ON THE WAVES AND INSTABILITY IN SELF-GRAVITATING MAGNETIC MOLECULAR CLOUDS WITH AMBIPOLAR DIFFUSION .1. PLANAR MODAL APPROACH

It is well established that molecular clouds are the main sites of act ive star formation in our Galaxy. The interaction of the three major p hysical agents in molecular clouds, i.e. the self-gravity, magnetic fi elds, and ambipolar diffusion, in the form of waves and instability, g overns the dynamics and evolution of molecular clouds. The present wor k 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 restric tions on the direction of the velocity perturbation which were used in previous studies. Thus, the wave number vector k is allowed to take a ny direction with respect to the mean field B-0. The exact general dis persion relation is found to be a seventh-order equation and can be re duced to a quartic equation as the first approximation about the small parameter x(rho) = rho(i,0)/rho(n,0), 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 Lambda and s igma, where h = V-A,V-n/C-n is the ratio between the Alfven speed and the sound speed in the neutrals, and the ''coupling factor'' sigma = n u(i)/omega(g,n) is the ratio between the average collision frequency o f a neutral with ions and the self-gravitation response frequency. It is shown that, in all directions, magnetic field only reduces the grow th rate but does not change the critical wave length for instability. The reduction of the growth rate depends on not only Lambda, the dimen sionless measure of the field strength, but also the direction of k as well as the coupling factor sigma. The frequencies and the dissipatio n rates of the Alfven waves and the fast and slow self-gravitating mag netosonic waves are calculated for all directions of k. The solutions of these waves are also given. Although the planar modal approach is i mportant in understanding the basic mechanism of magnetic waves and in stability, it does not take into account the three-dimensionality and the finite size of the cloud and is therefore only suitable to the loc al analysis. Thus, in order to discuss the global properties, we will develop a cylindrical modal approach in Part 2. There, we will also di scuss certain nonlinear effects and show their importance in leading t o a self-adjusting mechanism which slows down the global collapse at t he early stage of cloud evolution and refreshes the outward propagatin g Alfven and fast magnetosonic waves caused by star-forming or core-fo rming activities. In this way, a significant portion of the released g ravitational energy during the global collapse is turned into the magn etic waves to support the cloud against the global collapse itself.