Mapping the Galactic Halo VIII: Quantifying substructure
  We have measured the amount of kinematic substructure in the Galactic halo
using the final data set from the Spaghetti project, a pencil-beam high
latitude sky survey. Our sample contains 101 photometrically selected and
spectroscopically confirmed giants with accurate distance, radial velocity and
metallicity information. We have developed a new clustering estimator: the
"4distance" measure, which when applied to our data set leads to the
identification of 1 group and 7 pairs of clumped stars. The group, with 6
members, can confidently be matched to tidal debris of the Sagittarius dwarf
galaxy. Two pairs match the properties of known Virgo structures. Using models
of the disruption of Sagittarius in Galactic potentials with different degrees
of dark halo flattening, we show that this favors a spherical or prolate halo
shape, as demonstrated by Newberg et al. (2007) using SDSS data. One additional
pair can be linked to older Sagittarius debris. We find that 20% of the stars
in the Spaghetti data set are in substructures. From comparison with random
data sets we derive a very conservative lower limit of 10% to the amount of
substructure in the halo. However, comparison to numerical simulations shows
that our results are also consistent with a halo entirely built up from
disrupted satellites, provided the dominating features are relatively broad due
to early merging or relatively heavy progenitor satellites.
