Dead, undead, and zombie zones in protostellar disks as a function of stellar mass

Abstract

We investigate the viability of the magnetorotational instability (MRI) in X-ray ionized viscous accretion disks around both solar-type stars and very low mass stars. In particular, we determine the disk regions where the MRI can be shut off either by Ohmic resistivity (the so-called dead and undead zones) or by ambipolar diffusion (a region we term the zombie zone). We consider two stellar masses: M * = 0.7 M ⊙ and 0.1 M ⊙. In each case, we assume that: the disk surface density profile is that of a scaled Minimum Mass Solar Nebula, with M disk/M * = 0.01 as suggested by current data; disk ionization is driven primarily by stellar X-rays, complemented by cosmic rays and radionuclides; and the stellar X-ray luminosity scales with bolometric luminosity as LX /L * ≈ 10-3.5, as observed. Ionization rates are calculated with the MOCCASIN Monte Carlo X-ray transport code, and ionization balance determined using a simplified chemical network, including well-mixed 0.1 μm grains at various levels of depletion. We find that (1) ambipolar diffusion is the primary factor controlling MRI activity in disks around both solar-type and very low mass classical T Tauri stars. Assuming that the MRI yields the maximum possible field strength at each radius, we further find that: (2) the MRI-active layer constitutes only ∼5%-10% of the total disk mass; (3) the accretion rate (M) varies radially in both magnitude and sign (inward or outward), implying time-variable accretion as well as the creation of disk gaps and overdensities, with consequences for planet formation and migration; (4) achieving the empirical accretion rates in solar-type and very low mass stars requires a depletion of well-mixed small grains (via grain growth and/or settling) by a factor of 10-1000 relative to the standard dust-to-gas mass ratio of 10-2; and (5) the current non-detection of polarized emission from field-aligned grains in the outer disk regions is consistent with active MRI at those radii. © 2013. The American Astronomical Society. All rights reserved.