Formation, structure and evolution of the Giant Planets

1
Formation, structure and evolution of the Giant
Planets

• G.Magni

2
Internal structure of the Giant Planets
Giant planets store in their inner zones many
answers about the problems about the primordial
Solar System They are also natural
laboratories where make experiments outside on
high pressure physics (equation of state of high
pressure partially degenerate matter, phase
transitions, gas opacity, immiscibility and
sedimentation processes, magnetohydrodynamics)
3

• Physical parameters of the GP interiors

4
start
start
The internal structure of GP changes, during the
final evolutive phase, from a polytropic not very
far to perfect gas conditions, to a state with
high pressure thermodynamics of a H-He plus
ionized metals mixtures (Jupiter and Saturn) or
heterogeneous regions with remixing of volatile
and refractory components (Uranus and Neptune)
start
5
Magnetic field

• Jupiter and Saturn have very strong magnetic
  fields, closely aligned with the planets spin
  axis, and large magnetospheres
• The magnetic field of Uranus and Neptune are
  weaker, irregular and highly tilted with respect
  to the planets spin axis
• 
  J S
  U N
• Mean equatorial magnetic field(gauss) 4.28
  0.22 0.23 0.14
• Magnetic moment/MM(Earth) 20000
  600 50 25
• 
  (liquid metallic H)
  (H2O,NH3,CH4 ocean?)
  
• The periodic variation of the magnetic field
  gives us information on the true rotation of GP

6

• Heat sources

Accretion of material during the formation of
planets is likely the main source of primordial
heat The radiation flux coming from inside is
(except Uranus) comparable or larger than that
coming from the Sun, reflected or thermalized
7
Energy transport
The envelopes can mantain convective transport,
except in the subatmospheric region, when opacity
drops out (Guillot et al., 1994) and can be
considered largely adiabatic
8

• The internal heat source of GP comes from
  gravitational energy, either from gradual escape
  of primordial heat generated during the planets
  formation, and/or from previous or ongoing
  differentiation
• The excess of luminosity of Jupiter is consistent
  with an energy release due to accretion/contractio
  n dtcirca
• For Saturn, the primordial heat alone is not
  sufficient to explain excess heat
• For Uranus, the excess heat is extremely low,
  and also for Neptune the temperature drop from
  the initial temperature deducible by the heat
  equation is too low (200K) and inconsistent with
  the model of formation.

9

• Uranus has an excess heat extremely low, and
  also for Neptune the temperature drop from the
  initial temperature deducible by the heat
  equation is too low (200K) and inconsistent with
  the model of formation.
• For both the planets the convective transport
  must have been less efficient, at least in the
  external regions (rgt0.5 0.6 Rp)
• This could be due to strong gradients in chemical
  composition that can inhibite convection, but
  not in the mantle, in order to allow dynamo
  mechanism for magnetic field to be active. .
• The main differences between the two external
  planets seem to be the different extent of mixing
  of the constituents (Uranus, last impact oblique?
  less mixed Neptune, last impact frontal? more
  mixed)

10
(No Transcript)
11
Presence and mass of the core

• If a core is or not present in GP is one of the
  crucial questions that connects together
  formation, evolution, chemistry and internal
  structure of the planets.
• Large mass cores (10-30 MEarth) favour the
  nucleated instability formation mechanism
• Cores with small mass or nonexistent require some
  mechanism of depletion or complete melting in
  order to mantain the N.I. mechanism
• How much are GP differentiated?

12
adiabatic
isothermal
(nlt1, electronic degeneracy)
ad
is
(From Stevenson, 1982)
RSaturn lt RJupiter ? presence of a
core RUranus, RNeptune ltlt Rgas ? small envelope,
ice rich
13
Presence of a large core in a planet formed by
gas instability requires an higher enrichment by
planetesimals capture (part of the primordial
refractory elements must be used to form the core
and deplete the envelope) and time enough to
sedimentate them up to the center.
14
Equation of state

• The pressure-temperature profiles of the Giant
  Planets pass through a region of the hydrogen
  phase diagram where are present together thermal
  and pressure dissociation and ionization of
  hydrogen molecules and atoms.
• At the same time, the equation of state of helium
  is strongly far from perfect gas conditions, and
  high atomic weight elements give their contribute
  with a large amount of free electrons
• Theoretical calculations of the equations of
  state are difficult and strongly computer time
  consuming (Montecarlo simulations)
• In the last years, many progresses have resulted
  from the combination of experiments and
  theoretical studies

15

• One of the main open problems is a satisfactory
  treatment of H-Hehigh A.W.elements. The H-He
  mistures are generally treated interpolating
  between results on pure elements, but the volume
  additivity
• is not well applicable at extreme pressures
• In a recent work (Militzer, 2004) it is developed
  a Montecarlo simulation on a many body quantum
  system in order to define the thermodynamics of a
  H-He mixture(e,H and He nuclei), without the
  assumption of volume additivity. Chemical bonds,
  neutral and ionized atoms are found and
  classified during the simulation during the
  simulation.
• The Author finds discrepancies, for pressure
  values, of about 5-10 in case of pure elements
  , and a maximum error due the volume additivity
  assumption of 10

16
Opacity
The opacity is perhaps less important, but it can
influence the structure of the subatmospheric
regions of the envelope (Guillot et al.,1994).
A drop of opacity allows to a radiative layer to
exist in the outermost layers and modify the
thermal properties and the structure of the
planets (cooler interiors and slightly larger
cores)

The depth of the radiative layer depends
critically on the equation of state and on H2 and
alkali opacity at pressures of 10-100 kbar This
seems in any case to be only a minor effect on
the global thermal evolution, that is
essentially governed by convective transport
17

