title: Formation and Surface Density Evolution of Circumplanetary Disks and MRI

authors: Yuri I. Fujii, Satoshi Okuzumi, Takayuki Tanigawa, Shu-ichiro Inutsuka

abstract: Gaseous disks formed around gas giants are called circumplanetary disks. Circumplanetary disks are supposed to be the formation sites of satellites. Although understanding of disk evolution is required in developing the theory of satellite formation, the gas accretion rate and the surface density of circumplanetary disks are very uncertain. To understand the overall evolution of circumplanetary disks, we have to analyze the early formation phases of the disks and to understand the timing and condition of gap formation in protoplanetary disks. The latter will be possible with ALMA. In this work, we focus on the former. 
 We calculate the surface density evolution of the disk by solving the alpha-model equation of accretion disk with gas infall onto the disk that is provided by Tanigawa et al. (2012).  We try to determine the surface density of disks using the result of Okuzumi and Hirose (2011); we can determine the sizes of magnetorotational instability-active/inactive (MRI-active/inactive) layers and the resultant value of alpha. We find that MRI remains inactive in early phase of disk evolution. Our result suggests that MRI becomes important only after gap formation in protoplanetary disks where the gas infall rate onto the circumplanetary disk is substantially reduced.