Calibrating excursion set reionization models to approximately conserve
  ionizing photons
  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. In general, we find that biases in the inferred galaxy
properties when ignoring photon conservation are very modest. 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 $\sim 2.4\sigma$
(corresponding to $\sim -0.2$ in the power-law index). Our scheme is
implemented in the public code ${\tt 21cmFAST}$.
