Time-dependent evolution of the protoplanetary discs with magnetic winds
  We study the evolution of the protoplanetary discs (PPDs) in the presence of
magnetically driven winds with the stress relations motivated by the non-ideal
MHD disc simulations. Contribution of the magnetic winds in the angular
momentum removal and mass loss are described using these relations which are
quantified in terms of the plasma parameter. Evolution of the essential disc
quantities including the surface density, accretion rate and wind mass loss
rate are studied for a wide range of the model parameters. Two distinct phases
of the disc evolution are found irrespective of the adopted input parameters.
While at the early phase of the disc evolution, global disc quantities such as
its total mass and magnetic flux undergo non-significant reductions, their
rapid declines are found in the second phase of evolution. Duration of each
phase, however, depends upon the model parameters including magnetic wind
strength. Our model predicts that contributions of the magnetic winds in the
disc evolution are significant during the second phase. We then calculated
locus of points in the plane of the accretion rate and total disc mass
corresponding to an ensemble of evolving PPDs. Our theoretical isochrone tracks
exhibit reasonable fits to the observed PPDs in star forming regions Lupus and
$\sigma$-Orion.
