubickyj, O. et al. 2005, Icarus 179,
415 http//www.stsci.edu/institute/itsd/informatio
n/streaming/archive/MaySymposium2005
14
PLANET FORMATION
ASSEMBLING GAS GIANTS
FORMATION EARLY EVOLUTION OF PLANETARY SYSTEMS

M. ROZYCZKA NCAC WARSZAWA SPRING
SEMESTER 2008
Hubickyj, O. et al. 2005, Icarus 179,
415 http//www.stsci.edu/institute/itsd/informatio
n/streaming/archive/MaySymposium2005
15
PLANET FORMATION
ASSEMBLING GAS GIANTS
FORMATION EARLY EVOLUTION OF PLANETARY SYSTEMS

M. ROZYCZKA NCAC WARSZAWA SPRING
SEMESTER 2008
Hubickyj, O. et al. 2005, Icarus 179,
415 http//www.stsci.edu/institute/itsd/informatio
n/streaming/archive/MaySymposium2005
16
PLANET FORMATION
ASSEMBLING GAS GIANTS
FORMATION EARLY EVOLUTION OF PLANETARY SYSTEMS

M. ROZYCZKA NCAC WARSZAWA SPRING
SEMESTER 2008
Hubickyj, O. et al. 2005, Icarus 179,
415 http//www.stsci.edu/institute/itsd/informatio
n/streaming/archive/MaySymposium2005
17
PLANET FORMATION
ASSEMBLING GAS GIANTS
FORMATION EARLY EVOLUTION OF PLANETARY SYSTEMS

M. ROZYCZKA NCAC WARSZAWA SPRING
SEMESTER 2008
Hubickyj, O. et al. 2005, Icarus 179,
415 http//www.stsci.edu/institute/itsd/informatio
n/streaming/archive/MaySymposium2005
18
PLANET FORMATION
ASSEMBLING GAS GIANTS
?
FORMATION EARLY EVOLUTION OF PLANETARY SYSTEMS

M. ROZYCZKA NCAC WARSZAWA SPRING
SEMESTER 2008
Hubickyj, O. et al. 2005, Icarus 179,
415 http//www.stsci.edu/institute/itsd/informatio
n/streaming/archive/MaySymposium2005
19
PLANET FORMATION
ASSEMBLING GAS GIANTS
FORMATION EARLY EVOLUTION OF PLANETARY SYSTEMS

M. ROZYCZKA NCAC WARSZAWA SPRING
SEMESTER 2008
Hubickyj, O. et al. 2005, Icarus 179,
415 http//www.stsci.edu/institute/itsd/informatio
n/streaming/archive/MaySymposium2005
20
PLANET FORMATION
ASSEMBLING GAS GIANTS

• Effects of migration
• Disk with Ss7.5(r / 5.2 AU)-2
• start with an embryo of 0.6 M?,
• initially at 5.2, 8 or 15 AU
• viscosity parameter a 210-3
• model starting at 5.2 AU does
• not migrate

15
8
5.2
solids
gas
FORMATION EARLY EVOLUTION OF PLANETARY SYSTEMS

M. ROZYCZKA NCAC WARSZAWA SPRING
SEMESTER 2008
Alibert, Y. et al. 2005 AA 430, 1133
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PLANET FORMATION
ASSEMBLING GAS GIANTS
increasing Ss by 67 shortens evolution from 13
to 2 Myr (models 6L and 10L)

• more solids

• less opacity

lowering k to 2 of interstellar value shortens
evolution by a factor of 3
but not too strongly!

• limited mass of the core

• migration (type I)

FORMATION EARLY EVOLUTION OF PLANETARY SYSTEMS

M. ROZYCZKA NCAC WARSZAWA SPRING
SEMESTER 2008
22
PLANET FORMATION
ASSEMBLING GAS GIANTS
Md,0 0.16 M? Rd,0 40 AU
radial migration of solids increases Ss of the
final swarm
FORMATION EARLY EVOLUTION OF PLANETARY SYSTEMS

M. ROZYCZKA NCAC WARSZAWA SPRING
SEMESTER 2008
Kornet K. et al. 2002, AA 396, 977
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PLANET FORMATION
ASSEMBLING GAS GIANTS
Playing with opacity
FORMATION EARLY EVOLUTION OF PLANETARY SYSTEMS

M. ROZYCZKA NCAC WARSZAWA SPRING
SEMESTER 2008
Hubickyj, O. et al. 2005, Icarus 179,
415 http//www.stsci.edu/institute/itsd/informatio
n/streaming/archive/MaySymposium2005
24
PLANET FORMATION
ASSEMBLING GAS GIANTS

• Playing with opacity inconlusive
• Primary source of opacity in the envelope is
  dust grains. In a standard
• approach opacities with the interstellar dust
  size distribution are used.
• But material that enters a giant planet envelope
  has been modified from
• the original interstellar grains by
  coagulation and fragmentation.
• Moreover, grains drift toward the core,
  colliding and growing on the way.
• Recent calculations indicate that the opacity is
  roughly interstellar in the
• uppermost layers, where the grains reside for
  a relatively short time.
• Deeper in the atmosphere the opacity can be
  reduced over the interstellar
• value by as much as three orders of magnitude.
• The global effect of the grain size distribution
  on the contraction time
• of the envelope is unclear.

