Gravitational-wave astronomy with a physical calibration model

We carry out astrophysical inference for compact binary merger events in LIGO-Virgo’s first gravitational-wave transient catalog (GWTC-1) using a physically motivated calibration model. We demonstrate that importance sampling can be used to reduce the cost of what would otherwise be a computationally challenging analysis for signal-to-noise ratios of current gravitational-wave detections. We show that including the physical estimate for the calibration error distribution has negligible impact on the inference of parameters for the events in GWTC-1. Studying a simulated signal with matched filter signal-to-noise ratio $\mathrm{SNR}=200$, we project that a calibration error estimate typical of GWTC-1 is likely to be negligible for the current generation of gravitational-wave detectors. We argue that other sources of systematic error—from waveforms, prior distributions, and noise modeling—are likely to be more important. Finally, using the events in GWTC-1 as standard sirens, we infer an astrophysically informed improvement on the estimate of the calibration error in the LIGO interferometers.

Figure 1

Posterior distributions for an $\mathrm{SNR}=200$ GW150914-like event. The top panels show astrophysical parameters. The different shaded regions are $1\sigma$, $2\sigma$, and $3\sigma$ credible intervals. The red contours include the calibration error estimate while the blue contours do not. The black lines correspond to the injected properties of the source. The bottom panels show the reconstructed response function $R$. The red curves show the response curves averaged over calibration hyperparameters. The green curves show the response functions averaged over prior samples. The 95% credible intervals are indicated with translucent shading. The inclusion of the calibration envelope broadens the majority of astrophysical parameters by a modest amount. The sky localization of the event broadens noticeably with the inclusion of calibration error distribution, expanding by a factor of $\approx 2$ in a solid angle. This indicates the possibility that even for the loudest events observed, the calibration error estimate may not play a major role in the inferences made about the intrinsic properties of the source. It is interesting to note that constraining calibration model parameters at lower frequencies where the gravitational-wave signal is detected can inform the calibration model at higher frequencies where no signal is present.

Figure 2

Posterior distributions for GW170608. The top panels show astrophysical parameters. The different shaded regions are $1\sigma ,2\sigma$, and $3\sigma$ credible intervals. The red contours include the calibration error estimate while the blue contours do not. The inclusion of uncertainty in the calibration error leads to only marginal changes. The bottom panels show the reconstructed response function $R$. The red curves show the response curves averaged over calibration hyperparameters. The green curves show the response functions averaged over prior samples. The 95% credible intervals are indicated with translucent shading. The data are marginally informative about the calibration parameters.

Figure 3

Calibration response curve posterior distributions for both LIGO detectors informed by all events during the second observing run evaluated at the time of GW170729. Marginal shifts in the calibration error distributions are observed. The Bayes factor marginally favors the inclusion of the calibration error distribution over the zero-error hypothesis by 2.33.