Gravitational instability of filamentary molecular clouds, including
  ambipolar diffusion; Non-isothermal filament
  Recent observations of the filamentary molecular clouds show that their
properties deviate from the isothermal equation of state. Theoretical
investigations proposed that the logatropic and the polytropic equations of
state with negative indexes can provide a better description for these
filamentary structures. Here, we aim to compare the effects of these softer
non-isothermal equation of states with their isothermal counterpart on the
global gravitational instability of a filamentary molecular cloud. By
incorporating the ambipolar diffusion, we use the non-ideal
magnetohydrodynamics framework for a filament that is threaded by a uniform
axial magnetic field. We perturb the fluid and obtain the dispersion relation
both for the logatropic and polytropic equations of state by taking the effects
of magnetic field and ambipolar diffusion into account. Our results suggest
that, in absence of the magnetic field, a softer equation of state makes the
system more prone to gravitational instability. We also observed that a
moderate magnetic field is able to enhance the stability of the filament in a
way that is sensitive to the equation of state in general. However, when the
magnetic field is strong, this effect is suppressed and all the equations of
state have almost the same stability properties. Moreover, we find that for all
the considered equations of state, the ambipolar diffusion has destabilizing
effects on the filament.
