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Physics of Non-Universal Larson's Relation

From a new perspective, we re-examine self-gravity and turbulence jointly, in hopes of understanding the physical basis for one of the most important empirical relations governing clouds in the interstellar medium (ISM), the Larson's Relation relating velocity dispersion ($σ_R$) to cloud size ($R$). We report on two key new findings. First, the correct form of the Larson's Relation is $σ_R=α_v^{1/5}σ_{pc}(R/1pc)^{3/5}$, where $α_v$ is the virial parameter of clouds and $σ_{pc}$ is the strength of the turbulence, if the turbulence has the Kolmogorov spectrum. Second, the amplitude of the Larson's Relation, $σ_{pc}$, is not universal, differing by a factor of about two between clouds on the Galactic disk and those at the Galactic center, evidenced by observational data.