Detectability of compact intermediate-mass black hole binaries as low-frequency gravitational wave sources: The influence of dynamical friction of dark matter

Context. The spin of a black hole (BH) can significantly alter the density of dark matter (DM) in its vicinity, creating a density mini-spike. The dynamical friction (DF) between DM and the companion star of a BH can provide an efficient loss of angular momentum, driving the BH-main-sequence (MS) star binary to evolve toward a compact orbital system. Aims. We investigate the influence of DF from DM on the detectability of intermediate-mass black hole (IMBH)-MS binaries as low-frequency gravitational-wave (GW) sources. Methods. Taking into account DF from DM, we employed the detailed binary evolution code <ns0:monospace>MESA</ns0:monospace> to model the evolution of a large number of IMBH-MS binaries. Results. Our simulation shows that DF from DM can drive IMBH-MS binaries to evolve toward low-frequency GW sources when the donor-star mass is low, the spike index is high, or the initial orbital period is short. When the spike index is γ = 1.60, IMBH-MS binaries with donor-star masses of 1.0 − 3.4 M⊙ and initial orbital periods of 0.65 − 16.82 days can evolve toward visible LISA sources within a distance of 10 kpc. Conclusions. The DF from DM can enlarge the initial parameter space and prolong the bifurcation periods. In the low-frequency GW source stage, the X-ray luminosities of IMBH X-ray binaries are ∼1035 − 1036 erg s−1, making them ideal multi-messenger objects.