Structure and Stability of Filamentary Clouds Supported by Lateral
  Magnetic Field
  We have constructed two types of analytical models for an isothermal
filamentary cloud supported mainly by magnetic tension. The first one describes
an isolated cloud while the second considers filamentary clouds spaced
periodically. Both the models assume that the filamentary clouds are highly
flattened. The former is proved to be the asymptotic limit of the latter in
which each filamentary cloud is much thinner than the distance to the
neighboring filaments. We show that these models reproduce main features of the
2D equilibrium model of Tomisaka (2014) for filamentary cloud threaded by
perpendicular magnetic field. It is also shown that the critical mass to flux
ratio is $ M /\Phi = (2 \pi \sqrt{G}) ^{-1} $, where $ M $, $ \Phi $ and $ G $
denote the cloud mass, the total magnetic flux of the cloud, and the
gravitational constant, respectively. This upper bound coincides with that for
an axisymmetric cloud supported by poloidal magnetic fields. We applied the
variational principle for studying the Jeans instability of the first model.
Our model cloud is unstable against fragmentation as well as the filamentary
clouds threaded by longitudinal magnetic field. The fastest growing mode has a
wavelength several times longer than the cloud diameter. The second model
describes quasi-static evolution of filamentary molecular cloud by ambipolar
diffusion.
