Statistical link between the structure of molecular clouds and their density distribution

TL;DR

This paper develops a statistical framework linking the structure of molecular clouds to their density distributions, including power-law and continuous types, and explores their 2D projections.

Contribution

It introduces a class of equivalence for molecular clouds based on abstract scales and derives scaling relations for different density distributions.

Findings

Derived differential relationship between mean density and structure parameter.

Established relations between 2D and 3D scaling exponents.

Applicable to clouds with power-law, lognormal, or combined density distributions.

Abstract

We introduce the concept of a class of equivalence of molecular clouds represented by an abstract spherically symmetric, isotropic object. This object is described by use of abstract scales in respect to a given mass density distribution. Mass and average density are ascribed to each scale and thus are linked to the density distribution: a power-law type and an arbitrary continuous one. In the latter case, we derive a differential relationship between the mean density at a given scale and the structure parameter which defines the mass-density relationship. The two-dimensional (2D) projection of the cloud along the line of sight is also investigated. Scaling relations of mass and mean density are derived in the considered cases of power-law and arbitrary continuous distributions. We obtain relations between scaling exponents in the 2D and 3D cases. The proposed classes of equivalence are representative for the general structure of real clouds with various types of column-density distributions: power law, lognormal or combination of both.