• There are several possible departures from
  adiabaticity in GP interiors
• Near the planet cores, if conduction by
  degenerate electrons becomes important
• In the region at 1 Mbar, where helium can become
  insoluble in hydrogen
• At the molecular-metallic transition of hydrogen
• At P1 kbar, if alkali metals are strongly
  depleted
• In the meteorological layer (P0.4-40 bar, for
  water condensation

18
State of the art of the Equation of state (2002)
From Hubbard, Fortney and Lunine, 2002)
19

• A general model of EOS that can determine
  thermodynamical properties of H-He
• mixtures in a diagram P-T large enough for GP is
  still not at present available
• Several regions of the diagram P-T are covered by
  interpolations between theoretical
• models and experimental data on intermolecular
  forces and shock experiments
• The adiabats of Jupiter and Saturn cross two
  critical zones of the diagram - the
• phase transition liquid ( H2 ?H) and the
  immiscibility region of helium
• The transition H2(liquid)?H2(solid) and
  H(liquid)?H(solid) are better
• treated with theoretical models
• The transition H2?H presents discrepancies
  more than an order of
• magnitude between two current models (Saumon et
  al,1995 and Ross et
• al.,1998) and there is the question if it is a
  transition of order I or II, smooth or
• discontinuous. The location and the extension of
  the transition zone influences
• the miscibility and the distribution of helium
  and other minor components, and
• convective transport.

20
Helium precipitation

• The possibility that helium might have limited
  miscibility in fluid hydrogen (Salpeter, 1973)
  has very important consequences on the evolution
  of GP
• A study of the properties of H-He mixtures based
  on free-electron perturbation (not really
  satisfactory for helium) theory finds a three
  bands behaviour of the Helium miscibility, with
  maximum mixing values of 0.248, 0.21 and 0,
  respectively. The Jupiter-Saturn adiabats pass
  very close, and possibly intersect the transition
  , making possible He precipitation as He-rich
  droplets, at the upper boundary of the H zone
• More recent treatments (Klepeis et al., 1991,
  Pfaffenzeller, 1995) find very different
  results an enlarged and deeper immiscibility
  zone that supports thisprocess in Jupiter and
  Saturn, and on the contrary a shifted down that
  falls outside the adiabats of the planets

From Hubbard et al.,2002
Conrath Gautier (2000), revisiting Voyager
measurements, find helium abundances
(0.18ltYlt0.25) nearer to the present solar values.
In this case, the Saturn heat excess would
require another internal source
21
Thermal evolution of Jupiter and Saturn
crosses isolated planets
black dots Teff(Sun)constant
open circles Teff(Sun)time
dependent
From Hubbard et al., (1999, 2002)
The general cooling theory of Hubbard et
al.(1999) works very well for Jupiter and the fit
with the present state is independent on the
uncertainties for the H-He phase separation For
Saturn, the evolutive time is too short and a
source of thermal energy has to be found
(dY0.07, Hubbard et al.,1999)
22
Equation of state (EOS)
23
High pressure equation of state (2004)
Saumon and Guillot (ApJ,1999-2004)
24
Quantum Montecarlo computations of HHe EOS (end
of 2004)
Militzer (2004) The EOS is computed on a quantum
many-body system at nonzero temperature with
Montecarlo tecniques. The mixture of H and He is
represented by an ensemble of electrons, protons
and helium atoms. During the Montecarlo chain are
found and classified molecular bonds, neutral and
ionized states. The comparison with the EOS of
Saumon et al (1994) reveals a maximum discrepancy
of 10 in pressures and a failure of the volume
additivity assumption as well of 10
25
Optimized internal models

• The internal structures of Jovian planets can be
  inferred indirectly from their global
  characteristics
• The gravity field
• Where the gravitational momenta Jn can be
  measured during spacecraft flybys together with
  radio science tecniques

26

• The equation of state,defined by theoretical
  models constrained by high pressure experiments
• The internal rotation state, derived by
  nonthermal emission and magnetic field measures
• Boundary conditions, as mass, radius, thermal
  emission
• Some assumptions about structure and chemical
  composition
• If the number of parameters is not too large, the
  observational constraints can close the system of
  equations of the unknown terms of the density
  profile
• The informations on gravitational momenta and EOS
  are complementary knowledge of few
  gravitational momenta requires a good model for
  EOS, and viceversa (radio determination of Js of
  high order in the Cassini mission)

27

• Hubbard and Horedt (1983), and Hubbard and Marley
  (1989)build the first optimized models, based on
  J2,J4,J6 values for Jupiter and Saturn, and J2
  and J4 values for Neptune deduced by Voyager
  flybys.
• The cores, in HM model, exist and are compatible
  with the nucleated instability model, but are too
  dependent on a still uncertain equation of state

28

• Saumon and Guillot (2004), using the same set of
  Jns coming from Voyager data, but using refined
  EOS and new deuterium shock data, take on a deep
  examination of how the uncertainties in the EOS
  map into uncertainties in the internal structure
  of Jupiter and Saturn

29
(No Transcript)
30

• - Thermodynamical uncertainties directly
  propagate on global characteristics of the
  planets as core mass and
• thermal cooling timescales
• EOS that best fit with experimental shock data do
  not allow a good fit with observational data
  (short cooling timescales for Jupiter)
• The dispersion of the values of the core masses
  is still too large, particularly for Jupiter, to
  give a clear representation of the first phases
  of the core instability process
• It is necessary to have together best data on the
  gravitational moments from space missions and
  best equations of state in order to have a jump
  in quality of our knowledge of the interiors of
  the giant planets