  Filaments are ubiquitous in the universe. Recent observations have revealed
that stars and star clusters form preferentially along 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. 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 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 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
ratio of thermal to magnetic pressure, plasma beta. For typical cloud
conditions in the Milky Way spiral arms, we find lambda_sonic = 0.04-0.16 pc,
in excellent agreement with the filament width of 0.05-0.15 pc from
observations. Consistent with the theoretical model assumptions, we find that
the velocity dispersion inside the filaments is subsonic and supersonic
outside. We further explain the observed p=2 scaling of the filament density
profile, rho ~ r^(-p) with the collision of two planar shocks forming a
filament at their intersection.
