Evolution of a protoplanetary disc with the magnetic wind

Theoretical studies and numerical simulations of the protoplanetary discs (PPDs) indicate that magnetorotational instability (MRI) is a dominant mechanism in the accretion process. Recent observational evidence, however, implies that magnetic winds present in these systems. Launching the magnetic winds leads to further angular momentum removal and a higher mass accretion rate. Non-ideal MHD disc simulations have shown than there is a correlation with MRI and the magnetic winds. Thus exploring the structure of the PPDs with the magnetic winds plays a vital role. We present fully analytical solutions for the evolution of a PPD with the magnetic wind. Relations for the stress tensor components associated with the disc turbulence and the magnetic wind are motivated by recent MHD disc simulations. These relations are written in terms of the ratio of the gas and the magnetic pressures. In the case with a strong magnetic field, the role of the magnetic wind in the angular momentum removal is dominant. We show that a PPD undergoes a non-significant mass loss during the early stage of the evolution. But the mass loss rate is significantly amplified beyond a certain time. It seems that role of the magnetic wind in the older PPDs is more noticeable. We also indicate that the two-stage evolution of a PPD with the magnetic wind is more or less independent of the disc radial temperature distribution.