FORMATION EARLY EVOLUTION OF PLANETARY SYSTEMS

M. ROZYCZKA NCAC WARSZAWA SPRING
SEMESTER 2008
Movshovitz, N. Podolak, M. 2008, Icarus 194, 368
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PLANET FORMATION
ASSEMBLING GAS GIANTS
Three simulations of giant planet formation in
the Solar System including effects of type I and
II migration. The last row shows the real
giants. Red and blue segments of each circle show
the fraction of the planet made up of solids and
gas respectively.
FORMATION EARLY EVOLUTION OF PLANETARY SYSTEMS

M. ROZYCZKA NCAC WARSZAWA SPRING
SEMESTER 2008
Chambers, J. 2006 ApJ 652, L133 and
http//www.dtm.ciw.edu/chambers/chambers_planform.
html
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PLANET FORMATION
ASSEMBLING GAS GIANTS POPULATION SYNTHESIS
Type I migration neglected. Viscosity parameter a
10-4. Monte Carlo variables 1. stellar mass
0.7?M? ? 1.4 M? uniform distribution per
interval in log10(M?). 2. disk mass and size
described by fdisk ? enhancement factor of S
with respect to the standard based on MMSN.
Assumed Gaussian distribution of log10(
fdisk) with mean 0.25 and dispersion 1.
fdisk 0.7 for MMSN. 3. similar factor for
Z-enhancement. 4. exponential decay of the disk.
log10(tdecay) distributed uniformly between
6 and 7. 5. constant probability of planet
formation per interval in log10a.
Green and blue rocky and icy planets with
envelopes less massive than cores (filled
circles and crosses) and envelopes up to 10 times
more massive than cores (open circles). Orange
envelopes at least 10 times more massive than
cores.
FORMATION EARLY EVOLUTION OF PLANETARY SYSTEMS

M. ROZYCZKA NCAC WARSZAWA SPRING
SEMESTER 2008
Ida, S. Lin, D.N.C. 2004, ApJ 604, 388
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PLANET FORMATION
ASSEMBLING GAS GIANTS POPULATION SYNTHESIS
al maximum radius at which type II
migration can be halted au maximum
radius at which solid core can
accrete gas before disk disperses Ml
onset of rapid accretion Mu gas inflow ends
Planet desert
FORMATION EARLY EVOLUTION OF PLANETARY SYSTEMS

M. ROZYCZKA NCAC WARSZAWA SPRING
SEMESTER 2008
Ida, S. Lin, D.N.C. 2004, ApJ 604, 388
28
PLANET FORMATION
ASSEMBLING GAS GIANTS POPULATION SYNTHESIS
Green and blue rocky and icy planets with
envelopes less massive than cores (filled
circles and crosses) and envelopes up to 10 times
more massive than cores (open circles). Orange
envelopes at least 10 times more massive than
cores.
FORMATION EARLY EVOLUTION OF PLANETARY SYSTEMS

M. ROZYCZKA NCAC WARSZAWA SPRING
SEMESTER 2008
Ida, S. Lin, D.N.C. 2004, ApJ 604, 388
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PLANET FORMATION
ASSEMBLING GAS GIANTS POPULATION SYNTHESIS

• 1M? star
• viscosity parameter a 0.01
• type I migration with a rate
• reduced by a factor of 100
• type II migration

Monte Carlo variables 1. metallicity 2. Sg
(population derived from observational
constraints on disk masses) 3. disk decay
rate (photoevaporation) 4. initial orbit of the
core (assumed population uniform
distribution in log a)
failed cores
FORMATION EARLY EVOLUTION OF PLANETARY SYSTEMS

M. ROZYCZKA NCAC WARSZAWA SPRING
SEMESTER 2008
Mordasini, C. et al. 2008 ASPC in press
arXiv0710.5667
30
PLANET FORMATION
ASSEMBLING GAS GIANTS POPULATION SYNTHESIS
Currently detectable population with real
planets indicated by blue dots. Satistical
comparison 2D test 53 that both samples are
from the same distribution. 1D test for Msini
93 1D test for a 33
FORMATION EARLY EVOLUTION OF PLANETARY SYSTEMS

M. ROZYCZKA NCAC WARSZAWA SPRING
SEMESTER 2008
Mordasini, C. et al. 2008 ASPC in press
arXiv0710.5667
31
PLANET FORMATION
ASSEMBLING GAS GIANTS POPULATION SYNTHESIS
Type I migration neglected. Viscosity parameter a
10-3. Stellar mass 1 and 0.5 M?. Solids
water ice, sublimating at 150 K. Monte Carlo
variables 1. disk mass uniformly distributed
between 0.02 and 0.2 M?. 2. disk radius
uniformly distributed per interval in
log10(Rout). 3. constant probability of planet
formation per interval in log10a.
central star 1M?
FORMATION EARLY EVOLUTION OF PLANETARY SYSTEMS

