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 Hubble and Spitzer surveys. I find 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, and a single, passively evolving
burst, must be <100 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_{\sun} for the stellar initial mass
function (IMF; dN/dM \propto M^{\alpha}, \alpha=-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 is ruled out. In order to
maintain an ionized intergalactic medium from redshift 9 onwards, the stellar
IMF must have a slope of \alpha=-1.65 even if stars as massive as ~200 M_{\sun}
are formed. Correspondingly, if the intergalactic medium was ionized from
redshift 11 onwards, the IMF must have \alpha~-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\times10^{7} Msun/Mpc^3.Comment: 25 pages, 2 tables, 6 figures, ApJ, in press, v680 n
