The Stellar Initial Mass Function at the Epoch of Reionization

I provide estimates of the ultraviolet and visible light luminosity density at z ~ 6 after accounting for the contribution from faint galaxies below the detection limit of deep HST and Spitzer surveys. I find that the rest-frame V-band luminosity density is a factor of ~2-3 below the ultraviolet luminosity density at z ~ 6. This implies that the maximal age of the stellar population at z ~ 6, for a Salpeter initial mass function (IMF) and a single, passively evolving burst, must be lesssim100 Myr. If the stars in z ~ 6 galaxies are remnants of the star formation that was responsible for ionizing the intergalactic medium, reionization must have been a brief process that was completed at z < 7. This assumes the most current estimates of the clumping factor and escape fraction and a Salpeter slope extending up to 200 M_⊙ for the stellar IMF (dN/dM ~ M^α, α = -2.3). Unless the ratio of the clumping factor to escape fraction is less than 60, a Salpeter slope for the stellar IMF and reionization redshift higher than 7 are ruled out. In order to maintain an ionized intergalactic medium from redshift 9 onward, the stellar IMF must have a slope of α = -1.65 even if stars as massive as ~200 M_⊙ are formed. Correspondingly, if the intergalactic medium was ionized from redshift 11 onward, the IMF must have α = -1.5. The range of stellar mass densities at z ~ 6 straddled by IMFs which result in reionization at z > 7 is (1.3 +/- 0.4) × 10⁷ M_⊙ Mpc^-3.