Dark matter distributions around extreme mass ratio inspirals: effects of radial pressure and relativistic treatment

TL;DR

This paper examines how different models of dark matter distributions, especially those including radial pressure and relativistic effects, influence the orbital dynamics and gravitational wave signals of extreme mass ratio inspirals, highlighting the importance of accurate modeling.

Contribution

It introduces a relativistic treatment of dark matter around EMRIs, emphasizing the impact of radial pressure on orbital evolution and gravitational waveforms, which was not fully addressed before.

Findings

Radial pressure significantly alters orbital dynamics.

Relativistic models change gravitational waveform predictions.

Dark matter profile modeling affects detectability of EMRIs.

Abstract

We investigate different treatments of dark matter (DM) distributions surrounding extreme mass ratio inspirals (EMRIs) to assess their impact on orbital evolution and gravitational wave emission. Density profiles derived from the mass current and from the energy-momentum tensor using a distribution function yield consistent results, but both differ substantially from profiles obtained using an anisotropic fluid model based on Einstein cluster ansatz. We find that the inclusion of radial pressure significantly modifies both the orbital dynamics and the resulting gravitational wave waveforms. By analyzing waveform dephasing and mismatches, we show that a fully relativistic treatment of DM distributions can substantially alter the detectability thresholds of DM halos. Our results demonstrate that radial pressure and relativistic modeling of DM are essential for accurately describing the dynamics and observational signatures of EMRIs embedded in DM halos.