  We present high resolution simulations of two-fluid (ion-neutral) MHD
turbulence with resolutions as large as 512^3. The simulations are supersonic
and mildly sub-Alfvenic, in keeping with the conditions present in molecular
clouds. Such turbulence is thought to influence star formation processes in
molecular clouds because typical cores form on length scales that are
comparable to the dissipation scales of this turbulence in the ions. The
simulations are motivated by the fact that recent studies of isophotologue
lines in molecular clouds have found significant differences in the
linewidth-size relationship for neutral and ion species. The goals of this
paper are to explain those observations using simulations and analytic theory,
present a new set of density-based diagnostics by drawing on similar
diagnostics that have been obtained by studying single-fluid turbulence, and
show that our two-fluid simulations play a vital role in reconciling
alternative models of star formation. The velocity-dependent diagnostics
display a complementarity with the density-dependent diagnostics. We find that
the linewidth-size relationships show a prominent difference between ions and
neutrals when the line of sight is orthogonal to the mean field. This is
because the MHD waves in the ions differ from hydrodynamic waves in the
neutrals. We also find that the density probability distribution functions
(PDFs) show prominent differences between the ions and neutrals when the line
of sight is parallel to the mean field. This is because the velocity
fluctuations in the ions tend to produce column density fluctuations along
field lines. When the magnetic field makes an angle to the line of sight, both
observable differences should be visible. These diagnostics should be easy for
observers to test. This analysis assumes optically thin lines and a mean
magnetic field that is uniform in direction within a cloud.
