The Origin of Planetary System Architectures. I. Multiple Planet Traps in Gaseous Discs

The structure of planetary systems around their host stars depends on their initial formation conditions. Massive planets will likely be formed as a consequence of rapid migration of planetesimals and low mass cores into specific trapping sites in protoplanetary discs. We present analytical modeling of inhomogeneities in protoplanetary discs around a variety of young stars, - from Herbig Ae/Be to classical T Tauri and down to M stars, - and show how they give rise to planet traps. The positions of these traps define the initial orbital distribution of multiple protoplanets. We investigate both corotation and Lindblad torques, and show that a new trap arises from the (entropy-related) corotation torque. This arises at that disc radius where disc heating changes from viscous to stellar irradiation dominated processes. We demonstrate that up to three traps (heat transitions, ice lines and dead zones) can exist in a single disc, and that they move differently as the disc accretion rate $\dot{M}$ decreases with time. The interaction between the giant planets which grow in such traps may be a crucial ingredient for establishing planetary systems. We also demonstrate that the position of planet traps strongly depends on stellar masses and disc accretion rates. This indicates that host stars establish preferred scales of planetary systems formed around them. We discuss the potential of planet traps induced by ice lines of various molecules such as water and CO, and estimate the maximum and minimum mass of planets which undergo type I migration. We finally apply our analyses to accounting for the initial conditions proposed in the Nice model for the origin of our Solar system.