The large-scale structure of the halo of the Andromeda galaxy II.
  Hierarchical structure in the Pan-Andromeda Archaeological Survey
  The Pan-Andromeda Archaeological Survey is a survey of $>400$ square degrees
centered on the Andromeda (M31) and Triangulum (M33) galaxies that has provided
the most extensive panorama of a $L_\star$ galaxy group to large projected
galactocentric radii. Here, we collate and summarise the current status of our
knowledge of the substructures in the stellar halo of M31, and discuss
connections between these features. We estimate that the 13 most distinctive
substructures were produced by at least 5 different accretion events, all in
the last 3 or 4 Gyrs. We suggest that a few of the substructures furthest from
M31 may be shells from a single accretion event. We calculate the luminosities
of some prominent substructures for which previous estimates were not
available, and we estimate the stellar mass budget of the outer halo of M31. We
revisit the problem of quantifying the properties of a highly structured
dataset; specifically, we use the OPTICS clustering algorithm to quantify the
hierarchical structure of M31's stellar halo, and identify three new faint
structures. M31's halo, in projection, appears to be dominated by two
`mega-structures', that can be considered as the two most significant branches
of a merger tree produced by breaking M31's stellar halo into smaller and
smaller structures based on the stellar spatial clustering. We conclude that
OPTICS is a powerful algorithm that could be used in any astronomical
application involving the hierarchical clustering of points. The publication of
this article coincides with the public release of all PAndAS data products.
