Population synthesis and astrophysical inference for high-$z$ JWST galaxies

Observations of the high-$z$ Universe from JWST have revealed a new population of bright, early galaxies. A robust statistical interpretation of this data requires fast forward models that account for uncertainties in galaxy evolution and incorporate observational systematic effects. We present a probabilistic framework for population synthesis of high-$z$ galaxies and inference of their properties. Our framework is based on the semi-analytic galaxy-formation model Galacticus. To infer the astrophysical parameters governing high-$z$ galaxy evolution, we analyze JWST data from the CEERS and NGDEEP surveys and calculate the likelihood of observing individual objects in apparent magnitude--redshift space, for $z\geq8.5$ galaxy candidates. We include observational selection effects due to limited survey volume and depth, as well as photometric redshift uncertainties. We recover the posterior probability distribution for parameters describing star formation and outflow rates. We place an upper limit on the star formation timescale of $500~\mathrm{Myr}$ at a disk velocity of $50~\mathrm{km\ s}^{-1}$, and we infer a characteristic velocity at which the outflow mass-loading factor is $\sim 1$ of $150^{+280}_{-60}~\mathrm{km\ s}^{-1}$, both at $95\%$ confidence. Marginalizing over our astrophysical model, we find that galaxies in CEERS and NGDEEP data occupy halos with virial masses $10^{10\pm 0.5}~M_{\mathrm{\odot}}$ at $8.5\leq z\leq 12$, at $95\%$ confidence. The star formation timescale preferred by our fit is relatively short compared to typical values at lower redshifts, consistent with previous findings. The modeling and analysis framework presented here can enable systematic tests of high-$z$ galaxies' dust content, initial mass functions, and star formation burstiness in the future.