Stochastic Modeling of Star Formation Histories. III. Constraints from Physically Motivated Gaussian Processes

Galaxy formation and evolution involve a variety of effectively stochastic processes that operate over different timescales. The extended regulator model provides an analytic framework for the resulting variability (or “burstiness”) in galaxy-wide star formation due to these processes. It does this by relating the variability in Fourier space to the effective timescales of stochastic gas inflow, equilibrium, and dynamical processes influencing giant molecular clouds' creation and destruction using the power spectral density (PSD) formalism. We use the connection between the PSD and autocovariance function for general stochastic processes to reformulate this model as an autocovariance function, which we use to model variability in galaxy star formation histories (SFHs) using physically motivated Gaussian processes in log star formation rate (SFR) space. Using stellar population synthesis models, we then explore how changes in model stochasticity can affect spectral signatures across galaxy populations with properties similar to the Milky Way and present-day dwarfs, as well as at higher redshifts. We find that, even at fixed scatter, perturbations to the stochasticity model (changing timescales vs. overall variability) leave unique spectral signatures across both idealized and more realistic galaxy populations. Distributions of spectral features including H α and UV-based SFR indicators, H δ and Ca H and K absorption-line strengths, D _n (4000), and broadband colors provide testable predictions for galaxy populations from present and upcoming surveys with the Hubble Space Telescope, James Webb Space Telescope, and Nancy Grace Roman Space Telescope. The Gaussian process SFH framework provides a fast, flexible implementation of physical covariance models for the next generation of spectral energy distribution modeling tools. Code to reproduce our results can be found at https://github.com/kartheikiyer/GP-SFH .