Impact of dark matter spikes on the merger rates of Primordial Black Holes

Abstract: Mergers of Primordial Black Holes (PBHs) may contribute to the gravitational wave mergers detected by the LIGO-Virgo-KAGRA (LVK) Collaboration. We study the dynamics of PBH binaries dressed with dark matter (DM) spikes, for PBHs with extended mass functions. We analyze the impact of DM spikes on the orbital parameters of the PBH binaries formed in the early Universe and calculate their merger rates at the age of the Universe today. We consider two possible scenarios for the dynamics of the dressed binaries: assuming that either the DM spikes are completely evaporated from the binaries before merger or they remain static until the merger. Contrary to previous studies, we find that the presence of spikes may increase or decrease the present-day PBH merger rates, in some cases dramatically. Comparing with merger rates reported by the LVK Collaboration in the third Gravitational Wave Transient Catalog (GWTC-3), we derive approximate constraints on the fraction of Solar-mass PBHs in cold dark matter as $f_\mathrm{pbh}\leq \mathcal{O}(10^{-5} - 10^{-3})$, depending on the mass function. Our calculations are valid only for the idealized scenarios in which the DM spikes are either evaporated or static. However, they suggest that the impact of DM spikes on PBH merger rates may be more complicated than previously thought and motivate the development of a more general description of the merger dynamics, including feedback of the DM spikes in highly eccentric PBH binaries.