Interpreting ALMA non-detections of JWST super-early galaxies

Recent attempts to detect [OIII] 88$\mu$m emission from super-early ($z>10$) galaxy candidates observed by JWST have been unsuccessful. By using zoom-in simulations, we show that these galaxies are faint, and mostly fall below the local metal-poor $[\mathrm{O}\mathrm{I}\mathrm{I}\mathrm{I}]-\mathrm{S}\mathrm{F}\mathrm{R}$ relation as a result of their low ionization parameter, $U_{\mathrm{i}\mathrm{o}\mathrm{n}}\lesssim {10}^{-3}$. Such low $U_{\mathrm{i}\mathrm{o}\mathrm{n}}$ values are found in galaxies that are in an early assembly stage, and whose stars are still embedded in high-density natal clouds. However, the most luminous galaxy in our sample ($\mathrm{l}\mathrm{o}\mathrm{g}[L_{[\mathrm{O}\mathrm{I}\mathrm{I}\mathrm{I}]}\mathrm{/}{L}_{\odot }]=8.4$, $U_{\mathrm{i}\mathrm{o}\mathrm{n}}\approx 0.1$) could be detected by ALMA in only $2.8$ hrs.