| Issue |
A&A
Volume 710, June 2026
|
|
|---|---|---|
| Article Number | L3 | |
| Number of page(s) | 7 | |
| Section | Letters to the Editor | |
| DOI | https://doi.org/10.1051/0004-6361/202659228 | |
| Published online | 28 May 2026 | |
Letter to the Editor
The slope of the power spectrum of the density field in isothermal supersonic compressible turbulence
1
ENS de Lyon, Université Lyon 1, CNRS, CRAL, UMR 5574 Lyon, France
2
School of Physics, University of Exeter, Exeter EX4 4QL, UK
★ Corresponding author: This email address is being protected from spambots. You need JavaScript enabled to view it.
Received:
30
January
2026
Accepted:
2
May
2026
Abstract
The power spectrum (PS) of the density field in supersonic turbulence is a fundamental quantity that characterizes the statistical properties of the structures formed in compressible flows. It is also widely used to estimate the Mach number in the interstellar medium from simulation-derived relations. In this paper, we provide a first quantitative explanation for the evolution of the slope of the PS of the density field with the Mach number in homogeneous isotropic isothermal turbulence using a time-invariant quantity derived by Chandrasekhar, S. (1951, Proc. R. Soc. Lond. Ser. A, 210, 18). For simulated turbulent flows, the model reproduces the measured slopes for different widths of the inertial range and density variances very well. Our model also provides a comprehensive interpretation of the characteristic slopes of the PS of the density field measured in the interstellar medium. Based on these results, we stress that the Mach number cannot be reliably deduced from the slope of the PS of the density field. In closing, we discuss a resolution criterion that must be fulfilled to correctly simulate a turbulent flow with a given density PS slope.
Key words: turbulence / methods: analytical / ISM: structure
© The Authors 2026
Open Access article, published by EDP Sciences, under the terms of the Creative Commons Attribution License (https://creativecommons.org/licenses/by/4.0), which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.
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