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

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.