Research of Dark Matter Using Gravitational Waves in Black Hole Mergers

Abstract:

Dark matter is an invisible, gravitationally influenced component of the Universe that remains
one of the most significant unsolved problems in astrophysics - despite its gravitational
influence, it has yet to be directly detected or confirmed. In this paper, we investigate the
influence of dark matter on the dynamics of the motion of a binary black hole system when they
merge via gravitational wave signatures. We hypothesize that dark matter influences the inspiral
dynamics of binary systems through dynamical friction, which is reflected through the emitted
gravitational waves. Our main research question is: how do different dark matter density
profiles affect the gravitational wave signatures of intermediate mass-ratio inspirals (IMRIs)
during black hole mergers, and can these effects be used to indirectly detect dark matter? We
aim to model the intermediate mass ratio inspirals (IMRI) of Schwarzschild black holes placed

in different dark matter environments by applying Navarro-Frenk-White (NFW) and self-
interacting dark matter (SIDM) density profiles. Using Python simulations, we follow the

evolution of orbital parameters, such as eccentricity and semi-major axis, under vacuum and
dark matter conditions. Identifying observed variations in gravitational waveforms, in particular
in wave phasing and orbital decay rates, will provide a path to indirectly detect dark matter
using future space observatories such as LISA. In contrast to previous approaches focusing on
direct detection or cosmological observations, this study proposes a new method to investigate
dark matter by analyzing its dynamical effects on gravitational waves emitted in black hole
mergers.

Introduction:

Dark matter makes up about 85% of the matter of the Universe, but its properties remain largely

unknown due to the absence of electromagnetic interaction. Recent advances in gravitational-
wave astronomy offer a promising indirect approach to studying the gravitational effects of

dark matter. Black hole mergers, especially in the intermediate mass-ratio inspiral regime with
intermediate mass ratio, are sensitive probes of their astrophysical environment. The emitted
gravitational waves are shaped by the general theory of relativity and by perturbations caused
by the surrounding matter. We focus on the ability of dark matter to induce dynamical friction,
an effective drag force that affects the rate of binary inspirals. We hypothesize that the presence
of the dark matter halo changes the merger time and eccentricity of the evolution of binary
black holes. These changes should reflect observed variations in the gravitational wave signals,
which could potentially be detected by space observatories such as LISA. Thus, observing these
variations in gravitational waves could reveal the presence and properties of dark matter.

Literature Review:

Numerous theoretical studies investigated the dynamics of compact objects with dark matter.
Eda et al. (2015) suggested that dark matter bursts can leave traces in gravitational waveforms,
especially for intermediate mass-ratio inspirals. Becker et al. (2022) investigated how dark
matter spikes affect the orbital circularization of black holes. Shapiro & Paschalidis (2014) and
Boudaud et al. (2021) analyzed the Navarro-Frenk-White and SIDM dark matter profiles, which
determine how the dark matter density varies with radial distance, directly affecting the
gravitational force and orbital rate of change. This proposal has a strong foundation on these
studies by performing numerical simulations to compare orbital dynamics with and without
dark matter, offering visual and quantitative insight into the effects in different density models.

Methodology:​ 

We simulate a system composed of two Schwarzschild black holes in an IMRI configuration.
The primary object is assumed to be a supermassive black hole (105–106 M☉, where M☉
denotes the mass of the Sun), and the secondary is a stellar-mass black hole (~10 M☉). Their
orbital evolution is governed by gravitational wave radiation and the gravitational influence of
ambient dark matter.

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