Helical Fields and Filamentary Molecular Clouds II - Axisymmetric Stability and Fragmentation

In Paper I (Fiege & Pudritz, 1999), we constructed models of filamentary molecular clouds that are truncated by a realistic external pressure and contain a rather general helical magnetic field. We address the stability of our models to gravitational fragmentation and axisymmetric MHD-driven instabilities. By calculating the dominant modes of axisymmetric instability, we determine the dominant length scales and growth rates for fragmentation. We find that the role of pressure truncation is to decrease the growth rate of gravitational instabilities by decreasing the self-gravitating mass per unit length. Purely poloidal and toroidal fields also help to stabilize filamentary clouds against fragmentation. The overall effect of helical fields is to stabilize gravity-driven modes, so that the growth rates are significantly reduced below what is expected for unmagnetized clouds. However, MHD ``sausage'' instabilities are triggered in models whose toroidal flux to mass ratio exceeds the poloidal flux to mass ratio by more than a factor of $\sim 2$. We find that observed filaments appear to lie in a physical regime where the growth rates of both gravitational fragmentation and axisymmetric MHD-driven modes are at a minimum.