= Disk aspect ratio
{title2=$H/r$}
The aspect ratio of an <astrophysical disk> is its vertical thickness scale divided by cylindrical radius. A <thin disk> has $H/r\ll1$. In gas-supported vertical <hydrostatic equilibrium> with harmonic external gravity $-\Omega_z^2z$, $H/r\sim c_s/(r\Omega_z)$, where $\Omega_z$ is the <vertical epicyclic frequency> and $c_s$ is the <sound speed>. In a centrally dominated <Keplerian disk>, $\Omega_z=\Omega$, so this compares <sound speed> with orbital speed. If disk self-gravity supplies the vertical restoring force, the relation $H\sim c_s/\Omega$ requires replacement. A polytropic free-surface height and an isothermal scale height differ by model-dependent constants even though their aspect ratios have the same basic role.
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