Formation, structure and evolution of the Giant Planets

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Formation, structure and evolution of the Giant
Planets

• G.Magni

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Preliminary questionWhat is a giant
planet?Where it is placed, from stars to
terrestrial planets?Fast (and rough)
answeran object having mass between 0.1 and 10
Jupiter masses, with a gaseous envelope, rich in
H and He, gravitationally bound the the central
star
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Summary Questions

• What is the general subject and the specific
  plot of the play Formation of giant planets
  starting from a protostellar disk?
• What is the subject of the act Formation and
  evolution of OUR Jovian planets?
• What can we argue from the big amount of
  experimental data (space missions, observations)?
  
• How important is the effect of the observative
  selection effects (statistics on extrasolar
  planets, planetary surfaces much better known
  than the internal)?
• How are the main physical processes driving the
  GP formation?
• What do we know about their history?
• What we expect from the Cassini mission and from
  the future missions to better understand the GP
  formation?

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• Summary
  Problems
• Why it is difficult today to develop a general
  theory like a Theory of the planets?
• At present
• 1) Only one planetary system well known (our
  one)
• about 150 extrasolar planets strongly
  affected by observational selection effects
  (large mass, small distance from the central
  star, high eccentricity values privileged)
•  
• Formation, evolution and structure of the planets
  involve an extremely large amount of physical
  processes (neutral and ionized high pressure
  matter, plasma physics, phase transitions,
  chemical equilibrium and kinetics, interaction
  between solid particles.)
• Unlike star formation, the growth of a planet
  takes place in matter that is chemically and
  physically strongly disomogeneous (gas and solid
  particles, condensation and sublimation of
  volatiles, accretion of gas around solid bodies  

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4) In a planetary sistem, planets do not form as
single independent events, but their
evolutive tracks are strictly correlated one
another 5) The detectability and observability
of a growing primordial planet is very
difficult due to its low intrinsic luminosity ,
and has a short temporal window 6) The
evolutive timescales of the central star and of
the protoplanetary disk strongly influence
planetary formation and evolution. Slightly
different initial and boundary conditions can
produce (or inhibite) very different
planetary systems   7) What is missing up today
is, before of all, a good statistics of
extrasolar planets, a better knowledge of the
GP interiors and more informations on the
external Solar System (Kuiper Belt objects)
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1st step Our Solar Systemglobal
characteristicsregular propertiesregular
trendscomparison with the known sample of
extrasolar planets
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Formation process driven by long scale lenght
processes (gravitation?). The mutual interaction
among the growing planets during their formation
had to be not very important No similar
information for extrasolar planets
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SS Jovian planets, low eccentricity ExoP
strongly scattered eccentricity (collisional
processes) eccentricity growing with
distance (selection effect?)
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SS two classes of planets, mass vs.
distance ExoP large masses , slowly growing with
distance (selection effect, planetary migration)
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Virtual mass present massHHevolatiles ? Solar
nebula abundances Virtual mass distribution ?
regular trend (except Mars)
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Snow line in the minimum mass SN where
Psat(H2O,ice)P(SN)
There is a correlation among Giant Planets, snow
line and capture of volatiles
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In GP is present an increase of the density
gradient in their central regions Continuous
increase of Z (and/or Y) towards the center
(sedimentation of unsoluble elements) Or jump of
Z to larger values (presence of a rocky-icy core)
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Timescale constraints

• About 50 of the solar type young stars is
  rounded by disks or rings, 30 of them having
  masses compatible with our Planetary System
• It is also present a well defined correlation
  between mass of the disk and age of the disk
  itself
• However, it is very difficult and statistically
  unlikely, at least with the present observational
  tecniques, to directly observe a giant planet
  during its formation (only two hot Jupiters
  very close to the stars observed up today)
• The constraint on timescales coming from the
  observation of protostellar disks ranges from
  Tdisk lt105 yr (before the onset of the T-Tauri
  phase ) with Mdust100MEarth to Tdisk gt107 yr
  (b Pictoris disk) with strong dust depletion,
  Mdustlt 0.1MEarth

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(Montmerle, 1997)
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Chemical constraints
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• The composition of the gas of GP suggests that
• it comes from the primordial circumsolar disk
  (D/H for Jupiter and Saturn)
• but with depletion (gravitational?) processes
  for Helium,
• a substantial enrichment of refractories
  (capture of solid bodies) and
• an enrichment (at least for Jupiter) of volatile
  noble gases (capture of cold solid bodies)

