Protostellar Disk Evolution over Million-Year Timescales with a Prescription for Magnetized Turbulence
Dodson-Robinson, S. E.
Turner, N. J.
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Magnetorotational instability (MRI) is the most promising mechanism behind accretion in low-mass protostellar disks. Here we present the first analysis of the global structure and evolution of non-ideal MRI-driven T-Tauri disks on million-year timescales. We accomplish this in a 1+1D simulation by calculating magnetic diffusivities and utilizing turbulence activity criteria to determine thermal structure and accretion rate without resorting to a three-dimensional magnetohydrodynamical (MHD) simulation. Our major findings are as follows. First, even for modest surface densities of just a few times the minimum-mass solar nebula, the dead zone encompasses the giant planet-forming region, preserving any compositional gradients. Second, the surface density of the active layer is nearly constant in time at roughly 10 g cm-2, which we use to derive a simple prescription for viscous heating in MRI-active disks for those who wish to avoid detailed MHD computations. Furthermore, unlike a standard disk with constant-α viscosity, the disk midplane does not cool off over time, though the surface cools as the star evolves along the Hayashi track. Instead, the MRI may pile material in the dead zone, causing it to heat up over time. The ice line is firmly in the terrestrial planet-forming region throughout disk evolution and can move either inward or outward with time, depending on whether pileups form near the star. Finally, steady-state mass transport is an extremely poor description of flow through an MRI-active disk, as we see both the turnaround in the accretion flow required by conservation of angular momentum and peaks in Ṁ(R)bracketing each side of the dead zone. We caution that MRI activity is sensitive to many parameters, including stellar X-ray flux, grain size, gas/small grain mass ratio and magnetic field strength, and we have not performed an exhaustive parameter study here. Our 1+1D model also does not include azimuthal information, which prevents us from modeling the effects of Rossby waves.