Mass distribution of Pop III star clusters: A-SLOTH predictions for JWST observability

This study aims to model the expected luminosities of the first four Balmer-series transitions from Pop.\,III star-forming halos and assess their detectability with JWST/NIRSpec across $5 \le z \le 11$, while testing whether the massive Pop.\,III stellar systems required for detectability are physically expected to form. We use the semi-analytical code A-SLOTH with merger trees constructed from the extended Press-Schechter (EPS) formalism and cosmological $N$-body simulations targeting Milky Way-like halos and the halo population in an 8~Mpc$/h$ box. Predicted line fluxes are compared to JWST detection limits derived from the Exposure Time Calculator (ETC), assuming a 10\,000~s NIRSpec exposure at a signal-to-noise ratio of 5. For our default model parameters, Pop.\,III H$\alpha$ fluxes peak at $\sim10^{-20}$\,erg\,s$^{-1}$\,cm$^{-2}$, 1--2 orders of magnitude below the JWST detection threshold ($\sim6\times10^{-19}$\,erg\,s$^{-1}$\,cm$^{-2}$). The other Balmer lines are weaker than H$\alpha$ and are likewise undetectable. This is because, in our models, the massive Pop.\,III stellar systems required to generate detectable Balmer emission do not form. Pop.\,III star formation proceeds in short, feedback-regulated episodes that are terminated by radiative and supernova feedback, yielding young Pop.\,III stellar masses of only $\sim10^{1}$--$10^{4}\,\mathrm{M}_\odot$. In contrast, detectable Balmer emission would require Pop.\,III stellar masses of $M_{\star,\mathrm{III}}\gtrsim 10^{5}\,\mathrm{M}_\odot$, depending on the observable redshift.