A method for reconstructing the PDF of a 3D turbulent density field from 2D observations

TL;DR

This paper presents a novel method to reconstruct the 3D density PDF of turbulent fields from 2D observations, validated with simulations of molecular cloud turbulence, enabling better understanding of astrophysical turbulence.

Contribution

The paper introduces a new technique to derive the 3D density PDF from 2D column density data, linking the PDFs through a compression factor based on the power spectrum.

Findings

The 3D density PDF can be approximated from the 2D column density PDF.

The compression factor relates to the column density power spectrum.

The method is validated with hydrodynamic and magnetohydrodynamic turbulence simulations.

Abstract

We introduce a method for calculating the probability density function (PDF) of a turbulent density field in three dimensions using only information contained in the projected two-dimensional column density field. We test the method by applying it to numerical simulations of hydrodynamic and magnetohydrodynamic turbulence in molecular clouds. To a good approximation, the PDF of log(normalised column density) is a compressed, shifted version of the PDF of log(normalised density). The degree of compression can be determined observationally from the column density power spectrum, under the assumption of statistical isotropy of the turbulence.