Self-similar condensation of rotating magnetized self-gravitating isothermal filaments

¹ Laboratoire de radioastronomie millimétrique, UMR 8540 du CNRS, École normale supérieure et Observatoire de Paris, 24 rue Lhomond, 75231 Paris Cedex 05, France
² Department of Physics and Astronomy, Cardiff University, PO Box 913, 5 The Parade, Cardiff CF24 3YB, Wales, UK

Corresponding author: P. Hennebelle, patrick.hennebelle@ens.fr

Received: 1 February 2002
Accepted: 11 October 2002

Abstract

Ordinary differential equations describing the self-similar collapse of a rotating, magnetized, self-gravitating and isothermal filament are derived. Explicit homologous solutions are studied with special emphasis on the bifurcation that occurs at the magnetosonic critical point. It is shown that there is a critical value for the toroidal magnetic field slope at the origin above which no bifurcation occurs, the solution remains homologous, and below which the density and the poloidal magnetic field tend to zero at large radius (envelope) whereas the toroidal magnetic field and azimuthal velocity relax towards a constant value. A series of spatial profiles of density, velocity and magnetic field, potentially useful for comparison with numerical or observational studies, is obtained numerically and discussed.