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Lyman α emitters (LAEs) are galaxies that have been selected on the basis of a strong Lyα emission line in their spectra. Observational campaigns over the last decade have dramatically increased the sample of known LAEs, which now extends out to  z = 7. These discoveries have motivated numerous theoretical studies on the subject, which usually define LAEs in their models based on sharp Lyα luminosity and equivalent width (EW) cuts. While broadly representative, this procedure does not mimic the selection from observational programmes in detail, which instead use cuts in various colour spaces. In this paper, we investigate what implications this disjoint may have for theoretical studies that aim to model the observed population of LAEs. We construct an empirical model for the number density of star‐forming galaxies as a function of their ultraviolet (UV) and Lyα luminosity, utilizing measured constraints on the luminosity functions of drop‐out galaxies, and their luminosity‐dependent probability distribution function of Lyα EW. In particular, we investigate whether the LAE luminosity functions can be reproduced by defining LAEs using a ( z ‐dependent) Lyα luminosity and EW threshold. While we are able to reproduce the observed distribution of Lyα EW among LAEs out to rest‐frame  EW (REW) ∼ 200 Å, we find that our formalism  overpredicts  both the UV and Lyα luminosity functions of LAEs by a factor of 2–3, and is inconsistent with observations at the ∼95 per cent level. This tension is partially resolved if we assume the Lyα EW distribution of drop‐out galaxies to be truncated at REW ≳ 150 Å. However, the overprediction indicates that modelling LAEs with simple REW and luminosity cuts does not accurately mimic observed selection criteria, and can therefore lead to uncertainties in the predicted number density of LAEs. On the other hand, the predicted redshift evolution is not affected. We apply our formalism to drop‐out galaxies at  z  &gt; 6 and predict the luminosity functions of LAEs at   z = 7 ‐9 .

An empirical study of the relationship between Lyα and UV‐selected galaxies: do theorists and observers ‘select’ the same objects?