Dynamical relaxation and massive extrasolar planets

Following the suggestion of Black that some massive extrasolar planets may be associated with the tail of the distribution of stellar companions, we i nvestigate a scenario in which 5 less than or equal to N less than or equal to 100 planetary mass objects are assumed to form rapidly through a fragme ntation process occuring in a disc or protostellar envelope on a scale of 1 00 au. These are assumed to have formed rapidly enough through gravitationa l instability or fragmentation that their orbits can undergo dynamical rela xation on a time-scale of similar to 100 orbits. Under a wide range of initial conditions and assumptions, the relaxation pr ocess ends with either (i) one potential 'hot Jupiter' plus up to two 'exte rnal' companions, i.e. planets orbiting near the outer edge of the initial distribution; (ii) one or two 'external' planets or even none at all; (iii) one planet on an orbit with a semi-major axis of 10 to 100 times smaller t han the outer boundary radius of the inital distribution together with an ' external' companion. Most of the other objects are ejected and could contri bute to a population of free-floating planets. Apart from the potential 'ho t Jupiters', all the bound objects are on orbits with high eccentricity, an d also with a range of inclination with respect to the stellar equatorial p lane. We found that, apart from the close orbiters, the probability of endi ng up with a planet orbiting at a given distance from the central star incr eases with the distance. This is because of the tendency of the relaxation process to lead to collisions with the central star. The scenario we envisi on here does not impose any upper limit on the mass of the planets. We disc uss the application of these results to some of the more massive extrasolar planets.