# Theoretical model of the outer disk of TW Hya presently forming in-situ planets and comparison with models of AS 209 and HL Tau

## TL;DR

This paper presents a theoretical isothermal oscillatory density model of the TW Hya disk, comparing its properties with HL Tau and AS 209, revealing similarities and differences in disk structure and stability.

## Contribution

The study introduces a detailed isothermal density model for TW Hya's outer disk, highlighting its stability and comparing it with other protostellar disks, which is a novel approach.

## Key findings

- TW Hya's disk has a power-law density profile with index -0.2.
- TW Hya's disk is more dense centrally than HL Tau by a factor of 5.7.
- The disk shows stability with minimal centrifugal support.

## Abstract

We fit an isothermal oscillatory density model to the outer disk of TW Hya in which planets have presumably already formed and they are orbiting within four observed dark gaps. At first sight, this 52 AU small disk does not appear to be similar to our solar nebula; it shows several physical properties comparable to those in HL Tau (size $R_{\rm max}=102$ AU) and very few similarities to AS 209 ($R_{\rm max}=144$ AU). We find a power-law density profile with index $k=-0.2$ (radial densities $\rho(R) \propto R^{-1.2}$) and centrifugal support against self-gravity so small that it virtually guarantees dynamical stability for millions of years of evolution to come. Compared to HL Tau, the scale length $R_0$ and the core size $R_1$ of TW Hya are smaller only by factors of $\sim$2, reflecting the disk's half size. On the opposite end, the Jeans frequency $\Omega_J$ and the angular velocity $\Omega_0$ of the smaller core of TW Hya are larger only by factors of $\sim$2. The only striking difference is that the central density ($\rho_0$) of TW Hya is 5.7 times larger than that of HL Tau, which is understood because the core of TW Hya is only half the size ($R_1$) of HL Tau and about twice as heavy ($\Omega_J$). In the end, we compare the protostellar disks that we have modeled so far.