The JWST EXCELS Survey: A spectroscopic investigation of the ionizing properties of star-forming galaxies at 1<z<8

Charting the Epoch of Reionization demands robust assessments of what drives the production of ionizing photons in high-redshift star-forming galaxies (SFGs), and requires better predictive capabilities from current observations. Using a sample of $N=159$ SFGs at $1<z<8$, observed with deep medium-resolution spectroscopy from the JWST/NIRSpec EXCELS survey, we perform a statistical analysis of their ionizing photon production efficiencies (${\xi }_{\mathrm{i}\mathrm{o}\mathrm{n}}$). We consider ${\xi }_{\mathrm{i}\mathrm{o}\mathrm{n}}$, measured with Balmer line measurements, in relation to a number of key galaxy properties including; nebular emission line strengths ($W_{\lambda }(\mathrm{H}\alpha )$ and $W_{\lambda }$( [OIII])), UV luminosity ($M_{\mathrm{U}\mathrm{V}}$) and UV slope (${\beta }_{\mathrm{U}\mathrm{V}}$), as well as dust attenuation ($E(B-V{)}_{\mathrm{n}\mathrm{e}\mathrm{b}}$) and redshift. Implementing a Bayesian linear regression methodology, we fit ${\xi }_{\mathrm{i}\mathrm{o}\mathrm{n}}$ against the principal observables while fully marginalising over all measurement uncertainties, mitigating against the impact of outliers and determining the intrinsic scatter. Significant relations between ${\xi }_{\mathrm{i}\mathrm{o}\mathrm{n}}$ and $W_{\lambda }(\mathrm{H}\alpha )$, $W_{\lambda }$([OIII]) and ${\beta }_{\mathrm{U}\mathrm{V}}$ are recovered. Moreover, the weak trends with $M_{\mathrm{U}\mathrm{V}}$ and redshift can be fully explained by the remaining property dependencies. Expanding our analysis to multivariate regression, we determine that $W_{\lambda }(\mathrm{H}\alpha )$ or $W_{\lambda }$([OIII]), along with ${\beta }_{\mathrm{U}\mathrm{V}}$ and $E(B-V{)}_{\mathrm{n}\mathrm{e}\mathrm{b}}$, are the most important observables for accurately predicting ${\xi }_{\mathrm{i}\mathrm{o}\mathrm{n},0}$. The latter identifies the most common outliers as SFGs with relatively high $E(B-V{)}_{\mathrm{n}\mathrm{e}\mathrm{b}}\gtrsim 0.5$, possibly indicative of obscured star-formation or strong differential attenuation. Combining these properties enable ${\xi }_{\mathrm{i}\mathrm{o}\mathrm{n},0}$ to be inferred with an accuracy of $\sim 0.15$dex, with a population intrinsic scatter of ${\sigma }_{\mathrm{i}\mathrm{n}\mathrm{t}}\sim 0.035$dex.