M. ROZYCZKA NCAC WARSZAWA SPRING
SEMESTER 2008
Kornet, K. Wolf, S. 2006, AA 454, 989
32
PLANET FORMATION
ASSEMBLING GAS GIANTS POPULATION SYNTHESIS
FORMATION EARLY EVOLUTION OF PLANETARY SYSTEMS

M. ROZYCZKA NCAC WARSZAWA SPRING
SEMESTER 2008
Kornet, K. Wolf, S. 2006, AA 454, 989
33
PLANET FORMATION
ASSEMBLING GAS GIANTS

• Various population syntheses based on CAGC
  consistently predict
• planet desert
• huge population of failed cores
• Moreover,
• In CAGC gas giants may be limited to the regions
  alt20 AU
• (except for planets on eccentric orbits that
  are scattered from inner
• regions by dynamical instabilities in multiple
  gas giant systems).
• In disk fragmentation scenario gas giants are
  preferentially formed
• far from their host stars.
• The search for gas giants beyond 2030 AU may
  distinguish
• between the two scenarios.

FORMATION EARLY EVOLUTION OF PLANETARY SYSTEMS

M. ROZYCZKA NCAC WARSZAWA SPRING
SEMESTER 2008
Ida, S. Lin, D.N.C. 2004, ApJ 604, 388
34
VII. FORMATION OF TERRESTRIAL PLANETS
Beware of confusion authors engaged in
simulations of the growth of terrestrial planets
call the same objects planetesimals, cores,
embryos or protoplanets
FORMATION EARLY EVOLUTION OF PLANETARY SYSTEMS

M. ROZYCZKA NCAC WARSZAWA SPRING
SEMESTER 2008
35
PLANET FORMATION
ASSEMBLING INNER ROCKY PLANETS
Principal aims of the simulations 1. Get right
planets on right orbits 2. Get the right amount
of water 3. Get the right amount of iron-group
elements 4. Set limits on the original orbits of
giant planets
Principal difficulty Accurately integrate
N-body problems with N ? 102 for 108 yr
note formation of embryos is also a big-N-body
problem, but its timescale is much shorter (106
yr)
Highly specialized methods Bulirsch-Stroer and
symplectic integrators
FORMATION EARLY EVOLUTION OF PLANETARY SYSTEMS

M. ROZYCZKA NCAC WARSZAWA SPRING
SEMESTER 2008
36
PLANET FORMATION
ASSEMBLING INNER ROCKY PLANETS
Example of an N-body simulation of the growth
of terrestrial planets. At t 0 there are 150
embryos in the domain (14 with mass 0.1M? and
136 with mass 0.01M?)
movie chambers
FORMATION EARLY EVOLUTION OF PLANETARY SYSTEMS

M. ROZYCZKA NCAC WARSZAWA SPRING
SEMESTER 2008
Chambers, J. http//www.dtm.ciw.edu/chambers/chamb
ers_planform.html
37
PLANET FORMATION
ASSEMBLING INNER ROCKY PLANETS CHARACTERISTIC
EVOLUTIONARY PHASES
Initial condition embryos with isolation
masses
Isolation is overcome due to mutual stirring, and
collisions begin to occur
Horizontal bars show perihelion and aphelion
distances
FORMATION EARLY EVOLUTION OF PLANETARY SYSTEMS

M. ROZYCZKA NCAC WARSZAWA SPRING
SEMESTER 2008
Chambers, J.E. Wetherill, G.W. 1998 Icarus
136, 304
38
PLANET FORMATION
ASSEMBLING INNER ROCKY PLANETS CHARACTERISTIC
EVOLUTIONARY PHASES
The whole disk becomes dynamically excited
First protoplanet forms (arrow)
Horizontal bars show perihelion and aphelion
distances
FORMATION EARLY EVOLUTION OF PLANETARY SYSTEMS

M. ROZYCZKA NCAC WARSZAWA SPRING
SEMESTER 2008
Chambers, J.E. Wetherill, G.W. 1998 Icarus
136, 304
39
PLANET FORMATION
ASSEMBLING INNER ROCKY PLANETS CHARACTERISTIC
EVOLUTIONARY PHASES
The small objects are swept up
The largest surviving objects are isolated from
one another
Horizontal bars show perihelion and aphelion
distances
FORMATION EARLY EVOLUTION OF PLANETARY SYSTEMS

M. ROZYCZKA NCAC WARSZAWA SPRING
SEMESTER 2008
Chambers, J.E. Wetherill, G.W. 1998 Icarus
136, 304
40
PLANET FORMATION
ASSEMBLING INNER ROCKY PLANETS ... ? PULLING THEM
OUT OF CHAOS
Initial conditions in cases 7B, 8B and 9B differ
only in nodal longitudes of the embryos orbits
and in locations of the embryos on the orbits.
The evolution is highly stochastic, making it
difficult to to predict the kind of the final
planetary system that a particular protoplanetary
disk will produce
FORMATION EARLY EVOLUTION OF PLANETARY SYSTEMS

