Possible commensurabilities among pairs of extrasolar planets

Abstract

We investigate the possible commensurabilities to be expected when two protoplanets in the Jovian mass range, gravitationally interacting with each other and an external protoplanetary disc, are driven by disc-induced orbital migration of the outer protoplanet into a commensurability which is then maintained in subsequent evolution. We find that for a variety of protoplanet masses and typical protoplanetary disc properties, as well as the setting up of 2:1 commensurabilities of the type recently observed in GJ 876, 3:1 commensurabilities are often formed, in addition to 4:1, 5:1 and 5:2 commensurabilities which occur less frequently. The higher order commensurabilites are favoured when either one of the planets is massive, or the inner planet begins with a significant orbital eccentricity. Detection of such commensurabilities could yield important information relating to the operation of protoplanetary disc interactions during and shortly post-formation.