Disk-planets interactions and the diversity of period ratios in Kepler's multi-planetary systems

The Kepler mission is dramatically increasing the number of planets known in multi-planetary systems. Many adjacent planets have orbital period ratios near resonant values, with a tendency to be larger than required for exact first-order mean-motion resonances. This intriguing feature has been shown to be a natural outcome of orbital circularization of resonant planetary pairs due to star-planet tidal interactions. However, this feature holds in multi-planetary systems with periods longer than ten days, for which tidal circularization is unlikely to provide efficient divergent evolution of the planets orbits. Gravitational interactions between planets and their parent protoplanetary disk may instead provide efficient divergent evolution. For a planet pair embedded in a disk, we show that interactions between a planet and the wake of its companion can reverse convergent migration, and significantly increase the period ratio from a near-resonant value. Divergent evolution due to wake-planet interactions is particularly efficient when at least one of the planets opens a partial gap around its orbit. This mechanism could help account for the diversity of period ratios in Kepler's multiple systems comprising super-Earth to sub-jovian planets with periods greater than about ten days. Diversity is also expected for planet pairs massive enough to merge their gap. The efficiency of wake-planet interactions is then much reduced, but convergent migration may stall with a variety of period ratios depending on the density structure in the common gap. This is illustrated for the Kepler-46 system, for which we reproduce the period ratio of Kepler-46b and c.Comment: 15 pages, 11 figures, accepted for publication in Ap

Protoplanetary disks including radiative feedback from accreting planets

While recent observational progress is converging on the detection of compact regions of thermal emission due to embedded protoplanets, further theoretical predictions are needed to understand the response of a protoplanetary disk to the planet formation radiative feedback. This is particularly important to make predictions for the observability of circumplanetary regions. In this work we use 2D hydrodynamical simulations to examine the evolution of a viscous protoplanetary disk in which a luminous Jupiter-mass planet is embedded. We use an energy equation which includes the radiative heating of the planet as an additional mechanism for planet formation feedback. Several models are computed for planet luminosities ranging from $10^{-5}$ to $10^{-3}$ Solar luminosities. We find that the planet radiative feedback enhances the disk's accretion rate at the planet's orbital radius, producing a hotter and more luminous environement around the planet, independently of the prescription used to model the disk's turbulent viscosity. We also estimate the thermal signature of the planet feedback for our range of planet luminosities, finding that the emitted spectrum of a purely active disk, without passive heating, is appreciably modified in the infrared. We simulate the protoplanetary disk around HD 100546 where a planet companion is located at about 68 au from the star. Assuming the planet mass is 5 Jupiter masses and its luminosity is $\sim 2.5 \times 10^{-4} \, L_\odot$, we find that the radiative feedback of the planet increases the luminosity of its $\sim 5$ au circumplanetary disk from $10^{-5} \, \rm L_\odot$ (without feedback) to $10^{-3} \, \rm L_\odot$, corresponding to an emission of $\sim 1 \, \rm mJy$ in $L^\prime$ band after radiative transfer calculations, a value that is in good agreement with HD 100546b observations.Comment: 12 pages, 12 figures. Accepted for publication in The Astrophysical Journa

Influence of the circumbinary disk gravity on planetesimal accumulation in the Kepler 16 system

Recent observations from NASA's 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.Comment: Accepted for publication in A&

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

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.Comment: 6 pages, 5 figures, accepted for publication in ApJ

A substitute for the singular Green kernel in the Newtonian potential of celestial bodies

The "point mass singularity" inherent in Newton's law for gravitation represents a major difficulty in accurately determining the potential and forces inside continuous bodies. Here we report a simple and efficient analytical method to bypass the singular Green kernel 1/|r-r'| inside the source without altering the nature of the interaction. We build an equivalent kernel made up of a "cool kernel", which is fully regular (and contains the long-range -GM/r asymptotic behavior), and the gradient of a "hyperkernel", which is also regular. Compared to the initial kernel, these two components are easily integrated over the source volume using standard numerical techniques. The demonstration is presented for three-dimensional distributions in cylindrical coordinates, which are well-suited to describing rotating bodies (stars, discs, asteroids, etc.) as commonly found in the Universe. An example of implementation is given. The case of axial symmetry is treated in detail, and the accuracy is checked by considering an exact potential/surface density pair corresponding to a flat circular disc. This framework provides new tools to keep or even improve the physical realism of models and simulations of self-gravitating systems, and represents, for some of them, a conclusive alternative to softened gravity.Comment: Accepted for publication in A&A; 7 pages, color figure

Dust Traps in the Protoplanetary Disk MWC 758: Two Vortices Produced by Two Giant Planets?

