Tests of general relativity with the binary black hole signals from the LIGO-Virgo catalog GWTC-1

The detection of gravitational waves by Advanced LIGO and Advanced Virgo provides an opportunity to test general relativity in a regime that is inaccessible to traditional astronomical observations and laboratory tests. We present four tests of the consistency of the data with binary black hole gravitational waveforms predicted by general relativity. One test subtracts the best-fit waveform from the data and checks the consistency of the residual with detector noise. The second test checks the consistency of the low- and high-frequency parts of the observed signals. The third test checks that phenomenological deviations introduced in the waveform model (including in the post-Newtonian coefficients) are consistent with 0. The fourth test constrains modifications to the propagation of gravitational waves due to a modified dispersion relation, including that from a massive graviton. We present results both for individual events and also results obtained by combining together particularly strong events from the first and second observing runs of Advanced LIGO and Advanced Virgo, as collected in the catalog GWTC-1. We do not find any inconsistency of the data with the predictions of general relativity and improve our previously presented combined constraints by factors of 1.1 to 2.5. In particular, we bound the mass of the graviton to be $m_g\le 4.7\times {10}^{-23}\mathrm{eV}/c^2$ (90% credible level), an improvement of a factor of 1.6 over our previously presented results. Additionally, we check that the four gravitational-wave events published for the first time in GWTC-1 do not lead to stronger constraints on alternative polarizations than those published previously.

Figure 1

Survival function ($p=1-\mathrm{CDF}$) of the 90% credible upper limit on the network SNR (${\mathrm{SNR}}_{90}$) for each event (solid or dashed curves), compared to the measured residual values (vertical dotted lines). For each event, the value of the survival function at the measured ${\mathrm{SNR}}_{90}$ gives the $p$-value reported in Table 2 (markers). The colored bands correspond to uncertainty regions for a Poisson process and have half width $\pm p/\sqrt{N}$, with $N$ being the number of noise-only instantiations that yielded ${\mathrm{SNR}}_{90}^{\mathrm{n}}$ greater than the abscissa value.

Figure 2

Results of the inspiral-merger-ringdown consistency test for the selected binary black hole events (see Table 1). The main panel shows 90% credible regions of the posterior distributions of $(\mathrm{\Delta }{M}_{\mathrm{f}}/{\overline{M}}_{\mathrm{f}},\mathrm{\Delta }{a}_{\mathrm{f}}/{\overline{a}}_{\mathrm{f}})$, with the cross marking the expected value for GR. The side panels show the marginalized posteriors for $\mathrm{\Delta }{M}_{\mathrm{f}}/{\overline{M}}_{\mathrm{f}}$ and $\mathrm{\Delta }{a}_{\mathrm{f}}/{\overline{a}}_{\mathrm{f}}$. The thin black dashed curve represents the prior distribution, and the grey shaded areas correspond to the combined posteriors from the five most significant events (as outlined in Sec. 3 and Table 1).

Figure 3

Combined posteriors for parametrized violations of GR, obtained from all events in Table 1 with a significance of $\mathrm{FAR}<{(1000\text{yr})}^{-1}$ in both modeled searches. The horizontal lines indicate the 90% credible intervals, and the dashed horizontal line at 0 corresponds to the expected GR values. The combined posteriors on ${\phi }_i$ in the inspiral regime are obtained from the events which in addition exceed the SNR threshold in the inspiral regime (GW150914, GW151226, GW170104, GW170608, and GW170814), analyzed with imrphenompv2 (grey shaded region) and seobnrv4 (black outline). The combined posteriors on the intermediate and merger-ringdown parameters ${\beta }_i$ and ${\alpha }_i$ are obtained from events which exceed the SNR threshold in the postinspiral regime (GW150914, GW170104, GW170608, GW170809, GW170814, and GW170823), analyzed with imrphenompv2.

Figure 4

90% upper bounds on the absolute magnitude of the GR-violating parameters $\delta {\widehat{\phi }}_n$, from $-1$ through 3.5 PN in the inspiral phase. At each PN order, we show results obtained from each of the events listed in Table 1 that cross the SNR threshold in the inspiral regime, analyzed with imrphenompv2. Bounds obtained from combining posteriors of events detected with a significance that exceeds a threshold of $\mathrm{FAR}<{(1000\text{yr})}^{-1}$ in both modeled searches are shown for both analyses, using imrphenompv2 (filled diamonds) and seobnrv4 (empty diamonds).

Figure 5

90% credible upper bounds on the absolute value of the modified dispersion relation parameter $A_{\alpha }$. We show results for positive and negative values of $A_{\alpha }$ separately. Specifically, we give the updated versions of the results from combining together GW150914, GW151226, and GW170104 (first given in [6]), as well as the results from combining together all the events meeting our significance threshold for combined results (see Table 1). Picoelectronvolts (peV) provide a convenient scale, because $1\mathrm{peV}\simeq h\times 250\mathrm{Hz}$, where 250 Hz is roughly around the most sensitive frequencies of the LIGO and Virgo instruments.

Figure 6

Violin plots of the full posteriors on the modified dispersion relation parameter $A_{\alpha }$ calculated from the combined events, with the 90% credible interval around the median indicated.

Figure 7

Same as Fig. 2, except that the posteriors are computed using the nonprecessing-spin seobnrv4 waveforms.

Figure 8

Violin plots showing inspiral $\delta {\widehat{p}}_i$ posteriors for the individual binary black hole events of GWTC-1 [14] outlined in Sec. 3 (see the PI column of Table 1), using imrphenompv2 (shaded regions) and seobnrv4 (black solid lines). Thin horizontal lines indicate the 90% credible intervals, which show an overall statistical consistency with GR (dashed grey line).

Figure 9

Violin plots showing postinspiral $\delta {\widehat{p}}_i$ posteriors for the individual binary black hole events of GWTC-1 [14] outlined in Sec. 3 (see the PPI column of Table 1), using imrphenompv2. Thin horizontal lines indicate the 90% credible intervals, which show an overall statistical consistency with GR (dashed grey line).

Figure 10

Violin plots of the full posteriors for the modified dispersion relation parameter $A_{\alpha }$ for the individual binary black hole events of GWTC-1 [14], with the 90% credible interval around the median indicated. The events are ordered left to right by increasing median total mass. The filled violins are the imrphenompv2 results, while the unfilled violins give the seobnrv4 results for GW170729 and GW170814. Here ${\tilde{A}}_{\alpha }≔A_{\alpha }/({10}^{-19}{\mathrm{peV}}^{2-\alpha })$. We have let the much less constraining posteriors extend off the edges of the plots in order to show the more constraining posteriors in detail. The violin plots are scaled so that the maximum value of the posterior always has the same width, and these maximum values never occur off the plot.