Dark Matter Spike surrounding Supermassive Black Holes Binary and the nanohertz Stochastic Gravitational Wave Background

Recently, the NANOGrav, PPTA, EPTA and CPTA collaborations reported compelling evidence of the existence of the Stochastic Gravitational-Wave Background (SGWB). The amplitude and spectrum of this inferred gravitational-wave background align closely with the astrophysical predictions for a signal originating from the population of supermassive black-hole binaries. In light of these findings, we explore the possibility to detect dark matter spikes surrounding massive black holes, which could potentially impact the gravitational-wave waveform and modulate the SGWB. We demonstrate that the SMBH binary evolution induced by the combined effects of GW radiation and the dynamical friction of the dark matter spike exhibits detectable manifestations within the nHz frequency range of the SGWB.