Gravitational collapse of polytropic, magnetized, filamentary clouds

For the case in which the gas of a magnetized filamentary cloud obeys a polytropic equation of state, gravitational collapse of the cloud is studied using a simplified model. We concentrate on the radial distribution and restrict ourselves to a purely toroidal magnetic field. If the axial motions and poloidal magnetic fields are sufficiently weak, we could reasonably expect our solutions to be a good approximation. We show that while the filament experiences gravitational condensation and the density at the centre increases, the toroidal flux-to-mass ratio remains constant. A series of spatial profiles of density, velocity and magnetic field for several values of the toroidal flux-to-mass ratio and the polytropic index, is obtained numerically and discussed.