M. ROZYCZKA NCAC WARSZAWA SPRING
SEMESTER 2008
Chambers, J.E. Wetherill, G.W. 1998 Icarus
136, 304
41
PLANET FORMATION
ASSEMBLING INNER ROCKY PLANETS ROLE OF TYPE I
MIGRATION

• Simulation of oligarchic and post-oligarchic
  evolution
• with type I migration of embryos
• Embryos and planetesimals in an MMSN-like
  environment.
• Planetesimals are subject to radial drift
• Embryos accrete planetesimals and interact among
  themselves.
• Planetesimals do not interact with each other.
• Giant planets are neglected
• Two-stage modeling begins with a semi-analytic
  model of the oligarchic evolution of embryos with
  initially equal masses 1.510-4M? immersed in a
  swarm of planetesimals with masses 2.110-6M?
  (i.e. with radii of 100 km at assumed bulk
  density of 3 g cm-3).
• Initial conditions for N-body runs are drawn from
  semi-analytic model at
• t 0.3 Myr, when the number of embryos drops to
  40-50 due to merging.

FORMATION EARLY EVOLUTION OF PLANETARY SYSTEMS

M. ROZYCZKA NCAC WARSZAWA SPRING
SEMESTER 2008
McNeil, D. et al. 2006, AJ 130, 2884
42
PLANET FORMATION
ASSEMBLING INNER ROCKY PLANETS ROLE OF TYPE I
MIGRATION
The semi-analytic model calculates the mass the
migrating embryo would have at given t upon
achieving orbit indicated on the horizontal axis.
FORMATION EARLY EVOLUTION OF PLANETARY SYSTEMS

M. ROZYCZKA NCAC WARSZAWA SPRING
SEMESTER 2008
McNeil, D. et al. 2006, AJ 130, 2884
43
PLANET FORMATION
ASSEMBLING INNER ROCKY PLANETS ROLE OF TYPE I
MIGRATION
Initial conditions for N-body
FORMATION EARLY EVOLUTION OF PLANETARY SYSTEMS

M. ROZYCZKA NCAC WARSZAWA SPRING
SEMESTER 2008
McNeil, D. et al. 2006, AJ 130, 2884
44
PLANET FORMATION
ASSEMBLING INNER ROCKY PLANETS ROLE OF TYPE I
MIGRATION
FORMATION EARLY EVOLUTION OF PLANETARY SYSTEMS

M. ROZYCZKA NCAC WARSZAWA SPRING
SEMESTER 2008
McNeil, D. et al. 2006, AJ 130, 2884
45
PLANET FORMATION
ASSEMBLING INNER ROCKY PLANETS ROLE OF TYPE I
MIGRATION
Initial conditions for N-body
Large circles embryos (area proportional to
mass) lines through the circles indicate a width
of 10 Hill radii. Step-like line amount of
planetesimal material in semimajor axis bins of
width 0.1 AU.
FORMATION EARLY EVOLUTION OF PLANETARY SYSTEMS

M. ROZYCZKA NCAC WARSZAWA SPRING
SEMESTER 2008
McNeil, D. et al. 2006, AJ 130, 2884
46
PLANET FORMATION
ASSEMBLING INNER ROCKY PLANETS ROLE OF TYPE I
MIGRATION
FORMATION EARLY EVOLUTION OF PLANETARY SYSTEMS

M. ROZYCZKA NCAC WARSZAWA SPRING
SEMESTER 2008
McNeil, D. et al. 2006, AJ 130, 2884
47
PLANET FORMATION
ASSEMBLING INNER ROCKY PLANETS ROLE OF TYPE I
MIGRATION
History of embryos in C2 model. Area of the
circles scales linearly with embryo mass. For
each embryo three lines are drawn, corresponding
to the osculating values of the perihelion,
semimajor axis, and aphelion. Final spacings are
large enough for the system to be stable for 100
Myr The introduction of Jupiter and Saturn
should stir the embryos enough to enable
interactions and reduce the final number of
planets.
FORMATION EARLY EVOLUTION OF PLANETARY SYSTEMS

M. ROZYCZKA NCAC WARSZAWA SPRING
SEMESTER 2008
McNeil, D. et al. 2006, AJ 130, 2884
48
PLANET FORMATION
ASSEMBLING INNER ROCKY PLANETS ROLE OF TYPE I
MIGRATION
CONCLUSION The progenitors of the terrestrial
planets can survive type I migration proceeding
at near the nominal rate, provided the disc is
more massive than MMSN
FORMATION EARLY EVOLUTION OF PLANETARY SYSTEMS

