Electric heating and angular momentum transport in laminar models of protoplanetary discs

The vertical temperature structure of a protoplanetary disc bears on several processes relevant to planet formation, such as gas and dust grain chemistry, ice lines, and convection. The temperature profile is controlled by irradiation from the central star and by any internal source of heat such as might arise from gas accretion. We investigate the heat and angular momentum transport generated by the resistive dissipation of magnetic fields in laminar discs. We use local 1D simulations to obtain vertical temperature profiles for typical conditions in the inner disc (0.5-4 au). Using simple assumptions for the gas ionization and opacity, the heating and cooling rates are computed self-consistently in the framework of radiative non-ideal magnetohydrodynamics. We characterize steady solutions that are symmetric about the mid-plane and which may be associated with saturated Hall-shear unstable modes. We also examine the dissipation of electric currents driven by global accretion-ejection structures. In both cases we obtain significant heating for a sufficiently high opacity. Strong magnetic fields can induce an order-unity temperature increase in the disc mid-plane, a convectively unstable entropy profile, and a surface emissivity equivalent to a viscous heating of alpha similar to 10(-2). These results show how magnetic fields may drive efficient accretion and heating in weakly ionized discs where turbulence might be inefficient, at least for a range of radii and ages of the disc.