Thanatology in Protoplanetary Discs: the combined influence of Ohmic, Hall, and ambipolar diffusion on dead zones

Abstract: Protoplanetary discs are poorly ionised due to their low temperatures and high column densities, and are therefore subject to three "non-ideal" magnetohydrodynamic effects: Ohmic dissipation, ambipolar diffusion, and the Hall effect. The existence of magnetically driven turbulence in these discs has been a central question since the discovery of the magnetorotational instability. Early models considered Ohmic diffusion only and led to a scenario of layered accretion, in which a magnetically "dead" zone in the disc midplane is embedded within magnetically "active" surface layers at distances ~1-10 au from the central protostellar object. Recent work has suggested that a combination of Ohmic dissipation and ambipolar diffusion can render both the midplane and surface layers of the disc inactive and that torques due to magnetically driven outflows are required to explain the observed accretion rates. We reassess this picture by performing three-dimensional numerical simulations that include, for the first time, all three non-ideal MHD effects. We find that the Hall effect can generically "revive" dead zones by producing a dominant azimuthal magnetic field and a large-scale Maxwell stress throughout the midplane, provided the angular velocity and magnetic field satisfy Omega.B > 0. The attendant large magnetic pressure modifies the vertical density profile and substantially increases the disc scale height beyond its hydrostatic value. Outflows are produced, but are not necessary to explain accretion rates <10^{-7} Msun/yr. The flow in the disc midplane is essentially laminar, suggesting that dust sedimentation may be efficient. These results demonstrate that, if the MRI is relevant for driving mass accretion in protoplanetary discs, one must include the Hall effect to obtain even qualitatively correct results.