Geoscience Reference
In-Depth Information
25000
Fig. 9.4 Density profiles for massive Earth-like
planets. The composition of the planets shown is
similar to that of the Earth (33% iron core, 67%
silicate mantle with 0.1 of iron by mol).
A1M E -planet structure (blue) is almost
indistinguishable from that of Earth as inferred by
the Preliminary Reference Earth Model (dotted black)
(Dziewonski & Anderson, 1981). The discontinuities
in the curves are due to increases in density in the
mantle from phases transitions, from the boundary
between the mantle and the core, and the phase
transition between the outer core and inner core for
the 1 M E
20000
15000
10000
5000
...
1M
2M
10M
0
0
2000
4000
6000
8000
10000 12000
Radius (km)
planet case.
In addition, an equation of state (EOS) relating
density and entropy to pressure and tempera-
ture is needed. It is required to choose a priori
a composition for the planet, reflected in the
EOS implemented in the code. The end result is
a relation between planetary radius R ,mass M ,
composition X , and in the case of gaseous plan-
ets also age t , R
(see Figures 9.5 and 9.6). For compositions that
are solid, the temperature changes very little the
M-R relationships, while for compositions with a
volatile envelope, temperature has a large effect
on the radius, more pronounced for hydrogen (H)
and helium (He) but still important for H 2 Oen-
velopes (compare the blue lines corresponding to
H 2 O on Figures 9.5 and 9.6).
R ( M , X , t ), as well as all the
properties as a function of radius. Figures 9.4 and
9.5 show the density and pressure-temperature
profiles for rocky super-Earths. Indeed, one dif-
ference between the internal structure models of
solid and gaseous planets is that the latter needs
to account for a thermal evolution history. After
a planet forms, it cools and starts contracting. In
the case of solid planets this contraction is neg-
ligible in terms of the total radius of the planet,
while for gaseous planets the radius can change
by a factor of 2 within a few billions of years.
One limitation of all the models is that EOSs are
routinely extrapolated beyond the experimental
range. In particular, the pressure regime of super-
Earths (up to a few TPa, see Figure 9.4) is either too
high for empirical (experimentally determined)
EOS such as the Birch-Murnaghan EOS, widely
used for fitting experimental data, or too low for
the theoretical EOS valid at high-pressures (e.g.
Thomas-Fermi Dirac EOS) (Valencia et al ., 2009).
The procedure to infer the composition of an ex-
oplanet given its mass and radius is to test all the
compositions that can match the data. In practical
terms it means situating the data on a diagram
with different mass-radius relationships for the
different representative compositions considered
=
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10M
6000
5000
4000
1M
3000
ppv+mw
2000
pv+mw
ol+py
wd
+rw
+py
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0
0.01
0.1
1
10
Pressure (Mbar)
Fig. 9.5 Pressure-temperature structure of massive
Earth-like planets. The composition of the planets
shown is similar to that of the Earth (33% iron core,
67% silicate mantle with 0.1 of iron by mol). The
different mineral phases considered and their
boundaries (dashed lines) are shown: ol (olivine), py
(pyroxene), wd (wadsleyite), rg (ringwoodite), pv
(perovskite), mw (magnesiowustite) and ppv
(post-perovskite). The discontinuities in the curves are
due to boundary layers at the top and bottom of the
mantle where heat is conducted out, throughout the
rest the profile is adiabatic.
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