How Circumbinary Gas Giants Kepler-16 & Kepler-34 Could Have Formed

Modelling circumbinary protoplanetary disks II. Gas disk feedback on planetesimal dynamical and collisional evolution in the circumbinary systems Kepler-16 and 34

Authors:

Lines et al

Abstract:

Aims.

We investigate the feasibility of planetesimal growth in circumbinary protoplanetary disks around the observed systems Kepler- 16 and Kepler-34 under the gravitational influence of a precessing eccentric gas disk.

Methods.

We embed the results of our previous hydrodynamical simulations of protoplanetary disks around binaries into an N-body code to perform 3D, high-resolution, inter-particle gravity-enabled simulations of planetesimal growth and dynamics that include the gravitational force imparted by the gas.

Results.

Including the full, precessing asymmetric gas disk generates high eccentricity orbits for planetesimals orbiting at the edge of the circumbinary cavity, where the gas surface density and eccentricity have their largest values. The gas disk is able to efficiently align planetesimal pericenters in some regions leading to phased, non-interacting orbits. Outside of these areas eccentric planetesimal orbits become misaligned and overlap leading to crossing orbits and high relative velocities during planetesimal collisions. This can lead to an increase in the number of erosive collisions that far outweighs the number of collisions that result in growth. Gravitational focusing from the static axisymmetric gas disk is weak and does not significantly alter collision outcomes from the gas free case.

Conclusions.

Due to asymmetries in the gas disk, planetesimals are strongly perturbed onto highly eccentric orbits. Where planetesimals orbits are not well aligned, orbit crossings lead to an increase in the number of erosive collisions. This makes it difficult for sustained planetesimal accretion to occur at the location of Kepler-16b and Kepler-34b and we therefore rule out in-situ growth. This adds further support to our initial suggestions that most circumbinary planets should form further out in the disk and migrate inwards.

Modeling the Formation of Kepler-16 and Kepler-34 Circumbinary Exoplanetary Systems

Modelling circumbinary protoplanetary disks: I. Fluid simulations of the Kepler-16 and 34 systems

Authors:

Lines et al

Abstract:

The Kepler mission's discovery of a number of circumbinary planets orbiting close (a_p less than 1.1 au) to the stellar binary raises questions as to how these planets could have formed given the intense gravitational perturbations the dual stars impart on the disk. The gas component of circumbinary protoplanetary disks is perturbed in a similar manner to the solid, planetesimal dominated counterpart, although the mechanism by which disk eccentricity originates differs. This is the first work of a series that aims to investigate the conditions for planet formation in circumbinary protoplanetary disks. We present a number of hydrodynamical simulations that explore the response of gas disks around two observed binary systems: Kepler-16 and Kepler-34. We probe the importance of disk viscosity, aspect-ratio, inner boundary condition, initial surface density gradient, and self-gravity on the dynamical evolution of the disk, as well as its quasi steady-state profile. We find there is a strong influence of binary type on the mean disk eccentricity, e_d, leading to e_d = 0.02 - 0.08 for Kepler-16 and e_d = 0.10 - 0.15 in Kepler-34. The value of alpha-viscosity has little influence on the disk, but we find a strong increase in mean disk eccentricity with increasing aspect-ratio due to wave propagation effects. The choice of inner boundary condition only has a small effect on the surface density and eccentricity of the disk. Our primary finding is that including disk self-gravity has little impact on the evolution or final state of the disk for disks with masses less than 12.5 times that of the minimum-mass solar nebula. This finding contrasts with the results of self-gravity relevance in circumprimary disks, where its inclusion is found to be an important factor in describing the disk evolution.

Evolution of Circumbinary Exoplanets Around Eccentric Binaries

Evolution of circumbinary planets around eccentric binaries: The case of Kepler-34

Authors:

Kley et al

Abstract:

The existence of planets orbiting a central binary star system immediately raises questions regarding their formation and dynamical evolution. Recent discoveries of circumbinary planets by the Kepler space telescope has shown that some of these planets reside close to the dynamical stability limit where it is very difficult to form planets in situ. For binary systems with nearly circular orbits, such as Kepler-38, the observed proximity of planetary orbits to the stability limit can be understood by an evolutionary process in which planets form farther out in the disk and migrate inward to their observed position. The Kepler-34 system has a high orbital eccentricity of 0.52. Here, we analyse evolutionary scenarios for the planet observed around this system using two-dimensional hydrodynamical simulations.

The highly eccentric binary opens a wide inner hole in the disk which is also eccentric, and displays a slow prograde precession. As a result of the large, eccentric inner gap, an embedded planet settles in a final equilibrium position that lies beyond the observed location of Kepler-34b, but has the correct eccentricity. In this configuration the planetary orbit is aligned with the disk in a state of apsidal corotation.To account for the closer orbit of Kepler-34 b to the central binary, we considered a two-planet scenario and examined the evolution of the system through joint inward migration and capture into mean-motion resonances. When the inner planet orbits inside the gap of the disk, planet-planet scattering ensues. While often one object is thrown into a large, highly eccentric orbit, at times the system is left with a planet close to the observed orbit, suggesting that Kepler 34 might have had two circumbinary planets where one might have been scattered out of the system or into an orbit where it did not transit the central binary during the operation of Kepler.

Examining Kepler Circumbinary Planetary Systems With Single Planets

A dynamical stability study of Kepler Circumbinary planetary systems with one planet

Authors:

Chavez et al

Abstract:

To date, 17 circumbinary planets have been discovered. In this paper, we focus our attention on the stability of the Kepler circumbinary planetary systems with only one planet, i.e. Kepler-16, Kepler-34, Kepler-35, Kepler-38, Kepler-64 and Kepler-413. In addition to their intrinsic interest, the study of such systems is an opportunity to test our understanding of planetary system formation and evolution around binaries. The investigation is done by means of numerical simulations. We perform numerical integrations of the full equations of motion of each system with the aim of checking the stability of the planetary orbit. The investigation of the stability of the above systems consists of three numerical experiments. In the first one, we perform a long-term (1 Gyr) numerical integration of the nominal solution of the six Kepler systems under investigation. In the second experiment, we look for the critical semimajor axis of the six planetary orbits, and finally, in the third experiment, we construct two-dimensional stability maps on the eccentricity–pericentre distance plane. Additionally, using numerical integrations of the nominal solutions we checked if these solutions were close to the exact resonance.

Simulations of Kepler-34(AB)b's System

Forming Circumbinary Planets: N-body Simulations of Kepler-34

Authors:

Lines et al

Abstract:

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.