Self-consistent population spectral synthesis with FADO: II. Star
  formation history of galaxies in spectral synthesis methods
  The field of galaxy evolution will make a great leap forward in the next
decade as a consequence of the huge effort by the scientific community in
multi-object spectroscopic facilities. To maximise the impact of such incoming
data, the analysis methods must also step up, extracting reliable information
from the available spectra. In this paper, we aim to investigate the limits and
the reliability of different spectral synthesis methods in the estimation of
the mean stellar age and metallicity. The main question this work aims to
address is which signal-to-noise ratios (S/N) are needed to reliably determine
the mean stellar age and metallicity from a galaxy spectrum and how this
depends on the tool used to model the spectra. To address this question we
built a set of realistic simulated spectra containing stellar and nebular
emission, reproducing the evolution of a galaxy in two limiting cases: a
constant star formation rate and an exponentially declining star formation. We
degraded the synthetic spectra built from these two star formation histories
(SFHs) to different S/N and analysed them with three widely used spectral
synthesis codes, namely FADO, STECKMAP, and STARLIGHT. For S/N < 5 all three
tools show a large diversity in the results. The FADO and STARLIGHT tools find
median differences in the light-weighted mean stellar age of ~0.1 dex, while
STECKMAP shows a higher value of ~0.2 dex. Detailed investigations of the
best-fit spectrum for galaxies with overestimated mass-weighted quantities
point towards the inability of purely stellar models to fit the observed
spectra around the Balmer jump. Our results imply that when a galaxy enters a
phase of high specific star formation rate the neglect of the nebular continuum
emission in the fitting process has a strong impact on the estimation of its
SFH when purely stellar fitting codes are used, even in presence of high S/N
spectra.
