The Roles of Dust Growth in the Temperature Evolution and Snow Line Migration in Magnetically Accreting Protoplanetary Disks

The temperature structure of protoplanetary disks provides an important constraint on where in the disks rocky planets like our own form. Recent nonideal magnetohydrodynamical (MHD) simulations have shown that the internal Joule heating associated with magnetically driven disk accretion is inefficient at heating the disk midplane. A disk temperature model based on the MHD simulations predicts that in a disk around a solar-mass young star, the water snow line can move inside the current Earth's orbit within 1 Myr after disk formation. However, the efficiency of the internal Joule heating depends on the disk's ionization and opacity structures, both of which are governed by dust grains. In this study, we investigate these effects by combing the previous temperature model for magnetically accreting disks with a parameterized model for the grain size and vertical distribution. Grain growth enhances the gas ionization fraction and thereby allows Joule heating to occur closer to the midplane. However, growth beyond 10 \(\rm \mu m\) causes a decrease in the disk opacity, leading to a lower midplane temperature. The combination of these two effects results in the midplane temperature being maximized when the grain size is in the range 10-100 \(\rm \mu m\). Grain growth to millimeter sizes can also delay the snow line's migration to the 1 au orbit by up to a few Myr. We conclude that accounting for dust growth is essential for accurately modeling the snow line evolution and terrestrial planet formation in magnetically accreting protoplanetary disks.