Clump mass function at an early stage of molecular cloud evolution: I. A statistical approach

TL;DR

This paper presents a statistical method to derive the initial mass function of molecular cloud condensations formed through turbulence, revealing a power-law distribution consistent with observations.

Contribution

It introduces a novel statistical approach linking turbulence energy equipartition to the clump mass function in early molecular cloud evolution.

Findings

Clump mass function can be represented by multiple power laws.

High-mass slope is approximately -1, typical for fractal clouds.

Intermediate-mass part is shallower, aligning with observations.

Abstract

We derive the mass function of condensations (clumps) which were formed through a turbulent cascade over a range of spatial scales $L\le20$ pc during early, predominantly turbulent evolution of a molecular cloud. The approach rests upon the assumption of a statistical clump mass-density relationship $n\propto m^x$ with a scale dependence of the exponent $x$ obtained from equipartition relations between various forms of energy of clumps. The derived clump mass function (ClMF) could be represented by series of 2 or 3 power laws, depending on the chosen equipartition relation, the velocity scaling index and the type of turbulent forcing. The high-mass ClMF exhibits an average slope $\Gamma\simeq-1$, typical for fractal clouds, whereas its intermediate-mass part is shallower or flattened, in agreement with some observational studies.