The evolution of [OIII]$+\mathrm{H}\beta$ equivalent width from $\mathbf{z}\simeq \mathbf{3}-\mathbf{8}$: implications for the production and escape of ionizing photons during reionization

Accurately quantifying the ionizing photon production efficiency (${\xi }_{\mathrm{i}\mathrm{o}\mathrm{n}}$) 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]+$\mathrm{H}\beta$ emission lines ($W_{\lambda }$) and their physical properties. To supplement our high-redshift galaxies, we measure $W_{\lambda }$ 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 $W_{\lambda }$, increasing from $W_{\lambda }=310\pm 25\mathring{A}$ in VANDELS to $W_{\lambda }=540\pm 25\mathring{A}$ in our JWST-based sample. In the JWST sample at $z>7$, we find that $W_{\lambda }$ 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 $W_{\lambda }$ distribution, characterised by a more pronounced tail at lower $W_{\lambda }$, consistent with increasingly bursty star formation. Using $W_{\lambda }$ as a proxy for ${\xi }_{\mathrm{i}\mathrm{o}\mathrm{n}}$, and UV spectral slope as a proxy for LyC escape fraction ($f_{\mathrm{e}\mathrm{s}\mathrm{c}}$), we find a minority of galaxies with high ${\xi }_{\mathrm{i}\mathrm{o}\mathrm{n}}$ and $f_{\mathrm{e}\mathrm{s}\mathrm{c}}$ (e.g., $\mathrm{l}\mathrm{o}\mathrm{g}({\xi }_{\mathrm{i}\mathrm{o}\mathrm{n}}\mathrm{/}\mathrm{e}\mathrm{r}{\mathrm{g}}^{-1}\mathrm{H}\mathrm{z})\sim 25.6$ and $f_{\mathrm{e}\mathrm{s}\mathrm{c}}\sim 0.15$). 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 $\mathrm{l}\mathrm{o}\mathrm{g}({\xi }_{\mathrm{i}\mathrm{o}\mathrm{n}}\mathrm{/}\mathrm{e}\mathrm{r}{\mathrm{g}}^{-1}\mathrm{H}\mathrm{z})\sim 25.3$ and $f_{\mathrm{e}\mathrm{s}\mathrm{c}}\sim 0.05$. 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.