Stellar mass-to-light ratios from galaxy spectra: how accurate can they
  be?
  Stellar masses play a crucial role in the exploration of galaxy properties
and the evolution of the galaxy population. In this paper, we explore the
minimum possible uncertainties in stellar mass-to-light (M/L) ratios from the
assumed star formation history (SFH) and metallicity distribution, with the
goals of providing a minimum set of requirements for observational studies. We
use a large Monte Carlo library of SFHs to study as a function of galaxy
spectral type and signal-to-noise ratio (S/N) the statistical uncertainties of
M/L values using either absorption-line data or broad band colors. The accuracy
of M/L estimates can be significantly improved by using metal-sensitive indices
in combination with age-sensitive indices, in particular for galaxies with
intermediate-age or young stellar populations. While M/L accuracy clearly
depends on the spectral S/N ratio, there is no significant gain in improving
the S/N much above 50/pix and limiting uncertainties of 0.03 dex are reached.
Assuming that dust is accurately corrected or absent and that the redshift is
known, color-based M/L estimates are only slightly more uncertain than
spectroscopic estimates (at comparable spectroscopic and photometric quality),
but are more easily affected by systematic biases. This is the case in
particular for galaxies with bursty SFHs (high Hdelta at fixed D4000), the M/L
of which cannot be constrained any better than 0.15 dex with any indicators
explored here. Finally, we explore the effects of the assumed prior
distribution in SFHs and metallicity, finding them to be higher for color-based
estimates.
