2010ApJ...719.1454M

We present 230 realizations of a numerical model of planet formation in systems without gas giants. These represent a scenario in which protoplanets grow in a region of a circumstellar disk where water ice condenses and the surface density of solids is enhanced (the "ice line"), but fail to accrete massive gas envelopes before the gaseous disk is dispersed. Each simulation consists of a small number of gravitationally interacting oligarchs (protoplanets) and a much larger number of small bodies that represent the natal disk of planetesimals. Time zero of each simulation represents the epoch at which the gas has disappeared, and the dynamics are integrated for 5 billion years (Gyr). We investigate systems with varying initial number of oligarchs, oligarch spacing, location of the ice line, total mass in the ice line, and oligarch mean density. Systems become chaotic in ∼1 Myr but settle into stable configurations in 10-100 Myr. We find: (1) runs consistently produce a 5-9 M_⊕planet at a semimajor axis of 0.25-0.6 times the position of the ice line, (2) the distribution of planets' orbital eccentricities is distinct from, and skewed toward lower values than the observed distribution of (giant) exoplanet orbits, (3) Inner systems of two dominant planets (e.g., Earth and Venus) are not stable or do not form because of the gravitational influence of the innermost icy planet. The planets predicted by our model are unlikely to be detected by current Doppler observations. Microlensing is currently sensitive to the most massive planets found in our simulations, and may have already found several analogs. A scenario where up to 60% of stars host systems such as those we simulate is consistent with all the available data. We predict that, if this scenario holds, the NASA Kepler spacecraft will detect about 120 planets by two or more transits over the course of its 3.5 yr mission. Furthermore, we predict detectable transit timing variations exceeding 20 minutes due to the presence of additional outer planets. Future microlensing surveys will detect ∼130 analogs over a 5 yr survey, including a handful of multiple-planet systems. Finally, the Space Interferometry Mission (SIM-Lite) should be capable of detecting 96% of the innermost icy planets over the course of a 5 yr mission.