Ambipolar diffusion regulated collapse of filaments threaded by
  perpendicular magnetic fields
  We numerically reproduce the density profiles for filaments that are in
magnetohydrostatic and pressure equilibrium with their surroundings obtained in
Tomisaka (2014) and show that these equilibria are dynamically stable. If the
effect of ambipolar diffusion is considered, these filaments lose magnetic
support initiating cloud collapse. The filaments do not lose magnetic flux.
Rather the magnetic flux is redistributed within the filament from the centre
towards the envelope.
  The rate of the collapse is inversely proportional to the fractional
ionisation and two gravitationally-driven ambipolar diffusion regimes for the
collapse are observed as predicted in Mouschovias & Morton (1991). For high
values of the ionisation coefficient, that is $X \geq 10^{-7}$, the gas is
strongly coupled to the magnetic field and the Jeans length is larger than the
ambipolar diffusion length scale. Then the collapse is governed by
magnetically-regulated ambipolar diffusion. For $X \lesssim 10^{-8}$, the gas
is weakly coupled to the magnetic field and the magnetic support is removed by
gravitationally-dominated ambipolar diffusion. Here, neutrals and ions only
collide sporadically, that is the ambipolar diffusion length scale is larger
than the Jeans length.
  When decaying turbulence is included, additional support is provided to the
filament. This slows down the collapse of the filament even in the absence of a
magnetic field. When a magnetic field is present, the collapse rate increases
by a ratio smaller than for the non-magnetic case. This is because of a
speed-up of the ambipolar diffusion due to larger magnetic field gradients
generated by the turbulence and because the ambipolar diffusion aids the
dissipation of turbulence below the ambipolar diffusion length scale. The
highest increase in the rate is observed for the lowest ionisation coefficient
and the highest turbulent intensity.
