Detectability and Systematic Bias from First-Order Phase-Transition Dephasing in Kerr EMRIs

Abstract

We study gravitational-wave dephasing induced by an effective first-order phase transition in a Kerr extreme mass-ratio inspiral (EMRI). The transition is modeled phenomenologically as a finite-width restructuring of the dissipative flux sector, and its observational consequences are quantified with standard LISA matched-filter diagnostics. For a representative system with $M=2\times10^{5}M_\odot$, $μ=1.4M_\odot$, and $\hat a=0.90$, we obtain $ρ_{\rm B}=5.064$, $ρ_{\rm T}=4.073$, $ρ_{\rm R}=1.051$, and a mismatch $\mathcal M=2.986\times10^{-3}$ after maximization over extrinsic time and phase shifts. Although the normalized mismatch remains small, the accumulated phase difference grows to $ΔΦ_{22}^{\rm SF}\sim 5\times10^{3}\,\mathrm{rad}$, indicating that a narrow transition window can generate a large coherent deformation of the inspiral clock while leaving the waveform globally close to the baseline branch in detector-weighted norm. The resulting signal therefore lies in a bias-sensitive regime, characterized by small mismatch, order-unity residual norm, and large cumulative dephasing. Our results suggest that the dominant consequence of the transition sector is not loss of detectability, but loss of faithfulness for precision inference. This motivates future LISA EMRI waveform models that incorporate parameterized transition sectors directly into the waveform manifold.

Figures (8)

• Figure 1: Global summary of the first-order phase-transition imprint on the Kerr EMRI waveform. (a) Effective transition-control parameter $\Lambda$ as a function of the dominant-mode frequency $f_{22}$, with the mixed-phase interval highlighted. (b) Accumulated phase difference $\Delta\Phi_{22}^{\rm SF}$ between the baseline and transition branches. (c) Time-domain residual structure near the end of the inspiral. (d) Frequency-domain characteristic strains of the baseline, transition, and residual branches relative to the LISA sensitivity scale. The figure shows that a localized restructuring in the dissipative sector can generate a large coherent phase defect while the two main branches remain globally close in detector-weighted norm.
• Figure 2: Time-domain comparison of the baseline, transition, and residual strains as functions of time to cutoff. The baseline and transition waveforms remain visually close at early times but develop increasing phase slippage toward the end of the inspiral. The residual is therefore generated primarily by coherent dephasing rather than by a large amplitude mismatch.
• Figure 3: Characteristic strain of the baseline, transition, and residual waveforms compared with the LISA noise level. The baseline and transition branches remain close over most of the analyzed band, explaining the small mismatch, while the residual retains visible support near the upper inspiral band where the accumulated phase defect becomes most important.
• Figure 4: Detector-weighted mismatch after local intrinsic refitting of the baseline branch in a representative parameter plane, use $(M,\hat{a})$ . The benchmark point and the best-fit intrinsic baseline point should both be indicated. This figure is intended to test how effectively the transition waveform can be mimicked by nearby Kerr parameters.
• Figure 5: Fisher-bias diagnostic for the transition benchmark. Suggested implementations are either: (i) a bar chart of $|\Delta\theta_{\rm sys}|/\sigma$ for the dominant parameters, or (ii) Fisher confidence ellipses with the systematic-shift vector overlaid. This figure quantifies the extent to which the missing transition sector biases precision inference even when the normalized mismatch remains small.