Measuring the neutron star equation of state from EMRIs in dark matter environments with LISA

Abstract

Gravitational-wave observations of extreme mass-ratio inspirals (EMRIs) in vacuum are largely insensitive to the internal structure of the small compact companion. We show that this conclusion can change when the central black hole is surrounded by a dense dark matter environment. We compute, for the first time, the relativistic dynamical-friction force on a neutron star moving through a collisionless medium and its impact on the evolution of EMRIs embedded in dense dark matter spikes. We then perform a Bayesian parameter-estimation analysis of simulated LISA observations to assess the measurability of both spike properties and the companion's internal structure. We find that, in our fiducial dark matter spike models, EMRIs with signal-to-noise ratio (SNR) $\gtrsim 20$ already allow us to distinguish neutron star from black hole companions, while events with SNR $\gtrsim 400$ make it possible to discriminate between different neutron star equations of state.

Figures (7)

• Figure 1: Dynamical friction as a function of companion mass. Markers indicate the predicted onset of key features from a constant-density–sphere toy model for $u = \langle u\rangle_{9GM/c^2}$. A NS’s crust causes the toy model to overestimate the true values, particularly for SLy's thick crust.
• Figure 2: Marginal posteriors for the masses and spike density. Results are based on 4 years of observation data, with black dashed lines indicating the injected values.
• Figure 3: Bayes factors for EOS comparisons with different companion masses. Colored bands denote the Jeffreys-scale interpretation Jeffreys1939-JEFTOP-5 from "Trivial" (gray), to "Substantial", "Strong", "Very Strong", and "Decisive" (dark blue). Error bars show the nested-sampling evidence uncertainty. The SLy EOS cannot achieve a $2.2~\mathrm{M}_\odot$ configuration and is hence omitted.
• Figure 4: Minimum optimal signal-to-noise ratio accumulated after 4 years for distinguishing EMRIs with neutron star companions. Arrows point the SNR for binaries placed at $1~\mathrm{Gpc}$ distance. The vacuum-like region for the $10^5~\mathrm{M}_\odot$ case lies outside the plot.
• Figure 5: Difference in scattering cross-section for an extended toy object and a point mass. The dashed black line represents the accretion cross-section for a BH.