On Scaling Laws and Alfvenic Magnetic Fluctuations in Molecular Clouds

Under the basic assumption that the observed turbulent motions in molecular clouds are Alfvenic waves or turbulence, we emphasize that the Doppler broadening of molecular line profiles directly measures the velocity amplitudes of the waves instead of the Alfven velocity. Assuming an equipartition between the kinetic energy and the Alfvenic magnetic energy, we further propose the hypothesis that observed standard scaling laws in molecular clouds imply a roughly scale-independent fluctuating magnetic field, which might be understood as a result of strong wave-wave interactions and subsequent energy cascade. We predict that $\sigma_{v}\propto \rho^{-0.5}$ is a more basic and robust relation in that it may approximately hold in any regions where the spatial energy density distribution is primarily determined by wave-wave interactions, including gravitationally unbound regions. We also discuss the fact that a scale-independent $\sigma_{B}^{2}$ appears to contradict existing 1-D and 2-D computer simulations of MHD turbulence in molecular clouds.