Annual Report 2011 Max Planck Institute for Astronomy

ection and migration rate depends on the radial
slopes of the temperature and the gas surface density.
A good compromise for the numerical description
of the disks (which are in reality very complex,
3D-structures driven by magneto-hydrodynamical
processes) is provided by α-models, which describe
the disk as a rotating, viscous fluid which has an axisymmetric
structure.
2. A structure and evolution model for disk of solids.
This model yields the size, dynamical state and surface
density of the solid content of the disk. The
solids are initially in the form of dust. This dust
can grow in mass to form kilometer-sized planetesimals,
but also get destroyed again in collisions.
Additionally, they drift through the disk. These quantities
are used to calculate the accretion rate of solids
of the forming protoplanets.
3. An internal structure and evolution model of the
planet. This model calculates the internal, 1-D radial
structure of the interior of the planet. Both the solid
part and the gaseous envelope of the planet are considered.
The solid core is assumed to be differentiated
and consist of layers of iron, silicates, and if the
planet accreted outside of the snow-line, ices. For the
gaseous envelope, only primordial H/He envelopes
have been considered to date. During the formation
phase, the model calculates the amount of gas a core
can bind gravitationally. Low mass cores can only
bind tenuous atmospheres, while cores more massive
than roughly 10 Earth masses can trigger rapid,
runaway gas accretion, so that a giant planet forms.
After the formation phase, at constant mass, the temporal
evolution i.e. the contraction and cooling is calculated,
which yield radius and intrinsic luminosity
of a planet.
4. The last module addresses the various interactions
occurring during the formation process. These interaction
and feedbacks are in large parts responsible
for the complexity of the planet formation process.
Various interactions have to be modeled:
a) the interaction of the planet and the disk of solids
(planetesimals). The growing protoplanets not
only accrete planetesimals, but also influence their
dynamical state in terms of eccentricity and inclinations.
b) the interaction of the planets and the gaseous disk.
Due to gravitational interactions, the gaseous disk exerts
torques onto the planets, which causes them to
undergo radial migration. This orbital migration is
important in shaping the architectures of planetary
systems.
c) the interaction of the solid and the gaseous disk.
The drag felt by planetesimals causes the smaller bodies
to drift inwards. The temperature structure of the
gaseous disk also determines where in the disk which
solids can condensate, which in the end influences the
composition of the planets.
III.1 Planetary population synthesis 43
d) the interaction among planets. When several protoplanets
form in vicinity, they influence each other via
gravitational interactions. This can pump the eccentricity,
lead to scattering events and even ejections of
planets out of a planetary system. Migrating planets
can get caught into mean-motion resonances, which
can for example cause the outward migration of giant
planets.
e) the interaction between the planets and the star.
Planets at small orbital distances are subject to intense
stellar irradiation. This irradiation modifies the internal
structure of the planets, which affects their evolution.
The intense irradiation can also cause planets to
loose parts of their gaseous envelope.
f) the interaction between the star and the gaseous
disk. The temperature structure of the gaseous disk is
strongly influenced by the stellar radiation. The hard
radiation by the star drives the internal photoevaporation
of the disk, which is important for the lifetime of
the disks. Close to the star, the magnetic field of the
star can lead to the formation of a magnetospheric
cavity, which can halt migrating planets.
For the different processes, already relatively well established
physical descriptions are employed if possible.
Some simplifications are necessary (e.g. for computational
time restrictions), so that the global models rely
on the results of models and theoretical studies which focus
on one single aspect. In order to validate the models,
dedicated simulations are made which focus on relatively
well known individual planetary systems, in particular
the Solar System. But also some extrasolar systems
are studied individually, like for example the Kepler-11
system with at least six extrasolar planets, for which both
the masses and the radii are known.
The global formation models should output as many
observable quantities as possible, since in this case, one
can use combined constraints from many techniques.
The outputs should be: the mass, the orbital distance and
the eccentricity (for comparison with radial velocity and
microlensing results), the radius (which is a proxy for
the bulk composition) for the comparisons with transit
observations and the intrinsic luminosity for comparison
with discoveries made with direct imaging.
An exemplary output from the global formation model
used in the population synthesis calculations is shown
in Fig. III.1.3. It shows formation tracks in the mass-distance
plane. Planetary embryos are inserted at a given
starting semimajor axis into protoplanetary disk of varied
properties with an initial mass of 0.6 Earth masses.
They then grow by accreting planetesimals and gas, and
concurrently migrate due to the interaction with the gas
disk. The distribution of the final positions of the planets
(at the moment the protoplanetary disk goes away)
is eventually compared with the observed mass-distance
distribution (Fig. III.1.1). One can see that the outcome
of the formation process is of a high diversity, despite