= Tracer diffusion in a power-law accretion disk
{title2=$C_t-vC_Y=DC_{YY},\quad Y=\ln R,\ v=3\nu_0/2,\ D=\zeta\nu_0$}
In a steady <Keplerian accretion disk> with $\Sigma=\Sigma_0R^{-2}$, $\nu=\nu_0R^2$, and tracer diffusivity $k=\zeta\nu$, the trace <passive scalar> concentration obeys the displayed constant-coefficient <advection-diffusion equation> in logarithmic radius. Contaminant mass is proportional to $C\,dY$, because $2\pi R\sigma\,dR=2\pi\Sigma_0 C\,dY$. A radial impulse $C_0\delta(R-R_0)$ therefore has logarithmic amplitude $C_0/R_0$ and evolves by the <Gaussian heat kernel> centered at $\ln R_0-vt$. The full-line solution idealizes radii far from the disk boundaries.
Back to article page
