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تسجيل مستخدم جديدInfluence of the circumbinary disk gravity on planetesimal accumulation in the Kepler 16 system
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Recent observations from NASAs Kepler mission detected the first planets in circumbinary orbits. The question we try to answer is where these planets formed in the circumbinary disk and how far inside they migrated to reach their present location. We investigate the first and more delicate phase of planet formation when planetesimals accumulate to form planetary embryos. We use the hydrodynamical code FARGO to study the evolution of the disk and of a test population of planetesimals embedded in it. With this hybrid hydrodynamical--N--body code we can properly account for the gas drag force on the planetesimals and for the gravitational force of the disk on them. The numerical simulations show that the gravity of the eccentric disk on the planetesimal swarm excites their eccentricities to values much larger than those induced by the binary perturbations only within 10 AU from the stars. Moreover, the disk gravity prevents a full alignment of the planetesimal pericenters. Both these effects lead to large impact velocities, beyond the critical value for erosion. Planetesimals accumulation in circumbinary disks appears to be prevented close to the stellar pair by the gravitational perturbations of the circumbinary disk. The observed planets possibly formed in the outer regions of the disk and then migrated inside by tidal interaction with the disk.
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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.
The Kepler missions discovery of a number of circumbinary planets orbiting close (a_p < 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 th
e 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.
KH 15D is a system which consists of a young, eccentric binary, and a circumbinary disk which obscures the binary as the disk precesses. We develop a self-consistent model that provides a reasonable fit to the photometric variability that was observe
d in the KH 15D system over the past 60 years. Our model suggests that the circumbinary disk has an inner edge $r_{rm in}lesssim 1 {rm au}$, an outer edge $r_{rm out} sim {rm a few au}$, and that the disk is misaligned relative to the stellar binary by $sim$5-16 degrees, with the inner edge more inclined than the outer edge. The difference between the inclinations (warp) and longitude of ascending nodes (twist) at the inner and outer edges of the disk are of order $sim$10 degrees and $sim$15 degrees, respectively. We also provide constraints on other properties of the disk, such as the precession period and surface density profile. Our work demonstrates the power of photometric data in constraining the physical properties of planet-forming circumbinary disks.
Of the nine confirmed transiting circumbinary planet systems, only Kepler-47 is known to contain more than one planet. Kepler-47 b (the inner planet) has an orbital period of 49.5 days and a radius of about $3,R_{oplus}$. Kepler-47 c (the outer plane
t) has an orbital period of 303.2 days and a radius of about $4.7,R_{oplus}$. Here we report the discovery of a third planet, Kepler-47 d (the middle planet), which has an orbital period of 187.4 days and a radius of about $7,R_{oplus}$. The presence of the middle planet allows us to place much better constraints on the masses of all three planets, where the $1sigma$ ranges are less than $26,M_{oplus}$, between $7-43,M_{oplus}$, and between $2-5,M_{oplus}$ for the inner, middle, and outer planets, respectively. The middle and outer planets have low bulk densities, with $rho_{rm middle} < 0.68$ g cm$^{-3}$ and $rho_{rm outer} < 0.26$ g cm$^{-3}$ at the $1sigma$ level. The two outer planets are tightly packed, assuming the nominal masses, meaning no other planet could stably orbit between them. All of the orbits have low eccentricities and are nearly coplanar, disfavoring violent scattering scenarios and suggesting gentle migration in the protoplanetary disk.
We present the results of a study of the prospect of detecting habitable Trojan planets in the Kepler Habitable Zone circumbinary planetary systems (Kepler-16, -47, -453, -1647, -1661). We integrated the orbits of 10,000 separate N-body systems (N=4,
6), each with a one Earth-mass body in a randomly selected orbit near the L4 and L5 Lagrangian points of the host HZ circumbinary planet. We find that stable Trojan planets are restricted to a narrow range of semimajor axes in all five systems and limited to small eccentricities in Kepler-16, -47, and -1661. To assess the prospect of the detection of these habitable Trojan planets, we calculated the amplitudes of the variations they cause in the transit timing of their host bodies. Results show that the mean amplitudes of the transit timing variations (TTVs) correlate with the mass of the transiting planet and range from 70 minutes for Kepler-16b to 390 minutes for Kepler-47c. Our analysis indicates that the TTVs of the circumbinary planets caused by these Trojan bodies fall within the detectable range of timing precision obtained from the Kepler telescopes long-cadence data. The latter points to Kepler data as a viable source to search for habitable Trojan planets.
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