A combined PRIMER+MINERVA study of the evolution of $\mathbf{[O\mbox{III}]+Hβ}$ equivalent width from $\mathbf{z=3}$ to $\mathbf{z=8.5}$
We present an analysis of the evolution of $[O\,III]+\mathrm{H}β$ equivalent width ($W_λ$) over the redshift range $z=3$ to $z=8.5$, based on combining the JWST NIRCam PRIMER and MINERVA imaging in the UDS survey field. We find that the combined medium- and broad-band data set reduces the photometric redshift outlier rate to $η= 4.7\%$ at $m_{\rm F444W}\leq28$, a $42\%$ reduction compared with PRIMER imaging alone. We also demonstrate that the combined data set facilitates the accurate recovery of $[O\,III]+\mathrm{H}β$ equivalent widths in redshift bins centred on $z\sim3.2,\, 4.0,\, 5.0,\, 7.2,\, 8.3$; corresponding to the F210M, F250M, F300M, F410M and F460M filters. Based on a final sample of $N=1964$ galaxies with $M_{\rm UV}\leq-19.25$, we first provide new constraints on the bright end of the $z=7-8$ $[O\,III]+\mathrm{H}β$ luminosity function ($\log_{10}ϕ^{*} = -4.3_{-0.5}^{+0.2}$, $\log_{10}L^{*} = -43.4_{-0.2}^{+0.3}$), before proceeding to investigate the redshift evolution of $[O\,III]+\mathrm{H}β$ equivalent width. Using SED modelling based on non-parametric continuity star-formation histories, we find that the median $[O\,III]+\mathrm{H}β$ equivalent width monotonically increases with redshift, rising from $\mathrm{log}_{10}(W_λ)=2.54^{+0.01}_{-0.01}$ at $z\simeq 3$ to $\mathrm{log}_{10}(W_λ)=3.05^{+0.03}_{-0.03}$ at $z\simeq 8$. In tandem, the distribution of $\mathrm{log}_{10}(W_λ)$ is observed to become increasingly asymmetric with redshift, producing a fraction of extreme emission-line galaxies (EELGs, $W_λ>1000\,$Å) that reaches $f_{\rm EELG}=0.50\pm{0.10}$ by $z=8.3$. Our SED modelling results indicate that the physical driver of this evolution is increasingly bursty star-formation, with EELGs the result of particularly high specific star-formation rates over the 10 Myr prior to observation.