Geoscience Reference
In-Depth Information
of their atmospheres through low-resolution spec-
tra (Richardson
et al
., 2007; Swain
et al
., 2008,
to name a few) that tell us about their compo-
sition, thermal emission (Demory
et al
., 2007;
Charbonneau
et al
. 2008; Guillon
et al
., 2010, to
name a few) that tell us about their temperature,
and phase-curves (Knutson
et al
., 2007, Borucki
et al
., 2010, to name a few) that tell us about the
dynamics. While it is still a challenge to make
these observations for planets that do not possess
a massive atmosphere, telescopes are being de-
signed for this purpose. In fact, for one low-mass
planet already, GJ 1214b, a low-resolution spec-
trum has been obtained that has raised questions
about the composition of its atmosphere.
the ''super-Earths'' (mostly solid exoplanets) and
the gas-giants, it is important to keep in mind
that these properties lay in a continuum and not
on either side of one single mass-value threshold.
Out of these 10 planets with masses below
10 M
E
, only four have radii smaller than 2 R
E
,
which is the threshold that the Kepler team uses
to distinguish the super-Earths (radii between
1.3and2R
E
) from planets with an envelope of
volatiles, termed mini-Neptunes (radii between
2and6R
E
). Table 9.2 shows the characteristics of
the low-mass planets with the highest densities,
and their masses and radii are shown in Figure 9.3
(color coded by equilibrium temperature). How-
ever, to clearly assess the nature of a planet,
especially whether or not it has a substantial en-
velope, it is essential to conduct a careful analysis
of its composition and internal structure from its
mass and radius. Below we describe such models.
9.3
Composition of Planets
The first step towards characterizing a planet
is to learn about its composition. It is how we
learn about its nature and origin. Planets are
built from accretion of planetesimals (the initial
rocky/icy seeds of planet formation) that grow
to Mars size bodies and then beyond through
giant impacts, followed by gravitational accre-
tion of hydrogen and helium gas if any is still
present (Savronof, 1972). Thus, composition of a
solid planet reflects the initial chemical inven-
tory of the planetesimals that inherits the solar
nebula composition, plus any secondary forma-
tion processes such as giant planet collisions and
atmospheric evaporation.
As of April 2012, there have been 10 discover-
ies of planets with masses below 10 times that
of the Earth. This value of 10 M
E
is suggested
by theoretical models (e.g. Ida & Lin, 2004) to
be the threshold above which planets start ac-
creting substantial amounts of gas from the solar
nebula in a process called runaway gas accretion.
This suggests that planets that do not reach this
mass will not become gas giants. The exact mass
value for rapid accretion to take place, ending
in a gaseous planet, depends on the local condi-
tions of the protoplanetary disk (Rafikov, 2004).
Therefore, while using 10 M
E
is a convenient and
somewhat justified limit to distinguish between
9.3.1 Internal structure models
The methodology for an internal structure model
is to solve the structure equations for density
ρ
, pressure
P
, gravity
g
,mass
m
, temperature or
entropy as a function of radius
r
for a given plan-
etary mass. These can be either in differential
or integral form. Most exoplanet structure mod-
els integrate the differential equations from the
surface inwards. The following equations are one
example (Valencia
et al
., 2006),
ρ
2
(
r
)
g
(
r
)
K
s
(
r
)
dρ
dr
=
dp
dr
=−
ρ
(
r
)
g
(
r
)
dm
dr
=
4
πr
2
ρ
(
r
)
dg
dr
2
Gm
(
r
)
r
3
=
−
4
πGρ
(
r
)
(9.1)
where
K
s
is the adiabatic bulk modulus and
G
is the gravitational constant. For the rocky
planets the equation for temperature (not shown
here) usually reflects an adiabatic interior and a
conductive behavior at the top and bottom of the
mantle.
