Reconstruction of Galaxy Star Formation Histories through SED Fitting: The Dense Basis Approach

We introduce the Dense Basis method for Spectral Energy Distribution (SED) fitting. It accurately recovers traditional SED parameters, including M$_*$, SFR and dust attenuation, and reveals previously inaccessible information about the number and duration of star formation episodes and the timing of stellar mass assembly, as well as uncertainties in these quantities. This is done using basis Star Formation Histories (SFHs) chosen by comparing the goodness-of-fit of mock galaxy SEDs to the goodness-of-reconstruction of their SFHs. We train and validate the method using a sample of realistic SFHs at $z =1$ drawn from stochastic realisations, semi-analytic models, and a cosmological hydrodynamical galaxy formation simulation. The method is then applied to a sample of 1100 CANDELS GOODS-S galaxies at $1<z<1.5$ to illustrate its capabilities at moderate S/N with 15 photometric bands. Of the six parametrizations of SFHs considered, we adopt linear-exponential, bessel-exponential, lognormal and gaussian SFHs and reject the traditional parametrizations of constant (Top-Hat) and exponential SFHs. We quantify the bias and scatter of each parametrization. $15\%$ of galaxies in our CANDELS sample exhibit multiple episodes of star formation, with this fraction decreasing above $M_*>10^{9.5}M_\odot$. About $40\%$ of the CANDELS galaxies have SFHs whose maximum occurs at or near the epoch of observation. The Dense Basis method is scalable and offers a general approach to a broad class of data-science problems.