Resolving the ionizing photon budget crisis with JWST/NIRCam HII clumping constraints at z=6
We present a comprehensive study of the ionizing properties of 1721 galaxies at $5.6<z<6.5$ using deep JWST/NIRCam photometric imaging from the NEP, JADES, and PRIMER surveys spanning an unmasked area $\sim550$arcmin$^2$ across UV magnitudes $-22\lesssim M_{\rm UV}\lesssim-17.5$. Our $90\%$ stellar mass complete sample suggests little relation of UV slope with magnitude, $\beta_{\rm UV}=(-0.040\pm0.022)M_{\rm UV}-2.88^{+0.43}_{-0.44}$, implying $f_{\rm esc}^{\rm LyC}\simeq5\%$ based on calibrations from the Low-redshift Lyman Continuum Survey (LzLCS). We measure a constant ionizing photon production efficiency with UV magnitude, $\log_{10}(\xi_{\rm ion, 0}/\rm Hz\,erg^{-1}) = -0.006^{+0.019}_{-0.017}~M_{\rm UV} + 25.05^{+0.39}_{-0.34}$, consistent with HST canonical values. The total production rate of photons escaping into the IGM is computed as $\log_{10}(\dot{n}_{\rm ion}/\rm s^{-1}Mpc^{-3})=50.31^{+0.07}_{-0.06}$ for $M_{\rm UV}<-17$ galaxies from our star forming and smouldering UV luminosity functions (UVLFs), which differ in the faint-end slope ($\alpha_{\rm SFG}=-2.2\pm0.2$; $\alpha_{\rm sm}=-1.7\pm0.2$). Extrapolating to the latest UVLF turnover limits from the massive lensing galaxy cluster Abell S1063 ($M_{\rm UV, lim}=-13.5$) implies that a recombination-weighted HII clumping factor $C_{\rm HII, rec}=6.2^{+4.1}_{-2.1}$ is required to produce fully stably reionized at $z\simeq6$. A clumping factor of this magnitude resolves the ionizing photon budget crisis. Our methodology paves the way for indirect clumping measurements from galaxies which will provide insight into earlier stages of the EoR when the Ly$\alpha$-forest becomes saturated and more direct quasar measurements become impossible.