Efficiently Cooled Stellar Wind Bubbles in Turbulent Clouds I. Fractal Theory and Application to Star-Forming Clouds

TL;DR

This paper develops a fractal-based theory for wind-driven stellar bubbles in turbulent molecular clouds, explaining their cooling, expansion, and observational properties, with validation through hydrodynamic simulations.

Contribution

It introduces a new fractal surface model for stellar wind bubbles that accounts for enhanced cooling and altered expansion dynamics in turbulent environments.

Findings

Bubble radius scales as R ~ t^1/2 due to extreme cooling.

Predicted lower expansion velocities and pressures match observations.

Theory explains weak X-ray emission from observed bubbles.

Abstract

Winds from massive stars have velocities of 1000 km/s or more, and produce hot, high pressure gas when they shock. We develop a theory for the evolution of bubbles driven by the collective winds from star clusters early in their lifetimes, which involves interaction with the turbulent, dense interstellar medium of the surrounding natal molecular cloud. A key feature is the fractal nature of the hot bubble's surface. The large area of this interface with surrounding denser gas strongly enhances energy losses from the hot interior, enabled by turbulent mixing and subsequent cooling at temperatures T = 10^4-10^5 K where radiation is maximally efficient. Due to the extreme cooling, the bubble radius scales differently (R ~ t^1/2) from the classical Weaver77 solution, and has expansion velocity and momentum lower by factors of 10-10^2 at given R, with pressure lower by factors of 10^2 - 10^3. Our theory explains the weak X-ray emission and low shell expansion velocities of observed sources. We discuss further implications of our theory for observations of the hot bubbles and cooled expanding shells created by stellar winds, and for predictions of feedback-regulated star formation in a range of environments. In a companion paper, we validate our theory with a suite of hydrodynamic simulations.