The outer halo globular cluster system of M31 - III. Relationship to the
  stellar halo
  We utilise the final catalogue from the Pan-Andromeda Archaeological Survey
to investigate the links between the globular cluster system and field halo in
M31 at projected radii $R_p=25-150$ kpc. In this region the cluster radial
density profile exhibits a power-law decline with index $\Gamma=-2.37\pm0.17$,
matching that for the stellar halo component with [Fe/H] $<-1.1$. Spatial
density maps reveal a striking correspondence between the most luminous
substructures in the metal-poor field halo and the positions of many globular
clusters. By comparing the density of metal-poor halo stars local to each
cluster with the azimuthal distribution at commensurate radius, we reject the
possibility of no correlation between clusters and field overdensities with
high confidence. We use our stellar density measurements and previous kinematic
data to demonstrate that $\approx35-60\%$ of clusters exhibit properties
consistent with having been accreted into the outskirts of M31 at late times
with their parent dwarfs. Conversely, at least $\sim40\%$ of remote clusters
show no evidence for a link with halo substructure. The radial density profile
for this subgroup is featureless and closely mirrors that observed for the
apparently smooth component of the metal-poor stellar halo. We speculate that
these clusters are associated with the smooth halo; if so, their properties
appear consistent with a scenario where the smooth halo was built up at early
times via the destruction of primitive satellites. In this picture the entire
M31 globular cluster system outside $R_p=25$ kpc comprises objects accumulated
from external galaxies over a Hubble time of growth.
