[Paper Review] The impact of relativistic corrections on the detectability of dark-matter spikes with gravitational waves

Nicholas Speeney, Josu C. Aurrekoetxea+2 more|arXiv (Cornell University)|Apr 26, 2022

Pulsars and Gravitational Waves ResearchPhysics and Astronomy56 references83 citations

TL;DR

This paper investigates how relativistic corrections in dark matter (DM) spikes and dynamical friction affect the detectability of DM via gravitational waves from extreme mass-ratio inspirals (EMRIs). Using full general relativity to model DM spikes and post-Newtonian waveforms, it finds that relativistic effects significantly enhance signal dephasings and mismatches, improving DM detection prospects with LISA.

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.

Motivation & Objective

• Assess the impact of relativistic corrections on dark matter spike profiles in full general relativity.
• Model dynamical friction forces in a relativistic framework for compact binary systems near black holes.
• Integrate relativistic DM spike and drag effects into fast EMRI waveform models for improved signal fidelity.
• Quantify the detectability enhancement of DM signatures in gravitational wave signals from EMRIs.
• Provide analytical fits to relativistic DM spike profiles for a wide range of halo parameters.

Proposed method

• Numerically compute relativistic dark matter spike profiles using Eddington inversion in a Schwarzschild spacetime for Hernquist and NFW initial profiles.
• Derive analytical fits to the resulting spike profiles across a broad range of scale parameters (a, ρ₀, γ).
• Apply post-Newtonian (PN) formalism to compute gravitational wave dephasing due to relativistic corrections in both spike potential and dynamical friction.
• Incorporate relativistic dynamical friction torques into the FastEMRIWaveform (FEW) framework for circular orbits around nonspinning black holes.
• Use LISA noise models to compute signal mismatches and dephasings for realistic EMRI sources.
• Validate results against Newtonian approximations and quantify the relative importance of relativistic corrections.

Experimental results

Research questions

• RQ1 How do relativistic corrections alter the structure and density profile of dark matter spikes around black holes compared to Newtonian models?
• RQ2 To what extent do relativistic corrections to the dynamical friction force affect the orbital evolution of compact objects in EMRIs?
• RQ3 How do relativistic spike and drag effects influence the gravitational wave dephasing and mismatch in EMRI signals?
• RQ4 Can relativistic corrections significantly enhance the detectability of dark matter via gravitational wave observations with LISA?
• RQ5 What are the most effective analytical fits to relativistic DM spike profiles across varying halo parameters?

Key findings

• Relativistic corrections shift the peak of the dark matter spike closer to the black hole, from ~4Rₛ in Newtonian models to ~2Rₛ in general relativity, increasing central density.
• The inclusion of relativistic corrections in both the spike potential and dynamical friction leads to larger gravitational wave dephasings compared to Newtonian models.
• Mismatches between waveforms with and without dark matter spikes increase by up to a factor of 2 when relativistic corrections are included, enhancing detectability.
• The FEW waveform framework successfully incorporates relativistic DM effects with minimal computational overhead, enabling efficient parameter estimation.
• Relativistic dynamical friction contributes significantly to orbital decay, with corrections to Chandrasekhar's formula improving signal fidelity in high-SNR EMRI events.
• Analytical fits to relativistic spike profiles are accurate across a wide range of scale parameters, enabling fast and reliable modeling for future LISA data analysis.