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Ge 131
Chapter One
Motivation and Cosmochemical Background
Why study Planetary Interiors?
This is an area of science that has very few practitioners yet an importance
out of proportion to the numbers who study it. The reasons for its importance
are fourfold:
(1) It provides the explanatory basis for many phenomena that arise within a
planet (but have external manifestation). You can’t understand why certain
planets have volcanoes, why some planets have magnetic fields (and others do
not), and why Jupiter emits as much heat as it does without an understanding
of the insides of these bodies.
(2) It provides an essential part of the understanding of phenomena and
processes that are not intrinsically internal to the planet. For example, you
cannot claim any understanding of the history of Mars’ atmosphere if you are
ignorant of likely outgassing rates or of how the sputtering of the atmosphere
is affected by a magnetic field that varies through geologic time.
(3) It provides a unifying story. If you want to build a story of how the
planet formed and evolved to the present state, this will depend mainly on
understanding the interior.
(4) It provides a testing ground for fundamental physics (theory and lab)
under “extreme” conditions. Much of the interest in metallic hydrogen stems
from its inferred presence in Jupiter (and the implication that it is the most
common metal in the universe).
How does a Planet differ From a Rock or a Cloud of Gas?
The answer lies not in the composition, but in the conditions the material is
subjected to. A planet differs from small amounts of the same material for
two reasons: (1) Effect of gravity, leading to high pressures and a change in
material properties. (2) Inability of the planet to eliminate heat except by
becoming very hot internally (close to or at melting point in the case of solid
planets; hotter still in gaseous planets because of adiabatic heating alone).
Gravity does work on planet-forming materials. This changes their internal
energy (by compressing them). The gravitational energy per particle is
~GMµ/R (where G is the gravitational constant, M is the planet mass, µ is the
mass of the atom in question, and R is the planet radius). If we replace M by
4πρ av R3/3, where ρav is the average density of the planet, then the
gravitational energy is of order 4πGµρav R2/3. A typical electronic energy is
~1eV. For rocky materials (like Earth) the gravitational energy per atom
exceeds 1 eV for a body exceeding about 3000km (about the size of Mars).
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Less dense, lower molecular weight materials may require larger bodies, but
as we shall, see smaller energies than those needed to break bonds can be
important. In practice, any object exceeding of order 1000km in radius has
interesting internal physics.
Planets differ fundamentally from stars because their internal energy is not
primarily thermal energy. Suppose we equated the gravitational energy to
thermal energy (as we would for a star). The predicted temperature would
then be ~104 K for a Mars sized body and 4 x 104 K for Earth. The actual
temperature is smaller by a factor of ~ten, at least for Earth. Another way of
saying this is that αT < 0.1, where α is the coefficient of thermal expansion.
Planets are degenerate. Indeed, this is part of the definition of a planet: Bodies
less massive than 0.08 solar masses never achieve hydrogen burning and cool
to a degenerate state (a brown dwarf or giant planet). Planets may be “cold”
in the sense that their thermal energies are small compared to electronic
energies, but they are not cold in the sense of being well below the melting
point or Debye temperature of relevant materials.
What are Planets made of?
The best way to answer this question is to “ask the planet”; which means
deducing planetary composition from its observed properties. In practice, this
often does not work that well even for Earth. We do not have direct
observational evidence that Earth’s core is mostly iron; it could be an alloy of
niobium (which can have similar density and compression properties). We
must appeal at least in part to cosmochemical arguments: What is abundant as
a planet forming material? These arguments are necessarily plausible rather
than rigorous but strong nonetheless, because of the large differences in
cosmic abundance among material of similar chemistry.
Cosmic abundances of elements are determined by nuclear physics.
Hydrogen overwhelms because it is an elementary particle; helium is also
abundant because it is stable and can be formed in the Big Bang era. Heavier
elements (what astronomers call “metals”) are formed in stars and then
ejected into the interstellar medium, where the material then becomes
available to form our solar system. Combinations of alpha particles (i.e.
multiples of 4 mass units with proton number equal to neutron number) are
very favorable at low mass and 4 alphas (oxygen) is especially favorable
because of nuclear shell structure. So oxygen is the next most abundant
element followed closely by carbon. Neon (five alphas) and nitrogen (not a
combination of alphas) follow somewhat behind. Things get more complicated
as one goes to larger masses, but magnesium, silicon and iron are particularly
favored by nuclear physics. Iron is the “endpoint” of equilibrium
nucleosynthesis in the sense that heavier nuclei are less stable than it. Cosmic
abundances can be estimated by observations of the interstellar medium and
other stars.
