Filaments are ubiquitous in the universe. They are seen in cosmological structures, in the Milky Way centre and in dense interstellar gas. Recent observations have revealed that stars and star clusters form preferentially at the intersection of dense filaments. Understanding the formation and properties of filaments is therefore a crucial step in understanding star formation. Here we perform three-dimensional high-resolution magnetohydrodynamical simulations that follow the evolution of molecular clouds and the formation of filaments and stars within them. We apply a filament detection algorithm and compare simulations with different combinations of physical ingredients: gravity, turbulence, magnetic fields and jet/outflow feedback. We find that gravity-only simulations produce significantly narrower filament profiles than observed, while simulations that at least include turbulence produce realistic filament properties. For these turbulence simulations, we find a remarkably universal filament width of (0.10+/-0.02) pc, which is independent of the evolutionary stage or the star formation history of the clouds. We derive a theoretical model that provides a physical explanation for this characteristic filament width, based on the sonic scale (lambda_sonic) of molecular cloud turbulence. Our derivation provides lambda_sonic as a function of the cloud diameter L, the velocity dispersion sigma_v, the gas sound speed c_s and the strength of the magnetic field parameterised by plasma beta. For typical cloud conditions in the Milky Way spiral arms, we find theoretically that lambda_sonic = 0.04-0.16 pc, in excellent agreement with the filament width of 0.05-0.15 pc found in observations.
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