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Dead, Undead and Zombie Zones in Protostellar Disks as a Function of Stellar Mass

We investigate the viability of the magnetorotational instability (MRI) in 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 ampipolar diffusion (a region we term the Zombie Zone). We consider 2 stellar masses: Mstar = 0.7 and 0.1 Msun. In each case, we assume that: the disk surface density profile is that of a scaled Minimum Mass Solar Nebula, with Mdisk/Mstar ~ 0.01 as currently estimated; disk ionisation 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/Lstar ~ 10^-3.5, as observed. Ionization rates are calculated with the MOCCASIN code, and ionisation balance determined using a simplified chemical network, including well-mixed 0.1 um 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 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 (Mdot) 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 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.