Forming Cold Jupiters from Planetesimal Rings with Planet Population Synthesis Models

Recent exoplanet observations have provided rich information of cold Jupiters (CJs), typically defined as planets with masses larger than 0.3 Jupiter mass and orbital distances larger than 1 au. The orbital and mass distribution of CJs are important for constraining their formation history. It has been reported that the occurrence rate of giant planets increases with orbital period to the central star, and turns over at a location that roughly corresponds to the snow line of Sun-like stars. Further, the density distribution of CJs on the semi-major axis - mass diagram (in log-log scale) shows an inner boundary with an approximate slope of two. Such an inner boundary provides valuable constraints on the formation and evolution of CJs. Theories of planetesimal formation predicts that planetesimals can form within ring-like structures in the protoplanetary disk, typically near the snow line. We believe that these planetesimal rings with locally enhanced solid surface density can be preferable locations for giant planet formation. In this work. we aim at interpreting the two-dimensional (semi-major axis, mass) distribution of the observed CJs by assuming that these planets form within a planetesimal ring located near the water snow line. A planet population synthesis model (the Ida & Lin model) is used to compare the mass and orbital distribution of the synthetic planets with the observations. In particular, we focus on the occurrence of CJs with respective to the orbital distance and the slope of the inner boundary of CJ distribution on the semi-major axis - mass diagram. Our results suggest that if CJs form from planetesimal rings near the water snow line, the above-mentioned observational features can be reproduced. Our findings imply that with efficient core growth owing to the enhanced solid surface density, planetesimal ring structures near the snow line are ideal locations for cold giant planet formation.