On the evolution of multiple protoplanets embedded in a protostellar disc

Abstract

Context. Theory predicts that low mass protoplanets in a laminar protostellar disc will migrate into the central star prior to disc dispersal. It is known that protoplanets on orbits with eccentricity e > ∼ H/r, where H is the disc scale height and r is the radius, can halt or reverse their migration. Aims. We examine whether a system of interacting protoplanetary cores can excite and sustain significant eccentricity of the population, allowing some planetary cores to survive in the disc over its lifetime. Methods. We employ two distinct numerical schemes: an N-body code, adapted to include migration and eccentricity damping due to the gas disc via analytic prescriptions, and a hydrodynamics code that explicitly evolves a 2D protoplanetary disc model with embedded protoplanets. The former allows us to study the long term evolution, the latter to model the systems with greater fidelity but for shorter times. Results. After a brief period of chaotic interaction between the protoplanets that involves scattering, orbital exchange, collisions and the formation of co-orbital planets, we find that the system settles into a quiescent state of inward migration. Differential migration causes the protoplanets to form a series of mean motion resonances, such that a planet is often in resonance with both its interior and exterior neighbours. This helps prevent close encounters and leads to the protoplanetary swarm, or subgroups within it, migrating inward at a uniform rate. In about 2% of runs a single planet is scattered onto a distant orbit with significant eccentricity, allowing it to survive in the disc for ∼10 6 years. Over 20% of runs produce co-orbital planets that survive for the duration of the simulation, occupying mutual horseshoe or tadpole orbits. Conclusions. Disc-induced damping overwhelms eccentricity growth through planet-planet interactions, such that a protoplanetary swarm migrates inward. We suggest co-orbital planets may be observed in future exoplanet searches.

Orbital evolution of eccentric planets in radiative discs

“…Papaloizou & Larwood (2000) have also considered larger values for e and they find an extended eccentricity damping timescale such that de/dt ∝ e −2 if e > 1.1H/r. Cresswell & Nelson (2006) have performed hydrodynamical simulations of embedded small mass planets and find good agreement with the work by Papaloizou & Larwood (2000). These 2D results have been confirmed by Cresswell et al (2007) using fully 3D isothermal simulations.…”

Ten New and Updated Multiplanet Systems and a Survey of Exoplanetary Systems

“…HD 128311, a two-planet system, also appears to carry a signature of similar scattering (Sándor & Kley 2006 the required disk behavior and that predicted by hydrodynamical theories (Kley et al 2004). Simulations that include multiple protoplanets interacting with a protoplanet swarm show that most protoplanets will eventually accrete on to the star, leading to a planet occurrence rate lower than that observed (Cresswell & Nelson 2006). The increasing number of characterized multiplanet systems should help constrain these theories.…”

Accretion of Uranus and Neptune from inward-migrating planetary embryos blocked by Jupiter and Saturn

“…Second, the method of implementing in a N-body calculation synthetic forces computed from a 1D disk model is qualitatively reliable. It has been widely tested and used in similar studies, where it was shown to mimic the important gas effects on planets observed in genuine hydrodynamical simulations (e.g., Cresswell & Nelson 2006Morbidelli et al 2008).…”