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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.