On the interaction between embedded planets and the corotation region of protoplanetary discs

PhDDisc material in the corotation region librates with respect to low-mass planets on horseshoe trajectories. The exchange of angular momentum associated with this libration gives rise to the non-linear corotation torque (the horseshoe drag). For the first project described herein, we ran a suite of high-resolution 2D hydrodynamic simulations of low-mass (5 Earth mass) planets, at eccentricities 0 e < 0.3, embedded in both viscous protoplanetary discs with entropy relaxation and inviscid discs without. The attenuation of the corotation torque was obtained from these simulations and found to be well-fitted by an exponential decay with a characteristic ‘e-folding eccentricity’ that scales linearly with disc scale height. These results were tested with different disc scale heights between 0.03 and 0.1 and with a 10 Earth mass planet. In the second project in this thesis we sought to extend on these results by examining the case of an embedded 5 Earth mass planet in three dimensional discs. We found that our scaling relation held in this new case, confirming that it is possible to use 2D simulations with a softening parameter to capture the behaviour of the corotation torque. We investigated the time-averaged horseshoe width as a function of altitude and found that the corotation region extends from the midplane to around three scale heights, changing most near the midplane for eccentric planets. The final project looked at 3D radiative discs, under the influence of stellar irradiation, with more massive embedded planets capable of triggering gap formation. We use the pluto code to simulate a Jupiter mass planet at 5 AU in a protoplanetary disc. We describe our progress in understanding the process of gap formation in a case study of this class of hitherto undescribed disc.STFC PhD studentship

On the corotation torque for low-mass eccentric planets

SMF acknowledges the support of an STFC PhD studentship. The simulations presented in this paper were performed on the QMUL HPC facility purchased under the SRIF initiatives

Survivability of copper projectiles during hypervelocity impacts in porous ice: A laboratory investigation of the survivability of projectiles impacting comets or other bodies

AbstractDuring hypervelocity impact (>a few kms−1) the resulting cratering and/or disruption of the target body often outweighs interest on the outcome of the projectile material, with the majority of projectiles assumed to be vaporised. However, on Earth, fragments, often metallic, have been recovered from impact sites, meaning that metallic projectile fragments may survive a hypervelocity impact and still exist within the wall, floor and/or ejecta of the impact crater post-impact. The discovery of the remnant impactor composition within the craters of asteroids, planets and comets could provide further information regarding the impact history of a body. Accordingly, we study in the laboratory the survivability of 1 and 2mm diameter copper projectiles fired onto ice at speeds between 1.00 and 7.05kms−1. The projectile was recovered intact at speeds up to 1.50kms−1, with no ductile deformation, but some surface pitting was observed. At 2.39kms−1, the projectile showed increasing ductile deformation and broke into two parts. Above velocities of 2.60kms−1 increasing numbers of projectile fragments were identified post impact, with the mean size of the fragments decreasing with increasing impact velocity. The decrease in size also corresponds with an increase in the number of projectile fragments recovered, as with increasing shock pressure the projectile material is more intensely disrupted, producing smaller and more numerous fragments. The damage to the projectile is divided into four classes with increasing speed and shock pressure: (1) minimal damage, (2) ductile deformation, start of break up, (3) increasing fragmentation, and (4) complete fragmentation. The implications of such behaviour is considered for specific examples of impacts of metallic impactors onto Solar System bodies, including LCROSS impacting the Moon, iron meteorites onto Mars and NASA’s “Deep Impact” mission where a spacecraft impacted a comet

On the formation of planetary systems via oligarchic growth in thermally evolving viscous discs

GALC acknowledges the support of an STFC PhD studentship. The simulations presented in this paper were performed on the QMUL HPC facility purchased under the SRIF initiatives

Hydrocode modelling of hypervelocity impacts on ice

Experimental data are now widely available for the size of craters resulting from hypervelocity impacts of millimetre scale projectiles onto water ice targets. At such size scales the bowl shaped crater formed in ductile materials, or in larger scale impacts, is here surrounded by a large spallation zone due to the brittle nature of the ice. Modelling of these impacts therefore has to take account of this spallation. Here we used the iSALE2 hydrocode to simulate such impacts and compared the results to experimental data. We found that it was possible to reproduce the experimental data over a range of speeds (1–7 km s−1) for aluminium and copper projectiles. Initially, to reproduce the large spallation regions around the craters it was assumed that above a certain degree of damage, material was removed by spallation. However this simple one-parameter model failed to model the crater depth adequately. Accordingly, to obtain the best agreement of the simulations with the experimental data, a two-step ice strength was introduced, whereby above a critical amount of damage (0.95), the yield strength reduced from 1 MPa (intact) to 70 kPa (damaged). As a result, experimental data for crater depth and diameter and the results of the simulations agree to within 6% for diameter and 5% for depth over the impact energy range used in the experiments (1–240 J)

Survival of the impactor during hypervelocity collisions – I. An analogue for low porosity targets

Recent observations of asteroidal surfaces indicate the presence of materials that do not match the bulk lithology of the body. A possible explanation for the presence of these exogenous materials is that they are products of interasteroid impacts in the Main Belt, and thus interest has increased in understanding the fate of the projectile during hypervelocity impacts. In order to gain insight into the fate of impactor, we have carried out a laboratory programme, covering the velocity range of 0.38–3.50 km s?1, devoted to measuring the survivability, fragmentation and final state of the impactor. Forsterite olivine and synthetic basalt projectiles were fired on to low porosity (1 km s?1). After each shot, we examined the largest peridot fragments with Raman spectroscopy and no melt or alteration in the final state of the projectile was observed

The Role of Disc Self-Gravity in Circumbinary Planet Systems: II. Planet Evolution

We present the results of hydrodynamic simulations examining migration and growth of planets embedded in self-gravitating circumbinary discs. The binary star parameters are chosen to mimic those of the Kepler-16, -34 and -35 systems; the aim of this study is to examine the role of disc mass in determining the stopping locations of migrating planets at the edge of the cavity created by the central binary. Disc self-gravity can cause significant shrinkage of the cavity for disc masses in excess of 5--10 $\times$ the minimum mass solar nebula model. Planets forming early in the disc lifetime can migrate through the disc and stall at locations closer to the central star than is normally the case for lower mass discs, resulting in closer agreement between simulated and observed orbital architecture. The presence of a planet orbiting in the cavity of a massive disc can prevent the cavity size from expanding to the size of a lower mass disc. As the disc mass reduces over long time scales, this indicates that circumbinary planet systems retain memory of their initial conditions. Our simulations produce planetary orbits in good agreement with Kepler-16b without the need for self-gravity; Kepler-34 analogue systems produce wide and highly eccentric cavities, and self-gravity improves the agreement between simulations and data. Kepler-35b is more difficult to explain in detail due to it's relatively low mass, which results in the simulated stopping location being at a larger radius than that observed