The fragmentation of expanding shells I: Limitations of the thin--shell approximation

TL;DR

This study examines the limitations of the thin-shell approximation in gravitational fragmentation of expanding shells, highlighting the significant influence of external pressure and shell confinement on fragmentation behavior.

Contribution

The paper provides a comparative analysis using two numerical schemes to evaluate the thin-shell approximation's validity under different pressure conditions.

Findings

External pressure strongly affects fragmentation.

Pressure-confined shells align better with analytical models.

Hydrodynamic flows can suppress short-wavelength fragmentation.

Abstract

We investigate the gravitational fragmentation of expanding shells in the context of the linear thin--shell analysis. We make use of two very different numerical schemes; the FLASH Adaptive Mesh Refinement code and a version of the Benz Smoothed Particle Hydrodynamics code. We find that the agreement between the two codes is excellent. We use our numerical results to test the thin--shell approximation and we find that the external pressure applied to the shell has a strong effect on the fragmentation process. In cases where shells are not pressure--confined, the shells thicken as they expand and hydrodynamic flows perpendicular to the plane of the shell suppress fragmentation at short wavelengths. If the shells are pressure--confined internally and externally, so that their thickness remains approximately constant during their expansion, the agreement with the analytical solution is better.