A stepping stone toward detecting gravitational wave memory: a cumulative analysis with the full $(\ell=2, m=0)$ spherical harmonic using events from GWTC-4.0 and GWTC-5.0

Abstract

We perform Bayesian model selection to test for the presence of the $(\ell=2,m=0)$ spherical harmonic mode in gravitational wave events that have previously been identified as binary black hole mergers. As our signal model we use the quasi-circular, non-precessing IMRPhenomTHM_20 waveform model, which includes the oscillatory and displacement memory contributions. Including the oscillatory component of the (2,0) mode increases the signal-to-noise ratio and evidence for this mode, compared to testing only for the presence of gravitational wave memory. Our analysis thus constitutes a natural stepping stone toward detecting gravitational wave memory. We perform our analysis for the binary black hole signals identified in the GWTC-4.0 catalog, and for selected GWTC-5.0 events. In our Bayesian model comparison we find a cumulative $\log_{10}\mathcal{B}=1.38\pm0.79$ in favor of the presence of the (2,0) mode for the GWTC-4.0 catalog. We also stack the signal-to-noise ratio of the full (2,0) mode and of its individual contributions, obtaining results consistent with previous studies and reaching $\mathrm{SNR}_{\mathrm{memory}} = 0.89^{+0.29}_{-0.11}$ after approximately 7.5 months of O4a observations. In addition, we study the precessing candidate GW241127_061008, and find no additional evidence for the (2,0) mode when precession is included in IMRPhenomTPHM_20. Overall, our results provide an assessment of the observational support for the (2,0) mode in current gravitational wave data and allow us to discuss prospects for its future detection. We find that decisive statistical evidence will likely require a larger catalog, with an optimistic estimated number of events of $N_{\mathrm{events}} = 166^{+82}_{-55}$, based on the specific assumptions adopted in this work. We also expect that decisive evidence will require a more extensive waveform systematics study.