Ringdown Signatures of Dehnen Dark Matter Halos: Fluid Modes and Detectability with Space-Based Detectors

TL;DR

This study explores how gravitational-wave signals from black holes in dark matter halos can reveal properties of both the black holes and surrounding dark matter, using simulated waveforms and Bayesian analysis for future space-based detectors.

Contribution

It develops a relativistic framework for modeling dark matter effects on black hole ringdowns and assesses their detectability with upcoming gravitational-wave observatories.

Findings

Dark matter causes significant modifications to ringdown waveforms.

Profiles with spikes produce stronger signals, improving parameter inference.

Fluid modes appear at late times, indicating dark matter presence.

Abstract

In this work, we investigate the feasibility of using ringdown waveforms from supermassive black holes immersed in dark-matter halos to extract both the intrinsic black-hole parameters and those characterizing the surrounding matter distribution with future space-based gravitational-wave detectors. Building on the fully relativistic framework developed by Cardoso {\it et al.}, in which the dark-matter degrees of freedom are explicitly accounted for by minimal coupling to the gravitational sector, we construct numerical waveforms for a variety of Dehnen-type dark-matter profiles. We then convert these simulated waveforms into realistic data streams for future space-based gravitational-wave observatories, consistently implementing the second-generation Time-Delay Interferometry scheme in the analysis. We calculate the signal-to-noise ratios and perform a Bayesian parameter estimation to infer the model parameters, quantifying their measurability through the resulting posterior distributions. Our results indicate that the presence of dark matter can induce sizable modifications to the waveforms through the appearance of fluid modes at late times. Furthermore, dark-matter profiles with more pronounced spikes leave stronger imprints on the gravitational-wave signal, thereby enhancing the prospects for parameter inference with future space-based detectors such as LISA, Taiji, and TianQin.