# Theoretical models of the protostellar disks of AS 209 and HL Tau presently forming in-situ planets

## TL;DR

This paper presents isothermal oscillatory density models fitted to ALMA observations of the protoplanetary disks of AS 209 and HL Tau, revealing differences in core size and density that relate to planet formation regions.

## Contribution

It introduces a new application of isothermal oscillatory density models to observed disks, highlighting differences in core properties and stability conditions.

## Key findings

- HL Tau's core is significantly larger and denser than AS 209's core.
- Both disks exhibit stable density profiles with low centrifugal support.
- Four dark gaps are within HL Tau's core, none in AS 209.

## Abstract

We fit an isothermal oscillatory density model to two ALMA/DSHARP-observed disks, AS 209 and HL Tau, in which planets have presumably already formed and they are orbiting within the observed seven dark gaps in each system. These large disks are roughly similar to our solar nebula, albeit they exhibit milder radial density profiles and they enjoy lower centrifugal support. We find power-law density profiles with index $k=0.0$ (radial densities $\rho(R) \propto R^{-1}$) and centrifugal support against self-gravity so small that it guarantees dynamical stability for millions of years of evolution. The scale lengths of the models differ only by a factor of 1.9, but the inner cores of the disks are very different: HL Tau's core is 8.0 times larger and 3.6 times denser than the core of AS 209. This results in four dark gaps having formed within the core of HL Tau, whereas no dark gap is found in the core of AS 209. On the other hand, the Jeans frequencies and the angular velocities of the cores are comparable to within factors of 1.9 and 1.6, respectively.