A Possible Solution for the M/L-[Fe/H] Relation of Globular Clusters in
  M31: A metallicity and density dependent top-heavy IMF
  The observed mass-to-light ($M/L$) ratios of a large sample of GCs in M31
show an inverse trend with metallicity compared to what is expected from Simple
Stellar Population (SSP) models with an invariant canonical stellar IMF, in the
sense that the observed $M/L$ ratios decrease with increasing metallicity. We
show that incorporating the effect of dynamical evolution the SSP models with a
canonical IMF can not explain the decreasing $M/L$ ratios with increasing
metallicity for the M31 GCs. The recently derived top-heavy IMF as a function
of metallicity and embedded cluster density is proposed to explain the lower
than expected $M/L$ ratios of metal-rich GCs. We find that the SSP models with
a top-heavy IMF, retaining a metallicity- and cluster mass- dependent fraction
of the remnants within the clusters, and taking standard dynamical evolution
into account can successfully explain the observed $M/L-[Fe/H]$ relation of M31
GCs. Thus we propose that the kinematical data of GCs can be used to constrain
the top-heaviness of the IMF in GCs.
