Detector-Weighted Signatures of Localized Dissipative Transitions in Kerr EMRIs

Abstract

Abstract We study a parameterized localized modification of the dissipative evolution in a circular equatorial Kerr extreme mass-ratio inspiral (EMRI). We do not claim a unique mapping to a specific hadron--quark equation of state; instead, the transition sector is treated as a localized flux deformation with parameters $\{A_{\rm tr},f_c,\Delta f,p,q\}$. The reference inspiral uses real Teukolsky flux data from the Black Hole Perturbation Toolkit \texttt{CircularOrbitSelfForceData} repository, interpolating the tabulated Kerr circular-orbit fluxes in radius and spin. For a representative system with $M=2\times10^{5}M_\odot$, $\mu=1.4M_\odot$, $\hat a=0.90$, $A_{\rm tr}=10^{-6}$, $f_c=0.0165~{\rm Hz}$, and $\Delta f=0.009~{\rm Hz}$, we normalize the baseline waveform to $\rho_{\rm B}=30$. The transition waveform has $\rho_{\rm T}=30.000$, residual norm $\rho_{\rm R}=2.948$, and extrinsic-time-and-phase-maximized mismatch $\mathcal M_{\rm ext}=4.828\times10^{-3}$. A direct three-dimensional intrinsic profile refit reduces the mismatch to $5.95\times10^{-8}$ and shifts the best-fitting intrinsic parameters by $\Delta M/M=-3.32\times10^{-5}$, $\Delta\mu/\mu=2.11\times10^{-5}$, and $\Delta\hat a=-1.34\times10^{-6}$. In a zero-noise (Asimov) profile-likelihood calculation, the injected Kerr point has $\Delta\chi^2=8.67$ relative to the profiled best fit, outside the three-parameter 95\% contour but inside the 99\% contour for the adopted simplified likelihood. We also perform a six-parameter Fisher projection, but its condition number is $1.82\times10^{17}$ and the finite-difference step test does not converge; we therefore treat it only as a diagnostic of tangent-space degeneracy. The robust conclusion is that localized dissipative transitions can remain highly overlapping with nearby Kerr waveforms while producing detector-weighted residuals and a nominally significant profile-likelihood displacement in this restricted zero-noise waveform model.