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

TL;DR

This study explores how magnetic instabilities in protostellar disks depend on stellar mass, ionization, and dust properties, revealing limited MRI-active regions that influence accretion and planet formation.

Contribution

It provides a detailed analysis of MRI viability in disks around different stellar masses, incorporating ionization, dust depletion, and magnetic effects, which advances understanding of disk dynamics.

Findings

Ambipolar diffusion dominates MRI activity.

MRI-active layer is only 5-10% of disk mass.

Radial variation in accretion rates affects planet formation.

Abstract

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.