Resolving the ionizing photon budget crisis with JWST/NIRCam HII clumping constraints at z=6

TL;DR

This work addresses the ionizing photon budget crisis during the Epoch of Reionization by leveraging deep JWST/NIRCam photometry to construct a large, mass-complete sample of $5.6<z<6.5$ galaxies. It derives the ionizing photon production efficiency $\xi_{\rm ion,0}$ and the ionizing photon production rate $\dot{N}_{\rm ion,0}$ from Balmer and UV tracers, and combines these with a JWST-derived UV luminosity function to estimate the total ionizing emissivity $\dot{n}_{\rm ion}$ under both fixed and UV-mlope–dependent escape fraction scenarios. The analysis yields indirect constraints on the IGM HII clumping factor $C_{\rm HII, rec}$, finding $C_{\rm HII, rec}=6.2^{+4.1}_{-2.1}$ (based on a UVLF turnover at $M_{\rm UV, lim}=-13.5$) or $8.8^{+4.3}_{-2.5}$ with a fixed $f_{\rm esc}^{\rm LyC}=10\%$, implying that clumping can resolve the ionizing budget problem at $z\sim6$. The results demonstrate a pathway to indirect clumping measurements using galaxy populations, with implications for the reionization history, ISM/CGM escape physics, and the potential role of AGN, while highlighting modelling caveats tied to topology, SED assumptions, and the UV turnover of the UVLF.

Abstract

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, $β_{\rm UV}=(-0.040\pm0.022)M_{\rm UV}-2.88^{+0.43}_{-0.44}$, 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, $\log_{10}(ξ_{\rm ion, 0}/\rm Hz\,erg^{-1}) = -0.006^{+0.019}_{-0.017}~M_{\rm UV} + 25.05^{+0.39}_{-0.34}$, 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 ($α_{\rm SFG}=-2.2\pm0.2$; $α_{\rm sm}=-1.7\pm0.2$). 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$α$-forest becomes saturated and more direct quasar measurements become impossible.

Figures (17)

• Figure 1: Comparison of EaZy-py photo-z's derived from the Larson2023 template set with spec-z's collated from the DJA (v4.2). Colours indicate the photometric origin survey, where the larger markers show galaxies that are selected in the photometric sample, of which there are 39. The lower right inset panel shows the probability distribution in $\Delta z/(1+z_s)$ for the catalogue (shaded grey) and sample (navy blue outline), with NMAD and outlier fraction (defined as $\left|\Delta z/(1+z_s)\right| > 0.15$; dotted red lines in inset, and shaded grey in main plot) displayed. The $z_p=z_s$ line is shown in dashed black.
• Figure 2: Example SED fits for star forming (left figure, light blue) and smouldering galaxies (right figure, light red) in the JADES GOODS-South (within our "East" imaging) using the fiducial Bagpipes setup as outlined in \ref{['sec:Halpha_bagpipes']}. In the main panel of each figure, we show as the best-fit SED with shaded $16^{\rm th}-84^{\rm th}$ percentiles. An F090W/F200W/F444W false-colour cutout is shown in the lower right. The photometric magnitudes and SNRs are shown for each observed band; fluxes with $\rm SNR<2$ are shown as upper limits. Posterior redshift, $M_{\mathrm{UV}}$, and $\xi_{\rm ion, 0}$ PDFs are shown in the right hand panels and the star formation histories are shown in the lower left.
• Figure 3: Sample completeness curves from our mock JAGUAR catalogues Williams2018 coloured by EPOCHS v2 survey. Solid coloured lines show the average completeness of the combined catalogue for a particular survey and the thinner dashed lines show the results for each individual catalogue. The thick, dashed, black horizontal line shows the 90% completeness limit. We note that the brightest and most massive bins have a reduced sample size, and more JAGUAR realizations are required to average over this variance. Upper panel) Completeness defined in terms of $M_{\mathrm{UV}}$. Lower panel) Completeness curves defined in terms of input BEAGLE stellar mass, $M_{\star}$.
• Figure 4: Left panel)Bagpipes$\xi_{\rm ion, 0}$ priors for our fiducial setup (orange red), with BC03 and the standard Tacchella2022 "continuity bursty" SFH (sea green) and BPASS lognormal SFH (blue) also shown. Mean $\xi_{\rm ion, 0}$ results from UNCOVER by Atek2024 are shown for comparison. Right panel) Comparison of spectroscopic observed$\xi_{\rm ion, 0}$ measured from narrow H$\alpha$ fits to 71 $5.6<z<6.5$ NIRSpec PRISM/CLEAR spectra from the DJA against mock photometric measurements computed using our fiducial Bagpipes setup. The intrinsic (i.e. dust free) $\xi_{\rm ion, 0}$ upper prior limit from the left-hand panel is shown as a dashed grey line and the $1\sigma$$\xi_{\rm ion, 0}$ sensitivity limit at $\log_{10}(\xi_{\rm ion,0}/\rm Hz~erg^{-1})=25.0$ is shown in purple. We colour the $\xi_{\rm ion, 0}$ measurements by the photometrically determined V-band dust attenuation, $A_V$. The result of a bootstrapped KS goodness-of-fit test and corresponding $p$-value is shown in the lower right.
• Figure 5: $\xi_{\rm ion,0}-M_{\rm UV}$ derived from our 90% stellar mass complete sample. Darker shaded regions show the $16^{\rm th}-84^{\rm th}$ percentiles of the linear fit, with lighter shaded regions showing the scatter in the data. Fitting parameters are given in \ref{['tab:power_law_params']}. Wild bootstrap-binned data points calculated using \ref{['eq:wild_bootstrapping']} are displayed in $1~\rm dex$$M_{\mathrm{UV}}$ bins. Upper panel) Results are coloured by photometric origin field, with white stars showing measurements from our 71 selected NIRSpec/PRISM spectra. Lower panel) Results obtained for star forming (blue) and smouldering (red) subsamples. The respective contours show $\{1,2,3\}\sigma$ confidence intervals.