Extreme-Mass-Ratio Inspirals Embedded in Dark Matter Halo II: Chaotic Imprints in Gravitational Waves

TL;DR

This paper explores how chaos in the orbits of objects near black holes embedded in dark matter halos affects gravitational wave signals, revealing distinctive spectral features that could be detected by future observatories.

Contribution

It demonstrates the impact of chaotic dynamics on gravitational waveforms and introduces spectral and recurrence analysis methods to identify chaos in gravitational wave data.

Findings

Chaotic orbits produce broader frequency spectra in gravitational waves.

Chaotic signals show increased amplitude and energy emission.

Recurrence analysis reveals unique signatures of chaos in waveforms.

Abstract

We investigate the imprints of chaos in gravitational waves from extreme-mass-ratio inspirals configuration, where a stellar massive object, confined in a harmonic potential, orbits a supermassive Schwarzschild-like black hole embedded in a Dehnen-type dark matter halo. In our first paper [1], we demonstrated the system's transition from non-chaotic to chaotic dynamics by analyzing Poincar\'e sections, orbital evolution, and Lyapunov exponents across different energies and dark matter halo parameters. In this work, we compute the gravitational waveforms of the small celestial object along different chaotic and non-chaotic orbits by implementing the numerical kludge scheme. We further perform a spectral analysis of the gravitational waveforms from such orbits. In particular, we show that when the system is in a chaotic state, the gravitational wave signals are characterized by broader frequency spectra with finite widths, enhanced amplitude and energy emission rate, distinctly differentiating them from the signals generated during the system's non-chaotic state. Through recurrence analysis we also show that the time series of gravitational waveforms strain carry unique information on the motion of chaotic dynamics, which can be used to distinctly differentiate from non-chaotic to chaotic motion of the source. Furthermore, we discuss the potential detectability of these orbits for upcoming observatories like LISA, TianQin, and Taiji, emphasizing the significant potential for detecting chaotic imprints in gravitational waves to substantially enhance our understanding of chaotic dynamics in black hole physics and the dark matter environments of galactic nuclei.