Tracer diffusion in a power-law accretion disk ($C_t-v{C}_Y=D{C}_{YY},Y=\ln R,v=3{\nu }_0/2,D=\zeta {\nu }_0$)

In a steady Keplerian accretion disk with $\Sigma ={\Sigma }_0{R}^{-2}$, $\nu ={\nu }_0{R}^2$, 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 $CdY$, because $2\pi R\sigma dR=2\pi {\Sigma }_{0}CdY$. 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.