The impact of relativistic corrections on the detectability of dark-matter spikes with gravitational waves

Abstract

Black holes located within a dark matter cloud can create overdensity regions known as dark matter spikes. The presence of spikes modifies the gravitational-wave signals from binary systems through changes in the gravitational potential or dynamical friction effects. We assess the importance of including relativistic effects in both the dark matter distribution and the dynamical friction. As a first step we numerically calculate the particle dark matter spike distribution in full general relativity, using both Hernquist and Navarro-Frenk-White profiles in a Schwarzschild background, and we produce analytical fits to the spike profiles for a large range of scale parameters. Then we use a post-Newtonian prescription for the gravitational-wave dephasing to estimate the effect of relativistic corrections to the spike profile and to the dynamical friction. Finally we include the torques generated by dynamical friction in fast-to-generate relativistic models for circular extreme mass-ratio inspirals around a nonspinning black hole. We find that both types of relativistic corrections positively impact the detectability of dark matter effects, leading to higher dephasings and mismatches between gravitational-wave signals with and without dark matter spikes.

Dynamical friction in dark matter superfluids: The evolution of black hole binaries

“…Following the prescription laid out in refs. [75,78,79], one can estimate the dephasing cycles, which account for changes in the gravitational wave phase induced by dynamical friction within the DM spike. For simplicity, we approximate the orbit of the binary as circular, which is justified by the fact that dynamical friction circularizes inspiralling orbits within a DM spike [80].…”

“…(4.6) can be neglected. Rearranging and expanding to first order in ϵ, one obtains the following expression for r(Ω) [79],…”

“…Finally, following the comparison and discussion of figure 6, one can contrast these results with the ones for the case of collisionless dark matter (also discussed in ref. [79], where relativistic effects are taken into account). By looking at the red lines in figure 7, one can appreciate that dynamical friction for a collisionless rather than superfluid medium has a stronger role in driving the binary inspiral, also in the frequency range probed by LISA.…”

Solutions of the Einstein Equations for a Black Hole Surrounded by a Galactic Halo

“…Dynamical constraints on such dark-matter models of galaxies were studied in Lacroix (2018), while the impact of relativistic corrections on the detectability of dark-matter spikes with gravitational waves were considered in Speeney et al (2022). A general relativistic description of a black hole surrounded by a central region of a galaxy was given in Sadeghian et al (2013).…”