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Ordinary differential equations describing the self-similar collapse of arotating, magnetized, self-gravitating and isothermal filament are derived.Explicit homologous solutions are studied with special emphasis on thebifurcation that occurs at the magnetosonic critical point. It is shown thatthere is a critical value for the toroidal magnetic field slope at the originabove which no bifurcation occurs, the solution remains homologous, and belowwhich the density and the poloidal magnetic field tend to zero at large radius(envelope) whereas the toroidal magnetic field and azimuthal velocity relaxtowards a constant value. A series of spatial profiles of density, velocity andmagnetic field, potentially useful for comparison with numerical orobservational studies, is obtained numerically and discussed.Comment: Accepted for publication in A&

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