Vertical mass coordinate of a disk (source code)

= Vertical mass coordinate of a disk
{title2=$m(z)=\int_0^z\rho(z')\,dz'$}

In a reflection-symmetric <astrophysical disk>, the vertical mass coordinate measures <mass> per unit area above the midplane. It satisfies $dm=\rho\,dz$, so $\partial_m=\rho^{-1}\partial_z$ inside the material. If the total <surface density> is $\Sigma$, the upper face is $m=\Sigma/2$; the normalized coordinate $\zeta=2m/\Sigma$ ranges from zero to one. Integrals weighted by <mass density> become ordinary integrals in $m$, which is especially useful for <radiative diffusion> and the <density-weighted mean kinematic viscosity>.