Gravitational Fragmentation of Expanding Shells. I. Linear Analysis

TL;DR

This paper presents a linear perturbation analysis of expanding shells driven by HII regions, revealing enhanced growth rates of instabilities due to boundary effects and asymmetric density profiles, advancing understanding of gravitational fragmentation.

Contribution

It introduces a semi-analytic method for evolving the density profile and incorporates boundary effects, improving upon the thin-shell approximation in analyzing shell instabilities.

Findings

Growth rate is higher than previous thin-shell models.

Density profile evolves through three phases.

Boundary effects significantly influence instability growth.

Abstract

We perform a linear perturbation analysis of expanding shells driven by expansions of HII regions. The ambient gas is assumed to be uniform. As an unperturbed state, we develop a semi-analytic method for deriving the time evolution of the density profile across the thickness. It is found that the time evolution of the density profile can be divided into three evolutionary phases, deceleration-dominated, intermediate, and self-gravity-dominated phases. The density peak moves relatively from the shock front to the contact discontinuity as the shell expands. We perform a linear analysis taking into account the asymmetric density profile obtained by the semi-analytic method, and imposing the boundary conditions for the shock front and the contact discontinuity while the evolutionary effect of the shell is neglected. It is found that the growth rate is enhanced compared with the previous studies based on the thin-shell approximation. This is due to the boundary effect of the contact discontinuity and asymmetric density profile that were not taken into account in previous works.