Migration of giant planets in planetesimal discs

Monthly Notices of The Royal Astronomical Society, 2003

In this paper, we further develop the model for the migration of planets introduced by Del Popolo, Gambera & Ercan and extended to time-dependent planetesimal accretion discs by Del Popolo & Ekşi. More precisely, the assumption of Del Popolo & Ekşi that the surface density in planetesimals is proportional to that of the gas was released. Indeed, the evolution of the radial distribution of solids is governed by many processes: gas-solid coupling, coagulation, sedimentation, evaporation/condensation, so that the distribution of planetesimals emerging from a turbulent disc does not necessarily reflect that of the gas. In order to describe this evolution we use a method developed by Stepinski & Valageas, which, using a series of simplifying assumptions, is able to simultaneously follow the evolution of gas and solid particles for up to 107 yr. This model is based on the premise that the transformation of solids from dust to planetesimals occurs through hierarchical coagulation. Then, the distribution of planetesimals obtained after 107 yr is used to study the migration rate of a giant planet through the migration model introduced by Del Popolo, Gambera & Ercan. This allows us to investigate the dependence of the migration rate on the disc mass, on its time evolution and on the value of the dimensionless viscosity parameter α. We find that in the case of discs having a total mass of 10-3-10-1 Msolar, and 10-4 < α < 10-1, planets can migrate inward over a large distance while if Md < 10-3, Msolar the planets remain almost at their initial position for α > 10-3 and only in the case where α < 10-3 do the planets move to a minimum value of orbital radius of ~=2 au. Moreover, the observed distribution of planets in the period range 0-20 d can be easily obtained from our model. Therefore, dynamical friction between planets and the planetesimal disc provides a good mechanism to explain the properties of observed extrasolar giant planets.

2007

Planets embedded in a planetesimal disk will migrate as a result of angular momentum and energy conservation as the planets scatter the planetesimals that they encounter. A surprising variety of interesting and complex dynamics can arise from this apparently simple process. In this chapter, we review the basic characteristics of planetesimal-driven migration. We discuss how the structure of a planetary system controls migration. We describe how this type of migration can cause planetary systems to become dynamically unstable and how a massive planetesimal disk can save planets from being ejected from the planetary system during this instability. We examine how the solar system&#x27;s small-body reservoirs, particularly the Kuiper belt and Jupiter&#x27;s Trojan asteroids, constrain what happened here. We also review a new model for the early dynamical evolution of the outer solar system that quantitatively reproduces much of what we see. And finally, we briefly discuss how planetesim...

International Journal of Modern Physics D, 2003

In the current paper, we further improved the model for the migration of planets introduced and extended to time-dependent planetesimal accretion disks by Del Popolo. In the current study, the assumption of Del Popolo, that the surface density in planetesimals is proportional to that of gas, is relaxed. In order to obtain the evolution of planetesimal density, we use a method developed by Stepinski and Valageas which is able to simultaneously follow the evolution of gas and solid particles for up to 107 years. Then, the disk model is coupled to migration model introduced by Del Popolo in order to obtain the migration rate of the planet in the planetesimal. We find that the properties of solids known to exist in protoplanetary systems, together with reasonable density profiles for the disk, lead to a characteristic radius in the range 0.03–0.2 AU for the final semi-major axis of the giant planet.Hence our model can explain the properties of discovered extrasolar giant planets.

2003

In the current paper, we further improved the model for the migration of planets introduced in Del Popolo et al. (2001) and extended to time-dependent planetesimal accretion disks in Del Popolo and Eksi (2002). In the current study, the assumption of Del Popolo and Eksi (2002), that the surface density in planetesimals is proportional to that of gas, is released. In order to obtain the evolution of planetesimal density, we use a method developed in Stepinski and Valageas (1997) which is able to simultaneously follow the evolution of gas and solid particles for up to 10^7 yrs. Then, the disk model is coupled to migration model introduced in Del Popolo et al. (2001) in order to obtain the migration rate of the planet in the planetesimal. We find that the properties of solids known to exist in protoplanetary systems, together with reasonable density profiles for the disk, lead to a characteristic radius in the range 0.03-0.2 AU for the final semi-major axis of the giant planet.

Protostars and Planets V, 2007

The discovery of close orbiting extrasolar giant planets led to extensive studies of diskplanet interactions and the forms of migration that can result as a means of accounting for their location. Early work established the type I and type II migration regimes for low-mass embedded planets and high-mass gap-forming planets respectively. While providing an attractive means of accounting for close orbiting planets initially formed at several AU, inward migration times for objects in the Earth-mass range were found to be disturbingly short, making the survival of giant planet cores an issue. Recent progress in this area has come from the application of modern numerical techniques that make use of up-to-date supercomputer resources. These have enabled higher-resolution studies of the regions close to the planet and the initiation of studies of planets interacting with disks undergoing magnetohydrodynamic turbulence. This work has led to indications of how the inward migration of low- to intermediate-mass planets could be slowed down or reversed. In addition, the possibility of a new very fast type III migration regime, which can be directed inward or outward, that is relevant to partial gap-forming planets in massive disks has been investigated.

