2022MNRAS.509.5836L

Having accurate completeness functions is crucial to the determination of the rest-frame ultraviolet luminosity functions (UVLFs) all the way back to the epoch of reionization. Most studies use injection-recovery simulations to determine completeness functions. Although conceptually similar, published approaches have subtle but important differences in their definition of the completeness function. As a result, they implement different methods to determine the UVLFs. We discuss the advantages and limitations of existing methods using a set of mock observations, and then compare the methods when applied to the same set of Hubble Legacy Field (HLF) images. We find that the most robust method under all our mock observations is the one that defines completeness as a function of both input and output magnitude. Other methods considering completeness only as a function of either input or output magnitude may suffer limitations in a presence of photometric scatter and/or steep luminosity functions. In particular, when the flux scatter is >= 0.2 mag, the bias in the bright end of the UVLFs is on par with other systematic effects such as the lensing magnification bias. When tested on HLF images, all methods yield UVLFs that are consistent within 2σ confidence, suggesting that UVLF uncertainties in the literature are still dominated by small number statistics and cosmic variance. The completeness simulation code used in this study (GLACiaR2) is publicly released with this paper as a tool to analyse future higher precision data sets such as those expected from the James Webb Space Telescope.