Intermediate-mass-ratio inspirals with general dynamical friction in dark matter minispikes

TL;DR

This work investigates how DM minispikes influence IMRIs by incorporating a generalized dynamical friction that accounts for DM particles moving both slower and faster than the stellar-mass black hole. Using a DM density profile $ρ_ ext{DM}(r)∝ r^{-γ_ ext{sp}}$ and a phase-space distribution from Eddington’s formula, the authors couple dynamical-friction and GW emission to evolve the orbit, revealing a transition in eccentricity behavior around $γ_ ext{sp}=2$: slow-DM friction circularizes while fast-DM friction eccentricifies, with the fast component enhancing eccentricity at early times. They analyze GW characteristic strains, finding suppression at low frequencies and a shift of the peak to higher frequencies as $γ_ ext{sp}$ increases, and derive a quantitative relation linking the peak frequency $f(h_c^{\max})$ to $γ_ ext{sp}$, enabling potential constraints on DM minispike properties from future GW observations. Overall, the study provides a framework to use space-based GW detectors to probe the presence and density profile of DM around IMBHs via the imprint on orbital dynamics and GW spectra.

Abstract

The intermediate-mass-ratio inspirals (IMRIs) may be surrounded by dark matter (DM) minispikes. The dynamical friction from these DM minispike structures can affect the dynamics and the gravitational wave (GW) emission of the IMRIs. We analyze the effects of general dynamical friction, with a particular contribution from DM particles moving faster than the stellar-mass black hole in an eccentric IMRI. Our calculation show that these DM particles tends to eccentricify the orbit, therefore the evolution of the eccentricity depends on the competition between the fast moving DM particles and the slow moving DM particles. The results show that the dynamical friction enhances the eccentricity when $γ_\mathrm{sp}\lesssim2.0$, and the general dynamical friction is able to increase the eccentricity. We also analyze the effects of general dynamical friction on the GW characteristic strain. The results indicate that the characteristic strain is suppressed at lower frequencies, and the peak value of the characteristic strain occurs at higher frequencies as the power law index of DM minispike $γ_\mathrm{sp}$ increases. For the first time, a relation between the frequency peak value of characteristic strain of GWs and $γ_\mathrm{sp}$ is established. Using this analytical relation, the presence of DM and its halo density may be determined potentially from future GW data.

Figures (4)

• Figure 1: The evolution of eccentricity $e$ as a function of semilatus rectum $p$. The dot lines correspond to cases without phase space description. The dashdot lines correspond to the cases without the contribution of faster moving DM particles. The solid lines correspond to cases including the contribution of the faster moving DM particles. The black lines correspond to cases without DM. The red, blue and green lines correspond to a spike power law index $\gamma_\mathrm{sp}=1.5$,$2$ and $7/3$, respectively. Top panels: The evolution of $e$ with initial $p=5000\ m_1$. Lower panels: The evolution of $e$ with initial $p=10^5\ m_1$.
• Figure 2: The evolution of semimajor axis $a$ and eccentricity $e$ as functions of time $t$. The dot lines correspond to cases without phase space description. The dashdot lines correspond to cases without faster moving DM particles. The solid lines correspond to cases including the contribution of the faster moving DM particles. The black lines correspond to cases without DM halo. The red, blue and green lines correspond to a spike power law index $\gamma_\mathrm{sp}=1.5$,$2$ and $7/3$, respectively. Top panels: The evolution of $a$ and $e$ with initial $p=5000\ m_1$. Lower panels: The evolution of $a$ and $e$ with initial $p=10^5\ m_1$.
• Figure 3: The effects of dynamical friction on the characteristic strain $h^{(2)}_{+}$. The dot lines correspond to cases without phase space description. The dashdot lines correspond to cases without faster moving DM particles. The solid lines correspond to cases including the contribution of the faster moving DM particles. The black lines correspond to cases without DM. The red, blue and green lines correspond to a spike power law index $\gamma_\mathrm{sp}=1.5$,$2$ and $7/3$, respectively.
• Figure 4: The relation between the frequency peak values of GW characteristic strains and power law index of DM spike $\gamma_\mathrm{sp}$.The dot lines correspond to cases without phase space description. The dashdot lines correspond to the cases without the contribution of faster moving DM particles. The solid lines correspond to cases including the contribution of the faster moving DM particles.