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Effect of metallicity
In protostellar disks with high Z there is a
larger amount of refractory materials to form
protoplanetary cores and /or a higher opacity
that can influence planet formation. Besides,
more and more planets could have migrated up to
fall into the star. The litium overabundance is
instead a direct evidence of this last process
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• The steeper slope for GP can be
• produced by
• different physical conditions in different
  regions of the SN during planet formation
  (dependence on Sun distance of the mass accretion
  flux from the interstellar protosolar cloud ?
  Different turbulent regimes?)
• Lower accretion efficiency going outwards due to
  depletion of the SN (larger accretion times?
  Perturbation by previously formed inner planets?)

sM(virtual)/S (feeding zone)
The distribution is different (double slope) for
terrestrial planets and GP
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R(SN)40 AU
The best fit between present specific angular
momentum of the planets (mainly from GP) and of
SN defines a power law index for sigma of about
1.5 that is generally adopted as a standard
value
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The inclination of the spin axis of the sun can
be explained by a single impact of an object of 6
10 M(earth) (orbital migration) or 8 13
M(earth) capture from the Asteroids Belt
(resonant ejection)
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The mass of the impactor is compatible with the
accretional history of the planetesimals and of
the evolution of protoplanetary embryos
(Wetherill, 1988, )
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• Formation of giant planets seems to have at least
  two different mechanisms. The first produces
  planets with nearly circular orbits, low
  inclinations and eccentricities, regular trend in
  mass, distance and physical properties (up today,
  statistics only on our SS). The second brings to
  a population with very irregular distribution in
  physical and orbital parameters (strong selection
  effects) .
• In SS it is present a bimodality in the
  distribution of density, momentum of inertia and
  volatile abundances. The capture of gas starts
  abruptly, and then becomes less efficient, going
  outwards.
• There are many indications about the presence of
  a central core in all the GP

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Formation models must respect and explain

• temporal constraints
• mass distribution
• Existence of GP with very different values of
  distance from the central star and of
  eccentricities
• Abundance anomalies. General enrichment of C N
  O(?) with radial gradient. Helium depletion in
  Jupiter(?) and Saturn. D/H distribution
• Presence of central cores and relative formation
  mechanism
• Presence, structure and chemical properties of
  systems of regular satellites,

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Physical mechanisms for Giant Planet formation

• The G.P. formation is the most important
  gravitational phase transition after the birth
  of the star and of its gasdust quasi-keplerian
  disk

Constraints Lifetime of the disk 106 107 yr
due to dissipative mechanisms -turbulent
viscosity
-stellar wind
-tidal mass depletion due to
previously formed
planets or
companions in multiple systems
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Stability and instability factors in a Keplerian
disk

• Instability autogravitation inside gas and
  solid components
• dissipative processes 1
  radiative cooling
• 
  2 turbulent angular momentum transport
• 
  3 sticking processes among solid
  particles
• 
  4 condensation of volatiles in ices
• Stability 5 rotation a) non inertial forces
  transfer angular momentum referred
• to the Sun in angular
  momentum referred to the protoplanet
• (centrifugal barrier)
  b) differential rotation in SN disperses
• regions of the disk at
  different distances from the Sun and acts
• against thei
  aggregation
• 6 thermal pressure grows
  during contraction
• Gas gt processes 1 2 4 5 6
• Solid particles gt all the processes except 6
  

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A typical protoplanetary disks is in principle
stable. If the selfgravitation is low, in every
part of the disk there is a nearly exact
compensation among gravity of the star,
centrifugal forces and pressure. Small or large
scale radial and vertical motions can be present
(convection, turbulence, drag on the solid
particles, meridional circulation due to the weak
gas selfgravitation), but they do not destroy
the global equilibrium state. Density fluctuation
are quickly merged in the gas with a
timescale unless the mass of the disk is large
enough.

