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This paper is devoted to the study of the gravitational instability of amedium permeated by a uniform magnetic field along which a circularly polarizedAlfven wave propagates. We concentrate on the case of perturbations purelytransverse to the ambient field by means of direct numerical simulations of theMHD equations and of a linear stability analysis performed on a moderateamplitude asymptotic model. The Alfven wave provides an extra stabilizingpressure when the scale of perturbations is sufficiently large or smallcompared with the Jeans length $L_J$. However, there is a band of scales around$L_J$ for which the Alfven wave is found to have a destabilizing effect. Inparticular, when the medium is stable in absence of waves, the gravitationalinstability can develop when the wave amplitude lies in an appropriate range.This effect appears to be a consequence of the coupling between Alfven andmagnetosonic waves. The prediction based on a WKB approach that the Alfven wavepressure tensor is isotropic and thus opposes gravity in all directions is onlyrecovered for large amplitude waves for which the coupling between thedifferent MHD modes is negligible.Comment: submitted to A&

Twofold effect of Alfvén waves on the transverse gravitational instability