The Kepler mission has discovered about a dozen circumbinary planetary systems, all containing planets on ~ 1 AU orbits. We place bounds on the locations in the circumbinary protoplanetary disk, where these planets could have formed through collision
al agglomeration starting from small (km-sized or less) planetesimals. We first present a model of secular planetesimal dynamics that accounts for the (1) perturbation due to the eccentric precessing binary, as well as the (2) gravity and (3) gas drag from a precessing eccentric disk. Their simultaneous action leads to rich dynamics, with (multiple) secular resonances emerging in the disk. We derive analytic results for size-dependent planetesimal eccentricity, and demonstrate the key role of the disk gravity for circumbinary dynamics. We then combine these results with a simple model for collisional outcomes and find that in systems like Kepler 16, planetesimal growth starting with 10-100 m planetesimals is possible outside a few AU. The exact location exterior to which this happens is sensitive to disk eccentricity, density and precession rate, as well as to the size of the first generation of planetesimals. Strong perturbations from the binary in the inner part of the disk, combined with a secular resonance at a few AU inhibit the growth of km-sized planetesimals within 2 - 4 AU of the binary. In situ planetesimal growth in the Kepler circumbinary systems is possible only starting from large (few-km-sized) bodies in a low-mass disk with surface density less than 500 g/cm^2 at 1 AU.
Many exoplanets in close-in orbits are observed to have relatively high eccentricities and large stellar obliquities. We explore the possibility that these result from planet-planet scattering by studying the dynamical outcomes from a large number of
orbit integrations in systems with two and three gas-giant planets in close-in orbits (0.05 AU < a < 0.15 AU). We find that at these orbital separations, unstable systems starting with low eccentricities and mutual inclinations ($elesssim0.1$, $ilesssim0.1$) generally lead to planet-planet collisions in which the collision product is a planet on a low-eccentricity, low-inclination orbit. This result is inconsistent with the observations. We conclude that eccentricity and inclination excitation from planet-planet scattering must precede migration of planets into short-period orbits. This result constrains theories of planet migration: the semi-major axis must shrink by 1-2 orders of magnitude without damping the eccentricity and inclination.
We perform a systematic study of the dynamics of dust particles in protoplanetary disks with embedded planets using global 2-D and 3-D inviscid hydrodynamic simulations. Lagrangian particles have been implemented into magnetohydrodynamic code Athena
with cylindrical coordinates. We find two distinct outcomes depending on the mass of the embedded planet. In the presence of a low mass planet ($8 M_{oplus}$), two narrow gaps start to open in the gas on each side of the planet where the density waves shock. These shallow gaps can dramatically affect particle drift speed and cause significant, roughly axisymmetric dust depletion. On the other hand, a more massive planet ($>0.1 M_{J}$) carves out a deeper gap with sharp edges, which are unstable to the vortex formation. Particles with a wide range of sizes ($0.02<Omega t_{s}<20$) are trapped and settle to the midplane in the vortex, with the strongest concentration for particles with $Omega t_{s}sim 1$. The dust concentration is highly elongated in the $phi$ direction, and can be as wide as 4 disk scale heights in the radial direction. Dust surface density inside the vortex can be increased by more than a factor of 10$^2$ in a very non-axisymmetric fashion. For very big particles ($Omega t_{s}gg 1$) we find strong eccentricity excitation, in particular around the planet and in the vicinity of the mean motion resonances, facilitating gap opening there. Our results imply that in weakly turbulent protoplanetary disk regions (e.g. the dead zone) dust particles with a very wide range of sizes can be trapped at gap edges and inside vortices induced by planets with $M_{p}<M_{J}$, potentially accelerating planetesimal and planet formation there, and giving rise to distinctive features that can be probed by ALMA and EVLA.
Eclipsing binary DI Herculis (DI Her) is known to exhibit anomalously slow apsidal precession, below the rate predicted by the general relativity. Recent measurements of the Rossiter-McLauglin effect indicate that stellar spins in DI Her are almost o
rthogonal to the orbital angular momentum, which explains the anomalous precession in agreement with the earlier theoretical suggestion by Shakura. However, these measurements yield only the projections of the spin-orbit angles onto the sky plane, leaving the spin projection onto our line of sight unconstrained. Here we describe a method of determining the full three-dimensional spin orientation of the binary components relying on the use of the gravity darkening effect, which is significant for the rapidly rotating stars in DI Her. Gravity darkening gives rise to nonuniform brightness distribution over the stellar surface, the pattern of which depends on the stellar spin orientation. Using archival photometric data obtained during multiple eclipses spread over several decades we are able to constrain the unknown spin angles in DI Her with this method, finding that spin axes of both stars lie close to the plane of the sky. Our procedure fully accounts for the precession of stellar spins over the long time span of observations.
We investigate numerically the propagation of density waves excited by a low-mass planet in a protoplanetary disk in the nonlinear regime, using 2D local shearing box simulations with the grid-based code Athena at high spatial resolution (256 grid po
ints per scale height h). The nonlinear evolution results in the wave steepening into a shock, causing damping and angular momentum transfer to the disk. On long timescales this leads to spatial redistribution of the disk density, causing migration feedback and potentially resulting in gap opening. Previous numerical studies concentrated on exploring these secondary phenomena as probes of the nonlinear wave evolution. Here we focus on exploring the evolution of the basic wave properties, such as its density profile evolution, shock formation, post-shock wave behavior, and provide comparison with analytical theory. The generation of potential vorticity at the shock is computed analytically and is subsequently verified by simulations and used to pinpoint the shock location. We confirm the theoretical relation between the shocking length and the planet mass (including the effect of the equation of state), and the post-shock decay of the angular momentum flux carried by the wave. The post-shock evolution of the wave profile is explored, and we quantitatively confirm its convergence to the theoretically expected N-wave shape. The accuracy of various numerical algorithms used to compute the nonlinear wave evolution is also investigated: we find that higher order spatial reconstruction and high resolution are crucial for capturing the shock formation correctly.
