Fragmentation of Isothermal Sheet-Like Clouds. I: Solutions of Linear and Second-Order Perturbation Equations

Abstract

The fragmentation instability of an infinite isothermal gas layer is investigated in order to see whether the observed complex structures of many dense interstellar clouds are the results of fragmentation of parent sheet-like clouds. Linear perturbation theory for this sheet-like cloud is well-known, but to find the final result of growing perturbations, a nonlinear analysis is needed. As the first step, we obtain in this paper the solutions of the second-order perturbation equations, which will be useful to understand the nature of the nonlinear effect. From the analysis of the nonlinear effect, we found that, if fragments are initially elongated, they become elongated more and more as they go on collapsing. Hence most of collapsing fragments have structures of very slender cylinders. We also discuss the equilibrium and the collapse of an infinitely long isothermal cylinder.