Revisiting the Velocity Dispersion–Size Relation in Molecular Cloud Structures

Abstract

Structures in molecular ISM are observed to follow a power-law relation between the velocity dispersion and spatial size, known as Larson's first relation, which is often attributed to the turbulent nature of molecular ISM and imprints the dynamics of molecular cloud structures. Using the ¹³CO (J = 1–0) data from the Milky Way Imaging Scroll Painting survey, we built a sample with 360 structures having relatively accurate distances obtained from either the reddened background stars with Gaia parallaxes or associated maser parallaxes, spanning from 0.4 to ∼15 kpc. Using this sample and about 0.3 million pixels, we analyzed the correlations between velocity dispersion, surface/column density, and spatial scales. Our structure-wise results show power-law indices smaller than 0.5 in both the σ _v –R _eff and σ _v –R _eff · Σ relations. In the pixel-wise results, the is statistically scaling with the beam physical size (R _s ≡ ΘD/2) in form of . Meanwhile, in the inner Galaxy is statistically larger than the outer side. We also analyzed correlations between and the H₂ column density N(H₂), finding that stops increasing with N(H₂) after ≳10²² cm^‑2. The structures with and without high-column-density (>10²² cm^‑2) pixels show different relations, where the mean (std) ξ values are 0.38 (0.14) and 0.62 (0.27), respectively.