ABSTRACT
Short-period super-Earth-sized planets are common. Explaining how they form near their present orbits requires understanding the structure of the inner regions of protoplanetary discs. Previous studies have argued that the hot inner protoplanetary disc is unstable to the magnetorotational instability (MRI) due to thermal ionization of potassium, and that a local gas pressure maximum forms at the outer edge of this MRI-active zone. Here we present a steady-state model for inner discs accreting viscously, primarily due to the MRI. The structure and MRI-viscosity of the inner disc are fully coupled in our model; moreover, we account for many processes omitted in previous such models, including disc heating by both accretion and stellar irradiation, vertical energy transport, realistic dust opacities, dust effects on disc ionization, and non-thermal sources of ionization. For a disc around a solar-mass star with a standard gas accretion rate ($\dot{M}\, \sim \, 10^{-8}$ M⊙ yr−1) and small dust grains, we find that the inner disc is optically thick, and the accretion heat is primarily released near the mid-plane. As a result, both the disc mid-plane temperature and the location of the pressure maximum are only marginally affected by stellar irradiation, and the inner disc is also convectively unstable. As previously suggested, the inner disc is primarily ionized through thermionic and potassium ion emission from dust grains, which, at high temperatures, counteract adsorption of free charges on to grains. Our results show that the location of the pressure maximum is determined by the threshold temperature above which thermionic and ion emission become efficient.
The First Million Years of the Sun: A Calculation of the Formation and Early Evolution of a Solar Mass Star
