Let 2 represent the height above the midplane. Dotting the last equation with the unit vector z and transposing yields

Phi dz dz where PHI and pHI are, respectively, the pressure and mass density of the atomic gas. These two quantities are related by

Here the quantity cHI, which has the dimensions of velocity, represents the random internal motion of the medium. It is also the speed of sound, assuming the medium keeps a fixed temperature during passage of the waves. For an ideal gas, cHI is given in terms of the temperature and mean molecular weight by (RT/^)1/2, with R being the gas constant. If we assume that cHI does not vary with z, then substitution of equation (2.6) into (2.5) and a single integration yields the relation between p and :

"HI

* * Figure 2.6 Motion of HI gas in the Galaxy. * * Discrete clouds move away from the Galactic * midplane at z = 0, reaching an average dis* tance hm above and below it. This distance is * less than ht, the scale height for low-mass stars.

To make further progress, we need to specify the gravitational potential. This quantity is related to p*, the total mass density in the Galaxy, through Poisson's equation:

In a thin disk, we may safely ignore horizontal gradients and write (2.8) as

Most of the Galactic matter consists of low-mass stars, which have a scale height h* greater than that of the neutral gas (Figure 2.6). Hence, we may safely replace p*(z) in equation (2.9) by its midplane value p* (0). We then integrate this equation twice, noting that the gravitational force at the midplane, which is —d$g/dz, must vanish by symmetry. The resulting potential is given by

Equations (2.7) and (2.10) together imply that the cold neutral medium has a Gaussian distribution. The corresponding scale height is h-Hi =

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