The Density Distribution of Compressively-Forced Supersonic Turbulence Depends on the Driving Correlation Time

TL;DR

This paper investigates how the correlation time of driving accelerations influences the density distribution in compressively-driven supersonic turbulence, revealing significant effects on void formation and density fluctuations.

Contribution

It demonstrates that the driving correlation time critically affects density structures in compressively-driven turbulence, a factor previously underexplored in astrophysical turbulence models.

Findings

Longer correlation times lead to large, low-density voids.

Shorter correlation times produce narrower density distributions.

The correlation time may be much less than the eddy turnover time in supernova-driven turbulence.

Abstract

Supersonic turbulence plays a critical role in shaping astrophysical systems, from molecular clouds to the circumgalactic medium. Key properties of this turbulence include the Mach number, driving scale, and nature of the driving mechanism, which can be solenoidal (divergence-free), compressive (curl-free), or a mix of the two. A less studied property is the correlation time of the driving accelerations, $\tau_{\rm a}.$ While this timescale has a minimal impact on solenoidally-driven turbulence, we show that it has a strong impact on compressively-driven turbulence. Using high-resolution simulations with tracer particles, we analyze the evolution of density fluctuations, focusing on the PDF of the logarithmic density, $s$, and its rate of change, $\frac{ds}{dt},$ and the conditional statistics of $\frac{ds}{dt}$ and $\frac{d^2s}{dt^2}$. When the driving correlation time is comparable to the eddy turnover time, $\tau_{\rm a} \approx \tau_{\rm e},$ compressive driving leads to the formation of large, low-density voids in which the variance of $\frac{ds}{dt}$ is large. These are directly linked to sustained accelerated expansions, which results in a strong correlation between density and the divergence of the driving acceleration field. In contrast, when $\tau_{\rm a} \approx 0.1 \, \tau_{\rm e}$, compressive driving does not produce such voids, resulting in a narrower, less skewed distribution. We show using analytical estimates that $\tau_{\rm a}$ is may be significantly less than $\tau_{\rm e}$ in supernova-driven turbulence, highlighting the need to better understand the role of the driving correlation time in shaping the density structure of turbulent astrophysical systems.