The LAMOST spectroscopic survey of star clusters in M31. II.
  Metallicities, ages and masses
  We select from Paper I a sample of 306 massive star clusters observed with
the Large Sky Area Multi-Object Fibre Spectroscopic Telescope (LAMOST) in the
vicinity fields of M31 and M33 and determine their metallicities, ages and
masses. Metallicities and ages are estimated by fitting the observed integrated
spectra with stellar synthesis population (SSP) models with a pixel-to-pixel
spectral fitting technique. Ages for most young clusters are also derived by
fitting the multi-band photometric measurements with model spectral energy
distributions (SEDs). The estimated cluster ages span a wide range, from
several million years to the age of the universe. The numbers of clusters
younger and older than 1 Gyr are respectively 46 and 260. With ages and
metallicities determined, cluster masses are then estimated by comparing the
multi-band photometric measurements with SSP model SEDs. The derived masses
range from $\sim 10^{3}$ to $\sim 10^7$ $M_{\odot}$, peaking at $\sim 10^{4.3}$
and $\sim 10^{5.7}$ $M_{\odot}$ for young ($< 1$ Gyr) and old ($>1$ Gyr)
clusters, respectively. Our estimated metallicities, ages and masses are in
good agreement with available literature values. Old clusters richer than
[Fe/H] $\sim -0.7$ dex have a wide range of ages. Those poorer than [Fe/H]
$\sim -0.7$ dex seem to be composed of two groups, as previously found for
Galactic GCs -- one of the oldest ages with all values of metallicity down to
$\sim -2$ dex and another with metallicity increasing with decreasing age. The
old clusters in the inner disk of M\,31 (0 -- 30 kpc) show a clear metallicity
gradient measured at $-0.038\pm0.023$ dex/kpc.
