Interactions between planets and debris disks

The planetesimals which make up debris disks are dynamically perturbed by any planets that are present in the system; these perturbations influence the disk structure. By observing ~mm sized dust grains (which result from larger bodies colliding and grinding themselves down, and thus are expected to trace out the distribution of planetesimals) we can therefore make inferences about the planetary systems of stars with debris disks. For example, some of the best evidence for the history of our Solar System comes from studying the structure of the Sun's Asteroid and Edgeworth-Kuiper belts.

In the first instance this project is focusing on HD107146, a ~100Myr old solar-type star which hosts a relatively wide debris disk, extending from ~30 to 150AU. Recent ALMA observations of the disk suggest that there is a depletion in the surface density of planetesimals at around 80AU.

One possible explanation is that there is a planet of a few Earth masses on a circular orbit at ~80AU which is clearing the region immediately surrounding it of planetesimals. The exact shape of the depletion is not well-constrained, however: good fits to the observations are obtained from both a radial density profile that increases with distance but has a complete gap at ~80AU (as would be expected if there is a planet at the depletion), and a double-power-law profile that shows a partial depletion over a much broader range, which would require some other explanation.

Another idea that has been proposed is that a planet was scattered out into the disk on an eccentric orbit, and the observed structure is a result of the way the planet's orbit was circularised as it interacted with the disk. However, in cases where planets at large separations are seen and the debris disk is detected, the planet appears to have depleted the disk almost completely, in contrast to the relatively small depletion seen for HD107146; other scenarios should therefore be considered.

In this project we will consider how a multi-planet system would shape the disk; specifically, we will examine the effect of secular resonances. These occur where the precession rate of the planets equals that of the planetesimals in the disk, and act over long timescales to excite the eccentricities of these planetesimals. Objects on eccentric orbits will spend the majority of their time at distances not equal to their semi-major axis; this could therefore give rise to a depletion of the kind seen in the HD107146 system if there is a secular resonance at ~80AU.

We will begin by proposing a two-planet system, and aim to constrain the parameter space (consisting of the planet masses and distances) to as great an extent as possible by considering the requirements imposed by the observed disk structure and the secular interaction timescale.

N-body dynamical simulations will then be used to investigate the disk structures that would arise from various combinations of planets. The output from these simulations will also be post-processed to include the effect of disk depletion due to catastrophic collisions, which grind planetesimals into small particles which are blown out of the system by radiation pressure.

Having examined the specific example of HD107146, we aim to extend this secular analysis to other debris disks which show depletions; in the longer term we will also be considering more generally the observable effects of other types of planet-disk interaction.