# A Markov model for non-lognormal density distributions in compressive isothermal turbulence

## TL;DR

This paper introduces a Markov process-based model that captures the non-lognormal density distributions in compressive isothermal turbulence, accounting for shock-induced deviations and transient structure timescales.

## Contribution

It presents a simple, single-parameter analytic model explaining non-lognormal density PDFs in turbulence, validated against 1D and 3D simulation data.

## Key findings

- Model accurately describes density PDFs in simulations
- Quantifies deviations from lognormal distribution due to shocks
- Applicable to star formation studies in molecular clouds

## Abstract

Compressive isothermal turbulence is known to have a near lognormal density probability distribution function (PDF) with a width that scales with the sonic Mach number and nature of the turbulent driving (solenoidal vs compressive). However, the physical processes that mold the extreme high and low density structures in a turbulent medium can be different, with the densest structures being composed of strong shocks that evolve on shorter timescales than the low density fluid. The density PDF in a turbulent medium exhibits deviations from lognormal due to shocks, that increases with the sonic Mach number, which is often ignored in analytic models for turbulence and star formation. We develop a simple model for turbulence by treating it as a continuous Markov process, which explains both the density PDF and the transient timescales of structures as a function of density, using a framework developed in n Scannapieco & Safarzadeh (2018). Our analytic model depends on only a single parameter, the effective compressive sonic Mach number, and successfully describes the non-lognormal behavior seen in both 1D and 3D simulations of supersonic and subsonic compressive isothermal turbulence. The model quantifies the non-lognormal distribution of density structures in turbulent environments, and has application to star forming molecular clouds and star formation efficiencies.