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 JWST 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 given degeneracies and sensitivity limits. We introduce a population-level simulation-based inference framework that recovers the power spectrum of SFR fluctuations by forward modeling galaxy populations and distributions of rest-frame UV to rest-frame optical spectral features sensitive to such timescales. We adopt a stochastic SFH model based on a power spectral density (PSD) 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 PSD can be constrained sufficiently to distinguish between simulations (e.g., FIRE-2-like versus Illustris-like populations at >99% confidence for timescales < 100 Myr); (ii) simultaneously modeling stochastic fluctuations and the recent ( t L < 500 Myr) SFH slope is essential, as secular trends mimic burstiness in common diagnostics; (iii) frequent, intense bursts impose an outshining limit, biasing the inference to underestimate burstiness; and (iv) the PSD can be inferred to 95% confidence in both smooth and bursty populations under consistent modeling assumptions. This framework establishes that large, uniformly selected spectroscopic samples can place quantitative constraints on SFR timescales and associated feedback processes. The biggest unexplored systematic effects are fixed stellar population synthesis models and the assumption of perfect dust corrections; we will address these in future work.