A Fast and Accurate Calculation Scheme for Ionization Degrees in Protoplanetary and Circumplanetary Disks with Charged Dust Grains

TL;DR

This paper presents a rapid and precise semi-analytic method to calculate ionization degrees in protoplanetary and circumplanetary disks, accounting for dust grains, to better understand MRI activity and disk evolution.

Contribution

The authors develop a semi-analytic charge distribution model that accelerates ionization calculations in disks with dust grains, enabling extensive parameter studies.

Findings

MRI-inactive regions are extensive in circum-Jovian disks without dust.

Inclusion of dust grains significantly lowers ionization degrees.

Gas accretion rates in circumplanetary disks may be much smaller than previously estimated.

Abstract

We develop a fast and accurate calculation method for ionization degrees in protoplanetary and circumplanetary disks including dust grains. We apply our method to calculate the ionization degree of circumplanetary disks. It is important to understand the structure and evolution of protoplanetary/circumplanetary disks since they are thought to be the sites of planet/satellite formation. The turbulence that causes gas accretion is supposed to be driven by magnetorotational instability (MRI) that occurs only when the ionization degree is high enough for magnetic field to be coupled to gas. We calculate the ionization degrees in circumplanetary disks to estimate the sizes of MRI-inactive regions. We properly include the effect of dust grains because they efficiently capture charged particles and make ionization degree lower. Inclusion of dust grains complicates the reaction equations and requires expensive computation. In order to accelerate the calculation of ionization reactions, we develop a semianalytic method based on the charge distribution model proposed previously. This method enables us to study the ionization state of disks for a wide range of model parameters. For a previous model of circum-Jovian disk, we find that an MRI-inactive region covers almost all regions even without dust grains. This suggests that the gas accretion rates in circumplanetary disks are much smaller than previously thought.