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We propose a new, physically motivated fitting function for density PDFs in turbulent gas. Although it is known that when gas is isothermal, the PDF is approximately lognormal in the core, high-resolution simulations show large deviations…

Astrophysics of Galaxies · Physics 2013-07-02 Philip F. Hopkins

Molecular clouds exhibit lognormal probability density functions (PDF) of mass densities, which are thought to arise as a consequence of isothermal, supersonic turbulence. Star formation is then widely assumed to occur in perturbations in…

Astrophysics of Galaxies · Physics 2018-10-10 Evan Scannapieco , Mohammadtaher Safarzadeh

We conduct numerical experiments to determine the density probability distribution function (PDF) produced in supersonic, isothermal, self-gravitating turbulence of the sort that is ubiquitous in star-forming molecular clouds. Our…

Astrophysics of Galaxies · Physics 2021-08-10 Shivan Khullar , Christoph Federrath , Mark R. Krumholz , Christopher D. Matzner

The probability density function (PDF) of the logarithmic density contrast, $s=\ln (\rho/\rho_0)$, with gas density $\rho$ and mean density $\rho_0$, for hydrodynamical supersonic turbulence is well-known to have significant non-Gaussian…

Astrophysics of Galaxies · Physics 2022-11-16 James R. Beattie , Philip Mocz , Christoph Federrath , Ralf S. Klessen

We numerically study the volume density probability distribution function (n-PDF) and the column density probability distribution function (Sigma-PDF) resulting from thermally bistable turbulent flows. We analyze three-dimensional…

Astrophysics of Galaxies · Physics 2015-06-12 Adriana Gazol , Jongsoo Kim

Supersonic flows in the interstellar medium (ISM) are believed to be a key driver of the molecular cloud formation and evolution. Among molecular clouds' properties, the ratio between the solenoidal and compressive modes of turbulence plays…

Astrophysics of Galaxies · Physics 2022-05-18 Masato I. N. Kobayashi , Tsuyoshi Inoue , Kengo Tomida , Kazunari Iwasaki , Hiroki Nakatsugawa

The question of the shape of the density PDF for supersonic turbulence is addressed, using both analytical and numerical methods. For isothermal supersonic turbulence, the PDF is Log-Normal, with a width that scales approximately linearly…

Astrophysics · Physics 2007-05-23 AAke Nordlund , Paolo Padoan

Supersonic turbulence occurs in many environments, particularly in astrophysics. In the crucial case of isothermal turbulence, the probability density function (PDF) of the logarithmic density, $s$, is well measured, but a theoretical…

Astrophysics of Galaxies · Physics 2024-10-31 Evan Scannapieco , Liubin Pan , Edward Buie , Marcus Brüggen

We study the probability distribution function (PDF) of the mass density in simulations of supersonic turbulence with properties appropriate for molecular clouds. For this study we use Athena, a new higher-order Godunov code. We find there…

Astrophysics · Physics 2008-09-23 M. Nicole Lemaster , James M. Stone

We performed numerical simulations of supersonic isothermal turbulence driven by mostly compressive large-scale forcing, using both a static grid and adaptive mesh refinement with an effective resolution N=768^3. After a transient phase…

The probability distribution of density in isothermal, supersonic, turbulent gas is approximately lognormal. This behaviour can be traced back to the shock waves travelling through the medium, which randomly adjust the density by a random…

Astrophysics of Galaxies · Physics 2022-10-20 Branislav Rabatin , David C. Collins

Compressible turbulence shapes the structure of the interstellar medium of our Galaxy and likely plays an important role also during structure formation in the early Universe. The density PDF and the power spectrum of such compressible,…

Solar and Stellar Astrophysics · Physics 2013-09-25 Christoph Federrath

Turbulence is a complex phenomenon that plays a critical role in the interstellar medium (ISM). Previous simulations and observations show that the probability density function (PDF) of gas density in isothermal and compressible systems…

Astrophysics of Galaxies · Physics 2025-03-26 Xunchuan Liu

The probability density function (PDF) of the gas density in turbulent supersonic flows is investigated with high-resolution numerical simulations. In a systematic study, we compare the density statistics of compressible turbulence driven…

Astrophysics · Physics 2009-11-13 Christoph Federrath , Ralf S. Klessen , Wolfram Schmidt

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…

Astrophysics of Galaxies · Physics 2017-08-30 Jonathan Squire , Philip F. Hopkins

In star-forming clouds, high velocity flow gives rise to large fluctuations of density. In this work we explore the correlation between velocity magnitude (speed) and density. We develop an analytic formula for the joint probability…

Astrophysics of Galaxies · Physics 2023-08-02 Branislav Rabatin , David C. Collins

The density distribution of supersonic isothermal turbulence plays a critical role in many astrophysical systems. It is commonly approximated by a lognormal distribution with a variance of $\sigma_{s,{\rm V}}^2 \approx \ln(1 + b^2 M_{\rm…

Astrophysics of Galaxies · Physics 2026-01-15 Evan Scannapieco , Marcus Brüggen , Philipp Grete , Liubin Pan

The probability distribution function (PDF) of the mass surface density is an essential characteristic of the structure of molecular clouds or the interstellar medium in general. Observations of the PDF of molecular clouds indicate a…

Astrophysics of Galaxies · Physics 2015-06-18 Joerg Fischera

This paper investigates the statistical properties of isothermal turbulence in both the subsonic and supersonic regimes. The focus is on the influence of the Mach number ($Ma$) and the Reynolds number ($Re$) on both the space-local and…

Fluid Dynamics · Physics 2025-10-16 F. Thiesset , C. Federrath

We investigate the form of the one-point probability distribution function (pdf) for the density field of the interstellar medium using numerical simulations that successively reduce the number of physical processes included.…

Astrophysics · Physics 2014-10-13 J. Scalo , E. Vazquez-Semadeni , D. Chappell , T. Passot
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