Inside-out Planet Formation. V. Structure of the Inner Disk as Implied by the MRI

Abstract

The ubiquity of Earth- to super-Earth-sized planets found very close to their host stars has motivated in situ formation models. In particular, inside-out planet formation is a scenario in which planets coalesce sequentially in the disk, at the local gas pressure maximum near the inner boundary of the dead zone. The pressure maximum arises from a decline in viscosity, going from the active innermost disk (where thermal ionization yields high viscosities via the magnetorotational instability [MRI]) to the adjacent dead zone (where the MRI is quenched). Previous studies of the pressure maximum, based on α -disk models, have assumed ad hoc values for the viscosity parameter α in the active zone, ignoring the detailed MRI physics. Here we explicitly couple the MRI criteria to the α -disk equations, to find steady-state solutions for the disk structure. We consider both Ohmic and ambipolar resistivities, a range of disk accretion rates (10 −10 –10 −8   M ⊙ yr −1 ), stellar masses (0.1–1 M ⊙ ), and fiducial values of the non -MRI α -viscosity in the dead zone ( α DZ  = 10 −5 to 10 −3 ). We find that (1) a midplane pressure maximum forms radially outside the dead zone inner boundary; (2) Hall resistivity dominates near the inner disk midplane, perhaps explaining why close-in planets do not form in ∼50% of systems; (3) X-ray ionization can compete with thermal ionization in the inner disk, because of the low steady-state surface density there; and (4) our inner disks are viscously unstable to surface density perturbations.