Numerical Problems in Coupling Photon Momentum (Radiation Pressure) to Gas

Radiation pressure (RP; or photon momentum absorbed by gas) is important in a tremendous range of astrophysical systems. But we show the usual method for assigning absorbed photon momentum to gas in numerical radiation-hydrodynamics simulations (integrating over cell volumes or evaluating at cell centers) can severely under-estimate the RP force in the immediate vicinity around un-resolved (point/discrete) sources (and subsequently under-estimate its effects on bulk gas properties), unless photon mean-free-paths are highly-resolved in the fluid grid. The existence of this error is independent of the numerical radiation transfer (RT) method (even in exact ray-tracing/Monte-Carlo methods), because it depends on how the RT solution is interpolated back onto fluid elements. Brute-force convergence (resolving mean-free paths) is impossible in many cases (especially where UV/ionizing photons are involved). Instead, we show a 'face-integrated' method -- integrating and applying the momentum fluxes at interfaces between fluid elements -- better approximates the correct solution at all resolution levels. The 'fix' is simple and we provide example implementations for ray-tracing, Monte-Carlo, and moments RT methods in both grid and mesh-free fluid schemes. We consider an example of star formation in a molecular cloud with UV/ionizing RP. At state-of-the-art resolution, cell-integrated methods under-estimate the net effects of RP by an order of magnitude, leading (incorrectly) to the conclusion that RP is unimportant, while face-integrated methods predict strong self-regulation of star formation and cloud destruction via RP.