• Two possible accretion mechanisms for GP
• Gas gravitational instability
• Nucleated instability

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Stability of a Keplerian disk
timescales of thermal rearrangement, keplerian
dispersion and free-fall contraction of the
instability
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(optically thick disk)

• At Jupiter distance
• At Saturn distance

• The gas gravitational instability needs massive
  protoplanetary disks and produces massive giant
  gaseous planets
• Radial perturbations can fragment and give
  raise to several large protoplanets in similar
  orbits, in mutual interaction and competition
  (spreaded orbital elements, migration towards
  regions very close to the central star)
• Probable formation mechanism for a large part of
  the observed extrasolar planets

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Time evolution of gas instabilities
In a rotating disk, the exponential growth of the
instability is slowed down by adiabatic
compression, angular momentum transfer due to
noninertial forces and shock dissipation in
density waves. The evolutive time passes from
the free-fall time
to that of radiative cooling
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More realistic computations, using N-body codes
with SPH methods and 106 particles (Mayer et
al.,2002) or 3D hydrodynamical simulations
(Boss,2001) find that gravitational instabilities
can grow and survive also with 1 lt Q lt 1.75, and
M(SN) lt 0.1 M(Sun) if the SN is cold enough The
evolution, due to computing limitations, is
followed for few hundreths of years and is driven
from radiative losses and strongly dependent on
physical assumptions (energy transport,
opacity) The results are not significantly
different from the simple first order approach,
but seem well describe, specially in Mayers
approach, the possible formation and evolution of
extrasolar massive giant planets (survival of
several GP around the star after the first
strongly energetic dynamical phase) The
formation of the cores via sedimentation of
refractory elements requires the clumps to be
convectively stable for several thousands of
years
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Mayer et al.(2002) time evolution of gas
instability for Qmin1.75 (upper) and Qmin 1.4
(lower) after 160 and 350 years. rmax20AU and
MSN0.08MSun
Boss (2002) time evolution of gas
instability,after 304 years, Qmin1.3 (upper)
and local isothermal conditions (upper), and
after 345 years, Qmin1.1 and local adiabatic
conditions (lower). rmax20AU and MSN0.08MSun
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Nucleated Instability

• Current theories on the evolution and accretion
  of the solid component of SS (Safronov, 1962
  Wetherill, 1988) make likely the presence, in the
  GP region of bodies of several Earth masses,
  growing with timescales from 105 a 107 years
• Cores are formed first, through an accumulation
  mechanism, similar to the mechanism generally
  accepted for the formation of the terrestrial
  planets
• As the core grows larger, more and more nebular
  gas is collected in its sphere of influence,
  still holding quasi hydrostatic equilibrium,
  until a large and massive envelope is formed.
  The accretion rate of gas is nearly proportional
  to the accretion rate of the core

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• When a critical mass is reached, the static
  solution for the structure of the gas around the
  core is no more possible, and a dynamical phase
  begins.
• The gas accretion rate depends on the feedback
  mechanisms that drive the rearrangement of the
  boundary of the gaseous envelope the gas infall
  inside the protoplanets sphere of influence
  (Hill lobe).
• The feedback process essentially drives the
  accretion timescale
• At the same time, also planetesimals are
  collected, and they contribute to the core
  heating

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Hill surface defined by the potential of the
total force
Where the first term is the gravitational one due
to the protoplanet, the second is due to the Sun,
and the third is the centrifugal term coming from
the frame rotating with the protoplanet. The
accretion boundary is the highest closed isoline
around the protoplanet
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• Perri and Cameron (1972), Mizuno (1980), Wuchterl
  (1993), Pollack and Bodenheimer (1996) and others
  demonstrate that a static equilibrium structure
  for a gaseous envelope around a core, cannot
  exist beyond a critical value of the core mass,
  for predefinited external boundary conditions.
• The critical core mass value is reached when the
  selfgravitation energy of the gas becomes
  comparable with the gas-core gravitational
  energy, and depends on the thermodynamical
  properties of the gas, on the energetic balance
  with the surrounding SN and on the opacity of the
  gas ond of the dust. It can change, depending on
  the assumptions, also for two orders of
  magnitude.
• Even if more and more gas begins to be captured,
  if the critical value is overcome, the time
  evolution of the accretion phase it is not still
  completely clear and is strongly model dependent.
  

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From Stevenson (1988)
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• A gap between the envelope limit and the boundary
  of the Hill lobe is produced, that can be
  refilled by the gas of the SN. A dynamical phase
  stars up and the timescale becomes substantially
  smaller than the growth timescale of the core
• The dynamical phase is driven by the capability
  of the envelope to rearrange its structure. This
  depends on the opacity and on the luminosity
  that, growing, can again allow a nearly
  hydrostatic equilibrium structure.
• The increase of luminosity brings a loss of
  energy and a contraction of the envelope. So the
  accretion cannot be stopped.

