A supersonic turbulence origin of Larson's laws

Abstract

We revisit the origin of Larson's scaling laws describing the structure and kinematics of molecular clouds. Our analysis is based on recent observational measurements and data from a suite of six simulations of the interstellar medium, including effects of self-gravity, turbulence, magnetic field and multiphase thermodynamics. Simulations of isothermal supersonic turbulence reproduce observed slopes in linewidth-size and mass-size relations. Whether or not self-gravity is included, the linewidth-size relation remains the same. The mass-size relation, instead, substantially flattens below the sonic scale, as prestellar cores start to form. Our multiphase models with magnetic field and domain size 200 pc reproduce both scaling and normalization of the first Larson law. The simulations support a turbulent interpretation of Larson's relations. This interpretation implies that: (i) the slopes of linewidth-size and mass-size correlations are determined by the inertial cascade; (ii) none of the three Larson laws is fundamental; (iii) instead, if one is known, the other two follow from scale invariance of the kinetic energy transfer rate. It does not imply that gravity is dynamically unimportant. The self-similarity of structure established by the turbulence breaks in star-forming clouds due to the development of gravitational instability in the vicinity of the sonic scale. The instability leads to the formation of prestellar cores with the characteristic mass set by the sonic scale. The high-end slope of the core mass function predicted by the scaling relations is consistent with the Salpeter power-law index. Larson (1981) established that for many MCs their internal velocity dispersion, σu, is well correlated with the cloud size, L, and mass, m. Since the power-law form of the correlation, σu ∝ L 0.38 , and the power index, 0.38 ∼ 1/3, were similar to those of the Kolmogorov (1941a,b, hereafter K41) turbulence, he suggested that observed non-thermal linewidths may originate from a 'common hierarchy of interstellar turbulent motions'. The clouds would also appear mostly gravitationally bound and in approximate virial equilibrium, as there was a close positive correlation between their velocity dispersion and mass, σu ∝ m 0.20 . However, Larson suggested that these structures 'cannot have formed by simple gravitational collapse' and should be at least partly created by supersonic turbulence. This seminal paper preconceived many important ideas in the field and strongly influenced its development for the past 30 years.Myers (1983) studied 43 smaller dark clouds and confirmed the existence of significant linewidth-size and density-size correlations found earlier by Larson for larger MCs. He acknowledged that two distinct interpretations of the data are possible: (i) the linewidth-size relation also known as Larson's first law (σu ∝ R 0.5 ) arises from a Kolmogorov-like cascade of turbulent energy; (ii) the same c 2013 RAS

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