The fractal dimension of star-forming regions at different spatial scales in M33

TL;DR

This study analyzes the fractal distribution of stars, gas, and clouds in M33 across various scales, revealing a transition from turbulent to galactic dynamics around 500-1000 pc, and differences in distribution based on brightness and type.

Contribution

It provides the first detailed fractal analysis of multiple interstellar components in M33 over a wide range of spatial scales, identifying a characteristic transition scale.

Findings

Scale-free behavior at small scales

Transition to uniform distribution at 500-1000 pc

Different fractal dimensions for bright and faint stars

Abstract

We study the distribution of stars, HII regions, molecular gas, and individual giant molecular clouds in M33 over a wide range of spatial scales. The clustering strength of these components is systematically estimated through the fractal dimension. We find scale-free behavior at small spatial scales and a transition to a larger correlation dimension (consistent with a nearly uniform distribution) at larger scales. The transition region lies in the range 500-1000 pc. This transition defines a characteristic size that separates the regime of small-scale turbulent motion from that of large-scale galactic dynamics. At small spatial scales, bright young stars and molecular gas are distributed with nearly the same three-dimensional fractal dimension (Df <= 1.9), whereas fainter stars and HII regions exhibit higher values (Df = 2.2-2.5). Our results indicate that the interstellar medium in M33 is on average more fragmented and irregular than in the Milky Way.