Planet Traps in Protoplanetary Disks and the Formation and Evolution of Planetary Systems

One of the most fundamental problems in theories of planet formation in protoplanetary disks is planetary migration that arises from resonant, tidal interactions of forming planets with the natal disks. This rapid inward migration, also known as type I migration, leads to the well-known problem that its timescale is about two orders of magnitude shorter than the typical disk lifetime, so that (proto)planets plunge into the host stars within the disk lifetime. This provides a huge hurdle for understanding the statistical properties of observed extra solar planets that now amount to more than 700. In this thesis, we focus on one of the most general properties of protoplanetary disks - inhomogeneities. A large amount of theoretical and observational work currently suggests that protoplanetary disks are most likely to possess several kinds of inhomogeneities. Planetary migration is highly sensitive to the disk properties such as the surface density and temperature of disks, and the sensitivity leads to the formation of trapping sites for rapid type I migration at disk inhomogeneities. These local sites capturing planets undergoing migration are referred to as planet traps. We perform both analytical and numerical studies for exploring formation mechanisms of planet traps at disk inhomogeneities and their consequences for the formation and evolution of planetary systems. We focus on three kinds of the disk inhomogeneities: dead zones, ice lines, and transitions of heat sources in protoplanetary disks we refer to as heat transitions. Dead zones are an inevitable consequence of disk turbulence originating from magnetorotational instabilities (MRIs) that take place in (partially) ionized disks threaded by weak magnetic fields. One of the fundamental properties of the dead zone is a low level of turbulence there, which is the outcome of the high density, preventing the region from being ionized due to X-rays from the central stars and cosmic rays. Ice lines are formed due to low disk temperatures which lead to condensation of specific molecules there. Heat transitions arise as a consequence of the switching of the dominant heating process from viscous heating to stellar irradiation as the distance to the host stars increases. We summarize our major findings. 1) rapid dust settling arising in dead zones leaves a dusty wall at the outer edge of the dead zones beyond which the disks are quite turbulent, so that dust is fully mixed with the gas. Efficient heating of the wall by stellar irradiation and the subsequent backward heating of the dead zones by the wall result in a positive temperature gradient in the dead zones. This inversion in the temperature profiles leads to outward migration there. 2) Any protoplanetary disk is likely to possess up to three types of planet traps that are specified by characteristic disk radii (dead zone, ice line and heat transition traps). Disk evolution, driven by disk viscosity, lowers both the accretion rate and surface density of gas and moves traps inward at different rates. This suggests that the interactions of (proto)planets captured at different traps play the dominant role in constructing planetary system architectures. Furthermore, the distribution of planet traps depends largely on stellar masses and accretion rates, so that they are one of the principle parameters for regulating the (initial) scale of planetary systems. 3) Both multiplicity and mobility of planet traps are crucial for understanding the statistical properties of observed extra solar planets. For instance, the mass-period relation - observational manifestation that planetary mass is an increasing function of orbital periods - can be understood by constructing and following evolutionary tracks of accreting planets in planet traps. These three contribution are new results in the field.