Analytical models of rotating magnetized gas filaments

Several rotating molecular gas filaments with striking helical morphology have been observed in the Central Molecular Zone, including the Double Helix Nebula (DHN), the Galactic Centre Tornado (GCT), and the Pigtail Nebula (PTN). We present a model for isothermal, rotating, magnetized, pressure-truncated, non-self-gravitating filaments, as a model for these objects. We find a no v el analytical stationary solution for these molecular tornadoes by assuming a propagating torsional Alfv & eacute;n wave resulting in balance between toroidal magnetic stress and centrifugal force, as well as constant flux to mass ratio for the poloidal magnetic field. Our model allows for differential rotation and the density profile for the stationary solution goes asymptotically as r(-1) at large radius for a special case where the flux to mass ratios for the poloidal and toroidal fields are constant inside the filament. We subject our stationary solutions to a virial analysis and show that they satisfy the virial equation for cylindrical symmetry 2K + M = 0. Finally, we estimate the ratio of gravitational potential energy per unit length, W, to the bulk kinetic energy per unit length, K-0 , and calculate |W|/K-0 for the DHN, GCT, and PTN. Our estimates suggest that self-gravity is negligible in the DHN and the PTN and GCT are at most weakly self-gravitating. We also briefly address an application of our model to filamentary plasma lenses in the interstellar medium.