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• Strong disequilibrium phases can be anyhow
  possible (Wuchterl, 1993), and shock waves can
  slow, but probably not stop the accretion
  process.
• The accretion timescale depends essentially on
  the cooling time of the envelope (Safronov.1969).
  The envelope cutoff due to the Hill lobe causes a
  large variety of different equilibrium models
  with constant envelope radius Re RH but very
  different cooling times (103 105 years).
• The accretion process is strongly nonradial
  (asimmetry of the gravitational potential,
  velocity gradient of the gas in the SN,
  noninertial forces due to rotation). The 3D
  structure of the process can strongly affect the
  evolution and the relative timescales.

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Nucleated instability accretion models

• Pollack et al. (1996) use an evolutionary model
  having three major components
• The growth of the protoplanet is performed
  following the simultaneous growth of the central
  core by planetesimals capture and of the gaseous
  envelope due to the rearrangment of its external
  boundary
• The capture of planetesimals is computed with a
  central large body surrounded by a swarm of small
  bodies in the feeding zone, in the restricted
  three body approximation
• The structure of the protoplanet is integrated
  assuming spherical symmetry and quasi-hydrostatic
  equilibrium
• The (several) free parameters are adjusted to fit
  the properties of the Giant Planets and the
  constraints coming from protostellar disks (heavy
  elements overabundances and disk survival
  timescale).
• In Pollack et al.s model three main evolutionary
  phases can be identified 1) tlt5 105 yr -
  planetesimals accretion dominates 2) 5 105lttlt107
  yr - gas and planetesimals are comparable 3)
  t107yr runaway gas and planetesimals capture
  holds. This for Jupiter and Saturn. The accretion
  of Uranus and Neptune was terminated during the
  phase 2), as a result of the SN dissipation

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Time dependence of gas and planetesimals
accretion rate. Planetesimals capture runaway
at t0 and gasplanetesimals runaway at t8 106
yrs (Pollack et al., 1996)
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• The main limits of the models come from the large
  amount of initial assumptions, not all
  completely justified. Moreover, the gas accretion
  at the boundary of the Hill lobe is evaluated in
  spherical simmetry and without hydrodynamical
  effects. So, the runaway accretion is a
  mathematical artifact

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• A thorough study of the critical core mass and of
  its dependance on physical quantities and
  processes like opacity and convection, together
  with hydrodynamical calculations of the
  evolution of a protoplanet after the onset of
  the core nucleated instability have been
  performed by Wuchterl (1991, 1993, 1995, 2000).
• Wuchterl finds that
• The critical mass value depend strongly on the
  cooling process into the envelope. For purely
  radiative transport, the critical mass is
  independent on nebula density and mass accretion
  rate, and depends inversely on opacity and
  molecular weight (icy cores and Z-depleted
  nebulas have lower critical mass values). If
  convection holds, the critical mass depends
  inversely on molecular weight and density, and
  again does not depend on accretion rate

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• After the onset of the CNI the envelope starts
  to pulsate (driven by H2 dissociation) after a
  short contraction phase. This pulsation-driven
  wind depends directly on the nebula density. For
  more massive disks, a large convective region in
  the envelope appears and pulsation can be
  damped.
• The difference in envelope mass between Jupiter,
  Saturn, Uranus and Neptune derives frome this
  density dependent oscillation-damping mechanism.
• In spite of the complex physics treatment in
  Wuchterls models, (also time dependent
  convection), the main limitations in its results
  come from
• Spherical symmetry
• In the real SN the accretion of the envelope is
  very far from spherical symmetry
• Spherically simmetrical boundary conditions can
  be valid for a model in quasy-hydrostatic
  equilibrium, but can strongly bias the treatment
  of fast energetic processes like shocks or
  pulsations

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Nucleated instability 3D accretion model

• The model (Coradini and Magni, 1997, 2004)
  intends to treat the problem of the accretion
  onto the growing planet in the most possible
  general way, even if the physical treatment must
  be simplified. So
• A 3D mesh simulates the rotating Keplerian
  feeding zone, with the structure of the grid that
  takes into account the two main gravitational
  attractors (Sun and protoplanet)
• Spherical symmetry is abandoned everywhere, and
  the Hill lobe is only virtually present. Boundary
  conditions are only in the external edge of the
  SN, in radial and vertical direction, and in the
  mesh point corresponding to the protoplanet.
  However, quasi-hydrostatic equilibrium spherical
  structures for the envelope are computed at any
  time step, to define standard physical parameters
  as protoplanet mass, luminosity, effective
  temperature, effective radius of the region in
  quasi-equilibrium.

