Extreme mass ratio inspirals in rotating dark matter spikes

TL;DR

This paper investigates how rotating dark matter spikes around Kerr black holes influence gravitational wave signals from extreme mass ratio inspirals, highlighting the importance of including spin effects for detection and parameter estimation with LISA.

Contribution

It introduces a relativistic model for rotating dark matter spikes and assesses their impact on GW signals, emphasizing the role of black hole spin in detection prospects.

Findings

Spin of the primary black hole enhances DM spike detectability.

Dark matter environment effects are mostly negligible on the background metric.

Inclusion of spin effects improves future parameter estimation accuracy.

Abstract

Gravitational wave (GW) signals from extreme mass ratio inspirals (EMRIs) are a key observational target for the Laser Interferometer Space Antenna (LISA). The waveforms may be affected by the astrophysical environment surrounding the central black hole (BH), and in particular by the surrounding dark matter (DM) distribution. In this work, we consider the effect of a rotating DM "spike" around a central Kerr BH, and assess its detectability with LISA. Using a fully relativistic model for the rotating spike, we investigate its effect on the inspiral and hence on the emitted GW signals. We compute dephasings and mismatches to quantify how the spin of the primary BH affects the binary dynamics and the gravitational waveform. We show that the modifications due to the spin of the primary BH improve the detection prospects of DM spikes with LISA, and must be taken into account for future parameter estimation studies. We also estimate within post-Newtonian theory how the environment affects the background metric, and show that this effect is mostly negligible for the systems we consider.