Resolved ALMA and VLA observations indicate the existence of two dust traps in the protoplanetary disc MWC 758. By means of two-dimensional gas+dust hydrodynamical simulations post-processed with three-dimensional dust radiative transfer calculations, we show that the spirals in scattered light, the eccentric, asymmetric ring and the crescent-shaped structure in the (sub)millimetre can all be caused by two giant planets: a 1.5-Jupiter mass planet at 35 au (inside the spirals) and a 5-Jupiter mass planet at 140 au (outside the spirals). The outer planet forms a dust-trapping vortex at the inner edge of its gap (at ∼85 au), and the continuum emission of this dust trap reproduces the ALMA and VLA observations well. The outer planet triggers several spiral arms that are similar to those observed in polarized scattered light. The inner planet also forms a vortex at the outer edge of its gap (at ∼50 au), but it decays faster than the vortex induced by the outer planet, as a result of the disc’s turbulent viscosity. The vortex decay can explain the eccentric inner ring seen with ALMA as well as the low signal and larger azimuthal spread of this dust trap in VLA observations. Finding the thermal and kinematic signatures of both giant planets could verify the proposed scenario

The potential of discs from a "mean Green function"

By using various properties of the complete elliptic integrals, we have derived an alternative expression for the gravitational potential of axially symmetric bodies, which is free of singular kernel in contrast with the classical form. This is mainly a radial integral of the local surface density weighted by a regular "mean Green function" which depends explicitly on the body's vertical thickness. Rigorously, this result stands for a wide variety of configurations, as soon as the density structure is vertically homogeneous. Nevertheless, the sensitivity to vertical stratification | the Gaussian profile has been considered | appears weak provided that the surface density is conserved. For bodies with small aspect ratio (i.e. geometrically thin discs), a first-order Taylor expansion furnishes an excellent approximation for this mean Green function, the absolute error being of the fourth order in the aspect ratio. This formula is therefore well suited to studying the structure of self-gravitating discs and rings in the spirit of the "standard model of thin discs" where the vertical structure is often ignored, but it remains accurate for discs and tori of finite thickness. This approximation which perfectly saves the properties of Newton's law everywhere (in particular at large separations), is also very useful for dynamical studies where the body is just a source of gravity acting on external test particles.Comment: Accepted for publication in MNRAS, 11 page

The beta Pictoris system: Setting constraints on the planet and the disk structures at mid-IR wavelengths with NEAR

[abridged] We analyzed mid-infrared high-contrast coronagraphic images of the beta Pictoris system, taking advantage of the NEAR experiment using the VLT/VISIR instrument. The goal of our analysis is to investigate both the detection of the planet beta Pictoris b and of the disk features at mid-IR wavelengths. In addition, by combining several epochs of observation, we expect to constrain the position of the known clumps and improve our knowledge on the dynamics of the disk. To evaluate the planet b flux contribution, we extracted the photometry and compared it to the flux published in the literature. In addition, we used previous data from T-ReCS and VISIR, to study the evolution of the position of the southwest clump that was initially observed in the planetary disk back in 2003. While we did not detect the planet b, we were able to put constraints on the presence of circumplanetary material, ruling out the equivalent of a Saturn-like planetary ring around the planet. The disk presents several noticeable structures, including the known southwest clump. Using a 16-year baseline, sampled with five epochs of observations, we were able to examine the evolution of the clump: the clump orbits in a Keplerian motion with an sma of 56.1+-0.4 au. In addition to the known clump, the images clearly show the presence of a second clump on the northeast side of the disk and fainter and closer structures that are yet to be confirmed. We found correlations between the CO clumps detected with ALMA and the mid-IR images. If the circumplanetary material were located at the Roche radius, the maximum amount of dust determined from the flux upper limit around beta Pictoris b would correspond to the mass of an asteroid of 5 km in diameter. Finally, the Keplerian motion of the southwestern clump is possibly indicative of a yet-to-be-detected planet or signals the presence of a vortex.Comment: Accepted in Astronomy and Astrophysic