A Possible Solution for the $M/L-\mathrm{[Fe/H]}$ Relation of Globular
  Clusters in M31. II. the Age-Metallicity Relation
  This is the second of a series of papers in which we present a new solution
to reconcile the prediction of single stellar population (SSP) models with the
observed stellar mass-to-light ($M/L$) ratios of globular clusters (GCs) in M31
and its trend with respect to $\mathrm{[Fe/H]}$. In the present work our focus
is on the empirical relation between age and metallicity for GCs and its effect
on the $M/L$ ratio. Assuming that there is an anti-correlation between the age
of M31 GCs and their metallicity, we evolve dynamical SSP models of GCs to
establish a relation between the $M/L$ ratio (in the $V$ and $K$ band) and
metallicity. We then demonstrate that the established $M/L-\mathrm{[Fe/H]}$
relation is in perfect agreement with that of M31 GCs. In our models we
consider both the canonical initial mass function (IMF) and the top-heavy IMF
depending on cluster birth density and metallicity as derived independently
from Galactic GCs and ultra-compact dwarf galaxies by Marks et al. Our results
signify that the combination of the density- and metallicity-dependent
top-heavy IMF, the anti-correlation between age and metallicity, stellar
evolution and standard dynamical evolution yields the best possible agreement
with the observed trend of $M/L-\mathrm{[Fe/H]}$ for M31 GCs.
