Formation and Collapse of Nonaxisymmetric Protostellar Cores in Planar Magnetic Interstellar Clouds: Formulation of the Problem and Linear Analysis

We formulate the problem of the formation and collapse of nonaxisymmetric protostellar cores in weakly ionized, self-gravitating, magnetic molecular clouds. In our formulation, molecular clouds are approximated as isothermal, thin (but with finite thickness) sheets. We present the governing dynamical equations for the multifluid system of neutral gas and ions, including ambipolar diffusion, and also a self-consistent treatment of thermal pressure, gravitational, and magnetic (pressure and tension) forces. The dimensionless free parameters characterizing model clouds are discussed. The response of cloud models to linear perturbations is also examined, with particular emphasis on length- and timescales for the growth of gravitational instability in magnetically subcritical and supercritical clouds. We investigate their dependence on a cloud's initial mass-to-magnetic-flux ratio μ0 (normalized to the critical value for collapse), the dimensionless initial neutral-ion collision time τ̃ni,0, and also the relative external pressure exerted on a model cloud P̃ext. Among our results, we find that nearly critical model clouds have significantly larger characteristic instability length scales than do more distinctly sub- or supercritical models. Another result is that the effect of a greater external pressure is to reduce the critical length scale for instability. Numerical simulations showing the evolution of model clouds during the linear regime of evolution are also presented, and compared to the results of the dispersion analysis. They are found to be in agreement with the dispersion results, and confirm the dependence of the characteristic length- and timescales on parameters such as μ0 and P̃ext.