Astrophysical calibration of gravitational-wave detectors

We investigate a method to assess the validity of gravitational-wave detector calibration through the use of gamma-ray bursts as standard sirens. Such signals, as measured via gravitational-wave observations, provide an estimated luminosity distance that is subject to uncertainties in the calibration of the data. If a host galaxy is identified for a given source then its redshift can be combined with current knowledge of the cosmological parameters yielding the true luminosity distance. This will then allow a direct comparison with the estimated value and can validate the accuracy of the original calibration. We use simulations of individual detectable gravitational-wave signals from binary neutron star (BNS) or neutron star-black hole systems, which we assume to be found in coincidence with short gamma-ray bursts, to estimate any discrepancy in the overall scaling of the calibration for detectors in the Advanced LIGO and Advanced Virgo network. We find that the amplitude scaling of the calibration for the LIGO instruments could on average be confirmed to within $\sim 10\%$ for a BNS source within 100 Mpc. This result is largely independent of the current detector calibration method and gives an uncertainty that is competitive with that expected in the current calibration procedure. Confirmation of the calibration accuracy to within $\sim 20\%$ can be found with BNS sources out to $\sim 500\mathrm{Mpc}$.

Figure 1

The marginalized posterior probability distributions for some of the unknown parameters of a BNS system, including calibration scaling factors (surrounded by the thicker red borders) for the three detectors (H1, L1 and V1). The simulated signal was at a distance of 250 Mpc, had SNR of 7.9, 9.1 and 5.2 and percentage relative uncertainties in the calibration scale factors of 15%, 14% and 22% for each of the detectors respectively.

Figure 2

The marginalized posterior probability distributions for some of the unknown parameters of a NSBH system, including calibration scaling factors for the three detectors (H1, L1 and V1). The simulated signal was at a distance of 450 Mpc, had SNR of 9.7, 10.3 and 3.8 and percentage relative uncertainties in the calibration scale factors of 14%, 13% and 43% for each of the detectors respectively.

Figure 3

Distributions of the percentage accuracy at which the calibration scale factors can be determined for a three detector network using BNS systems (provided a coincident GRB is observed and can yield a distance estimate). The boxplots span the lower to upper quartile range of the distributions, with the median value shown as a horizontal line within the box and the mean shown as a white star. The dashed magenta line shows the percentage of sources drawn from the prior distribution that would be detectable at each distance value.

Figure 4

Distributions of the percentage accuracy at which the calibration scale factors can be determined for a three detector network if using NSBH systems (provided a coincident GRB is observed and can yield a distance estimate). The plot contents are the same as in Fig. 3.

Figure 5

Both figures show the cumulative fraction of true $\mathcal{C}$ values found within a given fractional credible interval versus the fractional credible interval for each detector for the BNS simulations at (a) 50 and (b) 500 Mpc. The grey shaded region is a 95% credible band for the expected deviations from diagonal.