Beyond the $α$ model: scaling the wind-driven accretion rate in protoplanetary disks using systematic non-ideal magnetohydrodynamical simulations
Magnetically driven mass accretion plays a key role in protoplanetary disk evolution and planet formation. However, the alpha prescription remains phenomenological, and how the accretion rate depends on basic disk quantities is still poorly understood. While local shearing-box simulations are computationally efficient, they suffer from a fundamental problem: the toroidal magnetic field generated by Keplerian shear accumulates within the computational domain, disrupting a field-line geometry consistent with global wind-driven accretion. In this study, we use the super-box-scale diffusion (SBD) scheme in non-ideal MHD shearing-box simulations. By damping the horizontally averaged horizontal magnetic fields, this scheme successfully mitigates the artificial field accumulation and maintains the field-line symmetry required for global wind-driven accretion for more than 500 orbital periods. Comparison with self-similar solutions supports the quantitative usefulness of the SBD method, showing good agreement in both the vertical structure and the plasma-beta dependence of the accretion rate. We then conduct a parameter survey using a magnetic diffusivity table, covering a wide range of disk radii, surface densities, magnetic field strengths, and dust-to-gas ratios. We demonstrate that the mass accretion rate follow power-law scaling relations in terms of three local disk properties: the midplane plasma beta, an effective ambipolar Elsasser number in ionized surface layers, and the thickness of the magnetically active layer. The scaling relations reproduce the numerical results to within a factor of 2-3 across the explored parameter space. The present scaling relations provide a framework for predicting the mass accretion rate from local disk physical quantities without invoking an alpha parameter.