= Surface density of a disk
{title2=$\Sigma$}
= Surface density
{synonym}
The \b[<surface density of a disk>] is the <mass density> integrated through its vertical column: $\Sigma(r)=\int_{-\infty}^{\infty}\rho(r,z)\,dz$. Its dimensions are <mass> per <area>. An axisymmetric annulus of width $dr$ therefore contains $dM=2\pi r\Sigma(r)dr$. This reduces a three-dimensional <mass> inventory to a radial one, which is useful in <viscous evolution of an accretion disk>. Distinct vertical profiles can have the same column <mass>, so $\Sigma$ alone does not determine the <vertical structure of an astrophysical disk>.
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