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Solar system abundances are determined from the solar photosphere. They
correlate well with the relative abundances of all but the most volatile
elements. CI chondrites ( “type one carbonaceous chondrites”), the most
primitive rocks in space, provide a guide to materials in the nebula from
which the planets formed. Of course, elemental abundances don’t tell you all
you want to know; one also needs to know the chemical form that the
materials take. Here is a complete list (the ppm and ppb numbers are mass
fractions)
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Here is a summary list, useful for understanding the most abundant elements :
Table 1: Solar system Abundances
Element
Number Fraction
Mass Fraction
H
He
O
C
Ne
N
Mg
Si
Fe
0.92
0.08
7 x 10 -4
4 x 10 -4
1.2 x 10 -4
1 x 10 -4
4 x10 -5
4 x 10 -5
3 x 10 -5
0.71
0.27
0.011
0.005
0.002
0.0015
0.001
0.0011
0.0016
One can also look at comets, though with far less accuracy (because we’ve
never had cometary material “in our hands” except in the form of
interplanetary dust particles, which have an uncertain relationship to bulk
composition).
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Of course, elemental abundances don’t tell you all you want to know; one
also needs to know the chemical form the materials take. To do this, one can
appeal to what is seen in the interstellar medium (which may survive partly
unaltered into comets and more distant planets).
Or one can look at meteorites themselves, but this is tricky since many
meteorites (even so-called “primitive” meteorites such as CI) have undergone
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processing, the details of which are poorly understood and might not
necessarily be the processing that took place by most planet forming
materials.
Or (as a last resort?) one can look at what equilibrium thermodynamics
predicts. This game is called “equilibrium condensation sequences”. It is done
in the context of imperfectly understood notions of what the nebular was
from which planets formed.
The game proceeds as follows: Take your expected elemental abundance and
specify a temperature and pressure. In the terrestrial zone, we might be
talking about T of order 1000K and P of order 10-4 bars (note how small this
especially since it means that the partial pressure of condensable materials is
orders of magnitude smaller). One then minimizes the Gibbs energy of the
system subject to all the degrees of freedom. This can be done for gradually
decreasing temperature to see what condenses out.
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(Taken from J. Lewis; all previous figs this chapter are from S. R. Taylor)
Simplistically, one could imagine using this as a guide to the composition of
planets. There are four pitfalls:
(1) Equilibrium thermodynamics may be irrelevant. This is certainly so at low
temperatures (the reactions don’t “go”; they are kinetically inhibited).
(2) Materials in a given zone of condensation need not necessarily be used at
that location to make a planet; mixing of materials may occur... this depends
on (imperfectly understood) aspects of the planetary formation process.
(3) Other chemistry may take place in the solid body precursors (“meteorite
parent bodies”) which alters the planet makeup.
(4) There might even be “physical sorting” (i.e. some material may survive
more readily in the planet accumulation process , depending on how easily
they are busted up in collision).Of course, this requires that some material is
completely lost (into the Sun; or out back to the interstellar medium).
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In any event, the speciation inside the planet will be at least partly determined
by the chemistry inside of the planet, regardless of the details of the materials
used to build the planet.
Examples of where the Nature of the Source Material may have Major
consequences for Planetary Structure:
(1) Suppose that the planet-forming material had lots of Fe but it was in
oxidized form (i.e. the iron reequilibrated with the nebula at below about
500K according to equilibrium thermodynamics). Then the planet might not
be able to form a metallic Fe core since the iron may remain in non-metallic
oxidized form. (It might still form a core of course, but not one that would be
necessarily metallic since FeO, for example, is an insulator, at least at low
pressures). Some of the oxidized iron may be reduced (e.g. by carbon).. this
may be important for the Galilean satellite cores. This issue of core formation
is an example of a compositional effect driven (in part) by the oxygen
fugacity of the system.
(2) According to elemental abundances, Mg/Si = 1.07. This is close to
pyroxene composition (e.g. MgSiO3). Yet we think Earth’s upper mantle (and
perhaps entire mantle) is more predominantly olivine composition (Mg2SiO4),
which has a much higher Mg/Si ratio. Maybe something happened during
planet formation that decreased Si relative to Mg (e.g. partial evaporation?)
Or maybe there is Si in earth’s core?
Examples of where the Nature of the Source Material does not have
Major consequences for Planetary Structure:
(1) Oxygen may have accreted onto Jupiter as both H2O and CO. But CO is
not stable (relative to CH4) deep in Jupiter’s atmosphere, so the form that O
takes in this planet does not depend on the form in which it arrived. (The total
amount of water might of course be affected since water easily condenses,
CO does not easily condense).
(2) Water ice may accrete onto icy satellite in amorphous form but it will
revert to crystalline form under the action of both heating and pressure inside
the body (if it is large enough, e.g. Titan).