Long-lived Magnetic-Tension-Driven Modes in a Molecular Cloud
  We calculate and analyze the longevity of magnetohydrodynamic (MHD) wave
modes that occur in the plane of a magnetic thin sheet. Initial turbulent
conditions applied to a magnetically subcritical cloud are shown to lead to
relatively rapid energy decay if ambipolar diffusion is introduced at a level
corresponding to partial ionization primarily by cosmic rays. However, in the
flux-freezing limit, as may be applicable to photoionized molecular cloud
envelopes, the turbulence persists at "nonlinear" levels in comparison with the
isothermal sound speed $\cs$, with one-dimensional rms material motions in the
range of $\approx 2\,\cs -5\,\cs$ for cloud sizes in the range of $\approx
2\,\pc - 16\,\pc$. These fluctuations persist indefinitely, maintaining a
significant portion of the initial turbulent kinetic energy. We find the
analytic explanation for these persistent fluctuations. They are
magnetic-tension-driven modes associated with the interaction of the sheet with
the external magnetic field. The phase speed of such modes is quite large,
allowing residual motions to persist without dissipation in the flux-freezing
limit, even as they are nonlinear with respect to the sound speed. We speculate
that long-lived large-scale MHD modes such as these may provide the key to
understanding observed supersonic motions in molecular clouds.
