Cue: A Fast and Flexible Photoionization Emulator for Modeling Nebular Emission Powered By Almost Any Ionizing Source

The complex physics governing nebular emission in galaxies, particularly in the early universe, often defy simple low-dimensional models. This has proven to be a significant barrier in understanding the (often diverse) ionizing sources powering this emission. We present Cue, a highly flexible tool for interpreting nebular emission across a wide range of abundances and ionizing conditions of galaxies at different redshifts. Unlike typical nebular models used to interpret extragalactic nebular emission, our model does not require a specific ionizing spectrum as a source, instead approximating the ionizing spectrum with a 4-part piece-wise power-law. We train a neural net emulator based on the CLOUDY photoionization modeling code and make self-consistent nebular continuum and line emission predictions. Along with the flexible ionizing spectra, we allow freedom in [O/H], [N/O], [C/O], gas density, and total ionizing photon budget. This flexibility allows us to either marginalize over or directly measure the incident ionizing radiation, thereby directly interrogating the source of the ionizing photons in distant galaxies via their nebular emission. Our emulator demonstrates a high accuracy, with $\sim$1% uncertainty in predicting the nebular continuum and $\sim$5% uncertainty in the emission lines. Mock tests suggest Cue is well-calibrated and produces useful constraints on the ionizing spectra when $S/N (\mathrm{H}_\alpha) \gtrsim 10$, and furthermore capable of distinguishing between the ionizing spectra predicted by single and binary stellar models. The compute efficiency of neural networks facilitates future applications of Cue for rapid modeling of the nebular emission in large samples and Monte Carlo sampling techniques.