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• Disk-like structures can form around the
  protoplanet, that can be identified as primordial
  satellitary disks.
• The structure of the protoplanet is computed
  taking into account radiative and convective
  transport, and the luminosity is produced by the
  energy released by the infalling
  gasplanetesimals, in the approximation of
  homologous variations of the structure.
• The thermal structure of the SN is computed with
  a simplified treatment of adiabaticradiative
  exchanges

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The grid
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Jupiter
Saturn
S
J
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Surface density in the central plane of SN at the
end of the accretion ( exploded view)
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Accretion time
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Mass inside the Hill lobe
Luminosity
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• Envelope radius
  Accretion time and
  cooling time

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Area where the gas has prograde motion ?Accretion
disk
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Mp 0.25 MSaturn
Mp 0. 5 MSaturn
Mp MSaturn
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• Results (3D model, Saturn)
• - A core of 15 MEarth accretes gas up to
  MSaturn in 104 years for a Minimum Mass
  Solar nebula
• - The pulsational instability mechanism seems
  to be not able to stop the accretion vgtcs
  well inside the envelope and in the strongly
  distorted flow paths near the Hill boundary,
  the gas finds in any case channels to fall onto
  the core
• The cooling time drives efficiently the accretion
  process, and flattens the curve (accretion time
  SN mass).
• Runaway phases
• can rise, but they are strongly model dependent
  

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What stops the accretion?

• Growing the protoplanet, the region from where
  the gas can be collected enlarges,
• and more and more matter could reach in principle
  the Hill lobe of the protoplanet
• For M(SN)0.02M(Sun), the feeding zones contain
  matter enough for several
• planets like Jupiter or Saturn.
• Several stopping mechanisms are possible
• Dissipation and/or photoevaporation of the SN (
  Safronov, 1969, Shu, 1982)
• Pulsational instability of the outer regions of
  the envelope
• Slowing down of the accretion efficiency due
  overheating of the envelope (runaway growth of
  outer planetesimals accretion due to planetary
  migration)
• Tidal confinement of the feeding zone and
  formation of a gap gas depleted around the
  protoplanet

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Evolution of Giant Planets
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• The way to the present state, asoon as the
  gaseous envelope has been accreted, is stillo
  long for a giant planet
• Giant planets, in their primordial evolutive
  phases, coexist with the disk where they have
  been born.
• At the same time, several planets already formed
  can mutually interact
• The central star is still not in Main Sequence
  and can be strongly active (bipolar flows,
  T-Tauri wind)
• The evolution of the young planet is so
  characterized by cooling and contraction of its
  envelope, and orbital changes that eventually
  drive it into the atmosphere of the star or
  towards the interstellar space

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Gap formation

• Papaloizou and Lin (1984) and Bryden et al.(1999)
  have firstly proposed that the accretion could be
  stopped by the formation of an annular gap that
  surrounds the orbit of the protoplanet, where the
  gas is strongly depleted and the accretion slowed
  for several orders of magnitude.
• Later on, the problem of gap formation has been
  examined by several authors (Artymowicz and
  Lubow, Winters et al., for example),
  investigating which the constraints about the
  main physical parameters (mass, density, thermal
  transport, turbulence) of the gas disk and of the
  growing planet that can produce the onset of a
  nearly gas free region around the protoplanet

From Bryden et al., 1999
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Interaction planet-disk

• Tidal interaction of a planet with the disk
  leads to the formation of spiral density
  perturbations that, because of the differential
  rotation, lead the planet in the inner region,
  and trail it in the outer region. Inner disk
  loses and outer disk gains angular momentum.
• Thus, the planet can progressively deplete of
  gas and solid matter an annular region along its
  orbit.
• The angular momentum exchange is asymmetric
  and the net balance can produce a torque that
  usually drives the planet to migrate inward.

