Turbulence and Magnetic Field Alignment in Small Molecular Clouds: The Role of Cloud Size, Mass, and Density

In this study, we investigate the relationship between turbulence (Δ V ) and different physical parameters in 22 isolated small molecular clouds and their cores, extending the analysis to a hierarchical scenario from core to cloud. Using 12 CO line width as a tracer of turbulence, we find that Δ V correlates with both cloud size and mass, following ∝ ( L cl ) 0.30 ± 0.04 and ∝ ( M cl ) 0.21 ± 0.08 . Further, the surface density of the clouds (Σ cl ) influences the Δ V – L cl relation, with Δ V ∝ ( L cl × Σ cl ) 0.50 ± 0.13 . This indicates that gravitational energy drives turbulence in clouds, indicating possible virial equilibrium. We observe that L cl correlates with M cl and volume gas density of the cloud ( ρ cl ), implying nearly constant Σ cl across the clouds. In cloud cores, C 18 O line-width data show complex behavior, with no direct correlation between Δ V and core size ( L co ). However, a positive correlation emerges when the surface density of the core is included in L co . Notably, the relation between volume gas density ( ρ co ) and core size ( L co ) deviates from constant core surface density. Our analysis reveals that turbulent pressure increases with gravitational pressure to maintain global equilibrium. Finally, on the core-to-cloud scale, physical relationships remain continuous, reflecting the interconnected nature of clouds and cores. Extending our previous work, where we demonstrated a nonlinear dependence of turbulence on the alignment of the local magnetic field in molecular clouds with the Galactic plane, we now compare observations with a theoretical model based on kinetic theory. Our result confirms that higher turbulence causes greater magnetic misalignment consistent with the derived second-order polynomial relationship.