Numerical problems in coupling photon momentum (radiation pressure) to gas

Abstract

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 centres) can severely underestimate the RP force in the immediate vicinity around unresolved (point/discrete) sources (and subsequently underestimate 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 underestimate 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.

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