Being WISE II: Reducing the Influence of Star Formation History on the
  Mass-to-Light Ratio of Quiescent Galaxies
  Stellar population synthesis models can now reproduce the photometry of old
stellar systems (age $>$ 2 Gyr) in the near-infrared (NIR) bands at 3.4 and
4.6$\mu$m (WISE W1 $\&$ W2 or IRAC 1 $\&$ 2). In this paper we derive stellar
mass-to-light ratios for these and optical bands, and confirm that the NIR M/L
shows dramatically reduced sensitivity to both age and metallicity compared to
optical bands, and further, that this behavior leads to significantly more
robust stellar masses for quiescent galaxies with [Fe/H] > -0.5 regardless of
star formation history (SFH). We then use realistic early-type galaxy SFHs and
metallicity distributions from the EAGLE simulations of galaxy formation to
investigate two methods to determine the appropriate M/L for a galaxy: 1) We
show that the uncertainties introduced by an unknown SFH can be largely removed
using a spectroscopically inferred luminosity-weighted age and metallicity for
the population to select the appropriate single stellar population (SSP)
equivalent M/L. Using this method, the maximum systematic error due to SFH on
the M/L of an early-type galaxy is $<$ 4$\%$ at 3.4 $\mu$m and typical
uncertainties due to errors in the age and metallicity create scatter of
$\lesssim$13$\%$. The equivalent values for optical bands are more than 2-3
times greater, even before considering uncertainties associated with internal
dust extinction. 2) We demonstrate that if the EAGLE SFHs and metallicities
accurately reproduce the true properties of early-type galaxies, the use of an
iterative approach to select a mass dependent M/L can provide even more
accurate stellar masses for early-type galaxies, with typical uncertainties $<$
9$\%$.
