The physical properties inferred from the spectral energy distributions of z > 3 galaxies have been influential in shaping our understanding of early galaxy formation and the role galaxies may play in cosmic reionization .
Of particular importance is the stellar mass density at early times which represents the integral of earlier star formation .
An important puzzle arising from the measurements so far reported is that the specific star formation rates ( sSFR ) evolve far less rapidly than expected in most theoretical models .
Yet the observations underpinning these results remain very uncertain , owing in part to the possible contamination of rest-optical broadband light from strong nebular emission lines .
To quantify the contribution of nebular emission to broad-band fluxes , we investigate the spectral energy distributions of 92 spectroscopically-confirmed galaxies in the redshift range 3.8 < z < 5.0 chosen because the H \alpha line lies within the Spitzer /IRAC 3.6 \mu m filter .
We demonstrate that the 3.6 \mu m flux is systematically in excess of that expected from stellar continuum alone , which we derive by fitting the SED with population synthesis models .
No such excess is seen in a control sample of spectroscopically-confirmed galaxies with 3.1 < z < 3.6 in which there is no nebular contamination in the IRAC filters .
From the distribution of our 3.6 \mu m flux excesses , we derive an H \alpha equivalent width distribution and consider the implications both for the derived stellar masses and the sSFR evolution .
The mean rest-frame H \alpha equivalent width we infer at 3.8 < z < 5.0 ( 270 Å ) indicates that nebular emission contributes at least 30 % of the 3.6 \mu m flux and , by implication , nebular emission is likely to have a much greater impact for galaxies with z \simeq 6 - 7 where both warm IRAC filters are contaminated .
Via our empirically-derived equivalent width distribution we correct the available stellar mass densities and show that the sSFR evolves more rapidly at z > 4 than previously thought , supporting up to a 5 \times increase between z \simeq 2 and 7 .
Such a trend is much closer to theoretical expectations .
Given our findings , we discuss the prospects for verifying quantitatively the nebular emission line strengths prior to the launch of the James Webb Space Telescope .