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We develop a fast and accurate calculation method for ionization degrees inprotoplanetary and circumplanetary disks including dust grains. We apply ourmethod to calculate the ionization degree of circumplanetary disks. It isimportant to understand the structure and evolution ofprotoplanetary/circumplanetary disks since they are thought to be the sites ofplanet/satellite formation. The turbulence that causes gas accretion issupposed to be driven by magnetorotational instability (MRI) that occurs onlywhen the ionization degree is high enough for magnetic field to be coupled togas. We calculate the ionization degrees in circumplanetary disks to estimatethe sizes of MRI-inactive regions. We properly include the effect of dustgrains because they efficiently capture charged particles and make ionizationdegree lower. Inclusion of dust grains complicates the reaction equations andrequires expensive computation. In order to accelerate the calculation ofionization reactions, we develop a semianalytic method based on the chargedistribution model proposed previously. This method enables us to study theionization state of disks for a wide range of model parameters. For a previousmodel of circum-Jovian disk, we find that an MRI-inactive region covers almostall regions even without dust grains. This suggests that the gas accretionrates in circumplanetary disks are much smaller than previously thought.

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