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 one group and seven pairs of clumped stars. The group, with six 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. using the Sloan Digital Sky Survey 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 that the dominating features are relatively broad due to early merging or relatively heavy progenitor satellites.