Ionizing properties of galaxies in JADES for a stellar mass complete sample: resolving the cosmic ionizing photon budget crisis at the Epoch of Reionization

We use NIRCam imaging from the JWST Advanced Deep Extragalactic Survey (JADES) to study the ionizing properties of a sample of 14 652 galaxies at $3 \le z_{\rm {phot}} \le 9$, 90 per cent 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 Prospector to fit all available photometry and infer galaxy properties. We find a significantly milder evolution of the ionizing photon production efficiency ($\xi _{\rm {ion}}$) with redshift and UV magnitude than previously reported. Interestingly, we observe two distinct populations in $\xi _{\rm {ion}}$, 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 $\xi _{\rm {ion}}$ normalization. We convolve the more representative $\log (\xi _{\rm {ion}} (z,\text{M}_{\rm {UV}}))$ relations (accounting for $\sim 97$ % of the sample), with luminosity functions from literature, to place constraints on the cosmic ionizing photon budget. By combining our results, we find that one of our models can match the observational constraints from the Ly $\alpha$ forest at $z\lesssim 6$. We conclude that galaxies with M$_{\rm {UV}}$ between $-16$ and $-20$, adopting a reasonable escape fraction, can produce enough ionizing photons to ionize the Universe, without exceeding the required ionizing photon budget.