A Lower Bound of Star Formation Activity in Ultra-high Redshift Galaxies Detected with JWST: Implications for Stellar Populations and Radiation Sources

Early results of JWST observations have delivered bright $z\gtrsim 10$ galaxy candidates in greater numbers than expected, enabling construction of the rest-frame UV luminosity functions (LFs). The LFs contain key information on the galaxy assembly history, star formation activity, and stellar population in the distant universe. Given an upper bound of the total baryonic mass inflow rate to galaxies from their parent halos estimated from abundance matching, we derive a lower bound on the product of the star formation and UV-photon production efficiency in galaxies at each redshift. This stringent constraint requires a high efficiency ($\gtrsim 10-30\%$) converting gas into stars, assuming a normal stellar population with a Salpeter-like mass distribution. The efficiency is substantially higher than those of typical nearby galaxies, but is consistent with those seen in starburst galaxies and super star clusters observed in the nearby universe. Alternatively, the star formation efficiency may be as low as a few percent, which is the average value for the entire galaxy population at $z\simeq 6$, if the stellar population is metal-free and drawn from a top-heavy mass distribution that produces more intense UV radiation. We discuss several other possible scenarios to achieve the constraint, for instance, energetic radiation produced from compact stellar-remnants and quasars, and propose ways to distinguish the scenarios by forthcoming observations.