Context. The future space missions Euclid and WFIRST-AFTA will use the Hα emission line to measure the redshifts of tens of millions of galaxies. The Hα luminosity function at z > 0.7 is one of the major sources of uncertainty in forecasting cosmological constraints from these missions. Aims. We construct unified empirical models of the Hα luminosity function spanning the range of redshifts and line luminosities relevant to the redshift surveys proposed with Euclid and WFIRST-AFTA. Methods. By fitting to observed luminosity functions from Hα surveys, we build three models for its evolution. Different fitting methodologies, functional forms for the luminosity function, subsets of the empirical input data, and treatment of systematic errors are considered to explore the robustness of the results. Results. Functional forms and model parameters are provided for all three models, along with the counts and redshift distributions up to z ∼ 2.5 for a range of limiting fluxes (F Hα > 0.5−3 × 10 −16 erg cm −2 s −1 ) that are relevant for future space missions. For instance, in the redshift range 0.90 < z < 1.8, our models predict an available galaxy density in the range 7700-130 300 and 2000-4800 deg −2 respectively at fluxes above F Hα > 1 and 2×10 −16 erg cm −2 s −1 , and 32 000-48 0000 for F Hα > 0.5×10 −16 erg cm −2 s −1 in the extended redshift range 0.40 < z < 1.8. We also consider the implications of our empirical models for the total Hα luminosity density of the Universe, and the closely related cosmic star formation history.

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