Geometry-Independent Determination of Radial Density Distributions in Molecular Cloud Cores and Other Astronomical Objects

TL;DR

This paper introduces a geometry-independent method to determine radial density profiles of astronomical objects from a single column density map, reducing bias and applicable to various objects, demonstrated on molecular cloud cores.

Contribution

The paper presents an analytical and numerical method that infers radial density profiles without assuming object geometry, based on contour self-similarity in column density maps.

Findings

Radial density profiles of molecular cloud cores are well described by an attenuated power law.

The method effectively removes geometric bias in density profile determination.

Application to 2MASS data demonstrates practical utility.

Abstract

We present a geometry-independent method for determining the shapes of radial volume density profiles of astronomical objects whose geometries are unknown, based on a single column density map. Such profiles are often critical to understand the physics and chemistry of molecular cloud cores, in which star formation takes place. The method presented here does not assume any geometry for the object being studied, thus removing a significant source of bias. Instead it exploits contour self-similarity in column density maps which appears to be common in data for astronomical objects. Our method may be applied to many types of astronomical objects and observable quantities so long as they satisfy a limited set of conditions which we describe in detail. We derive the method analytically, test it numerically, and illustrate its utility using 2MASS-derived dust extinction in molecular cloud cores. While not having made an extensive comparison of different density profiles, we find that the overall radial density distribution within molecular cloud cores is adequately described by an attenuated power law.