of gas, and which depends on whether dust is present at location $\boldsymbol{r}$. The packet traverses a path of length $\Delta r$ within a zone at position $\boldsymbol{r}$. The force is then $$\boldsymbol{f}_\mathrm{rad} = \left(\frac{1}{\Delta \, V \Delta \, t}\right) \, \rho(\boldsymbol{r}) \, \sum_p \frac{E_p}{c} \, \kappa(\lambda_p, \boldsymbol{r})\,  \Delta r \,  \hat{\boldsymbol{n}}_p \;.$$ The radiative acceleration $a_\mathrm{rad}$ is simply defined as $f_\mathrm{rad}/\rho$.

Our calculations apply the stationarity approximation, in which we solve the steady-state radiative transfer problem for a fixed gas density distribution. This approximation is justified if the radiative heating time scale and the radiative diffusion time scale are much shorter than the dynamical time scale.

For a sound speed of 200 km s$^{-1}$ and a characteristic length scale of 10 pc, the dynamical time is approximately $10^{12}$ seconds. Meanwhile, the photon diffusion time through the disk never exceeds $10^{11}$ seconds, and for many disk parameters the diffusion time is substantially shorter than that. The radiative heating time, estimated by dividing the thermal energy of the gas by the rate of radiative energy deposition, is $$\begin{aligned}
&t_\mathrm{heat} \approx \left(\frac {\rho \, k_B \, T_\mathrm{gas}}{\mu m_p}\right) \left( \frac{1}{\rho \, \kappa \, c \, a \, T_{\mathrm{rad}}^4  } \right) \nonumber \\
