The Validity of the Super-Particle Approximation during Planetesimal Formation

The formation mechanism of planetesimals in protoplanetary discs is hotly debated. Currently, the favoured model involves the accumulation of meter-sized objects within a turbulent disc, followed by a phase of gravitational instability. At best one can simulate a few million particles numerically as opposed to the several trillion meter-sized particles expected in a real protoplanetary disc. Therefore, single particles are often used as super-particles to represent a distribution of many smaller particles. It is assumed that small scale phenomena do not play a role and particle collisions are not modeled. The super-particle approximation can only be valid in a collisionless or strongly collisional system, however, in many recent numerical simulations this is not the case. In this work we present new results from numerical simulations of planetesimal formation via gravitational instability. A scaled system is studied that does not require the use of super-particles. We find that the scaled particles can be used to model the initial phases of clumping if the properties of the scaled particles are chosen such that all important timescales in the system are equivalent to what is expected in a real protoplanetary disc. Constraints are given for the number of particles needed in order to achieve numerical convergence. We compare this new method to the standard super-particle approach. We find that the super-particle approach produces unreliable results that depend on artifacts such as the gravitational softening in both the requirement for gravitational collapse and the resulting clump statistics. Our results show that short range interactions (collisions) have to be modelled properly.Comment: 10 pages, 7 figures, accepted for publication in Astronomy and Astrophysic

Erosive Hit-and-Run Impact Events: Debris Unbound

Erosive collisions among planetary embryos in the inner solar system can lead to multiple remnant bodies, varied in mass, composition and residual velocity. Some of the smaller, unbound debris may become available to seed the main asteroid belt. The makeup of these collisionally produced bodies is different from the canonical chondritic composition, in terms of rock/iron ratio and may contain further shock-processed material. Having some of the material in the asteroid belt owe its origin from collisions of larger planetary bodies may help in explaining some of the diversity and oddities in composition of different asteroid groups.Comment: 7 pages, 3 figure

Explaining the variability of WD 1145+017 with simulations of asteroid tidal disruption

Post-main-sequence planetary science has been galvanised by the striking variability, depth and shape of the photometric transit curves due to objects orbiting white dwarf WD 1145+017, a star which also hosts a dusty debris disc and circumstellar gas, and displays strong metal atmospheric pollution. However, the physical properties of the likely asteroid which is discharging disintegrating fragments remain largely unconstrained from the observations. This process has not yet been modelled numerically. Here, we use the N-body code PKDGRAV to compute dissipation properties for asteroids of different spins, densities, masses, and eccentricities. We simulate both homogeneous and differentiated asteroids, for up to two years, and find that the disruption timescale is strongly dependent on density and eccentricity, but weakly dependent on mass and spin. We find that primarily rocky differentiated bodies with moderate (~3-4 g/cm^3) bulk densities on near-circular (e <~ 0.1) orbits can remain intact while occasionally shedding mass from their mantles. These results suggest that the asteroid orbiting WD 1145+017 is differentiated, resides just outside of the Roche radius for bulk density but just inside the Roche radius for mantle density, and is more akin physically to an asteroid like Vesta instead of one like Itokawa.Comment: Accepted in MNRAS. Movies here!: http://www.star.bris.ac.uk/pcarter/WD1145_asteroid_disruption

Hiding in the Shadows II: Collisional Dust as Exoplanet Markers

Observations of the youngest planets ($\sim$1-10 Myr for a transitional disk) will increase the accuracy of our planet formation models. Unfortunately, observations of such planets are challenging and time-consuming to undertake even in ideal circumstances. Therefore, we propose the determination of a set of markers that can pre-select promising exoplanet-hosting candidate disks. To this end, N-body simulations were conducted to investigate the effect of an embedded Jupiter mass planet on the dynamics of the surrounding planetesimal disk and the resulting creation of second generation collisional dust. We use a new collision model that allows fragmentation and erosion of planetesimals, and dust-sized fragments are simulated in a post process step including non-gravitational forces due to stellar radiation and a gaseous protoplanetary disk. Synthetic images from our numerical simulations show a bright double ring at 850 $\mu$m for a low eccentricity planet, whereas a high eccentricity planet would produce a characteristic inner ring with asymmetries in the disk. In the presence of first generation primordial dust these markers would be difficult to detect far from the orbit of the embedded planet, but would be detectable inside a gap of planetary origin in a transitional disk.Comment: Accepted for publication in Ap

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

Explaining the variability of WD 1145+017 with simulations of asteroid tidal disruption

Post-main-sequence planetary science has been galvanised by the striking variability, depth and shape of the photometric transit curves due to objects orbiting white dwarf WD 1145+017, a star which also hosts a dusty debris disc and circumstellar gas, and displays strong metal atmospheric pollution. However, the physical properties of the likely asteroid which is discharging disintegrating fragments remain largely unconstrained from the observations. This process has not yet been modelled numerically. Here, we use the N-body code PKDGRAV to compute dissipation properties for asteroids of different spins, densities, masses, and eccentricities. We simulate both homogeneous and differentiated asteroids, for up to two years, and find that the disruption timescale is strongly dependent on density and eccentricity, but weakly dependent on mass and spin. We find that primarily rocky differentiated bodies with moderate (∼ 3−4 g/cm3 ) bulk densities on near-circular (e . 0.1) orbits can remain intact while occasionally shedding mass from their mantles. These results suggest that the asteroid orbiting WD 1145+017 is differentiated, resides just outside of the Roche radius for bulk density but just inside the Roche radius for mantle density, and is more akin physically to an asteroid like Vesta instead of one like Itokawa

Planetary embryo collisions and the wiggly nature of extreme debris discs

In this paper, we present results from a multi-stage numerical campaign to begin to explain and determine why extreme debris disk detections are rare, what types of impacts will result in extreme debris disks and what we can learn about the parameters of the collision from the extreme debris disks. We begin by simulating many giant impacts using a smoothed particle hydrodynamical code with tabulated equations of state and track the escaping vapour from the collision. Using an $N$-body code, we simulate the spatial evolution of the vapour generated dust post-impact. We show that impacts release vapour anisotropically not isotropically as has been assumed previously and that the distribution of the resulting generated dust is dependent on the mass ratio and impact angle of the collision. In addition, we show that the anisotropic distribution of post-collision dust can cause the formation or lack of formation of the short-term variation in flux depending on the orientation of the collision with respect to the orbit around the central star. Finally, our results suggest that there is a narrow region of semi-major axis where a vapour generated disk would be observable for any significant amount of time implying that giant impacts where most of the escaping mass is in vapour would not be observed often but this does not mean that the collisions are not occurring.Comment: 21 pages, 13 figures, 2 tables, accepted for publication in MNRA

How Not to Build Tatooine: The Difficulty of In Situ Formation of Circumbinary Planets Kepler 16b, Kepler 34b, and Kepler 35b

We study planetesimal evolution in circumbinary disks, focusing on the three systems Kepler 16, 34 and 35 where planets have been discovered recently. We show that for circumbinary planetesimals, in addition to secular forcing, eccentricities evolve on a dynamical timescale, which leads to orbital crossings even in the presence of gas drag. This makes the current locations of the circumbinary Kepler planets hostile to planetesimal accretion. We then present results from simulations including planetesimal formation and dust accretion, and show that even in the most favourable case of 100% efficient dust accretion, in situ growth starting from planetesimals smaller than ~10 km is difficult for Kepler 16b, Kepler 34b and Kepler 35b. These planets were likely assembled further out in the disk, and migrated inward to their current location.Comment: 5 pages, 3 figures, accepted for publication in ApJ