Gravitational radiation reaction around a static black hole surrounded by a Dehnen type dark matter halo

TL;DR

This work investigates gravitational radiation reaction for extreme mass ratio inspirals (EMRIs) around a Schwarzschild-like black hole embedded in a Dehnen-type dark matter halo. The authors derive the DM-modified metric, characterize bound equatorial orbits via the semimajor axis and eccentricity, and compute orbital periods and periastron precession by mapping between $(p,e)$ and the constants of motion, while incorporating GW backreaction, dynamical friction, and Bondi-Hoyle DM accretion. They find that higher central DM density $\rho_s$ and scale radius $r_s$ speed up inspiral by reducing the GW energy flux and enhancing orbital circularization, leading to stronger dephasing in the gravitational waveform. Leading-order quadrupole waveforms exhibit accumulative phase shifts compared to vacuum, implying potentially measurable DM-related signatures for space-based detectors like LISA and highlighting the importance of accounting for DM environments in EMRI modeling.

Abstract

We consider the motion of a particle in the geometry of a Schwarzschild-like black hole embedded in a dark matter (DM) halo with Dehnen type density profile and calculate the orbital periods along with the evolution of the semi-latus rectum and eccentricity for extreme mass ratio inspirals (EMRIs). Such a system emits gravitational waves (GWs), and the particle's orbit evolves under radiation reaction. We also consider the effects of dynamical friction and accretion of DM on the orbital parameters. We find that the eccentricity and semi-latus rectum decrease faster with respect to the case in which EMRI is in empty spacetime.

Figures (6)

• Figure 1: The effective potential for radial motion for $r_{s}=0.1$ and different values of $\rho_{s}$ (top panel); for $\rho_{s}=0.05$ and different values of $r_{s}$ (middle panel); for $\rho_{s}=0.05$ and $r_{s}=0.1$ (bottom panel).
• Figure 2: The results of the orbital periods and precessions for EMRIs in a Dehnen type DM halo with different values of $\rho_{s}$ and $r_{s}$.
• Figure 3: The energy and angular momentum fluxes for EMRIs in galaxies with a Dehnen type DM halo with different values of $\rho_{s}$ and $r_{s}$.
• Figure 4: The evolution of the orbital parameters $e(t)$ and $p(t)$ for different values of $\rho_{s}$ and $r_{s}$.
• Figure 5: Time-domain $h_+$ waveforms for EMRIs embedded in a Dehnen type DM halo with varying $\rho_s$ and $r_s$.