34 research outputs found
Dynamical corotation torques on low-mass planets
We study torques on migrating low-mass planets in locally isothermal discs.
Previous work on low-mass planets generally kept the planet on a fixed orbit,
after which the torque on the planet was measured. In addition to these static
torques, when the planet is allowed to migrate it experiences dynamical
torques, which are proportional to the migration rate and whose sign depends on
the background vortensity gradient. We show that in discs a few times more
massive than the Minimum Mass Solar Nebula, these dynamical torques can have a
profound impact on planet migration. Inward migration can be slowed down
significantly, and if static torques lead to outward migration, dynamical
torques can take over, taking the planet beyond zero-torque lines set by
saturation of the corotation torque in a runaway fashion. This means the region
in non-isothermal discs where outward migration is possible can be larger than
what would be concluded from static torques alone.Comment: 14 pages, 13 figures, accepted for publication in MNRA
Growing and moving planets in disks
Planets form in disks that are commonly found around young stars. The intimate relationship that exists between planet and disk can account for a lot of the exotic extrasolar planetary systems known today. In this thesis we explore disk-planet interaction using numerical hydrodynamical simulations. We study the growth and migration of embedded planets, as well as the condition for gap formation in the disk. These planetary gaps provide an important link to future observations of circumstellar disks.UBL - phd migration 201
The formation of systems with closely spaced low-mass planets and the application to Kepler-36
The Kepler-36 system consists of two planets that are spaced unusually close
together, near the 7:6 mean motion resonance. While it is known that mean
motion resonances can easily form by convergent migration, Kepler-36 is an
extreme case due to the close spacing and the relatively high planet masses of
4 and 8 times that of the Earth. In this paper, we investigate whether such a
system can be obtained by interactions with the protoplanetary disc. These
discs are thought to be turbulent and exhibit density fluctuations which might
originate from the magneto-rotational instability. We adopt a realistic
description for stochastic forces due to these density fluctuations and perform
both long term hydrodynamical and N-body simulations. Our results show that
planets in the Kepler-36 mass range can be naturally assembled into a closely
spaced planetary system for a wide range of migration parameters in a turbulent
disc similar to the minimum mass solar nebula. The final orbits of our
formation scenarios tend to be Lagrange stable, even though large parts of the
parameter space are chaotic and unstable.Comment: 13 pages, 8 figures, accepted for publication in MNRA
Migration of low-mass planets in inviscid disks: the effect of radiation transport on the dynamical corotation torque
Low-mass planets migrate in the type-I regime. In the inviscid limit, the
contrast between the vortensity trapped inside the planet's corotating region
and the background disk vortensity leads to a dynamical corotation torque,
which is thought to slow down inward migration. We investigate the effect of
radiative cooling on low-mass planet migration using inviscid 2D hydrodynamical
simulations. We find that cooling induces a baroclinic forcing on material
U-turning near the planet, resulting in vortensity growth in the corotating
region, which in turn weakens the dynamical corotation torque and leads to 2-3x
faster inward migration. This mechanism is most efficient when cooling acts on
a timescale similar to the U-turn time of material inside the corotating
region, but is nonetheless relevant for a substantial radial range in a typical
disk (5-50 au). As the planet migrates inwards, the contrast between the
vortensity inside and outside the corotating region increases and partially
regulates the effect of baroclinic forcing. As a secondary effect, we show that
radiative damping can further weaken the vortensity barrier created by the
planet's spiral shocks, supporting inward migration. Finally, we highlight that
a self-consistent treatment of radiative diffusion as opposed to local cooling
is critical in order to avoid overestimating the vortensity growth and the
resulting migration rate.Comment: 11 pages, 11 figures; accepted to MNRA
Buoyancy response of a disk to an embedded planet: a cross-code comparison at high resolution
In radiatively inefficient, laminar protoplanetary disks, embedded planets
can excite a buoyancy response as gas gets deflected vertically near the
planet. This results in vertical oscillations that drive a vortensity growth in
the planet's corotating region, speeding up inward migration in the type-I
regime. We present a comparison between PLUTO/IDEFIX and FARGO3D using 3D,
inviscid, adiabatic numerical simulations of planet-disk interaction that
feature the buoyancy response of the disk, and show that PLUTO/IDEFIX struggle
to resolve higher-order modes of the buoyancy-related oscillations, weakening
vortensity growth and the associated torque. We interpret this as a drawback of
total-energy-conserving, finite-volume schemes. Our results indicate that a
very high resolution or high-order scheme is required in shock-capturing codes
in order to adequately capture this effect.Comment: 13 pages, 17 figures, 1 table; accepted by MNRA
Forming Circumbinary Planets: N-body Simulations of Kepler-34
Observations of circumbinary planets orbiting very close to the central stars
have shown that planet formation may occur in a very hostile environment, where
the gravitational pull from the binary should be very strong on the primordial
protoplanetary disk. Elevated impact velocities and orbit crossings from
eccentricity oscillations are the primary contributors towards high energy,
potentially destructive collisions that inhibit the growth of aspiring planets.