M. ROZYCZKA NCAC WARSZAWA SPRING
SEMESTER 2008
McNeil, D. et al. 2006, AJ 130, 2884
49
PLANET FORMATION
ASSEMBLING INNER ROCKY PLANETS FOCUS ON MIXING
AND WATER
The paradox of watery Earth
Earth formed where water is liquid (T gt 273
K) Local planetesimals were dry The nearest
wet material was behind the snow line (T lt 150
K) HOW DID IT GET TO EARTHS ORBIT? 1. Earth
formed dry water was brought much later by
comets 2. Radial mixing of planetesimals was
efficient enough to bring water during the
formation of the Earth
FORMATION EARLY EVOLUTION OF PLANETARY SYSTEMS

M. ROZYCZKA NCAC WARSZAWA SPRING
SEMESTER 2008
50
PLANET FORMATION
ASSEMBLING INNER ROCKY PLANETS FOCUS ON MIXING
AND WATER
Simulations similar to C2 (slides 42-47) indicate
that extensive mixing is possible
FORMATION EARLY EVOLUTION OF PLANETARY SYSTEMS

M. ROZYCZKA NCAC WARSZAWA SPRING
SEMESTER 2008
McNeil, D. et al. 2006, AJ 130, 2884
51
PLANET FORMATION
ASSEMBLING INNER ROCKY PLANETS FOCUS ON MIXING
AND WATER
Water in asteroids
FORMATION EARLY EVOLUTION OF PLANETARY SYSTEMS

M. ROZYCZKA NCAC WARSZAWA SPRING
SEMESTER 2008
after Raymond, S. et al.. 2004, Icarus 168, 1
52
PLANET FORMATION
ASSEMBLING INNER ROCKY PLANETS FOCUS ON MIXING
AND WATER

• Modeling the process of terrestrial planet
  formation and water delivery
• as a function of several parameters of the
  protoplanetary system
• 42 simulations starting from 150-200 embryos and
  planetesimals
• Variable parameters
• Jupiters orbital radius, eccentricity, mass and
  time of formation
• Location of snow line (2 or 2.5 AU)
• Surface density of solids (8-10 g cm-2)
• Total mass of solids between Jupiter and 31
  resonance at 2.5 AU

FORMATION EARLY EVOLUTION OF PLANETARY SYSTEMS

M. ROZYCZKA NCAC WARSZAWA SPRING
SEMESTER 2008
Raymond, S. et al. 2004 Icarus 168, 1
53
PLANET FORMATION
ASSEMBLING INNER ROCKY PLANETS FOCUS ON MIXING
AND WATER
FORMATION EARLY EVOLUTION OF PLANETARY SYSTEMS

M. ROZYCZKA NCAC WARSZAWA SPRING
SEMESTER 2008
Raymond, S. et al. 2004 Icarus 168, 1
54
PLANET FORMATION
ASSEMBLING INNER ROCKY PLANETS FOCUS ON MIXING
AND WATER
Starting versus final locations of all embryos
and planetesimals incorporated into five planets
obtained in simulation 10 (shown in the last
slide)
FORMATION EARLY EVOLUTION OF PLANETARY SYSTEMS

M. ROZYCZKA NCAC WARSZAWA SPRING
SEMESTER 2008
Raymond, S. et al. 2004 Icarus 168, 1
55
PLANET FORMATION
ASSEMBLING INNER ROCKY PLANETS FOCUS ON MIXING
AND WATER
Systems with different eccentricity of Jupiters
orbit
FORMATION EARLY EVOLUTION OF PLANETARY SYSTEMS

M. ROZYCZKA NCAC WARSZAWA SPRING
SEMESTER 2008
Raymond, S. et al. 2004 Icarus 168, 1
56
PLANET FORMATION
ASSEMBLING INNER ROCKY PLANETS FOCUS ON MIXING
AND WATER
all 118 planets formed in 42 simulations
(including 12 with 2ltalt2.5 AU)
FORMATION EARLY EVOLUTION OF PLANETARY SYSTEMS

M. ROZYCZKA NCAC WARSZAWA SPRING
SEMESTER 2008
Raymond, S. et al. 2004 Icarus 168, 1
57
PLANET FORMATION
ASSEMBLING INNER ROCKY PLANETS FOCUS ON MIXING
AND WATER
all 43 planets formed with 0.8ltalt1.5 AU, i.e. in
the habitable zone
FORMATION EARLY EVOLUTION OF PLANETARY SYSTEMS

M. ROZYCZKA NCAC WARSZAWA SPRING
SEMESTER 2008
Raymond, S. et al. 2004 Icarus 168, 1
58
PLANET FORMATION
ASSEMBLING INNER ROCKY PLANETS FOCUS ON MIXING
AND WATER
CONCLUSIONS 1. Stochastic process, but some
trends are clear - increasing eJUP ?
drier terrestrial planets - increasing
MJUP ? fewer, more massive terrestrial planets
- increasing Ss ? fewer, more massive
terrestrial planets 2. All systems form 1-4
planets inside 2 AU. In most cases a planet forms
between 0.8-1.5 AU in 25 of cases between
0.9-1.1 AU 3. Terrestrial planets have a large
range in mass (0.23 to 3.85 M?) and water
content (dry to 300 Earth oceans Earth ocean
1.51024 g 2.510-4 M?) 4. Most of Earths
water was accreted during formation, from bodies
past the snow line 5. Terrestrial planets
are affected by giant planets! 6. A huge
diversity of extrasolar terrestrial planets
should be expected
FORMATION EARLY EVOLUTION OF PLANETARY SYSTEMS

