A General Theory of Turbulent Fragmentation

TL;DR

This paper presents a comprehensive analytic framework for understanding turbulent fragmentation in self-gravitating media, predicting properties like mass spectra, size relations, and collapse rates, while accounting for various physical effects.

Contribution

It generalizes previous models to include time-dependent gravo-turbulent fragmentation, rotation, magnetic fields, and complex equations of state, providing a unified predictive theory.

Findings

Fragmentation is always probabilistically gravitationally unstable.

Mass spectra and correlation functions are universal with weak dependence on media properties.

Suppression of fragmentation occurs with stiffer equations of state or different driving mechanisms.

Abstract

We develop an analytic framework to understand fragmentation in turbulent, self-gravitating media. Previously, we showed some properties of turbulence can be predicted with the excursion-set formalism. Here, we generalize to fully time-dependent gravo-turbulent fragmentation & collapse. We show that turbulent systems are always gravitationally unstable (in a probabilistic sense). The fragmentation mass spectra, size/mass relations, correlation functions, range of scales over which fragmentation occurs, & time-dependent rates of fragmentation are predictable. We show how this depends on bulk turbulent properties (Mach numbers & power spectra). We also generalize to include rotation, complicated equations of state, collapsing/expanding backgrounds, magnetic fields, intermittency, & non-normal statistics. We derive how fragmentation is suppressed with 'stiffer' equations of state or different driving mechanisms. Suppression appears at an 'effective sonic scale' where Mach(R,rho)~1. Gas becomes stable below this scale for polytropic gamma>4/3, but fragmentation still occurs on larger scales. The scale-free nature of turbulence and gravity generically drives mass spectra and correlation functions towards universal shapes, with weak dependence on many properties of the media. Correlated fluctuation structures, non-Gaussian density distributions, & intermittency have surprisingly small effects on the fragmentation process. This is because fragmentation cascades on small scales are 'frozen in' when large-scale modes push the 'parent' region above the collapse threshold; though they collapse, their statistics are only weakly modified by the collapse process. With thermal support, structure develops 'top-down' in time via fragmentation cascades; but strong rotational support reverses this to 'bottom-up' growth via mergers & introduces a maximal instability scale distinct from the Toomre scale.