The Shards of $\omega$ Centauri

We use the SDSS-Gaia catalogue to search for substructure in the stellar halo. The sample comprises 62\,133 halo stars with full phase space coordinates and extends out to heliocentric distances of $\sim 10$ kpc. As actions are conserved under slow changes of the potential, they permit identification of groups of stars with a common accretion history. We devise a method to identify halo substructures based on their clustering in action space, using metallicity as a secondary check. This is validated against smooth models and numerical constructed stellar halos from the Aquarius simulations. We identify 21 substructures in the SDSS-Gaia catalogue, including 7 high significance, high energy and retrograde ones. We investigate whether the retrograde substructures may be material stripped off the atypical globular cluster $\omega$~Centauri. Using a simple model of the accretion of the progenitor of the $\omega$~Centauri, we tentatively argue for the possible association of up to 5 of our new substructures (labelled Rg1, Rg3, Rg4, Rg6 and Rg7) with this event. This sets a minimum mass of $5 \times 10^8 M_\odot$ for the progenitor, so as to bring $\omega$~Centauri to its current location in action -- energy space. Our proposal can be tested by high resolution spectroscopy of the candidates to look for the unusual abundance patterns possessed by $\omega$~Centauri stars.