Extreme mass ratio inspirals in dark matter halos: dynamics and distinguishability of halo models

TL;DR

This work develops a fully relativistic framework for extreme mass ratio inspirals embedded in dark matter halos by modeling the halo with the Einstein cluster and analyzing axial and polar perturbations of a nonrotating BH. It computes GW fluxes and the adiabatic orbital evolution for DM profiles (Hernquist, NFW, Einasto) across a range of compactness, showing that environmental effects induce large phase dephasings, up to $\Delta\Phi \sim 10^3$ over a year, and that LISA can both detect the presence of DM halos and distinguish between halo models. The results highlight a linear scaling of dephasing with halo compactness and demonstrate robustness against changes in halo mass, profiles, and numerical details, while redshift corrections reduce but do not erase the effect. The study also establishes that fully relativistic modeling is essential, with PN approaches greatly underestimating or misrepresenting the cumulative phase shifts, and outlines future work to include BH spin, generic orbits, and integration into LISA data-analysis pipelines for DM constraints.

Abstract

The gravitational wave (GW) signals from extreme mass-ratio inspirals (EMRIs), a key target for the Laser Interferometer Space Antenna (LISA), will be affected in the presence of dark matter (DM) halos. In this paper we explore whether the effects of DM are detectable by LISA within a fully relativistic framework. We model the massive EMRI component as a nonrotating black hole (BH) surrounded by a DM halo. We compute axial and polar GW fluxes for circular orbits at linear order in the mass ratio for DM density profiles with varying mass and compactness. By comparing the phase evolution with vacuum systems, we find that DM halos can induce dephasings of tens to hundreds of radians over a one-year observation period. We demonstrate that even highly diluted DM distributions can significantly affect the emitted waveforms, and that the resulting GW signals can usually be distinguished from each other. While it is important to generalize these findings to more generic orbits and to spinning BHs, our results suggest that LISA could not only reveal the presence of DM halos, but also discriminate between different halo models.

Figures (7)

• Figure 1: Density profiles as a function of distance from a primary BH with mass $M = 10^6 M_\odot$. The purple-thick, green-medium, and orange-thin curves correspond to halo compactness values of $\mathcal{C} = 10^{-3}$, $\mathcal{C} = 10^{-4}$, and $\mathcal{C} = 10^{-5}$, respectively. The style of each curve indicates the DM model: Einasto (continuous), Hernquist (dashed), and NFW (dotted). The left and right panels correspond to DM halos with masses $M_\text{halo} = 10^{2} M_\text{BH}$ and $M_\text{halo} = 10^{3} M_\text{BH}$, respectively. Dashed and dotted vertical lines mark the initial orbital radius of a secondary object with mass $m_p = 10M_\odot$ and $m_p = 50M_\odot$, respectively, which evolves for one year around the primary before reaching the innermost stable circular orbit (ISCO). For reference, we also show in black the location of the coordinate radius of the BH horizon and the distance at which the DM profile vanishes.
• Figure 2: Top row: Ratio of GW fluxes emitted in vacuum to those in the presence of matter, plotted as a function of the secondary’s orbital radius. The primary BH mass is $M = 10^6 M_\odot$, the DM halo mass is $M_{\text{halo}} = 10^{2} M_{\text{BH}}$, and we consider two possible values of the secondary mass: $m_P = (10,50) M_\odot$. The purple solid, green dashed, and orange dotted lines represent halos with compactness values of $\mathcal{C} =(10^{-3},10^{-4},10^{-5})$. Markers along each curve indicate the initial orbital radius of the secondary, which evolves over either one year (filled markers) or six months (hollow markers) until plunge (see legend). Bottom row: Quadrupolar dephasing accumulated over one year (filled markers) and six months (hollow markers) during the evolution of the EMRIs. Labels on the top axes indicate the accumulated number of cycles in the vacuum case. The three different panels, from left to right, correspond to different DM density profiles.
• Figure 3: Same as Fig. \ref{['fig:dephasing_Mh100']}, but assuming a DM halo with $\text{M}_\text{halo} = 10^{3} \text{M}_\text{BH}$.
• Figure 4: Faithfulness density matrices for different DM profiles (Hernquist, NFW, and Einasto) of mass $M_{\text{halo}} = 10^{2} M_{\text{BH}}$, compared to the vacuum case and among each other. The three panels correspond to halo compactness values of $\mathcal{C} =(10^{-3}, 10^{-4}, 10^{-5})$. The upper and lower diagonals of each matrix display faithfulness values computed for systems with $(M_{\text{BH}}, m_p) = (10^6,10) M_\odot$ and $(M_{\text{BH}}, m_p) = (10^6,50) M_\odot$, respectively. Large (small) numbers in each cell indicate faithfulness values computed for a one-year (six-month) evolution, respectively.
• Figure 5: Same as Fig. \ref{['fig:faithfulness_Mh100']}, but for a halo mass of $M_\text{halo} = 10^{3} M_\text{BH}$.