Primordial-black-hole mergers in dark-matter spikes

It has been suggested that primordial black holes (PBHs) of roughly 30 solar masses could make up the dark matter and if so, might account for the recent detections by LIGO involving binary black holes in this mass range. It has also been argued that the super-massive black holes (SMBHs) that reside at galactic centers may be surrounded by extremely-dense dark-matter (DM) spikes. Here we show that the rate for PBH mergers in these spikes may well exceed the merger rate considered before in galactic dark-matter halos, depending on the magnitudes of two competing effects on the DM spikes: depletion of PBHs due to relaxation and replenishment due to PBHs in loss cone. This may provide a plausible explanation for the current rate of detection of mergers of 30-solar-mass black holes, even if PBHs make up a subdominant contribution to the dark matter. The gravitational-wave signals from such events will always originate in galactic centers, as opposed to those from halos, which are expected to have little correlation with luminous-galaxy positions.