M. ROZYCZKA NCAC WARSZAWA SPRING
SEMESTER 2008
Raymond, S. et al. 2004 Icarus 168, 1
59
PLANET FORMATION
ASSEMBLING INNER ROCKY PLANETS FOCUS ON MIXING
AND WATER

• Effects of the orbits of Jupiter and Saturn on
  the final planetary system
• 4 EJS simulations with the present (eccentric)
  orbits of Jupiter and Saturn 4 CJS simulations
  with nearly circular and coplanar orbits as
  predicted in recent models of the evolution of
  the outer Solar System
• Start from a distribution of 25 Mars-mass
  embryos and 1000 planetesimals 1/40 as massive
  as the embryos (large number of interacting
  bodies allows for a more accurate treatment of
  dynamical friction)
• Different random number seeds to generate
  orbital parameters in each simulation
• Bodies with perihelion at less than 0.1 AU are
  assumed to hit the Sun those with an aphelion
  distance greater than 10 AU (i.e. crossing both
  Jupiter and Saturn) are assumed to be ejected
  from the system.
• Migration of Jupiter and Saturn is not included.

FORMATION EARLY EVOLUTION OF PLANETARY SYSTEMS

M. ROZYCZKA NCAC WARSZAWA SPRING
SEMESTER 2008
OBrien, D.P. et al. 2006, Icarus 184, 29
60
PLANET FORMATION
ASSEMBLING INNER ROCKY PLANETS FOCUS ON MIXING
AND WATER
Simulations EJS Jupiter and Saturn have their
present (slightly excentric) orbits
FORMATION EARLY EVOLUTION OF PLANETARY SYSTEMS

M. ROZYCZKA NCAC WARSZAWA SPRING
SEMESTER 2008
OBrien, D.P. et al. 2006, Lunar Planetary Sc.
XXXVII, 2347 also Icarus 184, 29
61
PLANET FORMATION
ASSEMBLING INNER ROCKY PLANETS FOCUS ON MIXING
AND WATER
Simulations CJS Jupiter and Saturn have
coplanar and circular orbits
FORMATION EARLY EVOLUTION OF PLANETARY SYSTEMS

M. ROZYCZKA NCAC WARSZAWA SPRING
SEMESTER 2008
OBrien, D.P. et al. 2006, Lunar Planetary Sc.
XXXVII, 2347 also Icarus 184, 29
62
PLANET FORMATION
ASSEMBLING INNER ROCKY PLANETS FOCUS ON MIXING
AND WATER
CONCLUSIONS 1. In each simulation a stable system
of terrestrial planets is formed within 250 Myr.
2. In EJS simulations the asteroid belt is
rapidly cleared of embryos, such that they
are less likely to end up in the final
terrestrial planets 3. Substantial radial mixing
occurs. In CJS simulations, the mass fraction of
material from beyond 2.5 AU in the final
planets ranges from 1.638 (with a median of
15), compared to 0.31.5 in EJS 4. As far
as abundances of water and iron-group elements
are concerned, final CJS planets are more
consistent with the Earth than final EJS
planets 5. However, CJS planets are (on the
average) too massive compared to the actual
Earth-like ones, and their center of mass is too
far from the Sun. In those respects, EJS
planets beter fit to the Solar System 6. If
Jupiter and Saturn did indeed start out on orbits
as eccentric as they are today, an
alternative source of water for Earth is likely
necessary
FORMATION EARLY EVOLUTION OF PLANETARY SYSTEMS

M. ROZYCZKA NCAC WARSZAWA SPRING
SEMESTER 2008
OBrien, D.P. et al. 2006, Icarus 184, 29
63
PLANET FORMATION
ASSEMBLING INNER ROCKY PLANETS FOCUS ON MIXING
AND WATER

• High-resolution simulations of the final stage in
  the formation of terrestrial planets
• Jupiter on a cirular orbit
• Initially 1000-2000 embryos and planetesimals
• Three sets of initial conditions

FORMATION EARLY EVOLUTION OF PLANETARY SYSTEMS

M. ROZYCZKA NCAC WARSZAWA SPRING
SEMESTER 2008
Raymond, S. et al. 2006 Icarus 183, 265 and
http//lasp.colorado.edu/7Eraymond/
64
PLANET FORMATION
ASSEMBLING INNER ROCKY PLANETS FOCUS ON MIXING
AND WATER
Simulation 0 1885 initial particles Jupiter at
5.5 AU
movie raymond1
FORMATION EARLY EVOLUTION OF PLANETARY SYSTEMS

