Discrete diffusion Lyman-alpha radiative transfer

Due to its accuracy and generality, Monte Carlo radiative transfer (MCRT) has emerged as the prevalent method for Ly$\alpha$ radiative transfer in arbitrary geometries. The standard MCRT encounters a significant efficiency barrier in the high optical depth, diffusion regime. Multiple acceleration schemes have been developed to improve the efficiency of MCRT but the noise from photon packet discretization remains a challenge. The discrete diffusion Monte Carlo (DDMC) scheme has been successfully applied in state-of-the-art radiation hydrodynamics (RHD) simulations. Still, the established framework is not optimal for resonant line transfer. Inspired by the DDMC paradigm, we present a novel extension to resonant DDMC (rDDMC) in which diffusion in space and frequency are treated on equal footing. We explore the robustness of our new method and demonstrate a level of performance that justifies incorporating the method into existing Ly$\alpha$ codes. We present computational speedups of $\sim 10^2$-$10^6$ relative to contemporary MCRT implementations with schemes that skip scattering in the core of the line profile. This is because the rDDMC runtime scales with the spatial and frequency resolution rather than the number of scatterings - the latter is typically $\propto \tau_0$ for static media, or $\propto (a \tau_0)^{2/3}$ with core-skipping. We anticipate new frontiers in which on-the-fly Ly$\alpha$ radiative transfer calculations are feasible in 3D RHD. More generally, rDDMC is transferable to any computationally demanding problem amenable to a Fokker-Planck approximation of frequency redistribution.