2013ApJ...775...53H

We present a Monte Carlo model for the structure of low-mass (total mass <25 M_⊕) planetary systems that form by the in situ gravitational assembly of planetary embryos into final planets. Our model includes distributions of mass, eccentricity, inclination, and period spacing that are based on the simulation of a disk of 20 M_⊕, forming planets around a solar-mass star, and assuming a power-law surface density distribution that drops with distance a as ∝ a.^–1.5. The output of the Monte Carlo model is then subjected to the selection effects that mimic the observations of a transiting planet search such as that performed by the Kepler satellite. The resulting comparison of the output to the properties of the observed sample yields an encouraging agreement in terms of the relative frequencies of multiple-planet systems and the distribution of the mutual inclinations when moderate tidal circularization is taken into account. The broad features of the period distribution and radius distribution can also be matched within this framework, although the model underpredicts the distribution of small period ratios. This likely indicates that some dissipation is still required in the formation process. The most striking deviation between the model and observations is in the ratio of single to multiple systems in that there are roughly 50% more single-planet candidates observed than are produced in any model population. This suggests that some systems must suffer additional attrition to reduce the number of planets or increase the range of inclinations.