5 research outputs found
Hydrodynamics of embedded planets' first atmospheres - III. The role of radiation transport for super-Earth planets
The population of close-in super-Earths, with gas mass fractions of up to 10%
represents a challenge for planet formation theory: how did they avoid runaway
gas accretion and collapsing to hot Jupiters despite their core masses being in
the critical range of ? Previous
three-dimensional (3D) hydrodynamical simulations indicate that atmospheres of
low-mass planets cannot be considered isolated from the protoplanetary disc,
contrary to what is assumed in 1D-evolutionary calculations. This finding is
referred to as the recycling hypothesis. In this Paper we investigate the
recycling hypothesis for super-Earth planets, accounting for realistic 3D
radiation hydrodynamics. Also, we conduct a direct comparison in terms of the
evolution of the entropy between 1D and 3D geometries. We clearly see that 3D
atmospheres maintain higher entropy: although gas in the atmosphere loses
entropy through radiative cooling, the advection of high entropy gas from the
disc into the Bondi/Hill sphere slows down Kelvin-Helmholtz contraction,
potentially arresting envelope growth at a sub-critical gas mass fraction.
Recycling, therefore, operates vigorously, in line with results by previous
studies. However, we also identify an "inner core" -- in size 25% of
the Bondi radius -- where streamlines are more circular and entropies are much
lower than in the outer atmosphere. Future studies at higher resolutions are
needed to assess whether this region can become hydrodynamically-isolated on
long time-scales.Comment: 16 pages, 12 figures, accepted for publication at MNRA
Torque wiggles -- a robust feature of the global disc-planet interaction
Gravitational coupling between planets and protoplanetary discs is
responsible for many important phenomena such as planet migration and gap
formation. The key quantitative characteristics of this coupling is the
excitation torque density -- the torque (per unit radius) imparted on the disc
by planetary gravity. Recent global simulations and linear calculations found
an intricate pattern of low-amplitude, quasi-periodic oscillations in the
global radial distribution of torque density in the outer disc, which we call
torque wiggles. Here we show that torque wiggles are a robust outcome of global
disc-planet interaction and exist despite the variation of disc parameters and
thermodynamic assumptions (including -cooling). They result from
coupling of the planetary potential to the planet-driven density wave freely
propagating in the disc. We developed analytical theory of this phenomenon
based on approximate self-similarity of the planet-driven density waves in the
outer disc. We used it, together with linear calculations and simulations, to
show that (a) the radial periodicity of the wiggles is determined by the global
shape of the planet-driven density wave (its wrapping in the disc) and (b) the
sharp features in the torque density distribution result from constructive
interference of different azimuthal (Fourier) torque contributions at radii
where the planetary wake crosses the star-planet line. In the linear regime the
torque wiggles represent a weak effect, affecting the total (integrated) torque
by only a few per cent. However, their significance should increase in the
non-linear regime, when a gap (or a cavity) forms around the perturber's orbit.Comment: 19 pages, 15 figures, submitted to MNRA
Planetary population synthesis
In stellar astrophysics, the technique of population synthesis has been
successfully used for several decades. For planets, it is in contrast still a
young method which only became important in recent years because of the rapid
increase of the number of known extrasolar planets, and the associated growth
of statistical observational constraints. With planetary population synthesis,
the theory of planet formation and evolution can be put to the test against
these constraints. In this review of planetary population synthesis, we first
briefly list key observational constraints. Then, the work flow in the method
and its two main components are presented, namely global end-to-end models that
predict planetary system properties directly from protoplanetary disk
properties and probability distributions for these initial conditions. An
overview of various population synthesis models in the literature is given. The
sub-models for the physical processes considered in global models are
described: the evolution of the protoplanetary disk, the planets' accretion of
solids and gas, orbital migration, and N-body interactions among concurrently
growing protoplanets. Next, typical population synthesis results are
illustrated in the form of new syntheses obtained with the latest generation of
the Bern model. Planetary formation tracks, the distribution of planets in the
mass-distance and radius-distance plane, the planetary mass function, and the
distributions of planetary radii, semimajor axes, and luminosities are shown,
linked to underlying physical processes, and compared with their observational
counterparts. We finish by highlighting the most important predictions made by
population synthesis models and discuss the lessons learned from these
predictions - both those later observationally confirmed and those rejected.Comment: 47 pages, 12 figures. Invited review accepted for publication in the
'Handbook of Exoplanets', planet formation section, section editor: Ralph
Pudritz, Springer reference works, Juan Antonio Belmonte and Hans Deeg, Ed
Hydrodynamics of embedded planets' first atmospheres - III. The role of radiation transport for super-Earth planets
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Formation of a planetary Laplace resonance through migration in an eccentric disk
Context. Orbital mean motion resonances in planetary systems originate from dissipative processes in disk-planet interactions that lead to orbital migration. In multi-planet systems that host giant planets, the perturbation of the protoplanetary disk strongly affects the migration of companion planets.
Aims. By studying the well-characterized resonant planetary system around GJ 876 we aim to explore which effects shape disk-driven migration in such a multi-planet system to form resonant chains.
Methods. We modelled the orbital migration of three planets embedded in a protoplanetary disk using two-dimensional locally isothermal hydrodynamical simulations. In order to explore the effect of several disk characteristics, we performed a parameter study by varying the disk thickness, α viscosity, mass as well as the initial position of the planets. Moreover, we have carefully analysed and compared simulations with various boundary conditions at the disk’s inner rim.
Results. We find that due to the high masses of the giant planets in this system, substantial eccentricity can be excited in the disk. This results in large variations of the torque acting on the outer lower mass planet, which we attribute to a shift of Lindblad and corotation resonances as it approaches the eccentric gap that the giants create. Depending on disk parameters, the migration of the outer planet can be stopped at the gap edge in a non-resonant state. In other models, the outer planet is able to open a partial gap and to circularize the disk again, later entering a 2:1 resonance with the most massive planet in the system to complete the observed 4:2:1 Laplace resonance.
Conclusions. Disk-mediated interactions between planets due to spiral waves and excitation of disk eccentricity by massive planets cause deviations from smooth inward migration of exterior lower mass planets. Self-consistent modelling of the disk-driven migration of multi-planet systems is thus mandatory. Constraints can be placed on the properties of the disk during the migration phase, based on the observed resonant state of the system. Our results are compatible with a late migration of the outermost planet into the resonant chain, when the giant planet pair already is in resonance