M. ROZYCZKA NCAC WARSZAWA SPRING
SEMESTER 2008
Raymond, S. et al. 2006 Icarus 183, 265 and
http//lasp.colorado.edu/7Eraymond/
65
PLANET FORMATION
ASSEMBLING INNER ROCKY PLANETS
An example of the effective feeding zones of the
planets
FORMATION EARLY EVOLUTION OF PLANETARY SYSTEMS

M. ROZYCZKA NCAC WARSZAWA SPRING
SEMESTER 2008
Raymond, S. et al. 2006 Icarus 183, 265
66
PLANET FORMATION
ASSEMBLING INNER ROCKY PLANETS FOCUS ON MIXING
AND WATER
FORMATION EARLY EVOLUTION OF PLANETARY SYSTEMS

M. ROZYCZKA NCAC WARSZAWA SPRING
SEMESTER 2008
Raymond, S. et al. 2007, Astrobiology 7, 66
67
PLANET FORMATION
ASSEMBLING INNER ROCKY PLANETS FOCUS ON MIXING
AND WATER
CONCLUSIONS 1. The feeding zones of the
terrestrial planets widen and move outward in
time 2. The asteroid belt is cleared of gt99 of
its mass due to mutual scattering of embryos
and planetesimals onto unstable orbits (e.g. mean
motion resonances with Jupiter). In time
these bodies are removed via ejections, or
by colliding with bodies closer to the Sun 3.
Each planet formed in simulations has at least
five Earth oceans of water 4. Significant
fraction of the delivered water is in the form of
planetesimal-sized bodies. Some planets can
also accrete a large amount of water in the form
of a few large embryos in a hit or miss
process 5. Mars is generally much too large
FORMATION EARLY EVOLUTION OF PLANETARY SYSTEMS

M. ROZYCZKA NCAC WARSZAWA SPRING
SEMESTER 2008
Raymond, S. et al. 2006 Icarus 183, 265 and
2007, Astrobiology 7, 66
68
PLANET FORMATION
ASSEMBLING INNER ROCKY PLANETS SURVIVING THE
MIGRATION OF GAS GIANTS
The problem of migrating giants
What happens to slowly assembling embryos and
planetesimals when a rapidly formed gas giant
migrates across the inner part of its
protoplanetary disk? Can we expect any
Earth-like planets in systems with Hot Jupiters?
FORMATION EARLY EVOLUTION OF PLANETARY SYSTEMS

M. ROZYCZKA NCAC WARSZAWA SPRING
SEMESTER 2008
69
PLANET FORMATION
ASSEMBLING INNER ROCKY PLANETS EFFECTS OF THE
MIGRATION OF GAS GIANTS
Simulations of terrestrial planet growth during
and after giant planet migration Protoplanetary
disk of gas and solids, extending from 0.25 to 10
AU Drag from the gaseous disk taken into account
The solids 17 M? of rocky/icy material, evenly
divided between 80 Moon-toMars-sized embryos and
1200 planetesimals Inner disk iron-rich and
water-poor outer disk water-rich and
iron-poor Five initial configurations of randomly
distributed embryos and planetesimals A giant
planet migrates in 105 years from 5 AU to 0.25
AU In some simulations another (stationary) giant
is present at 10 AU
FORMATION EARLY EVOLUTION OF PLANETARY SYSTEMS

M. ROZYCZKA NCAC WARSZAWA SPRING
SEMESTER 2008
Mandell, A.M. et al. 2007, ApJ 660, 823 Raymond,
S. et al. 2006, Science 313, 1413
70
PLANET FORMATION
ASSEMBLING INNER ROCKY PLANETS EFFECTS OF THE
MIGRATION OF GAS GIANTS
FORMATION EARLY EVOLUTION OF PLANETARY SYSTEMS

M. ROZYCZKA NCAC WARSZAWA SPRING
SEMESTER 2008
Mandell, A.M. et al. 2007, ApJ 660, 823
71
PLANET FORMATION
ASSEMBLING INNER ROCKY PLANETS EFFECTS OF THE
MIGRATION OF GAS GIANTS
simulation JD5 (red box in the next slide)
movies raymond2 raymond3
FORMATION EARLY EVOLUTION OF PLANETARY SYSTEMS

M. ROZYCZKA NCAC WARSZAWA SPRING
SEMESTER 2008
Mandell, A.M. et al. 2007, ApJ 660, 823 Raymond,
S. et al. 2006, Science 313, 1413 and
http//lasp.colorado.edu/7Eraymond/
72
PLANET FORMATION
ASSEMBLING INNER ROCKY PLANETS EFFECTS OF THE
MIGRATION OF GAS GIANTS
FORMATION EARLY EVOLUTION OF PLANETARY SYSTEMS

