It's More Complicated Than You Think: A Forward Model to Infer the Recent Star Formation History, Bursty or Not, of Galaxy Populations

Abstract: Observations of the early Universe (z > 4) with the James Webb Space Telescope reveal galaxy populations with a wide range of intrinsic luminosities and colors. Bursty star formation histories (SFHs), characterized by short-term fluctuations in the star formation rate (SFR), may explain this diversity, but constraining burst timescales and amplitudes in individual galaxies is challenging due to degeneracies and sensitivity limits. We introduce a population-level simulation-based inference framework that recovers the power and timescales of SFR fluctuations by forward-modeling galaxy populations and distributions of rest-UV to rest-optical spectral features sensitive to star formation timescales. We adopt a stochastic SFH model based on a power spectral density formalism spanning 1 Myr-10 Gyr. Using simulated samples of N=500 galaxies at z~4 with typical JWST/NIRSpec uncertainties, we demonstrate that: (i) the power of SFR fluctuations can be measured with sufficient precision to distinguish between simulations (e.g., FIRE-2-like vs. Illustris-like populations at >99% confidence for timescales < 100 Myr); (ii) simultaneously modeling stochastic fluctuations and the recent (t_L < 500 Myr) average SFH slope is essential, as secular trends otherwise mimic burstiness in common diagnostics; (iii) frequent, intense bursts impose an outshining limit, and bias inference toward underestimating burstiness due to the obscuration of long-timescale power; and (iv) the power of SFR fluctuations can be inferred to 95% confidence across all timescales in both smooth and bursty populations. This framework establishes a novel and robust method for placing quantitative constraints on the feedback physics regulating star formation using large, uniformly selected spectroscopic samples.