Debris disks as signposts of terrestrial planet formation II. Dependence of exoplanet architectures on giant planet and disk properties

We present models for the formation of terrestrial planets, and the collisional evolution of debris disks, in planetary systems that contain multiple marginally unstable gas giants. We previously showed that in such systems, the dynamics of the giant planets introduces a correlation between the presence of terrestrial planets and cold dust, i.e., debris disks, which is particularly pronounced at lambda similar to 70 mu m. Here we present new simulations that show that this connection is qualitatively robust to a range of parameters: the mass distribution of the giant planets, the width and mass distribution of the outer planetesimal disk, and the presence of gas in the disk when the giant planets become unstable. We discuss how variations in these parameters affect the evolution. We find that systems with equal-mass giant planets undergo the most violent instabilities, and that these destroy both terrestrial planets and the outer planetesimal disks that produce debris disks. In contrast, systems with low-mass giant planets efficiently produce both terrestrial planets and debris disks. A large fraction of systems with low-mass (M less than or similar to 30 M-circle plus) outermost giant planets have final planetary separations that, scaled to the planets' masses, are as large or larger than the Saturn-Uranus and Uranus-Neptune separations in the solar system. We find that the gaps between these planets are not only dynamically stable to test particles, but are frequently populated by planetesimals. The possibility of planetesimal belts between outer giant planets should be taken into account when interpreting debris disk SEDs. In addition, the presence of similar to Earth-mass seeds in outer planetesimal disks causes the disks to radially spread to colder temperatures, and leads to a slow depletion of the outer planetesimal disk from the inside out. We argue that this may explain the very low frequency of > 1 Gyrold solar-type stars with observed 24 mu m excesses. Our simulations do not sample the full range of plausible initial conditions for planetary systems. However, among the configurations explored, the best candidates for hosting terrestrial planets at similar to 1 AU are stars older than 0.1-1 Gyr with bright debris disks at 70 mu m but with no currently-known giant planets. These systems combine evidence for the presence of ample rocky building blocks, with giant planet properties that are least likely to undergo destructive dynamical evolution. Thus, we predict two correlations that should be detected by upcoming surveys: an anti-correlation between debris disks and eccentric giant planets and a positive correlation between debris disks and terrestrial planets.