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

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 $\gamma_\mathrm{sp}\lesssim2.0$, 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 $\gamma_\mathrm{sp}$ increases. For the first time, a relation between the frequency peak value of characteristic strain of GWs and $\gamma_\mathrm{sp}$ is established. Using this analytical relation, the presence of DM and its halo density may be determined potentially from future GW data.