Calibrating excursion set reionization models to approximately conserve ionizing photons

Abstract: The excursion set reionization framework is widely used, due to its speed and accuracy in reproducing the 3D topology of reionization. However, it is known that it does not conserve photon number. Here, we introduce an efficient, on-the-fly recipe to approximately account for photon conservation. Using a flexible galaxy model shown to reproduce current high-$z$ observables, we quantify the bias in the inferred reionization history and galaxy properties resulting from the non-conservation of ionizing photons. Using a mock 21-cm observation, we perform inference with and without correcting for ionizing photon conservation. We find that ignoring photon conservation results in very modest biases in the inferred galaxy properties, for our fiducial model. The notable exception is in the power-law scaling of the ionizing escape fraction with halo mass, which can be biased from the true value by $\sim2.4\sigma$ (corresponding to $\sim0.2$ in the power-law index). Our scheme is implemented in the public code ${\tt 21cmFAST}$.