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

Abstract: The black hole (BH) spin could significantly change the density of dark matter (DM) in its vicinity, creating a mini-spike of the density of DM. 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 orbit system. We investigate the influence of the DF of DM on the detectability of intermediate-mass black hole (IMBH)-MS binaries as low-frequency gravitational wave (GW) sources. Taking into account the DF of DM, we employ the detailed binary evolution code MESA to model the evolution of a large number of IMBH-MS binaries. Our simulation shows that the DF of DM can drive those IMBH-MS binaries to evolve toward low-frequency GW sources for a low donor-star mass, a high spike index, or a short initial orbital period. When the spike index $\gamma=1.60$, those IMBH-MS binaries with donor-star masses of $1.0-3.4~ M_{\odot}$ and initial orbital periods of $0.65-16.82~ \rm days$ could potentially evolve into visible LISA sources within a distance of $10~\rm kpc$. The DF of DM can enlarge the initial parameter space and prolong the bifurcation periods. In the low-frequency GW source stage, the X-ray luminosities of those IMBH X-ray binaries are $\sim 10^{35}-10^{36}~\rm erg\,s^{-1}$, hence they are ideal multimessenger objects.