Tests of general relativity with GW150914

TL;DR

GW150914 enables tests of general relativity in the strong-field, dynamical regime of a binary black-hole merger. The authors employ two independent IMR waveform families (EOBNR and IMRPhenom) and parameterized GR-deviation frameworks to examine waveform phasing, remnant properties, QNM content, and GW dispersion. Across residual analyses, IMR consistency, QNM searches, and dispersion bounds, they find no statistically significant GR violations, establishing a 90% CL lower bound on the graviton Compton wavelength of 10^13 km. The study demonstrates GR’s validity in genuine strong-field gravity and outlines a path for tighter constraints with future louder detections and a broader detector network.

Abstract

The LIGO detection of GW150914 provides an unprecedented opportunity to study the two-body motion of a compact-object binary in the large velocity, highly nonlinear regime, and to witness the final merger of the binary and the excitation of uniquely relativistic modes of the gravitational field. We carry out several investigations to determine whether GW150914 is consistent with a binary black-hole merger in general relativity. We find that the final remnant's mass and spin, as determined from the low-frequency (inspiral) and high-frequency (post-inspiral) phases of the signal, are mutually consistent with the binary black-hole solution in general relativity. Furthermore, the data following the peak of GW150914 are consistent with the least-damped quasi-normal mode inferred from the mass and spin of the remnant black hole. By using waveform models that allow for parameterized general-relativity violations during the inspiral and merger phases, we perform quantitative tests on the gravitational-wave phase in the dynamical regime and we determine the first empirical bounds on several high-order post-Newtonian coefficients. We constrain the graviton Compton wavelength, assuming that gravitons are dispersed in vacuum in the same way as particles with mass, obtaining a $90\%$-confidence lower bound of $10^{13}$ km. In conclusion, within our statistical uncertainties, we find no evidence for violations of general relativity in the genuinely strong-field regime of gravity.

Figures (8)

• Figure 1: Upper panel: cumulative distribution function (CDF) of $\log$ Bayes factor -- the logarithm of the ratio of Bayesian evidences between two competing models -- for the signal-versus-noise and signal-versus-glitch BayesWave models, computed for 100 4-s stretches of data around GW150914. Lower Panel: cumulative distribution function (CDF) of the 95% credible upper bound on network coherent-burst SNR, denoted SNR$_{95}$, again computed for 100 instrument-noise segments. In both panels, we indicate with dashed lines the $\log$ Bayes factors and upper bound on coherent-burst SNR corresponding to the residuals obtained after subtracting the most probable waveform from GW150914.
• Figure 2: MAP estimate and 90% credible regions for the waveform (upper panel) and GW frequency (lower panel) of GW150914 as estimated by the LALInference analysis GW150914-PARAMESTIM. The solid lines in each panel indicate the most probable waveform from GW150914 GW150914-PARAMESTIM and its GW frequency. We mark with a vertical line the instantaneous frequency $f_{\rm GW}^{\rm end \,insp} = 132$ Hz, which is used in the IMR consistency test to delineate the boundary between the frequency-domain inspiral and post-inspiral parts (see Fig. \ref{['fig:regions']} below for a representation of the most probable waveform's amplitude in frequency domain).
• Figure 3: Frequency regions of the parameterized waveform model as defined in the text and in Ref. Khan:2015jqa. The plot shows the absolute value of the frequency-domain amplitude of the most-probable waveform from GW150914 GW150914-PARAMESTIM. The inspiral region (cyan) from 20 Hz to $\sim$55 Hz corresponds to the early and late inspiral regimes. The intermediate region (red) goes from $\sim$ 55 Hz to $\sim$ 130 Hz. Finally, the merger--ringdown region (orange) goes from $\sim$ 130 Hz to the end of the waveform.
• Figure 4: Top panel: 90% credible regions in the joint posterior distributions for the mass $M_f$ and dimensionless spin $a_f$ of the final compact object as determined from the inspiral (dark violet, dashed) and post-inspiral (violet, dot-dashed) signals, and from a full inspiral--merger--ringdown analysis (black). Bottom panel: Posterior distributions for the parameters $\Delta M_f/M_f$ and $\Delta a_f/a_f$ that describe the fractional difference in the estimates of the final mass and spin from inspiral and post-inspiral signals. The contour shows the $90\%$ confidence region. The plus symbol indicates the expected GR value $(0,0)$.
• Figure 5: $90\%$ credible regions in the joint posterior distributions for the damped-sinusoid parameters $f_0$ and $\tau$ (see main text), assuming start times $t_0 = t_M + 1,3,5,6.5$ ms, where $t_M$ is the merger time of the MAP waveform for GW150914. The black solid line shows the $90\%$ credible region for the frequency and decay time of the $\ell =2$, $m=2$, $n=0$ (i.e., the least damped) QNM, as derived from the posterior distributions of the remnant mass and spin parameters.