Measuring the speed of gravitational waves from the first and second observing run of Advanced LIGO and Advanced Virgo

The speed of gravitational waves for a single observation can be measured by the time delay among gravitational-wave detectors with Bayesian inference. Then multiple measurements can be combined to produce a more accurate result. From the near simultaneous detection of gravitational waves and gamma rays originating from GW170817/GRB 170817A, the speed of gravitational wave signal was found to be the same as the speed of the gamma rays to approximately one part in ${10}^{15}$. Here we present a different method of measuring the speed of gravitational waves, not based on an associated electromagnetic signal but instead by the measured transit time across a geographically separated network of detectors. While this method is far less precise, it provides an independent measurement of the speed of gravitational waves. For GW170817, a binary neutron star inspiral observed by Advanced LIGO and Advanced Virgo, by fixing sky localization of the source at the electromagnetic counterpart the speed of gravitational waves is constrained to 90% confidence interval (0.97c, 1.02c), where c is the speed of light in a vacuum. By combing ten binary black hole (BBH) events and the binary neutron star event from the first and second observing runs of Advanced LIGO and Advanced Virgo, the 90% confidence interval is narrowed down to (0.97c, 1.01c). The accurate measurement of the speed of gravitational waves allows us to test the general theory of relativity. We further interpret these results within the test framework provided by the gravitational standard-model extension (SME). In doing so, we obtain simultaneous constraints on four of the nine nonbirefringent, nondispersive coefficients for Lorentz violation in the gravity sector of the SME and place limits on the anisotropy of the speed of gravity.

Figure 1

Marginalized posterior distributions of $v_g$ for GW170817. The solid line is obtained from the run with fixing $\alpha$ and $\delta$ at the electromagnetic counterpart, whereas the dashed line obtained from the run without fixing $\alpha$ and $\delta$.

Figure 2

Posterior distributions of $v_g$ for ten BBH events: GW150914, GW151012, GW151226, GW170104, GW170608, GW170729, GW170809, GW170814, GW170818, GW170823, and combined posterior. The combined posterior is computed using Eq. (7).

Figure 3

Posterior distributions of $v_g$ for ten BBH and a BNS detected in O1 and O2: GW150914, GW151012, GW151226, GW170104, GW170608, GW170729, GW170809, GW170814, GW170817, GW170818, GW170823, and combined posterior. For GW170817, $\alpha$ and $\delta$ are free parameters in the top plot, in the bottom plot $\alpha$ and $\delta$ are fixed at the electromagnetic counterpart.

Figure 4

The 90% confidence regions for the sky localizations of all GW events detected in O1 and O2. The solid contours are obtained from the posteriors where the speed of gravitational waves is fixed at the speed of light, and the dashed contours show the results for $v_g$ as a free parameter. Top: events detected by Advanced LIGO and Advanced Virgo (GW170729, GW170809, GW170814, GW170817, GW170818); middle: events detected by the two Advanced LIGO detectors in O2 (GW170104, GW170608, GW170823); bottom: events detected in O1 (GW150914, GW151012, GW151226).

Figure 5

The distribution of ${\overline{s}}_{jm}$ values implied by the events listed on lines 2, 5, 6, and 8 of Table 1. Numbers above the plots show best values with a one sigma range.

Figure 6

The distribution of ${\overline{s}}_{jm}$ values implied by the events listed on lines 2, 5, 7, and 8 of Table 1. That is, relative to Fig. 5, the sky position of GW170817 is fixed. Numbers above the plots show best values with a one sigma range.