Constraining unmodeled physics with compact binary mergers from GWTC-1

We present a flexible model to describe the effects of generic deviations of observed gravitational-wave signals from modeled waveforms in the LIGO and Virgo gravitational-wave detectors. With the detection of 11 gravitational-wave events from the GWTC-1 catalog, we are able to constrain possible deviations from our modeled waveforms. In this paper, we present our coherent spline model that describes the deviations, then choose to validate our model on an example phenomenological and astrophysically motivated departure in waveforms based on extreme spontaneous scalarization. We find that the model is capable of recovering the simulated deviations. By performing model comparisons, we observe that the spline model effectively describes the simulated departures better than a normal compact binary coalescence (CBC) model. We analyze the entire GWTC-1 catalog of events with our model and compare it to a normal CBC model, finding that there are no significant departures from the modeled template gravitational waveforms used.

Figure 1

Simulated phase deviation $\delta \varphi$ for extreme spontaneous scalaraization toy model.

Figure 2

Simulated amplitude deviation $\delta A$ for extreme spontaneous scalaraization toy model.

Figure 3

Corner plots showing the one- and two-dimensional marginalized posterior distributions for simulated parameters for PE runs on the unmodified signal with spline model on (purple) or off (pink). This demonstrates the impact of the model flexibility on astrophysical parameter uncertainties.

Figure 4

Corner plots showing the one- and two-dimensional marginalized posterior distributions for simulated parameters for PE runs on the modified signal with spline model on (purple) or off (pink). This demonstrates inaccuracies in parameter estimation performed on signals containing deviations from the physically modeled waveforms.

Figure 5

Spline interpolation of unmodified (left) and modified (right) signal deviations. One and two $\sigma$ credible intervals (gray) and the median spline (red) are shown with top panel the amplitude deviations and middle panel the phase deviations. In the bottom frame, we plot the node position posterior distributions, which you can see clump toward the frequency of deviations in the modified case in the bottom right most panel, while they are more uniformly distributed for the unmodified case as they are exploring the prior.

Figure 6

Posterior quantile of the spline interpolant that 0-deviation corresponds to for the simulated unmodified (pink) and modified (purple) signals.

Figure 7

The DIC value from spline-model-off run minus spline-on run for different simulated phase deviations. Green shaded regions are where the spline model is preferred, and the red shaded region is where the spline model off is preferred.

Figure 8

Spline interpolation of GW170823 with 1 and $2\sigma$ credible intervals (gray) and the median spline interpolant (red) shown.

Figure 9

Spline interpolation of GW170729 with 1 and $2\sigma$ credible intervals (gray) and the median spline interpolant (red) shown.

Figure 10

Spline interpolation of GW170729 with $1\sigma$ percent credible intervals shown, comparing runs on GW170729 with calibration turned on/off and using a HOM waveform also with calibration turned off.

Figure 11

Quantile of spline interpolation that 0-deviation corresponds to for GWTC-1 events. (Different choices of $f_{\mathrm{low}}$ and sampling rates were chosen for some events.)

Figure 12

Spline interpolation of GW170817 with 1 and $2\sigma$ credible intervals (gray) and the median spline interpolant (red) shown.

Figure 13

DIC of spline model-off run minus DIC of spline model-on run for GWTC-1 events and simulated signals. Simulated modified signals are denoted with the magnitude of phase deviation jump in degrees. Negative values correspond to spline model disfavored, while positive values show the spline model favored.

Figure 14

DIC of spline-model-off run minus DIC of spline-model-on run for GWTC-1 events and simulated signals. DICs in this plot are calculated with half of the variance degree of freedom penalty term. Simulated modified signals are denoted with the magnitude of phase deviation jump in degrees. Negative values correspond to spline model disfavored, while positive values show the spline model favored.