# The distribution of density in supersonic turbulence

## TL;DR

This paper introduces a shock-based model for density statistics in supersonic turbulence, predicting key properties like probability distribution and variance, with reasonable agreement to simulations and potential for future extensions.

## Contribution

The paper presents a novel, physically motivated model for density statistics in supersonic turbulence based on shock structures, improving understanding of ISM physics.

## Key findings

- Model predicts density probability distribution and intermittency.
- Good qualitative agreement with numerical simulations.
- Framework adaptable to more complex physical processes.

## Abstract

We propose a model for the density statistics in supersonic turbulence, which play a crucial role in star-formation and the physics of the interstellar medium (ISM). Motivated by [Hopkins, MNRAS, 430, 1880 (2013)], the model considers the density to be arranged into a collection of strong shocks of width $\sim\! \mathcal{M}^{-2}$, where $\mathcal{M}$ is the turbulent Mach number. With two physically motivated parameters, the model predicts all density statistics for $\mathcal{M}>1$ turbulence: the density probability distribution and its intermittency (deviation from log-normality), the density variance-Mach number relation, power spectra, and structure functions. For the proposed model parameters, reasonable agreement is seen between model predictions and numerical simulations, albeit within the large uncertainties associated with current simulation results. More generally, the model could provide a useful framework for more detailed analysis of future simulations and observational data. Due to the simple physical motivations for the model in terms of shocks, it is straightforward to generalize to more complex physical processes, which will be helpful in future more detailed applications to the ISM. We see good qualitative agreement between such extensions and recent simulations of non-isothermal turbulence.