Effect of dark matter halo environment on GW memory signal

TL;DR

This work investigates how a surrounding dark matter halo, modeled by a Hernquist-type profile (with and without a spike), affects gravitational-wave memory from a central black hole. It combines geodesic-deviation analysis under a passing GW pulse with the Bondi-Sachs formalism at null infinity to quantify the memory contribution and embed it into ringdown templates, enabling potential extraction of halo parameters from memory signals. The results show that the memory imprint depends nontrivially on halo parameters, notably decreasing with increasing M/a, and that spike and non-spike halos yield distinct trajectory modifications; a memory-corrected total waveform h^{total} exhibits a nonlinear dependence on M/a, captured by a cubic fit h^{total} ≈ 0.002(M/a) − 0.001(M/a)^2 + 0.0001(M/a)^3. This covariant framework links local geodesic dynamics to asymptotic memory through BMS flux-balance laws and offers a pathway to probe dark matter environments around black holes with future GW detectors, including LISA, via memory signatures.

Abstract

In this paper, we study the gravitational wave (GW) memory effect for a black hole embedded in a dark matter halo described by a Hernquist-type density profile, both with and without a spike. We first solve the geodesic equations in this spacetime under the influence of a GW pulse to examine how the combined effects of the dark matter halo and the GW pulse modify the geodesic deviation equation and particle trajectories. We then investigate how the memory effect manifests in the waveform in the presence of the dark matter halo. To do that, we analyze the memory contribution at asymptotic null infinity using the Bondi-Sachs formalism and, in particular, the Bondi-Metzner-Sachs (BMS) flux balance laws associated with BMS symmetries. This framework allows us to quantify the GW memory contribution to the waveform, incorporate it into the ringdown waveform templates, and thereby provide a possible avenue for extracting information about the dark matter halo parameters.

Figures (8)

• Figure 1: Plot showing the evolution of the geodesic $\phi$ in the presence (solid lines) and absence (dashed lines) of a GW pulse, for a dark matter halo with $M/a = 0.1$ (red), $M/a = 0.3$ (brown), and $M/a = 0.5$ (blue).
• Figure 2: Plot showing the evolution of the separation $\Delta\phi$ (as defined in \ref{['Delta_def']}) in the presence (solid lines) and absence (dashed lines) of a GW pulse, for a dark matter halo with $M/a = 0.1$ (black), $M/a = 0.3$ (red), and $M/a = 0.5$ (blue).
• Figure 3: Plot of the evolution of separation $\Delta \phi$ (as defined in \ref{['Delta_def']}) in presence of DM with spike (Green) and DM without spike (Magenta) for $M/a=0.1$, where the solid lines represent the evolution in presence of GW pulse and the dashed lines represent the evolution in absence of GW pulse.
• Figure 4: Comparison of trajectories before and after the GW pulse.
• Figure 5: Plots of the trajectory before and after the GW pulse in the absence and presence of a dark matter halo.