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

The future space missions Euclid and WFIRST-AFTA will use the Halpha emission line to measure the redshifts of tens of millions of galaxies. The Halpha luminosity function at z>0.7 is one of the major sources of uncertainty in forecasting cosmological constraints from these missions. We construct unified empirical models of the Halpha luminosity function spanning the range of redshifts and line luminosities relevant to the redshift surveys proposed with Euclid and WFIRST-AFTA. By fitting to observed luminosity functions from Halpha 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. 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_Halpha>0.5 - 3 x 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--13300 and 2000--4800 deg^-2 respectively at fluxes above F_Halpha>1 and 2 x 10^-16 erg cm^-2 s^-1, and 32000--48000 for F_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 Halpha luminosity density of the Universe, and the closely related cosmic star formation history.