The Origin of Jovian Planets in Protostellar Disks: The Role of Dead Zones

The final masses of Jovian planets are attained when the tidal torques that they exert on their surrounding protostellar disks are sufficient to open gaps in the face of disk viscosity, thereby shutting off any further accretion. In sufficiently well ionized disks, the predominant form of disk viscosity originates from the magnetorotational instability (MRI) that drives hydromagnetic disk turbulence. In the region of sufficiently low ionization rate, the so-called dead zone, turbulence is damped and we show that lower mass planets will be formed. We considered three ionization sources (X-rays, cosmic rays, and radioactive elements) and determined the size of a dead zone for the total ionization rate by using a radiative, hydrostatic equilibrium disk model developed by Chiang and coworkers. We studied a range of surface mass density (Σ0 = 103-105 g cm-2) and X-ray energy (kTX = 1-10 keV). We also compared the ionization rate of such a disk by X-rays with cosmic rays and find that the latter dominate X-rays in ionizing protostellar disks unless the X-ray energy is very high (5-10 keV). Among our major conclusions are that for typical conditions, dead zones encompass a region extending out to several AU, the region in which terrestrial planets are found in our solar system. Our results suggest that the division between low- and high-mass planets in exosolar planetary systems is a consequence of the presence of a dead zone in their natal protoplanetary disks. We also find that the extent of a dead zone is mainly dependent on the disk's surface mass density. Our results provide further support for the idea that Jovian planets in exosolar systems must have migrated substantially inward from their points of origin.