Terrestrial planet formation in exoplanetary systems with a giant planet on an external orbit

The Epsilon Eridani and 47 UMa extrasolar systems both have moderately massive planets orbiting relatively far away from the central star (at 3.3 and beyond 2.1 AU, respectively). This peculiarity makes them possible candidates for harboring terrestrial planets in their inner regions since the external giant planet might not have inhibited planet growth in the neighborhood of the star. Here we numerically investigate how the accretion of terrestrial planets may have been affected by the presence of the detected giant planets in external orbits. The uncertain timing of the giant planet formation with respect to the planetesimal accumulation process lead us to consider two possible scenarios: 1) the perturbing massive planet was fully formed when the planetesimals in the inner zone were still in their early phases of accumulation, and 2) the giant planet reached its final mass only later on when lunar-sized embryos were already present in the inner disk. In the first case we have used a deterministic numerical algorithm to compute the relative velocity distribution in a swarm of planetesimals affected by the gravitational perturbations of the giant planet and, possibly, by gas drag. The second scenario is explored by using the symplectic algorithm by Chambers (1999) to simulate the late stage of terrestrial planet formation. The Epsilon Eridani system turns out to be a very hostile environment for planetary formation in the terrestrial region when the giant planet formed early. The planet's high eccentricity (0.608) induces very large relative velocities between planetesimals in inner orbits and collisions result mostly in disruption rather than accretion. On the other hand, if large embryos had enough time to form before the completion of the giant planet, they can accrete each other in giant impacts and coalesce into a few terrestrial planets within 0.8 AU from the star. For the 47 UMa system the situation is quite similar. The large mass of the inner giant planet excites large eccentricities among the planetesimals in the terrestrial region preventing accumulation. However, the damping effect on the relative velocities caused by gas drag opens a chance for accretion in a small region around the star inside 0.3 AU. The second and more distant planet recently discovered around 47 Uma does not significantly affect the encounter velocity distribution in the inner regions of the system. As for Epsilon Eridani, orderly growth of lunar-sized embryos takes place within 0.8 AU in presence of a late-formed giant planet. In either case, beyond 0.8 AU planetesimals or planetary embryos are rapidly removed by the massive planet perturbations.