Title: Co-evolution of dust grains and protoplanetary disks II: structure and evolution of protoplanetary disks; an analytical approach

Abstract: In our previous study (Tsukamoto {\it et al.} 2023), we investigated formation and early evolution of protoplanetary disks with 3D non-ideal magnetohydrodynamics simulations considering dust growth, and found that the modified equations of the conventional steady accretion disk model which consider the magnetic braking, { dust growth} and ambipolar diffusion reproduce the disk structure obtained from simulations very well. In this paper, as a sequel of the our previous study, we analytically investigate the structure and evolution of protoplanetary disks corresponding to Class 0/I young stellar objects using the modified steady accretion disk model combining an analytical model of envelope accretion. We estimate that the disk radius is several AU at disk formation epoch and increases to several 100 AU at the end of the accretion phase. The disk mass is estimated to be $0.01 M_\odot \lesssim M_{\rm disk} \lesssim 0.1 M_\odot$ for a disk with radius of several 10 AU and mass accretion rate of $\dot{M}_{\rm disk} \sim 10^{-6} M_\odot {\rm yr^{-1}}$. We also found that, with typical disk ionization rates and moderate mass accretion rate ($\dot{M}_{\rm disk}\gtrsim10^{-8} M_\odot {\rm yr^{-1}}$), magneto-rotational instability is suppressed in the disk because of low plasma $\beta$ and efficient ambipolar diffusion. We argue that the radial profile of specific angular momentum (or rotational velocity) at the disk outer edge should be continuously connected to that of the envelope if the disk evolves by magnetic braking, and should be discontinuous if the disk evolves by internal angular momentum transport process such as gravitational instability or magneto-rotational instability. Future detailed observations of the specific angular momentum profile around the disk outer edge are important for understanding the angular momentum transport mechanism of protoplanetary disks.