Alfvén wave support of a dwarf molecular cloud I. An isothermal model

Dwarf (or dark) molecular clouds and molecular clumps have a lifetime which is greater than their dynamical time and must therefore be, in an average sense, in mechanical equilibrium. Equilibrium perpendicular to a global magnetic field is by magnetic forces and it is proposed that along the field the gas is supported by an Alfvén wave pressure force. A selfconsistent analytical model, utilising a WKB approximation, is developed for such support. It is found that Alfvén waves are indeed a good candidate for this support, generating model cloud thicknesses consistent with observations. The effect of damping by the linear process of ion-neutral friction is considered. It is found that the damping of the waves is not a necessary condition for the support of the cloud although weak damping is an advantage. The possible sources of these waves are discussed.