N-body Simulations of Satellite Formation around Giant Planets: Origin of Orbital Configuration of the Galilean Moons

As the number of discovered extrasolar planets has been increasing, diversity of planetary systems requires studies of new formation scenarios. It is important to study satellite formation in circumplanetary disks, which is often viewed as analogous to formation of rocky planets in protoplanetary disks. We investigated satellite formation from satellitesimals around giant planets through N-body simulations that include gravitational interactions with a circumplanetary gas disk. Our main aim is to reproduce the observable properties of the Galilean satellites around Jupiter through numerical simulations, as previous N-body simulations have not explained the origin of the resonant configuration. We performed accretion simulations based on the work of Sasaki et al. (2010), in which an inner cavity is added to the model of Canup & Ward (2002, 2006). We found that several satellites are formed and captured in mutual mean motion resonances outside the disk inner edge and are stable after rapid disk gas dissipation, which explains the characteristics of the Galilean satellites. In addition, owing to the existence of the disk edge, a radial compositional gradient of the Galilean satellites can also be reproduced. An additional objective of this study is to discuss orbital properties of formed satellites for a wide range of conditions by considering large uncertainties in model parameters. Through numerical experiments and semianalytical arguments, we determined that if the inner edge of a disk is introduced, a Galilean-like configuration in which several satellites are captured into a 2:1 resonance outside the disk inner cavity is almost universal. In fact, such a configuration is produced even for a massive disk and rapid type I migration. This result implies the inevitability of a Galilean satellite formation in addition to providing theoretical predictions for extrasolar satellites.Comment: 20 pages, 9 figures, accepted for publication in Ap

Suppression of type I migration by disk winds

Planets less massive than Saturn tend to rapidly migrate inward in protoplanetary disks. This is the so-called type I migration. Simulations attempting to reproduce the observed properties of exoplanets show that type I migration needs to be significantly reduced over a wide region of the disk for a long time. However, the mechanism capable of suppressing type I migration over a wide region has remained elusive. The recently found turbulence-driven disk winds offer new possibilities. We investigate the effects of disk winds on the disk profile and type I migration for a range of parameters that describe the strength of disk winds. We also examine the in situ formation of close-in super-Earths in disks that evolve through disk winds. The disk profile, which is regulated by viscous diffusion and disk winds, was derived by solving the diffusion equation. We carried out a number of simulations and plot here migration maps that indicate the type I migration rate. We also performed N-body simulations of the formation of close-in super-Earths from a population of planetesimals and planetary embryos. We define a key parameter, Kw, which determines the ratio of strengths between the viscous diffusion and disk winds. For a wide range of Kw, the type I migration rate is presented in migration maps. These maps show that type I migration is suppressed over the whole close-in region when the effects of disk winds are relatively strong (Kw < 100). From the results of N-body simulations, we see that type I migration is significantly slowed down assuming Kw = 40. We also show that the results of N-body simulations match statistical orbital distributions of close-in super-Earths.Comment: 5 pages, 4 figures, accepted for publication in A&A Letter

Formation of terrestrial planets in disks evolving via disk winds and implications for the origin of the solar system's terrestrial planets

Recent three-dimensional magnetohydrodynamical simulations have identified a disk wind by which gas materials are lost from the surface of a protoplanetary disk, which can significantly alter the evolution of the inner disk and the formation of terrestrial planets. A simultaneous description of the realistic evolution of the gaseous and solid components in a disk may provide a clue for solving the problem of the mass concentration of the terrestrial planets in the solar system. We simulate the formation of terrestrial planets from planetary embryos in a disk that evolves via magnetorotational instability and a disk wind. The aim is to examine the effects of a disk wind on the orbital evolution and final configuration of planetary systems. We perform N-body simulations of sixty 0.1 Earth-mass embryos in an evolving disk. The evolution of the gas surface density of the disk is tracked by solving a one-dimensional diffusion equation with a sink term that accounts for the disk wind. We find that even in the case of a weak disk wind, the radial slope of the gas surface density of the inner disk becomes shallower, which slows or halts the type I migration of embryos. If the effect of the disk wind is strong, the disk profile is significantly altered (e.g., positive surface density gradient, inside-out evacuation), leading to outward migration of embryos inside ~ 1 AU. Disk winds play an essential role in terrestrial planet formation inside a few AU by changing the disk profile. In addition, embryos can undergo convergent migration to ~ 1 AU in certainly probable conditions. In such a case, the characteristic features of the solar system's terrestrial planets (e.g., mass concentration around 1 AU, late giant impact) may be reproduced.Comment: 8 pages, 4 figures, accepted for publication in A&

Eccentricity Trap: Trapping of Resonantly Interacting Planets near the Disk Inner Edge

Using orbital integration and analytical arguments, we have found a new mechanism (an "eccentricity trap") to halt type I migration of planets near the inner edge of a protoplanetary disk. Because asymmetric eccentricity damping due to disk-planet interaction on the innermost planet at the disk edge plays a crucial role in the trap, this mechanism requires continuous eccentricity excitation and hence works for a resonantly interacting convoy of planets. This trap is so strong that the edge torque exerted on the innermost planet can completely halt type I migrations of many outer planets through mutual resonant perturbations. Consequently, the convoy stays outside the disk edge, as a whole. We have derived semi-analytical formula for the condition for the eccentricity trap and predict how many planets are likely to be trapped. We found that several planets or more should be trapped by this mechanism in protoplanetary disks that have cavities. It can be responsible for the formation of non-resonant, multiple, close-in super-Earth systems extending beyond 0.1AU. Such systems are being revealed by radial velocity observations to be quite common around solar-type stars.Comment: 24 pages, 7 figures, accepted for publication in Ap

Evolution of Protoplanetary Discs with Magnetically Driven Disc Winds

Aims: We investigate the evolution of protoplanetary discs (PPDs hereafter) with magnetically driven disc winds and viscous heating. Methods: We consider an initially massive disc with ~0.1 Msun to track the evolution from the early stage of PPDs. We solve the time evolution of surface density and temperature by taking into account viscous heating and the loss of the mass and the angular momentum by the disc winds within the framework of a standard alpha model for accretion discs. Our model parameters, turbulent viscosity, disc wind mass loss, and disc wind torque, which are adopted from local magnetohydrodynamical simulations and constrained by the global energetics of the gravitational accretion, largely depends on the physical condition of PPDs, particularly on the evolution of the vertical magnetic flux in weakly ionized PPDs. Results: Although there are still uncertainties concerning the evolution of the vertical magnetic flux remaining, surface densities show a large variety, depending on the combination of these three parameters, some of which are very different from the surface density expected from the standard accretion. When a PPD is in a "wind-driven accretion" state with the preserved vertical magnetic field, the radial dependence of the surface density can be positive in the inner region <1-10 au. The mass accretion rates are consistent with observations, even in the very low level of magnetohydrodynamical turbulence. Such a positive radial slope of the surface density gives a great impact on planet formation because (i)it inhibits the inward drift or even results in the outward drift of pebble/boulder-sized solid bodies, and (ii) it also makes the inward type-I migration of proto-planets slower or even reversed. Conclusions: The variety of our calculated PPDs should yield a wide variety of exoplanet systems.Comment: 16 pages, 11 figures embedded, accepted by A&A (comments are welcome