Disk Stability and Neutral Hydrogen as a Tracer of Dark Matter
  We derive the projected surface mass distribution Sigma_M for spherically
symmetric mass distributions having an arbitrary rotation curve. For a galaxy
with a flat rotation curve and an ISM disk having a constant Toomre stability
parameter, Q, the ISM surface mass density Sigma_g as well as Sigma_M both fall
off as 1/R. We use published data on a sample of 20 well studied galaxies to
show that ISM disks do maintain a constant Q over radii usually encompassing
more than 50% of the HI mass. The power law slope in Sigma_g covers a range of
exponents and is well correlated with the slope in the epicyclic frequency.
This implies that the ISM disk is responding to the potential, and hence that
secular evolution is important for setting the structure of ISM disks. We show
that the gas to total mass ratio should be anti-correlated with the maximum
rotational velocity, and that the sample falls on the expected relationship. A
very steep fall off in Sigma_g is required at the outermost radii to keep the
mass and angular momentum content finite for typical rotation curve shapes, and
is observed. The observation that HI traces dark matter over a significant
range of radii in galaxies is thus due to the disks stabilising themselves in a
normal dark matter dominated potential. This explanation is consistent with the
cold dark matter paradigm.