Monthly Notices of the Royal Astronomical Society

Protoplanetary discs are thought to be truncated at orbital periods of around 10 d. Therefore, the origin of rocky short-period planets with P &lt; 10 d is a puzzle. We propose that many of these planets may form through the Type-I migration of planets locked into a chain of mutual mean motion resonances. We ran N-body simulations of planetary embryos embedded in a protoplanetary disc. The embryos experienced gravitational scatterings, collisions, disc torques, and dampening of orbital eccentricity and inclination. We then modelled Kepler observations of these planets using a forward model of both the transit probability and the detection efficiency of the Kepler pipeline. We found that planets become locked into long chains of mean motion resonances that migrate in unison. When the chain reaches the edge of the disc, the inner planets are pushed past the edge due to the disc torques acting on the planets farther out in the chain. Our simulated systems successfully reproduce the obs...

The discovery of close orbiting extrasolar giant planets led to extensive studies of disk planet interactions and the forms of migration that can result as a means of accounting for their location. Early work established the type I and type II migration regimes for low mass embedded planets and high mass gap forming planets respectively. While providing an attractive means of accounting for close orbiting planets intially formed at several AU, inward migration times for objects in the earth mass range were found to be disturbingly short, making the survival of giant planet cores an issue. Recent progress in this area has come from the application of modern numerical techniques wich make use of up to date supercomputer resources. These have enabled higher resolution studies of the regions close to the planet and the initiation of studies of planets interacting with disks undergoing MHD turbulence. This work has led to indications of how the inward migration of low to intermediate mass planets could be slowed down or reversed. In addition, the possibility of a new very fast type III migration regime, that can be directed inwards or outwards, that is relevant to partial gap forming planets in massive disks has been investigated.

Astronomy & Astrophysics, 2013

Context. The strength and direction of migration of embedded low mass planets depends on the disc's structure. It has been shown that, in discs where the viscous heating is balanced by radiative transport, the migration can be directed outwards, a process which extends the lifetime of growing planetary embryos. Aims. In this paper we investigate the influence of a constantṀ-flux through the disc, as well as the influence of the disc's metallicity on the disc's thermodynamics. We focus onṀ discs, which have a net mass flux through them. Utilizing the resulting disc structure, we determine the regions of outward migration in the disc. Methods. We perform numerical hydrosimulations ofṀ discs with viscous heating, radiative cooling and stellar irradiation in 2D in the r-z-plane. We use the explicit/implicit hydrodynamical code FARGOCA that includes a full tensor viscosity and stellar irradiation, as well as a two temperature solver that includes radiation transport in the flux-limited diffusion approximation. The migration of embedded planets is studied by using torque formulae. Results. For a disc of gas surface density Σ G and viscosity ν, we find that the discs thermal structure depends on the product Σ G ν and the amount of heavy elements, while the migration of planets additionally to the mentioned quantities, depends on the amount of viscosity ν itself. As a result of this, the disc structure can not be approximated by simple power laws. During the lifetime of the disc, the structure of the disc changes significantly in a non-linear way in the inner parts. In the late stages of the discs evolution (characterised by lowṀ), outward migration is only possible if the metallicity of the disc is high. For low metallicity, planets would migrate inwards and could potentially be lost to the star. Conclusions. The presented disc structures and migration maps have important consequences on the formation of planets, as they can give hints on the different formation mechanisms for different types of planets as a function of metallicity.

Astronomy & Astrophysics, 2011

Context. The migration of planets plays an important role in the early planet-formation process. An important problem has been that standard migration theories predict very rapid inward migration, which poses problems for population synthesis models. However, it has been shown recently that low-mass planets (20-30 M Earth ) that are still embedded in the protoplanetary disc can migrate outwards under certain conditions. Simulations have been performed mostly for planets at given radii for a particular disc model. Aims. Here, we plan to extend previous work and consider different masses of the disc to quantify the influence of the physical disc conditions on planetary migration. The migration behaviour of the planets will be analysed for a variety of positions in the disc. Methods. We perform three-dimensional (3D) radiation hydrodynamical simulations of embedded planets in protoplanetary discs. We use the explicit-implicit 3D hydrodynamical code NIRVANA that includes full tensor viscosity, and implicit radiation transport. For planets on circular orbits at various locations we measure the radial dependence of the torques for three different planetary masses.

Astronomy and Astrophysics, 2008

Context. The formation of resonant pairs of planets in exoplanetary systems involves planetary migration in the protoplanetary disc. After a resonant capture, the subsequent migration in this configuration leads to a large increase of planetary eccentricities if no damping mechanism is applied. This has led to the conclusion that the migration of resonant planetary systems cannot occur over large radial distances and has to be terminated sufficiently rapidly through disc dissipation. Aims. In this study, we investigate whether the presence of an inner disc might supply an eccentricity damping of the inner planet, and if this effect could explain the observed eccentricities in some systems. Methods. To investigate the influence of an inner disc, we first compute hydrodynamic simulations of giant planets orbiting with a given eccentricity around an inner gas disc, and measure the effect of the latter on the planetary orbital parameters. We then perform detailed long term calculations of the GJ 876 system. We also run N-body simulations with artificial forces on the planets mimicking the effects of the inner and outer discs. Results. We find that the influence of the inner disc can not be neglected, and that it might be responsible for the observed eccentricities. In particular, we reproduce quite well the orbital parameters of a few systems engaged in 2:1 mean motion resonances : GJ 876, HD 73 526, HD 82 943 and HD 128 311. Finally, we derive analytically the effect that the inner disc should have on the inner planet to reach a specific orbital configuration with a given damping effect of the outer disc on the outer planet. Conclusions. We conclude that an inner disc, even though difficult to model properly in hydro-dynamical simulations, should be taken into account because of its damping effect on the eccentricity of the inner planet. By including this effect, we can explain quite naturally the observed orbital elements of the pairs of known resonant exoplanets.