Detecting gravitational-wave memory with LIGO: implications of GW150914

TL;DR

It is estimated that Advanced LIGO operating at design sensitivity may be able to make a signal-to-noise ratio 3 (5) detection of memory with ∼35 (90) events with masses and distance similar to GW150914.

Abstract

It may soon be possible for Advanced LIGO to detect hundreds of binary black hole mergers per year. We show how the accumulation of many such measurements will allow for the detection of gravitational-wave memory: a permanent displacement of spacetime that comes from strong-field, general relativistic effects. We estimate that Advanced LIGO operating at design sensitivity may be able to make a signal-to-noise ratio 3(5) detection of memory with ~35 (90) events with masses and distance similar to GW150914. We highlight the importance of incorporating higher-order gravitational-wave modes for parameter estimation of binary black hole mergers, and describe how our methods can also be used to detect higher-order modes themselves before Advanced LIGO reaches design sensitivity.

Figures (4)

• Figure 1: Gravitational-wave time series of the higher-order modes for an edge-on binary with parameters consistent with GW150914 abbott16_detectionabbott16_PE, where the vertical axis $\Delta h_{\ell m}$ is defined in Eqn. (\ref{['delta_strain']}). The red curve shows the $\Delta h_{22}$ mode, which is identically zero, implying the GW polarization angle $\psi$ and phase at coalescence $\phi_c$ are degenerate variables. The blue trace shows $\sum_\ell\sum_m\Delta h_{\ell m}$ for $\ell=2,3$ and all corresponding values of $\left|m\right|>0$. The fact that $\Delta h_{\ell m}\neq0$ implies that higher-order modes can be used to break the $\psi$ degeneracy and thus determine the sign of the memory.
• Figure 2: Gravitational-wave strain time series using parameters consistent with GW150914 abbott16_detectionabbott16_PE. The top panel shows the strain time series with GW memory (blue curve) and without (black). The bottom panel shows only the memory-induced strain series, where the blue curve uses the maximum likelihood parameters for GW150914 abbott16_detectionabbott16_PE. The red dotted and dashed curves are binaries at the same distance (410 Mpc) and with the same orientation ($\theta=140^\circ$), but equal mass binaries with $m_{1,2}=20\,M_\odot$ and $50\,M_\odot$ respectively (cf. $65\,M_\odot$ for the blue curve). Inset: the solid blue curve shows a zoomed-in version of the blue curve from the bottom panel, while the dashed curve is after a high-pass filter to show the signal visible in aLIGO.
• Figure 3: Evolution of the cumulative signal-to-noise $\left<\hbox{S/N}_{\rm tot}\right>$ as a function of the number of binary black hole mergers. All binaries have the same distance and mass as the maximum likelihood parameters of GW150914, but have random distributions of inclination, polarisation and sky position. In the top panel, the solid curves represent the expectation value and the shaded region is the one-sigma uncertainties. The blue curve sums the memory signal-to-noise contribution from all binaries, and the red curve assigns memory $\left<\hbox{S/N}\right>=0$ for those binaries where the polarisation angle, and hence the sign of the memory cannot be determined. The bottom panel shows 20 individual realisations of the red curve in the top panel. One particular realisation is highlighted in red; the binaries assigned $\left<\hbox{S/N}\right>=0$ are shown with blue crosses. In both panels, the horizontal dashed and solid lines show $\left<\hbox{S/N}_{\rm tot}\right>=3$ and $5$ respectively.
• Figure 4: Evolution of the cumulative Bayes factor as a function of the number of binary black hole mergers. All binaries have the same distance and mass as the maximum likelihood parameters of GW150914, but have random distributions of inclination, polarisation and sky position. The thick, solid curves represent the expectation value and the shaded region is the one-sigma uncertainties. The blue curve sums the memory signal-to-noise contribution from all binaries, and the red curve assigns memory $\left<\hbox{S/N}\right>=0$ for those binaries where the polarisation angle, and hence the sign of the memory cannot be determined. We also show in grey 10 individual realisations from the red curve.