Ionising properties of galaxies in JADES for a stellar mass complete sample: resolving the cosmic ionising photon budget crisis at the Epoch of Reionisation

We use NIRCam imaging from the JWST Advanced Deep Extragalactic Survey (JADES) to study the ionising properties of a sample of 15721 galaxies at $3 \leq z_{\rm{phot}} \leq 9$, 90\% complete in stellar mass down to log(M$_{\star}$/[M$_{\odot}$])$\approx 7.5$. Out of the full sample, 1620 of the galaxies have spectroscopic redshift measurements from the literature. We use the spectral energy distribution fitting code \texttt{Prospector} to fit all available photometry and infer galaxy properties. We find a significantly milder evolution of the ionising photon production efficiency (\xion\/) with redshift and UV magnitude than previously reported. Interestingly, we observe two distinct populations in \xion\/, distinguished by their burstiness (given by SFR$_{10}$/SFR$_{100}$). Both populations show the same evolution with $z$ and M$_{\rm{UV}}$, but have a different \xion\/ normalisation. We convolve the more representative $\log(\xi_{\rm{ion}} (z,\text{M}_{\rm{UV}}))$ relations (accounting for $\sim96$\% of the sample), with luminosity functions from literature, to place constraints on the cosmic ionising photon budget. By combining our results, we find that one of our models can match the observational constraints from the \lya\/ forest at $z\lesssim6$. We conclude that galaxies with M$_{\rm{UV}}$ between $-16$ and $-20$, adopting a reasonable escape fraction, can produce enough ionising photons to ionise the Universe, without exceeding the required ionising photon budget.