Bayesian inference for tidal heating with extreme mass ratio inspirals

Extreme mass ratio inspirals (EMRIs) provide unique probes of near-horizon dissipation through the tidal heating. We present a full Bayesian analysis of tidal heating in equatorial eccentric EMRIs by performing injection-recovery studies and inferring posterior constraints on the reflectivity parameter $|\mathcal{R}|^2$ while sampling in the full EMRI parameter space. We find that in the strong-field regime the posterior uncertainties are smaller, indicating a stronger constraining capability on the tidal heating. Using two-year signals with an optimal signal-to-noise ratio (SNR) of $ρ=50$, EMRIs can put bounds on $|\mathcal{R}|^2$ at the level of $10^{-3}$–$ 10^{-4}$ for a rapidly spinning central object. Moreover, we show that neglecting the tidal heating can induce clear systematic biases in the intrinsic parameters of the EMRI system. These results establish EMRIs as promising precision probes for detecting and constraining black hole event horizons.

💡 Research Summary

This paper investigates the prospect of using extreme‑mass‑ratio inspirals (EMRIs) observed by space‑based gravitational‑wave detectors such as LISA to measure the near‑horizon dissipation known as tidal heating. In general relativity a Kerr black hole absorbs gravitational‑wave flux at its horizon, acting as a one‑way membrane. Alternative compact objects (e.g. exotic compact objects, ECOs) may replace the horizon with a partially reflecting surface. The authors parametrize this deviation with a dimensionless reflectivity coefficient |𝑅|², where 𝑅=0 corresponds to a perfectly absorbing Kerr black hole and |𝑅|²=1 to a perfectly reflecting surface.

The study proceeds through four main stages. First, they construct a fully relativistic adiabatic EMRI waveform model at the zero‑post‑adiabatic (0PA) level, based on Teukolsky‑derived energy and angular‑momentum fluxes. The horizon contribution to these fluxes is multiplied by (1‑|𝑅|²), thereby incorporating the reflectivity directly into the orbital evolution. The waveform generation uses the FastEMRIWaveforms code, which provides efficient evaluation of the 0PA model while retaining the necessary strong‑field accuracy.

Second, they create a suite of simulated signals (injection) for a fiducial system: a central black hole of mass M=10⁶ M⊙ with spin a=0.95 M, a stellar‑mass secondary of μ=10 M⊙, and a two‑year observation window. The signal‑to‑noise ratio is fixed at ρ=50, a realistic value for a moderately loud EMRI in LISA. They explore a grid of initial orbital parameters (semi‑latus rectum pᵢ and eccentricity eᵢ) covering the region where the inspiral remains in band for the full two years. Two injection cases are considered: (i) the standard Kerr case with |𝑅|²=0, and (ii) a small deviation with |𝑅|²=0.01.

Third, a Bayesian inference framework is built. The likelihood is the usual Gaussian form based on the LISA I‑channel response, and priors are taken to be broad and mostly uniform (e.g., |𝑅|²∈