  The Cold Neutral Medium (CNM) is an important part of the galactic gas cycle
and a precondition for the formation of molecular and star forming gas, yet its
distribution is still not fully understood. In this work we present extremely
high resolution simulations of spiral galaxies with time-dependent chemistry
such that we can track the formation of the CNM, its distribution within the
galaxy, and its correlation with star formation. We find no strong radial
dependence between the CNM fraction and total HI due to the decreasing
interstellar radiation field counterbalancing the decreasing gas column density
at larger galactic radii.However, the CNM fraction does increase in spiral arms
where the CNM distribution is clumpy, rather than continuous, overlapping more
closely with H2. The CNM doesn't extend out radially as far as HI, and the
vertical scale height is smaller in the outer galaxy compared to HI with no
flaring. The CNM column density scales with total midplane pressure and
disappears from the gas phase below values of PT/kB =1000 K/cm3. We find that
the star formation rate density follows a similar scaling law with CNM column
density to the total gas Kennicutt-Schmidt law. In the outer galaxy we produce
realistic vertical velocity dispersions in the HI purely from galactic dynamics
but our models do not predict CNM at the extremely large radii observed in HI
absorption studies of the Milky Way. We suggest that extended spiral arms might
produce isolated clumps of CNM at these radii.
