Impact of the $(\ell=2,m=0)$ spherical harmonic mode with memory on parameter estimation for ground-based detectors

TL;DR

This work extends the IMRPhenomTHM waveform model to include the full $ (ell=2,m=0) $ mode, incorporating both the nonoscillatory memory and the oscillatory ringdown content, to assess how memory-aware modeling affects parameter estimation for current and next-generation ground-based detectors. Using zero-noise injections across LIGO with A$^{ ext{#}}$ sensitivity, CE, and ET networks, it quantifies biases arising when the $ (2,0) $ mode is neglected, with a focus on mass, spin, and distance–inclination degeneracies. The results show that neglecting the full $ (2,0) $ mode can induce notable biases in individual-spin estimates for certain edge-on, high-SNR configurations, while the distance–inclination improvement from the mode is limited when higher-order modes are present. In 3G detector networks, the qualitative conclusions remain, though increased SNR improves overall parameter precision; the study emphasizes the importance of including the complete $ (2,0) $ mode for accurate inference in precision GW astronomy. These findings have direct implications for waveform modeling choices in parameter estimation pipelines and for designing analyses that maximize information from subdominant harmonics and memory.

Abstract

We recently presented an efficient and accurate waveform model for the $(2,0)$ spherical harmonic mode including both the displacement memory contribution and the ringdown oscillations for aligned-spin binary black holes in quasi-circular orbits. The model we developed is constructed in time domain and implemented within the computationally efficient IMRPhenomTHM waveform model. In this article, we employ it to perform in-depth parameter estimation studies for future ground-based detectors, specifically considering LIGO A$^{\#}$, Cosmic Explorer, and the Einstein Telescope, combining them in different detector networks. While previous studies have reviewed the impact of the memory contribution in parameter estimation, we assess the effect of incorporating the complete mode in the analysis on the posterior estimation of source parameters, performing zero-noise injections of high signal-to-noise ratio signals. We investigate the impact of this mode on the distance-inclination degeneracy and compare its impact in edge-on and face-on configurations. We find that including this mode helps mitigate biases in the estimation of individual spin components, which may otherwise arise when the mode is neglected.

Figures (19)

• Figure 1: Dependence on the mass ratio of the maximum of the strain amplitude (in geometric units, $G=c=1$) for equal-spin systems of the full $(2,0)$ spherical harmonic (green squares), the oscillatory component (blue circles) and the memory component (orange stars) of this mode. The left panel corresponds to a configuration with high negative spins, the middle panel to a nonspinning system, and the right panel to a configuration with high positive spins.
• Figure 2: Sensitivity curves of LIGO A$^{\#}$, Einstein Telescope (ET-D) and Cosmic Explorer (CE1) detectors used in the injections, taken from Sensitivitycurves.
• Figure 3: Joint posterior distributions of the mass ratio ($q$) and chirp mass ($\mathcal{M}$) for the eight injections in order from left to right and top to bottom. The black lines correspond to the injected parameter values.
• Figure 4: Joint posterior distributions of the individual spin $z$ components ($\chi_{1z}$ and $\chi_{2z}$) for the eight injections in order from left to right and top to bottom. The black lines correspond to the injected parameter values.
• Figure 5: Joint posterior distributions of the luminosity distance ($d_L$) and inclination ($\theta_{\text{JN}}$). Left panel corresponds to Injection 4. Right panel compares the recovery with only the dominant $(2,\pm2)$ mode, adding the memory (result taken from Xu:2024ybt), and adding the full $(2,0)$ mode when the higher modes are neglected both in the injection and the recovery. This corresponds to Injection 5 with the modified sky location and trigger time. The black lines correspond to the injected parameter values.