11 research outputs found
On type-I migration near opacity transitions. A generalized Lindblad torque formula for planetary population synthesis
We give an expression for the Lindblad torque acting on a low-mass planet
embedded in a protoplanetary disk that is valid even at locations where the
surface density or temperature profile cannot be approximated by a power law,
such as an opacity transition. At such locations, the Lindblad torque is known
to suffer strong deviation from its standard value, with potentially important
implications for type I migration, but the full treatment of the tidal
interaction is cumbersome and not well suited to models of planetary population
synthesis. The expression that we propose retains the simplicity of the
standard Lindblad torque formula and gives results that accurately reproduce
those of numerical simulations, even at locations where the disk temperature
undergoes abrupt changes. Our study is conducted by means of customized
numerical simulations in the low-mass regime, in locally isothermal disks, and
compared to linear torque estimates obtained by summing fully analytic torque
estimates at each Lindblad resonance. The functional dependence of our modified
Lindblad torque expression is suggested by an estimate of the shift of the
Lindblad resonances that mostly contribute to the torque, in a disk with sharp
gradients of temperature or surface density, while the numerical coefficients
of the new terms are adjusted to seek agreement with numerics. As side results,
we find that the vortensity related corotation torque undergoes a boost at an
opacity transition that can counteract migration, and we find evidence from
numerical simulations that the linear corotation torque has a non-negligible
dependency upon the temperature gradient, in a locally isothermal disk.Comment: Appeared in special issue of "Celestial Mechanics and Dynamical
Astronomy" on Extrasolar Planetary System
Recent developments in planet migration theory
Planetary migration is the process by which a forming planet undergoes a
drift of its semi-major axis caused by the tidal interaction with its parent
protoplanetary disc. One of the key quantities to assess the migration of
embedded planets is the tidal torque between the disc and planet, which has two
components: the Lindblad torque and the corotation torque. We review the latest
results on both torque components for planets on circular orbits, with a
special emphasis on the various processes that give rise to additional, large
components of the corotation torque, and those contributing to the saturation
of this torque. These additional components of the corotation torque could help
address the shortcomings that have recently been exposed by models of planet
population syntheses. We also review recent results concerning the migration of
giant planets that carve gaps in the disc (type II migration) and the migration
of sub-giant planets that open partial gaps in massive discs (type III
migration).Comment: 52 pages, 18 figures. Review article to be published in "Tidal
effects in Astronomy and Astrophysics", Lecture Notes in Physic
Giant Planet Formation and Migration
© 2018, The Author(s). Planets form in circumstellar discs around young stars. Starting with sub-micron sized dust particles, giant planet formation is all about growing 14 orders of magnitude in size. It has become increasingly clear over the past decades that during all stages of giant planet formation, the building blocks are extremely mobile and can change their semimajor axis by substantial amounts. In this chapter, we aim to give a basic overview of the physical processes thought to govern giant planet formation and migration, and to highlight possible links to water delivery.S.-J. Paardekooper is supported by a Royal Society University Research Fellowship. A. Johansen is supported by the Knut and Alice Wallenberg Foundation, the Swedish Research Council (grant 2014-5775) and the European Research Council (ERC Starting Grant 278675-PEBBLE2PLANET)
Angular momentum exchange during secular migration of two-planet systems
We investigate the secular dynamics of two-planet coplanar systems evolving
under mutual gravitational interactions and dissipative forces. We consider two
mechanisms responsible for the planetary migration: star-planet (or
planet-satellite) tidal interactions and interactions of a planet with a
gaseous disc. We show that each migration mechanism is characterized by a
specific law of orbital angular momentum exchange. Calculating stationary
solutions of the conservative secular problem and taking into account the
orbital angular momentum leakage, we trace the evolutionary routes followed by
the planet pairs during the migration process. This procedure allows us to
recover the dynamical history of two-planet systems and constrain parameters of
the involved physical processes.Comment: 20 pages, 9 figures, accepted for publication in Celestial Mechanics
and Dynamical Astronomy (special issue on Exoplanets
PlanetâDisk Interactions
Tides come from the fact that different parts of a system do not
fall in exactly the same way in a non-uniform gravity field. In the
case of a protoplanetary disk perturbed by an orbiting, prograde
protoplanet, the protoplanet tides raise a wake in the disk which
causes the orbital elements of the planet to change over time. The
most spectacular result of this process is a change in the
protoplanet's semi-major axis, which can decrease by orders of
magnitude on timescales shorter than the disk lifetime. This drift
in the semi-major axis is called planetary migration, and is the
most important aspect of planetâdisk interactions. In this chapter,
we first describe how the planet and disk exchange angular momentum
and energy at the Lindblad and corotation resonances. Next we
review the various types of planetary migration that have so far
been contemplated: type I migration, which corresponds to low-mass
planets (less than a few Earth masses) triggering a linear disk
response; type II migration, which corresponds to massive planets
(typically at least one Jupiter mass) that open up a gap in the
disk; ârunawayâ or type III migration, which corresponds to
sub-giant planets that orbit in massive disks; and stochastic or
diffusive migration, which is the migration mode of low- or
intermediate-mass planets embedded in turbulent disks. Third, we
discuss questions linked to the planet eccentricity, in particular
how the eccentricity is affected by the planetâdisk interaction.
Fourth, we discuss the various numerical schemes that have been used
to describe planetâdisk interactions. We discuss their strengths
and weaknesses, and list the results that numerical simulations have
achieved over the past decade
Dynamical friction on hot bodies in gaseous, opaque media, and application to embedded protoplanets
A massive and luminous perturber moving across an opaque gas is subjected to a force different from the gravitational friction that it would experience if it were cold. The heat released by the perturber diffuses in the surrounding gas, where it gives rise to a low density region behind the perturber that exerts a force (that we call heating force) in the direction of motion, thus opposed to the standard dynamical friction. We present numerical simulations with nested meshes that confirm the analytical expression of the heating force in the limits of a low and high Mach number, respectively, and we present simulations that show that the dynamical friction exerted on a cold perturber in a gas with thermal diffusion is markedly different from that in an adiabatic gas. We then present numerical simulations of low-mass protoplanets embedded in opaque, viscous discs, that show that when these bodies have a sufficiently large luminosity their eccentricity and inclination can be excited to values comparable to the aspect ratio of the disc. We finally present numerical experiments with very high resolution that try to resolve the flow within the Bondi sphere, in an attempt to study the dependence of the heating force as a function of the ratio of the diffusive to acoustic times across the Bondi radius
Disk Surface Density Transitions as Protoplanet Traps
Astrophysical Journal, 642, pp. 478-487, http://dx.doi.org./10.1086/500967International audienc