Predictions for the Correlation between Giant and Terrestrial Extrasolar Planets in Dynamically Evolved Systems

Abstract

The large eccentricities of many giant extrasolar planets may represent the endpoint of gravitational scattering in initially more crowded systems. If so, the early evolution of the giant planets is likely to be more restrictive of terrestrial planet formation than would be inferred from the current, dynamically quiescent configurations. Here we study statistically the extent of the anticorrelation between giant planets and terrestrial planets expected in a scattering model. We use marginally stable systems of three giant planets, with a realistic range of planetary masses, as a simple model for the initial conditions prior to scattering, and we show that after scattering the surviving planets reproduce well the known extrasolar planet eccentricities beyond a > 0.5 AU. By tracking the minimum periastron values of all planets during the evolution, we derive the distribution of orbital radii across which strong perturbations (from crossing orbits) are likely to affect low-mass planet formation. We find that scattering affects inner planet formation at orbital separations less than 50% of the final periastron distance, qfm, of the innermost massive planet in approximately 30% of the realizations and can occasionally influence planet formation at orbital separations less than 20% of qfm. The domain of influence of the scattering massive planets increases as the mass differential between the massive planets decreases. Observational study of the correlation between massive and terrestrial extrasolar planets in the same system has the potential to constrain the origin of planetary eccentricity.