The evolution of [OIII]$+\rm{H}β$ equivalent width from $\mathbf{z\simeq3-8}$: implications for the production and escape of ionizing photons during reionization
Accurately quantifying the ionizing photon production efficiency ($ξ_\rm{ion}$) of $z>6$ star-forming galaxies (SFGs) is necessary to understand their contribution to reionization. We investigate the ionizing properties of N=279 SFGs selected at $z=6.9-7.6$ from the JWST Cycle-1 imaging programmes; PRIMER and JADES. We use BAGPIPES to consistently infer the equivalent widths of their [OIII]+$\rm{Hβ}$ emission lines ($W_λ$) and their physical properties. To supplement our high-redshift galaxies, we measure $W_λ$ photometrically for a sample of N=253 $z=3.2-3.6$ SFGs selected from the VANDELS spectroscopic survey. Comparing these samples, we find a strong apparent redshift evolution in their median $W_λ$, increasing from $W_λ=310\pm25\,Å$ in VANDELS to $W_λ=540\pm25\,Å$ in our JWST-based sample. In the JWST sample at $z>7$, we find that $W_λ$ correlates with both stellar mass and UV luminosity, with high-mass, $M_{ UV}-$faint galaxies producing systematically weaker emission lines. Moreover, we discover a departure from the standard log-normal shape of the $W_λ$ distribution, characterised by a more pronounced tail at lower $W_λ$, consistent with increasingly bursty star formation. Using $W_λ$ as a proxy for $ξ_\rm{ion}$, and UV spectral slope as a proxy for LyC escape fraction ($f_\rm{esc}$), we find a minority of galaxies with high $ξ_\rm{ion}$ and $f_\rm{esc}$ (e.g., $\rm{log(ξ_{ion}/erg^{-1}Hz})\sim25.6$ and $f_\rm{esc}\sim0.15$). However, we find that the LyC photon budget at $z>7$ is dominated by galaxies with more moderate output, close to the sample median of $\rm{log(ξ_{ion}/erg^{-1}Hz})\sim25.3$ and $f_\rm{esc}\sim0.05$. This is consistent with estimates for the number of LyC photons required to power reionization at $z>7$, with no evidence for over or under-production.