# Theoretical model of HD 163296 presently forming in-situ planets and comparison with the models of AS 209, HL Tau, and TW Hya

## TL;DR

This paper models the HD 163296 protoplanetary disk using an isothermal oscillatory density model, comparing its properties with other disks to understand planet formation in situ.

## Contribution

It introduces a detailed isothermal density model for HD 163296 and compares its physical properties with those of similar disks, highlighting similarities and differences.

## Key findings

- HD 163296's disk is comparable in size and structure to AS 209.
- The disk shows a small inner core radius, possibly due to unresolved planets.
- Physical parameters of HD 163296 are similar to those of other modeled disks.

## Abstract

We fit an isothermal oscillatory density model to the disk of HD 163296 in which planets have presumably already formed and they are orbiting at least within the four observed dark gaps. This 156 AU large axisymmetric disk shows various physical properties comparable to those of AS 209, HL Tau, and TW Hya that we have modeled previously; but it compares best to AS 209. The disks of HD 163296 and AS 209 are comparable in size and they share similar values of the power-law index $k\approx 0$ (a radial density profile of the form $\rho(R)\propto R^{-1}$), the rotational parameter $\beta_0$ (to within a factor of 3); a relatively small inner core radius (although this parameter for HD 163296 is exceptionally small, $R_1\simeq 0.15$ AU, presumably due to unresolved planets in the inner 50 AU); the scale length $R_0$ and the Jeans gravitational frequency $\Omega_J$ (to within factors of 1.4); the equation of state ($c_0^2/\rho_0$) and the central density $\rho_0$ (to within factors of 2); and the core angular velocity $\Omega_0$ (to within a factor of 4.5). In the end, we compare all six nebular disks that we have modeled so far.