In this work, we conduct high resolution, inter-particle gravity enabled N-body
simulations to investigate the feasibility of planetesimal growth in the
Kepler-34 system. We improve upon previous work by including planetesimal disk
self-gravity and an extensive collision model to accurately handle
inter-planetesimal interactions. We find that super-catastrophic erosion events
are the dominant mechanism up to and including the orbital radius of
Kepler-34(AB)b, making in-situ growth unlikely. It is more plausible that
Kepler-34(AB)b migrated from a region beyond 1.5 AU. Based on the conclusions
that we have made for Kepler-34 it seems likely that all of the currently known
circumbinary planets have also migrated significantly from their formation
location with the possible exception of Kepler-47(AB)c.Comment: 6 pages, 5 figures, accepted for publication in ApJ
Vortex migration in protoplanetary disks
We consider the radial migration of vortices in two-dimensional isothermal
gaseous disks. We find that a vortex core, orbiting at the local gas velocity,
induces velocity perturbations that propagate away from the vortex as density
waves. The resulting spiral wave pattern is reminiscent of an embedded planet.
There are two main causes for asymmetries in these wakes: geometrical effects
tend to favor the outer wave, while a radial vortensity gradient leads to an
asymmetric vortex core, which favors the wave at the side that has the lowest
density. In the case of asymmetric waves, which we always find except for a
disk of constant pressure, there is a net exchange of angular momentum between
the vortex and the surrounding disk, which leads to orbital migration of the
vortex. Numerical hydrodynamical simulations show that this migration can be
very rapid, on a time scale of a few thousand orbits, for vortices with a size
comparable to the scale height of the disk. We discuss the possible effects of
vortex migration on planet formation scenarios.Comment: 13 pages, 13 figures, accepted for publication in Ap
Rapid inward migration of planets formed by gravitational instability
The observation of massive exoplanets at large separation from their host
star, like in the HR 8799 system, challenges theories of planet formation. A
possible formation mechanism involves the fragmentation of massive
self-gravitating discs into clumps. While the conditions for fragmentation have
been extensively studied, little is known of the subsequent evolution of these
giant planet embryos, in particular their expected orbital migration. Assuming
a single planet has formed by fragmentation, we investigate its interaction
with the gravitoturbulent disc it is embedded in. Two-dimensional
hydrodynamical simulations are used with a simple prescription for the disc
cooling. A steady gravitoturbulent disc is first set up, after which
simulations are restarted including a planet with a range of masses
approximately equal to the clump's initial mass expected in fragmenting discs.
Planets rapidly migrate inwards, despite the stochastic kicks due to the
turbulent density fluctuations. We show that the migration timescale is
essentially that of type I migration, with the planets having no time to open a
gap. In discs with aspect ratio ~ 0.1 at their forming location, planets with a
mass comparable to, or larger than Jupiter's can migrate in as short as 10000
years, that is, about 10 orbits at 100 AU. Massive planets formed at large
separation from their star by gravitational instability are thus unlikely to
stay in place, and should rapidly migrate towards the inner parts of
protoplanetary discs, regardless of the planet mass.Comment: 13 pages, 10 figures, accepted for publication in MNRA
Numerical convergence in self-gravitating shearing sheet simulations and the stochastic nature of disc fragmentation
We study numerical convergence in local two-dimensional hydrodynamical
simulations of self-gravitating accretion discs with a simple cooling law. It
is well-known that there exists a steady gravito-turbulent state, in which
cooling is balanced by dissipation of weak shocks, with a net outward transport
of angular momentum. Previous results indicated that if cooling is too fast
(typical time scale 3/Omega, where Omega is the local angular velocity), this
steady state can not be maintained and the disc will fragment into
gravitationally bound clumps. We show that, in the two-dimensional local
approximation, this result is in fact not converged with respect to numerical
resolution and longer time integration. Irrespective of the cooling time scale,
gravito-turbulence consists of density waves as well as transient clumps. These
clumps will contract because of the imposed cooling, and collapse into bound
objects if they can survive for long enough. Since heating by shocks is very
local, the destruction of clumps is a stochastic process. High numerical
resolution and long integration times are needed to capture this behaviour. We
have observed fragmentation for cooling times up to 20/Omega, almost a factor 7
higher than in previous simulations. Fully three-dimensional simulations with a
more realistic cooling prescription are necessary to determine the effects of
the use of the two-dimensional approximation and a simple cooling law.Comment: 15 pages, 10 figures, accepted for publication in MNRA