Coradini and Magni, 2004
- There is a strong connection between planet
migration, gap onset, physical and
thermodynamical conditions inside the
protoplanetary disk, and evolutive history of the
central star, that strongly influence the
evolution of the Giant Planets (see extrasolar
planets)
Lubow et al., 1999
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• If waves experience damping of any kind their
  energy and angular momentum get transferred to
  the disk fluid disk evolves
• The dissipation takes place in the farther
  branches of the density waves, where non-linear
  growth holds and shock phenomena can be active
• Dissipative mechanisms can be turbulent viscous
  shear or radiative cooling of the fronts of the
  waves, heated by gas compression .
• Both the cooling process and viscous dissipation
  are scarcely efficient in the linear region of
  the wave, but can produce a significant
  transport of energy and angular momentum along
  the nonlinear branches
• Turbulent viscosity is difficult to describe in a
  correct way because it is difficult to find and
  correctly describe the energy source that feeds
  it (convection, MHD instabilities, gas-dust
  interface). The most common way to model it is
  through the a-parameter of the Shakura-Sunyaev
  model

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Feedback mechanisms

• - In an inviscid disk the characteristic
  timescales of gap opening and tidal migration are
• - While planetary torques repel disk away, planet
  might migrate out of the forming gap. This is
  important for small planets
• - Feedback from the surface density
  inhomogeneities slows the migration facilitating
  gap opening (Ward Hourigan89) but the non
  conservation of vertical hydrostatic equilibrium
  near the edges of the gap fills the gap.
• - Viscosity opposes gap formation by filling the
  gap
• The theory of gap opening requires that three
  simultaneous effects have to be considered
  simultaneously
• Realistic density wave damping
• Planetary migration
• Contribution of feedback mechanisms

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Important timescales

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Gap formation in an inviscid disk
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Numerical models
From Balbus et al.,2003
From Bryden et al.,1999
From Trilling et al.,1999
Numerical models have studied with sophisticated
methods (SPH smoothed particles, 2D and 3D
hydrodynamics, MHD turbulence the process
gapmigration in the phase space of the physical
parameters governing them. While it is difficult
to give a direct correlation between a regular
system like our one and the rearrangement, driven
by the gapmigration process, of the primordial
planetary system (Bryden et al.,1999, Balbus et
al.,2003), the large variety of dynamical and
physical characteristics of extrasolar planets
well agree with the large spectrum of evolutive
patterns produced by this process (Tirring et
al.,1999)
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Migration driven by secular perturbations

• The dynamical evolution of GP does not end when
  the first gas driven phase (gas and/or
  nucleated instability, gap formation and tidal
  migration) is exhausted due the dissipation of
  the SN gas, leaving a planetary system possibly
  quite different from that we know today. The
  rearrangement of the system can be produced
  again by interactions among solid bodies
  (planets residual planetesimals disk) with
  timescales of 106 108 years.
• All the models studyng this process are based on
  N-bodies numerical integrations, and choose a
  certain number of free parameters (number,
  masses, initial distances of planets, mass and
  structure of the planetesimals disk, number of
  objects contained inside) that are varied in
  order to obtain the best representation of the
  present Solar System and of some dynamical
  parameters.
• The agreement between the numerical planetary
  system and the present is generally good, but
  often the initial values of free parameters are
  not sufficiently justified by reasonable
  hypotheses

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• Thommes et al. (1999)
• The authors assume that, starting from a system
  of four or five protoplanets placed between the
  present orbits of Jupiter and Saturn, plus an
  external planetesimal disk, it is possible to
  explain the actual position of Uranus and Neptune
  and their depletion of H and He.
• Uranus and Neptune migrate from the initial
  position, between Jupiter and Saturn distances,
  and circularize their orbits owing to
  interactions with the planetesimals disk.
• Jupiter and Saturn can firstly accrete the gas
  envelope, gain mass being able to scatter the
  orbits of the other protoplanets (or eject them
  outside the SS).
• The model can explain the morphology of the
  Kuiper Belt and of the scattered disk
• The most questionable assumption of this model is
  the initial position of the cores in a very
  narrow belt (5-10 AU). What happened in the outer
  regions?

