The scale height of gas traced by [CII] in the Galactic plane
  The distribution of various interstellar gas components and the pressure in
the interstellar medium (ISM) is a result of the interplay of different
dynamical mechanisms and energy sources on the gas in the Milky Way. The scale
heights of the different gas tracers, such as HI and CO, are a measure of these
processes. The scale height of [CII] emission in the Galactic plane is
important for understanding those ISM components not traced by CO or HI. We
determine the average distribution of [CII] perpendicular to the plane in the
inner Galactic disk and compare it to the distributions of other key gas
tracers, such as CO and HI. We calculated the vertical, z, distribution of
[CII] in the inner Galactic disk by adopting a model for the emission that
combines the latitudinal, b, spectrally unresolved BICE survey, with the
spectrally resolved $Herschel$ Galactic plane survey of [CII] at b = 0 deg. Our
model assumed a Gaussian emissivity distribution vertical to the plane, and
related the distribution in z to that of the latitude b using the spectrally
resolved [CII] Herschel survey as the boundary solution for the emissivity at
b=0 deg. We find that the distribution of [CII] perpendicular to the plane has
a full-width half-maximum of 172 pc, larger than that of CO, which averages
~110 pc in the inner Galaxy, but smaller than that of HI, ~230 pc, and is
offset by -28 pc. We explain the difference in distributions of [CII], CO, and
HI as due to [CII] tracing a mix of ISM components. Models of hydrostatic
equilibrium of clouds in the disk predict different scale heights, for the same
interstellar pressure. The diffuse molecular clouds with [CII] but no CO
emission likely have a scale height intermediate between the low density atomic
hydrogen HI clouds and the dense CO molecular clouds.
