Polytropic models of filamentary interstellar clouds - II. Helical magnetic fields

We study the properties of magnetized cylindrical polytropes as models for interstellar filamentary clouds, extending the analysis presented in a companion paper. We formulate the general problem of magnetostatic equilibrium in the presence of a helical magnetic field, with the aim of determining the degree of support or compression resulting from the magnetization of the cloud. We derive scale-free solutions appropriate to describe the properties of the envelopes of filaments at radii larger than the flat-density region. In these solutions, the polytropic exponent determines the radial profiles of the density and the magnetic field. The latter decreases with radius less steeply than the density, and field lines are helices twisted over cylindrical surfaces. A soft equation of state supports magnetic configurations that preferentially compress and confine the filament, whereas in the isothermal limit the field provides support. For each value of the polytropic exponent, the Lorentz force is directed outwards or inwards depending on whether the pitch angle is below or above some critical value which is a function of the polytropic exponent only.