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We have performed systemmatic local linear stability analysis on a radiallystratified infinite self-gravitating cylinder of rotating plasma under theinfluence of magnetic field. In order to render the system analyticallytractable, we have focussed solely on the axisymmetric modes of perturbations.Using cylindrical coordinate system, we have derived the critical linear massdensity of a non-rotating filament required for gravitational collapse to ensuein the presence of azimuthal magnetic field. Moreover, for such filamentsthreaded by axial magnetic field, we show that the growth rates of the modeshaving non-zero radial wavenumber are reduced more strongly by the magneticfield than that of the modes having zero radial wavenumber. More importantly,our study contributes to the understanding of the stability property ofrotating astrophysical filaments that are more often than not influenced bymagnetic fields. In addition to complementing many relevant numerical studiesreported the literature, our results on filaments under the influence ofmagnetic field generalize some of the very recent analytical works(e.g.,~\citet{jog2014}, etc.). For example, here we prove that even a weakmagnetic field can play a dominant role in determining stability of thefilament when the rotation timescale is larger than the free fall timescale. Afilamentary structure with faster rotation is, however, comparatively morestable for the same magnetic field. The results reported herein, due to stronglocality assumption, are strictly valid for the modes for which one can ignorethe radial variations in the density and the magnetic field profiles.

Stability of Rotating Self-Gravitating Filaments:Stability of Rotating Self-Gravitating Filaments: Effects of Magnetic Field