On the waves and instability in self-gravitating magnetic molecular clouds with ambipolar diffusion Part 2: Cylindrical modal approach and nonlinear effects

The dynamics and evolution of molecular clouds, which are the main sites of active star formation in our Galaxy, are governed by the interaction of the self-gravity, magnetic fields, and ambipolar diffusion, in the form of waves and instability. In our earlier paper (Part 1), we carried out a detailed planar modal analysis. The present paper (Part 2) is an extension of Part 1 in order to include the three-dimensionality and the finite size of the cloud as well as the nonlinear effects. A cylindrical modal approach is developed to take into account the three-dimensionality and the finite size of the cloud as well as the special direction of the mean field B ₀. Dispersion relation and solutions of such cylindrical modes are obtained. It is shown that, in the most unstable direction (∥ B ₀), the growth rate is considerably reduced by the finite lateral size compared with the planar mode of the same wavelength. Nonlinear effects of the magnetic field and magnetic waves are discussed, with particular attention paid to their dependence on the coupling factor σ which is the ratio between the mean collision frequency of a neutral with ions and the gravitational response frequency. It is shown that fast magnetosonic waves are as important as Alfvén waves in the global support of the cloud. In order that the lower limit of the wavelengths in the moderately dissipative range of such waves is small compared with the cloud size, σ should be larger than 5. It is also shown that σ should be larger than 7.3 in order for the density growth of the neutral fluid in a free-fall time to be smaller than 30%. A typical value of σ ≈ 11 in molecular clouds is estimated. This corresponds to an ionization rate ζ = 10^?17 and a metal depletion δ = 0.1. For the clouds with such value of σ, both the density growth and the flux loss are smaller than 20% in a free-fall time. It is shown that a self-adjusting mechanism is able to slow down the global collapse at the early stage of cloud evolution in terms of the interaction between the global collapse and the then existing Alfvén and fast magnetosonic waves, which originate from the inhomogeneous velocity and density distributions in the cloud. Such interaction will not only strengthen these waves, but also create outwards decaying amplitudes of the field perturbation and therefore generate outward net magnetic forces to support the cloud against global collapse. The same mechanism also works for refreshing the outwards propagating Alfvén and fast magnetosonic waves caused by star-forming or core-forming activities, if the total energy supply rate due to these activities is lower than the total dissipation rate of these waves. In this way, a significant portion of the released gravitational energy during the global collapse is tapped and turned into the magnetic waves to slow down the global collapse itself. In terms of such a mechanism, the property that the dissipation rate of Alfvén and fast magnetosonic waves increases with the wave number leads to a simple explanation of the coexistence of the global quasi-stability and the local instability (formation of dense cores) in molecular clouds with cloud mass much larger than the Jeans mass.     

On the clumpy structure of molecular clouds

Two-dimensional hydrodynamic calculations for a self-gravitating, magnetic and compressible medium are carried out. The results based on numerical simulations show that the joint effect of the nonlinearity of the hydrodynamic equations and self-gravity is the mechanism for generating the observed complex structure of molecular clouds (e.g. clumps and filaments). In addition, parameters such as the evolution time of molecular clouds, the density contrast, fractal dimension, and the velocity probability distribution are derived. Their possible relation to the observed properties of molecular clouds are discussed.