Spin-induced quadrupole moment based test for eccentric binaries

TL;DR

This work extends the spin-induced quadrupole moment BH-nature test to eccentric binaries, demonstrating that neglecting eccentricity can bias BH/non-BH inferences and mimic non-BH signatures. Using a combination of Fisher information matrix analysis and full Bayesian parameter estimation with the TaylorF2Ecc waveform, the authors quantify eccentricity-induced systematics across LIGO-like, Cosmic Explorer, and LISA–like detector configurations. They show that eccentricity biases can dominate statistical errors for realistic ejections (e.g., $e_0\sim0.1$ at 20 Hz for current detectors, smaller thresholds for next-generation detectors), leading to misestimation of $\delta\kappa_i$, mass ratio $q$, and $\boldsymbol{\chi}_{\rm eff}$, and potentially misclassifying BH binaries as non-BH systems. The results underscore the necessity of including eccentricity in SIQM tests to reliably probe BH nature and inform formation channels, with extensions to precession and tidal effects proposed for future work.

Abstract

The spin-induced quadrupole moment-based test of black hole nature is routinely used to probe the true nature of detected binary signals, assuming a circular orbit. We extend the applicability of the method to binaries in eccentric orbits. Considering simulated signals of varying masses, spins, and signal strengths, we demonstrate how the systematic errors resulting from neglecting orbital eccentricity compare with the statistical errors, using a semi-analytic Fisher matrix-based formalism that accounts for both current and future detectors. Further, we quantify the systematic errors by developing a Bayesian inference framework for the current detector network. The inspiral-only aligned spin gravitational wave waveform model for eccentric binaries, TaylorF2Ecc, is employed. For the current detector network, neglecting an initial eccentricity of $e_0^{\rm inj}=0.1$ defined at $20\,\mathrm {Hz} $ can lead to a serious bias in binary parameter inference. Notably, a nearly equal-mass, moderately spinning binary black hole in an eccentric orbit can be identified as a non-black hole binary with extreme spins and asymmetric masses. We demonstrate the criticality of biased estimates that may arise when neglecting the orbital eccentricity while performing tests of black hole nature and discuss prospects.

Figures (5)

• Figure 1: The statistical error on the spin-induced quadrupole moment parameter $\sigma_{\delta\kappa_s}$ is plotted in dashed lines. The systematic error on the spin-induced quadrupole moment parameter $\Delta\theta_{\delta\kappa_s}$ is shown as a function of eccentricity.
• Figure 2: For three binary choices, $q=0.875$, $(\boldsymbol{\chi}_1, \boldsymbol{\chi}_2) = (0.3, 0.1)$ (blue), $q=0.5$, $(\boldsymbol{\chi}_1, \boldsymbol{\chi}_2) = (0.3, 0.1)$ (orange), $(\boldsymbol{\chi}_1, \boldsymbol{\chi}_2) = (0.3, 0.1)$ and $q=0.5$, $(\boldsymbol{\chi}_1, \boldsymbol{\chi}_2) = (0.5, 0.4)$ (green), $\delta\kappa_1$ is estimated considering a simulated binary system in eccentric orbit with initial orbital eccentricity $e_0^{\rm inj}=0.1$ and recovered employing a quasi-circular waveform model. The mass ratio effect is negligible. However, a slowly spinning binary exhibits a larger bias compared to a rapidly spinning binary.
• Figure 3: The posteriors on the mass ratio and effective spin parameter are shown for three binary configurations. The injected signals are eccentric, but are analysed using a quasi-circular waveform model that includes the $\delta\kappa$ parameter. The injected mass ratio values are $q = 0.875,0.5,0.5$, and the corresponding effective spin values are $\boldsymbol{\chi_{\rm eff}} = 0.20, 0.23, 0.46$, plotted in green, orange, and blue curves, respectively. The posterior estimates are shifted from their injected values, with the extent of the bias determined by the respective binary configuration.
• Figure 4: Posteriors on $\delta\kappa_1$ considering a simulated binary of eccentricity $e_0^{\rm inj}=0.1$ (solid histogram) and $e_0^{\rm inj}=0.05$ (dotted histograms). Both these injections, when recovered with the eccentric model, provide results consistent with a binary BH value. In contrast, the circular recovery of the $e_0^{\rm inj}=0.1$ injection lead to severe bias in the $\delta\kappa_1$ estimate (dashed histogram). The vertical lines represent the $90\%$ credible highest probability density regions.
• Figure 5: Impact of excluding eccentricity while analysing an eccentric binary system is illustrated for two cases, for a binary BH analysis (left, $\theta_{\rm BBH}$) and SIQM analysis (right, $\theta_{\rm BBH}, \delta\kappa_i$). The black star represents the injected value. Red and blue scatter plots represent analysis assuming circular and eccentric recovery, respectively. Ignoring eccentricity in the SIQM analysis can lead to mis-identifying a nearly-equal mass, slowly spinning binary BH as a mass-asymmetric binary with evidence for rapid spins.