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The best run
Integration time t5 106 years At t0 rJ5.3
AU rS9 AU rC16.35 AU rC27.6
AU Planetesimals disk 10 AU lt r lt 60 AU At
t5 106 yr rJ4.9 AU rS10.2 AU rC119.7
AU rC231.1 AU
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• Morbidelli et al. (2005)
• A planetary system with initial quasi-circular,
  coplanar orbits would have evolved to the current
  orbital configuration of the SS, provided that
  crossed their 12 orbital resonance.
• This resonance crossing could have occurred as
  the GP migrated due their gravitational
  interactions with a planetesimals disk.
• The four planets start with their present mass.
  The initial positions of Jupiter and Saturn are
  forced to be close to their 12 resonance
• The (hot or cold) disk of planetesimals has a
  total mass of 10-50 MEarth and is composed of
  1000-5000 bodies
• During migration, the eccentricities and mutual
  inclinations of the planets are damped by their
  gravitational interaction with the disk of
  planetesimals (dynamical friction).
• The crossing of the resonance 12 causes a sudden
  jump on eccentricities and inclinations of
  Jupiter and Saturn has a drastic effect on the
  whole planetary system.
• The final orbital configuration depends on the
  planetary configuration immediately after the
  resonance crossing

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• Results
• Explorating with several simulation the phase
  space of the initial parameters of the planetary
  system, the best runs seem to reproduce the
  most important chacteristics of the giant planets
  orbits, namely final semimajor axes,
  eccentricities and mutual inclinations.
• The survivability of the regular satellites of
  Jupiter and Saturn is assured during their close
  encounters (rltRHill), but not that of the
  irregular satellites. This give a constraint on
  the time of theit capture.
• The model can explain the Late Heavy Bombardment
  (700 My after the planets formed. This was due
  both to the rapid migration of the planets, that
  destabilized the outer disk of planetesimals, and
  to the strong perturbation of the asteroid belt
• The orbital characteristics of the Jupiters
  Trojan asteroids can be explained if they were
  captured during a short period of time, just
  after the crossing of the 12 resonance, when the
  dyinamics of the Trojan region was chaotic

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• The model of Morbidelli et al. finds in a very
  brilliant way very well a channel in the space of
  the possible evolutive histories, through which
  we can reach a very satisfactory agreement with
  the present SS. The problem is their initial
  planetary system is realistic?

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• A new model origin of the large eccentricities
  of extrasolar planets (Namouni, 2005)
• The existence of phases of continuous
  acceleration due to mass loss (asymmetrical
  bipolar jets or winds from protoplanetary disks)
  can explain many of the peculiarities of the
  orbital parameters of extrasolar planets (higly
  scattered in eccentricities and semimajor axes)
• Two modes of eccitation of eccentricities are
  possible secular, for planets closer to the
  star, and star acceleration smaller than
  gravitational acceleration of the companion, and
  sudden, at large distances, when the two
  accelerations are comparable.
• Depending on the duration, direction and time
  dependence of the acceleration, not only large
  eccentricities can be excited, but also inward
  migration and ejection (in multiplanet systems)
  
• In multiplanet systems the distribution of final
  eccentricities can give constraints on the
  parameters of the acceleration processes
  (duration and alignment) and also on the physical
  mechanism producing it.
• The Namouni model starts from a known physical
  process, that can be utilized in reasonable
  conditions in order to explain a large variety of
  orbital characteristics of extrasolar planets

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• I modelli di evoluzione planetaria con
  modellizzazione contemporanea gapmigrazionepertu
  rbazioni secolari riescono a render conto di
  tutta una serie di evidenze osservative,
  intervenendo sui parametri fisici (massa ed
  evoluzione termica del disco, entità dello shear
  viscoso, popolazione di planetesimi) che
  governano il fenomeno. Più difficile è adattare
  il modello ai singoli sistemi planetari. Poiché
  ci sono ancora molte incertezze nella
  modellizzazione, linversione dai dati
  osservativi ai parametri base dei modelli non è
  facilmente praticabile.
• Le probabili grandi differenze nelle condizioni
  iniziali e nelle storie evolutive dei vari
  sistemi planetari fin qui osservati è comunque in
  accordo con la grande varietà di situazioni
  osservate, che sarebbe probabilmente ancora più
  grande se non ci fosse leffetto della selezione
  osservativa.
• La migrazione planetaria deve avere
  verosimilmente unincidenza molto diversa. Certi
  sistemi planetari possono essere completamente
  spariti cadendo sulla stella centrale, mentre il
  altri, come il nostro, le perturbazioni sono
  state soltanto un effetto secondario