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

TL;DR

This work addresses whether dynamical friction from a dark-matter mini-spike around an intermediate-mass black hole can steer IMBH-MS binaries into low-frequency gravitational-wave sources detectable by space-based detectors like LISA. Using a MESA-based binary evolution framework that includes a DM DF prescription with a spike profile, the authors map how donor mass, spike index, and initial orbital period govern orbital decay and the emergence of LISA-visible sources, including potential multimessenger signatures. They identify a critical spike index γ_cr ≈ 1.66 and a bifurcation period near P_{orb,i} ≈ 5.93 days, delineating parameter spaces that yield detectable GW signals at distances up to 10 kpc, with associated X-ray luminosities in the 10^{35}-10^{36} erg s^{-1} range. The results imply that DM DF can significantly enhance the formation rate and observability of IMBH binaries as low-frequency GW sources, offering a promising avenue for multimessenger astrophysics and indirect DM probes.

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 $γ=1.60$, 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.

Figures (10)

• Figure 1: The DM density profiles with different spike indices around an IMBH of $M_{\rm BH}=1000~ M_{\odot}$. The vertical orange dashed line represents a radius of $r=2.93\times10^{12}~\rm cm$, which is the orbital separation of a system consisting of a $1000~M_\odot$ IMBH and a $1~M_\odot$ MS star in an orbit of 1.0 day.
• Figure 2: Evolution of IMBH-MS binaries with an initial orbital period of $P_{\rm orb,i}=1.0~\rm day$ and different initial donor-star masses in the orbital period vs. stellar age diagram (top panel) and orbital period vs. donor-star mass diagram (bottom panel) when $\gamma=1.60$. The open circles, solid triangles, and solid stars indicate the beginning of RLOF, the onset when IMBH binaries are visible by LISA at distances of 1 kpc and 10 kpc, respectively. These sources are invisible for LISA at a distance of 1 kpc after those open triangles.
• Figure 3: Evolution of IMBH-MS binaries with $P_{\rm orb, i}=1.0~\rm day$ and different massive donor stars in the orbital period vs. stellar age diagram (top panel) and orbital period vs. donor-star mass diagram (bottom panel) when $\gamma=1.80$. The meanings of those symbols are the same as Figure \ref{['fig:1.60a']}.
• Figure 4: Evolution of IMBH binaries with $P_{\rm orb,i}=1~\rm day$ and different donor-star masses in the characteristic strain vs. GW frequency diagram when $\gamma=1.60$ (top panel) and $\gamma=1.80$ (bottom panel). The blue curve is the sensitivity curve of LISA originating from the numerical calculation of a mission duration of 4 yr. The red and green curves are the sensitivity curves of TianQin Wang2019 and Taiji ruan20, respectively.
• Figure 5: Evolution of IMBH-MS binaries with $M_{\rm d,i}=3.0~ M_{\odot}$, $P_{\rm orb,i}=1.0 ~\rm day$, and different spike indices in the orbital period vs. stellar age diagram. The meanings of those symbols are same to Figure \ref{['fig:1.60a']}.