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The future space missions Euclid and WFIRST-AFTA will use the Halpha emissionline to measure the redshifts of tens of millions of galaxies. The Halphaluminosity function at z>0.7 is one of the major sources of uncertainty inforecasting cosmological constraints from these missions. We construct unifiedempirical models of the Halpha luminosity function spanning the range ofredshifts and line luminosities relevant to the redshift surveys proposed withEuclid and WFIRST-AFTA. By fitting to observed luminosity functions from Halphasurveys, we build three models for its evolution. Different fittingmethodologies, functional forms for the luminosity function, subsets of theempirical input data, and treatment of systematic errors are considered toexplore the robustness of the results. Functional forms and model parametersare provided for all three models, along with the counts and redshiftdistributions up to z~2.5 for a range of limiting fluxes (F_Halpha>0.5 - 3 x10^-16 erg cm^-2 s^-1) that are relevant for future space missions. Forinstance, in the redshift range 0.90<z<1.8, our models predict an availablegalaxy density in the range 7700--13300 and 2000--4800 deg^-2 respectively atfluxes above F_Halpha>1 and 2 x 10^-16 erg cm^-2 s^-1, and 32000--48000 forF_Halpha>0.5 x 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 Halphaluminosity density of the Universe, and the closely related cosmic starformation history.

Modelling the number density of Halpha emitters for future spectroscopic near-IR space missions