Dark matter distributions around extreme mass ratio inspirals: effects of radial pressure and relativistic treatment

TL;DR

We address how dark matter halos around massive black holes influence extreme mass ratio inspirals (EMRIs) by developing a fully relativistic DM model that includes nonzero radial pressure. The authors derive Hernquist-type density profiles using both a distribution-function approach (yielding $\rho_T$ and $\rho_J$ with $p_r$) and an anisotropic-fluid model ( $\rho_C$ with $p_r=0$ ), and solve the Einstein equations to obtain the background metric for each case. They then evolve circular EMRIs under GW radiation reaction and dynamical friction in these halos and compute GW waveforms and mismatches. They find that radial pressure significantly alters orbital evolution and waveforms, that fully relativistic treatment lowers detectability thresholds allowing halos with compactness as small as $M/a_0\sim10^{-5}$ to be observable with LISA, and that neglecting radial pressure or relativistic effects can substantially misestimate EMRI observables. This work underscores the necessity of incorporating environmental effects in EMRI modeling for accurate astrophysical and fundamental physics in the LISA era.

Abstract

We investigate different treatments of dark matter (DM) distributions surrounding extreme mass ratio inspirals (EMRIs) to assess their impact on orbital evolution and gravitational wave emission. Density profiles derived from the mass current and from the energy-momentum tensor using a distribution function yield consistent results, but both differ substantially from profiles obtained using an anisotropic fluid model based on Einstein cluster ansatz. We find that the inclusion of radial pressure significantly modifies both the orbital dynamics and the resulting gravitational wave waveforms. By analyzing waveform dephasing and mismatches, we show that a fully relativistic treatment of DM distributions can substantially alter the detectability thresholds of DM halos. Our results demonstrate that radial pressure and relativistic modeling of DM are essential for accurately describing the dynamics and observational signatures of EMRIs embedded in DM halos.

Figures (8)

• Figure 1: The energy density distribution. The blue and black curves correspond to the halo size of $a_0 = 100 M$ and $a_0 = 10^4 M$, respectively. The solid, dashed and dot-dashed lines denote $\rho_\text{T}(r)$, $\rho_\text{C}(r)$ and $\rho_\text{J}(r)$, respectively.
• Figure 2: The dependence of $\rho_\text{T}$ on $r$ and the compactness $M/a_0$. The right panel is plotted at $r=10M_\text{BH}$.
• Figure 3: The density ratio $\rho_\text{T}/\rho_\text{J}$ near the central MBH. The blue and black curves correspond to the halo size of $a_0 = 100 M$ and $a_0 = 10^4 M$, respectively.
• Figure 4: The ratio between $p_r$ and $\rho_\text{T}$. The blue and black curves correspond to the halo size of $a_0 = 100 M$ and $a_0 = 10^4 M$, respectively.
• Figure 5: The energy fluxes due to the dynamical friction and gravitational radiation from GWs. We take $a_0=100M$.