Evolution of the Water Snow Line in Magnetically Accreting Protoplanetary Disks

Abstract

The low water content of the terrestrial planets in the solar system suggests that the protoplanets formed within the water snow line. Accurate prediction of the snow line location moving with time provides a clue to constraining the formation process of the planets. In this paper, we investigate the migration of the snow line in protoplanetary disks whose accretion is controlled by laminar magnetic fields, which have been proposed by various nonideal magnetohydrodynamic (MHD) simulations. We propose an empirical model of the disk temperature based on our nonideal MHD simulations, which show that the accretion heating is significantly less efficient than that in turbulent disks, and calculate the snow line location over time. We find that the snow line in magnetically accreting laminar disks moves inside the current Earth’s orbit within 1 Myr after star formation, whereas the time for the conventional turbulent disk is much longer than 1 Myr. This result suggests that either the rocky protoplanets formed in such an early phase of the disk evolution, or the protoplanets moved outward to the current orbits after they formed close to the protosun.

A global two-layer radiative transfer model for axisymmetric, shadowed protoplanetary disks

“…However, recent studies of the magnetohydrodynamics of weakly ionized protoplanetary disks have shown that accretion heating favors the disk surface because the midplane region is too poorly ionized to sustain a large electric current (Hirose & Turner 2011;Mori et al 2019). These models predict that the magnetohydrodynamic accretion heating can raise the midplane temperature only when the disk opacity is high enough (Béthune & Latter 2020;Mori et al 2021). This suggests that stellar irradiation rather than internal heating may determine the location of the water snow line.…”

Nucleation and growth of iron pebbles explains the formation of iron-rich planets akin to Mercury

“…We take into account that a part of the mass accretion rate will not lead to heating, if the angular momentum is transported by large-scale disc winds (Mori et al 2021). Hence δ/α, with α representing the total angular transport and δ representing the local turbulence, gives the fraction of mass transported via turbulence and hence leading to heating.…”

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

“…For disks around solar-type stars, they found that the snow line migrates inside 1 au within the first ∼ 10 5 yr after star formation. The classical viscous model also predicts inward migration of the snow line, but the snow line's arrival time at 1 au in the MHD disk model is an order of magnitude longer in the model assuming vertically uniform viscosity (see Figure 6 of Mori et al 2021). The MHD model suggests that planetary embryos at 1 au could have accreted a larger amount of water ice (see also Sato et al 2016), strongly constraining scenarios for the inner solar system formation.…”

“…Second, dust grains are the dominant source of disk opacity, and their size and spatial distribution control the disk's cooling rate (e.g., Oka et al 2011). Mori et al (2021) assumed that submicron-sized grains are abundant in the disks 1 ; however, it is more likely that most of the small grains in the inner few au region grow to larger solid particles or bodies in the first 1 Myr of disk evolution (e.g., Birnstiel et al 2010). As the abundance of small dust grains decreases, the ionization fraction increases, whereas the disk opacity decreases.…”

“…Their net effect is not obvious, because an increased ionization fraction results in a Joule heating layer closer to the midplane, while a decreased opacity results in more efficient radiative cooling. Mori et al (2021) were unable to study the net effect of the two in a self-consistent manner because they determined the disk's ionization faction and opacity independently.…”