A Coherent Study of Emission Lines from Broad-Band Photometry: Specific Star-Formation Rates and [OIII]/H{β} Ratio at 3 < z < 6

We measure the H{\alpha} and [OIII] emission line properties as well as specific star-formation rates (sSFR) of spectroscopically confirmed 3<z<6 galaxies in COSMOS from their observed colors vs. redshift evolution. Our model describes consistently the ensemble of galaxies including intrinsic properties (age, metallicity, star-formation history), dust-attenuation, and optical emission lines. We forward-model the measured H{\alpha} equivalent-widths (EW) to obtain the sSFR out to z~6 without stellar mass fitting. We find a strongly increasing rest-frame H{\alpha} EW that is flattening off above z~2.5 with average EWs of 300-600A at z~6. The sSFR is increasing proportional to (1+z)^2.4 at z<2.2 and (1+z)^1.5 at higher redshifts, indicative of a fast mass build-up in high-z galaxies within e-folding times of 100-200Myr at z~6. The redshift evolution at z>3 cannot be fully explained in a picture of cold accretion driven growth. We find a progressively increasing [OIII]{\lambda}5007/H{\beta} ratio out to z~6, consistent with the ratios in local galaxies selected by increasing H{\alpha} EW (i.e., sSFR). This demonstrates the potential of using "local high-z analogs" to investigate the spectroscopic properties and relations of galaxies in the re-ionization epoch.