= Surface density of a size-sorted dust burst
{title2=$\Sigma=\frac{m_d(4-\alpha)}{\pi(r_0^2-r^2)[1-\eta^{4-\alpha}]}(t/T_r)^{4-\alpha}$}
For initial dust mass $m_d$ in a ring at $r_0$ with a fixed-diameter <power-law size distribution> of index $\alpha<4$, <burst transport under inverse-size radial drag> maps radius to diameter $D_r=2\gamma t/(r_0^2-r^2)$. Set $T_r=t_r(D_{\max})$ and $\eta=D_{\min}/D_{\max}$. The <surface density> is the azimuthal average: $2\pi r\Sigma\,dr=(\pi\rho K/6)D_r^{3-\alpha}dD_r$. Since $dD_r/dr=2rD_r/(r_0^2-r^2)$, <mass normalization of a power-law size distribution> gives the displayed expression. It is supported where $\eta\le t/T_r\le1$. It applies at $t>0$ before removal at the radius in question; the initial state is a delta-function ring. A local angular density needs additional phase information.
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