On the evolution of multiple protoplanets embedded in a protostellar disc

Free access article

Issue		A&A Volume 450, Number 2, May I 2006


Page(s)		833 - 853
Section		Planets and planetary systems
DOI		http://dx.doi.org/10.1051/0004-6361:20054551

A&A 450, 833-853 (2006)
DOI: 10.1051/0004-6361:20054551

On the evolution of multiple protoplanets embedded in a protostellar disc

P. Cresswell and R. P. Nelson

Astronomy Unit, Queen Mary, University of London, Mile End Rd, London, E1 4NS, UK
e-mail: P.Cresswell@qmul.ac.uk

(Received 19 November 2005 / Accepted 17 January 2006)

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 $e \ga H/r$ , 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 ${\sim} 10^6$ 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.

Key words: stars: planetary systems: protoplanetary disks -- planets and satellites: formation -- stars: planetary systems: formation

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