Self-consistent Ring Model in Protoplanetary Disks: Temperature Dips and Substructure Formation

Rings and gaps are ubiquitous in protoplanetary disks. Larger dust grains will concentrate in gaseous rings more compactly due to stronger aerodynamic drag. However, the effects of dust concentration on the ring's thermal structure have not been explored. Using MCRT simulations, we self-consistently construct ring models by iterating the ring's thermal structure, hydrostatic equilibrium, and dust concentration. We set up rings with two dust populations having different settling and radial concentration due to their different sizes. We find two mechanisms that can lead to temperature dips around the ring. When the disk is optically thick, the temperature drops outside the ring, which is the shadowing effect found in previous studies adopting a single-dust population in the disk. When the disk is optically thin, a second mechanism due to excess cooling of big grains is found. Big grains cool more efficiently, which leads to a moderate temperature dip within the ring where big dust resides. This dip is close to the center of the ring. Such a temperature dip within the ring can lead to particle pileup outside the ring and feedback to the dust distribution and thermal structure. We couple the MCRT calculations with a 1D dust evolution model and show that the ring evolves to a different shape and may even separate to several rings. Overall, dust concentration within rings has moderate effects on the disk's thermal structure, and a self-consistent model is crucial not only for protoplanetary disk observations but also for planetesimal and planet formation studies.