Evolution of Protoplanetary Discs with Magnetically Driven Disc Winds
  Aims: We investigate the evolution of protoplanetary discs (PPDs hereafter) with magnetically driven disc winds and viscous heating. Methods: We consider an initially massive disc with ~0.1 Msun to track the evolution from the early stage of PPDs. We solve the time evolution of surface density and temperature by taking into account viscous heating and the loss of the mass and the angular momentum by the disc winds within the framework of a standard alpha model for accretion discs. Our model parameters, turbulent viscosity, disc wind mass loss, and disc wind torque, which are adopted from local magnetohydrodynamical simulations and constrained by the global energetics of the gravitational accretion, largely depends on the physical condition of PPDs, particularly on the evolution of the vertical magnetic flux in weakly ionized PPDs. Results: Although there are still uncertainties concerning the evolution of the vertical magnetic flux remaining, surface densities show a large variety, depending on the combination of these three parameters, some of which are very different from the surface density expected from the standard accretion. When a PPD is in a "wind-driven accretion" state with the preserved vertical magnetic field, the radial dependence of the surface density can be positive in the inner region <1-10 au. The mass accretion rates are consistent with observations, even in the very low level of magnetohydrodynamical turbulence. Such a positive radial slope of the surface density gives a great impact on planet formation because (i)it inhibits the inward drift or even results in the outward drift of pebble/boulder-sized solid bodies, and (ii) it also makes the inward type-I migration of proto-planets slower or even reversed. Conclusions: The variety of our calculated PPDs should yield a wide variety of exoplanet systems. 
Takeru K. Suzuki, Masahiro Ogihara, Alessandro Morbidelli, Aur\'elien   Crida, and Tristan Guillot
astro-ph.EP astro-ph.SR