SIMBAD references

Non-ideal MHD effects play an important role in the gas dynamics in protoplanetary disks (PPDs). This paper addresses the influence of non-ideal MHD effects on the magnetorotational instability (MRI) and angular momentum transport in PPDs using the most up-to-date results from numerical simulations. We perform chemistry calculations using a complex reaction network with standard prescriptions for X-ray and cosmic-ray ionizations. We first show that whether or not grains are included, the recombination time is at least one order of magnitude less than the orbital time within five disk scale heights, justifying the validity of local ionization equilibrium and strong coupling limit in PPDs. The full conductivity tensor at different disk radii and heights is evaluated, with the MRI active region determined by requiring that (1) the Ohmic Elsasser number Λ be greater than 1 and (2) the ratio of gas to magnetic pressure β be greater than β_min(Am) as identified in the recent study by Bai & Stone, where Am is the Elsasser number for ambipolar diffusion. With full flexibility as to the magnetic field strength, we provide a general framework for estimating the MRI-driven accretion rate {dot}M and the magnetic field strength in the MRI active layer. We find that the MRI active layer always exists at any disk radius as long as the magnetic field in PPDs is sufficiently weak. However, the optimistically predicted {dot}M in the inner disk (r = 1-10 AU) appears insufficient to account for the observed range of accretion rates in PPDs (around 10^–8 M_☉/yr) even in the grain-free calculation, and the presence of solar abundance sub-micron grains further reduces {dot}M by one to two orders of magnitude. Moreover, we find that the predicted {dot}M increases with radius in the inner disk where accretion is layered, which would lead to runaway mass accumulation if disk accretion is solely driven by the MRI. Our results suggest that stronger sources of ionization and/or additional mechanisms such as magnetized wind are needed to explain the observed accretion rates in PPDs. In contrast, our predicted {dot}M is on the order of 10^–9 M_☉/yr in the outer disk, consistent with the observed accretion rates in transitional disks.