 Disk scale height

The disk scale height measures the vertical spread of matter or pressure. For an isothermal, non-self-gravitating thin disk, $\rho (z)={\rho }_0\exp [-z^2/(2H^2)]$ and $H=c_s/{\Omega }_z$. Stronger vertical gravity confines the same gas more tightly; a higher sound speed makes it thicker. Here $H$ is a standard deviation, not a sharp surface; a polytropic surface uses a different convention.^[ref]