Recoiled star clusters in the Milky Way halo: N-body simulations and a candidate search through the SDSS

During the formation of the Milky Way, ?100 central black holes (BHs) may have been ejected from their small host galaxies as a result of asymmetric gravitational wave emission. We previously showed that many of these BHs are surrounded by a compact cluster of stars that remained bound to the BH during the ejection process. In this paper, we perform long-term N-body simulations of these star clusters to determine the distribution of stars in these clusters today. These numerical simulations, reconciled with our FokkerPlanck simulations, show that the stellar density profile follows a power law with slope similar to-2.15, and show that large-angle scattering and tidal disruptions remove 2090 per cent of the stars by similar to 1010 yr. We then analyse the photometric and spectroscopic properties of recoiled clusters accounting for the small number of stars in the clusters. We use our results to perform a systematic search for candidates in the Sloan Digital Sky Survey. We find no spectroscopic candidates, in agreement with our expectations from the completeness of the survey. Using generic photometric models of present-day clusters, we identify similar to 100 recoiling cluster candidates. Follow-up spectroscopy would be able to determine the nature of these candidates.