21 Balmer Jump Street: The Nebular Continuum at High Redshift and Implications for the Bright Galaxy Problem, UV Continuum Slopes, and Early Stellar Populations

We study, from both a theoretical and observational perspective, the physical origin and spectroscopic impact of extreme nebular emission in high-redshift galaxies. The nebular continuum, which can appear during extreme starbursts, is of particular importance as it tends to redden UV slopes and has a significant contribution to the UV luminosities of galaxies. Furthermore, its shape can be used to infer the gas density and temperature of the ISM. First, we provide a theoretical background, showing how different stellar populations (SPS models, IMFs, and stellar temperatures) and nebular conditions impact observed galaxy spectra. We demonstrate that, for systems with strong nebular continuum emission, 1) UV fluxes can increase by up to 0.7~magnitudes (or more in the case of hot/massive stars) above the stellar continuum, which may help reconcile the surprising abundance of bright high-redshift galaxies and the elevated UV luminosity density at $z>10$, 2) at high gas densities, UV slopes can redden from $\beta\lesssim-2.5$ to $\beta\sim-1$, 3) observational measurements of $\xi_{ion}$ are grossly underestimated, and 4) UV downturns from two-photon emission can masquerade as DLAs. Second, we present a dataset of 58 galaxies observed with NIRSpec on JWST at $2.5