Annual Report 2011 Max Planck Institute for Astronomy

46 III. Selected Research Areas
R [R Earth ]
15
10
5
0
Kepler–18d
Kepler–9b
Kepler–9c
Kepler–11e
Uranus
Kepler–11d
Neptune
Uranus
Neptune
Kepler–11f
Kepler–10c
Kepler–11c
Fig. III.1.6: Mass-radius diagram of synthetic planets with a
primordial H/He envelope at an age of 5 Gyrs together with all
planets in- and outside of the Solar System with a known mass
and radius, and a semimajor axis of at least 0.1 AU (as in the
model). The colors indicate the fraction of heavy elements in
it adds constraints that go beyond the position of a planet
in the mass-distance plot. Fig. III.1.6 shows a comparison
of the observed mass-radius relationship of actual
and synthetic planets as found in a recent population
synthesis calculation. These calculations do not only
model the formation of the planets, but also their evolution
once the protoplanetary disk has disappeared. The
global shape of the planetary mass-radius relation can
be understood from the core accretion paradigm, and the
basic properties of matter as expressed in the equations
of state: Low-mass planets can only bind tenuous H/He
envelopes, since their Kelvin-Helmholtz timescale for
envelope contraction during the formation phase is long
compared to the typical lifetime of a protoplanetary disk.
Therefore, the top left corner in the M – R plane remains
empty, as no low-mass, gas-dominated planets come into
existence. Also the bottom right corner remains empty.
This is due to the fact that massive cores necessarily
cause rapid runaway gas accretion, so that their composition
is dominated by envelope gas. No massive, solid
dominated planets come into existence that would populate
the bottom right corner. One notes that the synthetic
and most actual planets populate the same location in the
mass-radius plane.
10
CoRoT–9b
Saturn
10 2
M [M Earth ]
Jupiter
HD 17156b
HD 80606b
CoRoT–10b
KOI–423b
10 3 10 4
Credit: C. Mordasini
the synthetic planets. The black symbols (bottom) for example
correspond to solid-dominated low-mass planets which contain
at most 1 % of H/He, while the most massive planets (orange,
top) consist of at least 99 % H/He.
From the position of a planet in the mass-radius relationship,
it is possible to deduce (within some limits due
to degeneracies) the bulk composition of a planet. This
is due to the fact that for a given total mass, planets with
a higher fraction of solid elements (iron, silicates, and
possibly ices) relative to H/He have a smaller radius.
The plot shows that depending on the mass range, there
are many different associated radii, reflecting a large diversity
in potential interior compositions. These different
compositions are in turn due to the different formation
histories. It is for example found that planets at large
distances typically contain a higher fraction of solid elements,
since the mass of planetesimals available to accrete
(the isolation mass) increases for currently accepted
disk models with distance.
The interior structure of a planet also varies depending
on the place where it has accreted matter. Planets that
accrete mainly outside of the ice line will contain large
amounts of ices. This leaves traces in the bulk composition,
and possibly also in the atmospheric composition.
Future global models of planet formation and evolution
should therefore include detailed descriptions for the
(chemical) composition of planets, and consider for example
also other envelope types than just primordial H/