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.
