Analytical solutions for the evolution of MHD wind-driven accretion discs

Abstract

ABSTRACT We present new analytical solutions for the evolution of protoplanetary discs (PPDs) where magnetohydrodynamic (MHD) wind-driven processes dominate. Our study uses a 1D model which incorporates equations detailing angular momentum extraction by MHD winds and mass-loss rates. Our solutions demonstrate that the disc retains its initial state during the early phases; however, it rapidly evolves towards a self-similar state in the later stages of disc evolution. The total disc mass undergoes a continuous decline over time, with a particularly rapid reduction occurring beyond a certain critical time threshold. This gradual decrease in mass is influenced by the wind parameters and the initial surface density of the disc. In the MHD wind-dominated regime, we show that the disc’s lifespan correlates positively with the magnetic lever arm up to a certain threshold, irrespective of the initial disc size. PPDs with a larger magnetic lever arm are found to maintain significantly higher total disc mass over extended periods compared to their counterparts. The mass ejection-to-accretion ratio increases in efficient wind scenarios and is further amplified by a steeper initial surface density profile. Our analysis also reveals varied evolutionary trajectories in the plane of accretion rate and total disc mass, influenced by magnetic parameters and initial disc size. In scenarios with efficient MHD winds, discs with bigger sizes have extended operation time for mechanisms governing planet formation.