Magnetic Turbulence and Thermodynamics in the Inner Region of Protoplanetary Discs

Abstract

Using radiation magnetohydrodynamics simulations with realistic opacities and equation of state, and zero net magnetic flux, we have explored thermodynamics in the inner part of protoplanetary discs where magnetic turbulence is expected. The thermal equilibrium curve consists of the upper, lower, and middle branches. The upper (lower) branch corresponds to hot (cool) and optically very (moderately) thick discs, respectively, while the middle branch is characterized by convective energy transport near the midplane. Convection is also the major energy transport process near the low surface density end of the upper branch. There, convective motion is fast with Mach numbers reaching $\gtrsim 0.01$, and enhances both magnetic turbulence and cooling, raising the ratio of vertically-integrated shear stress to vertically-integrated pressure by a factor of several. This convectively enhanced ratio seems a robust feature in accretion discs having an ionization transition. We have also examined causes of the S-shaped thermal equilibrium curve, as well as the thermal stability of the equilibrium solutions. Finally, we compared our results with the disc instability models used to explain FU Ori outbursts. Although the thermal equilibrium curve in our results also exhibits bistability, the surface density contrast across the bistability is an order of magnitude smaller, and the stress-to-pressure ratios in both upper and lower branches are two orders of magnitude greater, than those favored in the disc instability models. It therefore appears likely that FU Ori outbursts are not due solely to a thermal-viscous limit cycle resulting from accretion driven by local magnetic turbulence.