# Models of Saturn's protoplanetary disk forming in-situ its regular satellites and innermost rings before the planet is formed

## TL;DR

This study models Saturn's early protoplanetary disk, revealing its unique steep density profile, narrow extent, and rotational characteristics, which differ from Jupiter and Uranus, providing insights into satellite and ring formation before planet formation.

## Contribution

It presents a detailed isothermal oscillatory density model of Saturn's primordial disk, highlighting its distinct properties and stability, unlike previous models of other giant planets' disks.

## Key findings

- Saturn's disk has a steep power-law index of -4.5.
- The disk's radial extent is very narrow, less than 0.9 Gm.
- The core density and rotation rate are comparable to Jupiter's core.

## Abstract

We fit an isothermal oscillatory density model of Saturn's protoplanetary disk to the present-day major satellites and innermost rings D/C and we determine the radial scale length of the disk, the equation of state and the central density of the primordial gas, and the rotational state of the Saturnian nebula. This disk does not look like the Jovian and Uranian disks that we modeled previously. Its power-law index is extremely steep ($k=-4.5$) and its radial extent is very narrow ($\Delta R\lesssim 0.9$ Gm), its rotation parameter that measures centrifugal support against self-gravity is somewhat larger ($\beta_0=0.0431$), as is its radial scale length (395 km); but, as was expected, the size of the Saturnian disk, $R_{\rm max}=3.6$ Gm, takes just an intermediate value. On the other hand, the central density of the compact Saturnian core and its angular velocity are both comparable to that of Jupiter's core (density of $\approx 0.3$~g~cm$^{-3}$ in both cases, and rotation period of 5.0 d versus 6.8 d); and significantly less than the corresponding parameters of Uranus' core. As with the other primordial nebulae, this rotation is sufficiently slow to guarantee the disk's long-term stability against self-gravity induced instabilities for millions of years of evolution.