The Nature of H$\beta+$[O{\sc iii}] and [O{\sc ii}] emitters to $z \sim 5$ with HiZELS: stellar mass functions and the evolution of EWs

We investigate the properties of $\sim7000$ narrow-band selected galaxies with strong H$\beta+$[OIII] and [OII] nebular emission lines from the High-$z$ Emission Line Survey (HiZELS) between $z \sim 0.8 - 5.0$. Our sample covers a wide range in stellar mass ($M\sim10^{7.5 - 12.0}$ M$_\odot$), rest-frame equivalent widths (EW$_\mathrm{rest}\sim 10 - 10^5$ \AA), and line luminosities ($L\sim10^{40.5 - 43.2}$ erg s$^{-1}$). We measure the H$\beta+$[OIII] and [OII]-selected stellar mass functions out to $z \sim 3.5$ and find that both $M_\star$ and $\phi_\star$ increases with cosmic time, which may be due to the [OIII] selection including an increasing fraction of AGN at lower redshifts. The [OII]-selected stellar mass functions show a constant $M_\star\sim10^{11.6}$ M$_\odot$ and a strong, increasing evolution with cosmic time in $\phi_\star$ in line with H$\alpha$ studies. We also investigate the EW$_\mathrm{rest}$ evolution as a function of redshift with a fixed mass range (10$^{9.5 - 10.0}$ M$_\odot$) and find an increasing trend best represented by $(1+z)^{3.81\pm0.14}$ and $(1+z)^{2.72\pm0.19}$ up to $z\sim 2$ and $\sim 3$ for H$\beta$+[OIII] and [OII] emitters, respectively. This is the first time that the EW evolution has been directly measured for H$\beta+$[OIII] and [OII] emitters up to these redshifts. There is evidence for a slower evolution for $z > 2$ in the H$\beta+$[OIII] EW and a decreasing trend for $z > 3$ in the [OII] EW evolution, which would imply low [OII] EW at the highest redshifts and higher [OIII]/[OII] line ratios. This suggests that the ionization parameter at higher redshift may be significantly higher than the local Universe. Our results set the stage for future near-IR space-based spectroscopic surveys to test our extrapolated predictions and also produce $z > 5$ measurements to constrain the high-$z$ end of the EW$_\mathrm{rest}$ and [OIII]/[OII] evolution.