Binary Black Hole Cross-Correlations with Galaxies

Dark matter (DM) is required to explain the flattening of galaxy rotation curves. A possible dark matter candidate is primordial black holes (PBHs). These PBHs don’t necessarily live within the same area as stellar black holes (SBHs). This is because DM is required at large radii to flatten the rotation curves, while SBHs would be concentrated within galaxies where stars are forming. We study whether gravitational waves can be used to locate binary black holes (BBHs) within galaxies. The distance from the galaxy can be used toindicate if the BBHs that produced these GWs are either stellar or PBHs. The method investigated is the angular cross-correlation between galaxies and BBHs looking at two approaches. We first investigate theoretically the angular cross-correlation when BBHs are distributed according to an isothermal sphere profile with a lower radius cutoff. Second we validate using simulations. We find that the lower cutoff manifests itself as a peak in the angular cross-correlation. We study how well we can determine the peak position by varying the number of GWs. We find that the peak isn’t effected by the number of GWs until between 1000 and 10000 events. At thispoint the resolution of the simulation becomes a problem, seen as a bias to larger peaks. We then investigate a few observational challenges such as galaxy clustering, uncertainty on BBH positions and reduced sky access. We find that the methods are robust. However the uncertainty on BBHs positions has a bias to smaller values. We then check to what effect changing the limits of the isothermal profile effects the peak position, finding that it is mostly determined by the lower limit. Overall we conclude that with as few as O(10 − 1000) well localized GW events, a typical scale of correlation between galaxies and BBHs can be determined.