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. 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. Taking into account DF from DM, we employed the detailed binary evolution code MESA to model the evolution of a large number of IMBH-MS binaries. 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 ̊m days can evolve toward visible LISA sources within a distance of 10 ̊m kpc. 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 ∼ 10^ ̊m erg, s^ making them ideal multi-messenger objects.
Jia et al. (Thu,) studied this question.