Parametrising Star Formation Histories

We examine the star formation histories (SFHs) of galaxies in smoothed particle hydrodynamics (SPH) simulations, compare them to parametric models that are commonly used in fitting observed galaxy spectral energy distributions, and examine the efficacy of these parametric models as practical tools for recovering the physical parameters of galaxies. The commonly used tau-model, with SFR ~ exp(-t/tau), provides a poor match to the SFH of our SPH galaxies, with a mismatch between early and late star formation that leads to systematic errors in predicting colours and stellar mass-to-light ratios. A one-parameter lin-exp model, with SFR ~ t*exp(-t/tau), is much more successful on average, but it fails to match the late-time behavior of the bluest, most actively star-forming galaxies and the passive, "red and dead" galaxies. We introduce a 4-parameter model, which transitions from lin-exp to a linear ramp after a transition time, which describes our simulated galaxies very well. We test the ability of these parametrised models to recover (at z=0, 0.5, and 1) the stellar mass-to-light ratios, specific star formation rates, and stellar population ages from the galaxy colours, computed from the full SPH star formation histories using the FSPS code of Conroy et al. (2009). Fits with tau-models systematically overestimate M/L by ~ 0.2 dex, overestimate population ages by ~ 1-2 Gyr, and underestimate sSFR by ~ 0.05 dex. Fits with lin-exp are less biased on average, but the 4-parameter model yields the best results for the full range of galaxies. Marginalizing over the free parameters of the 4-parameter model leads to slightly larger statistical errors than 1-parameter fits but essentially removes all systematic biases, so this is our recommended procedure for fitting real galaxies.