lko-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 (eg. clumps and filaments). IR 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.
Two-dimensional compressible turbulence in a self-gravitating, magnetic interstellar medium is calculated as an initial value problem. It is shown that even if the initial density distribution is homogeneous and the initial velocity distribution contains only a few Fourier components, the nonlinear interaction among the Fourier components will generate more and more Fourier components and lead to a turbulent and fractal structure in the interstellar medium. The calculations are carried out for three different initial states. In order to see the time evolution, detailed density distributions and fractal dimensions of the density contours are calculated at three moments of time for each of the initial states. The results show that the fractal dimension remains almost the same (~1.4–1.5), although the detailed density distribution has changed considerably. The insensibility of the fractal dimension of density contours to both the initial conditions and the evolution time is in good agreement with observations of molecular clouds in the interstellar medium.
It is well established that molecular clouds are the main sites of active star formation in our Galaxy. The interaction of the three major physical agents in molecular clouds, i.e the self-gravity, magnetic fields, and ambipolar diffusion, in the form of waves and instability, governs the dynamics and evolution of molecular clouds. The present work is a new effort on this subject.This work consists of two parts. In Part 1, we complete the planar modal analysis by removing the restrictions on the direction of the velocity perturbation which were used in previous studies. Thus, the wave number vector k is allowed to take any direction with respect to the mean field B,, . The exact general dispersion relation is found to be a seventh-order equation and can be reduced to a quartic equation as the first approximation about the small parameter x,, = pi,O/pn,O, the density ratio between ions and neutrals. The growth rate contour maps in the k plane are obtained for various values of the basic dimensionless parameters A and a. where A = VA,,/Cn is the ratio between the Alfvkn speed and the sound speed in the neutrals, and the "coupling factor" Q = v i /~g , n is the ratio between the average collision frequency of a neutral with ions and the self-gravitation response frequency. It is shown that, in all directions, magnetic field only reduces the growth rate but does not change the critical wave length for instability. The reduction of the growth rate depends on not only A, the dimensionless measure of the field strength, but also the direction of k as well as the coupling factor Q. The frequencies and the dissipation rates of the Alfvh waves and the fast and slow self-gravitating magnetosonic waves are calculated for all directions of k. The solutions of these waves are also given.Although the planar modal approach is important in understanding the basic mechanism of magnetic waves and instability. it does not take into account the three-dimensionality and the finite size of the cloud and is therefore only suitable to the local analysis. Thus, in order to discuss the global properties, we will develop a cylindrical modal approach in Part 2. There, we will also discuss certain nonlinear effects and show their importance in leading to a self-adjusting mechanism which slows down the global collapse at the early stage of cloud evolution and refreshes the outward propagating Alfvkn and fast magnetosonic waves caused by star-forming or core-forming activities. In this way, a significant portion of the released gravitational energy during the global collapse is turned into the magnetic waves to support the cloud against the global collapse itself. * This will also be justified by numerical calculations. Cf. Section 5 and Fig. 3. Actually. this conclusion holds even for o-00 (the MHD limit) except the special case klB,,. Condition (3.39) is replaced by ~C~,~~~.,/(V:,~+CSI)''~ if and only if u-+= and kLB, (for detailed discussions, see Appendix C).
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