# Temperature Structure in the Inner Regions of Protoplanetary Disks: Inefficient Accretion Heating Controlled by Nonideal Magnetohydrodynamics

## TL;DR

This study uses advanced MHD simulations to show that Joule heating is inefficient in the inner regions of protoplanetary disks, making irradiation the dominant heating source and challenging traditional viscous heating models.

## Contribution

The paper demonstrates that nonideal MHD effects suppress Joule heating in the inner disk, highlighting irradiation as the primary temperature source and providing new insights into disk thermal structure.

## Key findings

- Joule heating occurs mainly above the midplane, not at it.
- Midplane temperature is dominated by irradiation heating.
- Hall effect influences Joule heating depending on magnetic field alignment.

## Abstract

The gas temperature in protoplanetary disks (PPDs) is determined by a combination of irradiation heating and accretion heating, with the latter conventionally attributed to turbulent dissipation. However, recent studies have suggested that the inner disk (a few AU) is largely laminar, with accretion primarily driven by magnetized disk winds, as a result of nonideal magnetohydrodynamic (MHD) effects from weakly ionized gas, suggesting an alternative heating mechanism by Joule dissipation. We perform local stratified MHD simulations including all three nonideal MHD effects (ohmic, Hall, and ambipolar diffusion) and investigate the role of Joule heating and the resulting disk vertical temperature profiles. We find that in the inner disk, as ohmic and ambipolar diffusion strongly suppress electrical current around the midplane, Joule heating primarily occurs at several scale heights above the midplane, making the midplane temperature much lower than that with the conventional viscous heating model. Including the Hall effect, Joule heating is enhanced/reduced when the magnetic fields threading the disks are aligned/anti-aligned with the disk rotation, but it is overall ineffective. Our results further suggest that the midplane temperature in the inner PPDs is almost entirely determined by irradiation heating, unless viscous heating can trigger thermal ionization in the disk innermost region to self-sustain magnetorotational instability turbulence.