M. ROZYCZKA NCAC WARSZAWA SPRING
SEMESTER 2008
Raymond, S. et al. 2006, Science 313, 1413
73
PLANET FORMATION
ASSEMBLING INNER ROCKY PLANETS EFFECTS OF THE
MIGRATION OF GAS GIANTS
CONCLUSIONS 1. Very water-rich, Earth-mass
planets form from surviving material outside the
giant planets orbit, often in the habitable
zone and with low orbital eccentricities. 2.
Earth-mass planets can also form interior to the
migrating Jovian planet. 3. The surviving planets
can be divided into three classes - Hot
Earths interior to the giant planet orbit
- normal terrestrial planets between the giant
planet and 2.5 AU - outer planets beyond
2.5 AU, whose accretion was not completed by the
end of the simulation. 4. More than a
third of the known systems of giant planets may
harbor Earth-like planets.
FORMATION EARLY EVOLUTION OF PLANETARY SYSTEMS

M. ROZYCZKA NCAC WARSZAWA SPRING
SEMESTER 2008
Mandell, A.M. et al. 2007, ApJ 660, 823 Raymond,
S. et al. 2006, Science 313, 1413
74
MATURE PLANETS
STABILITY OF PLANETARY SYSTEMS
Consider planets m1 and m2 orbiting a star of
mass M on circular orbits a1 and a2. The
stability of the system depends on the relative
spacing D such that
a2 a1(1 D ) Let m1 ? m1 /M and m2 ?
m2 /M . Then for m1 , m2 1 it was shown
analytically that systems with
D gtDmin 2.40(m1 m2 )1/3 are stable. Caution
this is a sufficient condition, but it has not
been proved that it is also a necessary one. The
analytic result does not say anything about
systems with D lt Dmin.
FORMATION EARLY EVOLUTION OF PLANETARY SYSTEMS

M. ROZYCZKA NCAC WARSZAWA SPRING
SEMESTER 2008
Armitage, P. J. 2007, arXivastro-ph/0701485
75
MATURE PLANETS
STABILITY OF PLANETARY SYSTEMS
For Jupiter and Saturn Dmin 0.26, whereas the
actual separation D 0.83, i.e. a planetary
system composed solely of Jupiter and Saturn on
circular orbits would be stable at all
times. The analysis can be extended onto nonzero
eccentricities, but it does not apply to systems
with more than 2 planets. No absolute stability
bound is known for any system with more than 3
planets. For a multiplanet system a plausible
but mathematically unfounded expectation is that
it goes unstable if any pair of neighbouring
planets substantially violates the critical
two-planet separation
FORMATION EARLY EVOLUTION OF PLANETARY SYSTEMS

M. ROZYCZKA NCAC WARSZAWA SPRING
SEMESTER 2008
Armitage, P. J. 2007, arXivastro-ph/0701485
76
MATURE PLANETS
STABILITY OF PLANETARY SYSTEMS
One can also expect that planetary systems become
more stable with increasing orbital separations.
Numerical experiments confirm this
conjecture. Mutual Hill radius
FORMATION EARLY EVOLUTION OF PLANETARY SYSTEMS

M. ROZYCZKA NCAC WARSZAWA SPRING
SEMESTER 2008
Chambers, J. http//star.arm.ac.uk/jec/res-plane
ts.html
77
MATURE PLANETS
STABILITY OF PLANETARY SYSTEMS
Packed Planetary Systems (PPS) hypothesis The
majority of planetary systems appear dynamically
full, i.e. there is no room in them for a stable
orbit between known planetary orbits, so
additional companions cannot exist between those
known. PPS suggests that planet formation is an
efficient process if a planet is dynamically
alowed, it exists or wherever there is room
for a planet to form, it does form
FORMATION EARLY EVOLUTION OF PLANETARY SYSTEMS

M. ROZYCZKA NCAC WARSZAWA SPRING
SEMESTER 2008
Barnes, R.. 2008 http//www.lpl.arizona.edu/rory
/prediction/
78
MATURE PLANETS
STABILITY OF PLANETARY SYSTEMS
Packed Planetary Systems (PPS) hypothesis PPS is
able to make verifiable predictions. A small
percentage of the early-discovered planetary
systems did contain stable gaps. PPS implied
there must be planets in them that had not yet
been discovered because they were at or below
detection limits. The discovery of the HD 74156
d confirmed the existence of a planet with period
and minimum mass predicted by PPS (it was the
first succesful prediction since that of
Neptune!) Another success of PPS concerns the
system 55 Cnc, in which the predicted planet f
was discovered
FORMATION EARLY EVOLUTION OF PLANETARY SYSTEMS

M. ROZYCZKA NCAC WARSZAWA SPRING
SEMESTER 2008
Barnes, R.. 2008 http//www.lpl.arizona.edu/rory
/prediction/
79
MATURE PLANETS
STABILITY OF PLANETARY SYSTEMS
FORMATION EARLY EVOLUTION OF PLANETARY SYSTEMS

M. ROZYCZKA NCAC WARSZAWA SPRING
SEMESTER 2008
Barnes, R. Gozdziewski, K. Raymond, S. 2008,
arXiv0804.4496v1 figure http//www.lpl.arizona
.edu/rory/prediction/