2025ApJ...980..252B

In this study, we investigate the relationship between turbulence (ΔV) 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 ¹²CO line width as a tracer of turbulence, we find that ΔV correlates with both cloud size and mass, following $\propto {({L}_{\mathrm{cl}})}^{0.30\pm 0.04}$ and $\propto {({M}_{\mathrm{cl}})}^{0.21\pm 0.08}$. Further, the surface density of the clouds (Σ_cl) influences the ΔV-L_cl relation, with ${\rm{\Delta }}V\propto {({L}_{\mathrm{cl}}\times {\Sigma }_{\mathrm{cl}})}^{0.50\pm 0.13}$. 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, C¹⁸O line-width data show complex behavior, with no direct correlation between ΔV 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.