Effect of calibration errors on Bayesian parameter estimation for gravitational wave signals from inspiral binary systems in the advanced detectors era

By 2015 the advanced versions of the gravitational-wave detectors Virgo and LIGO will be online. They will collect data in coincidence with enough sensitivity to potentially deliver multiple detections of gravitation waves from inspirals of compact-object binaries. This work is focused on understanding the effects introduced by uncertainties in the calibration of the interferometers. We consider plausible calibration errors based on estimates obtained during LIGO’s fifth and Virgo’s third science runs, which include frequency-dependent amplitude errors of $\sim 10\%$ and frequency-dependent phase errors of $\sim 3\mathrm{degrees}$ in each instrument. We quantify the consequences of such errors estimating the parameters of inspiraling binaries. We find that the systematics introduced by calibration errors on the inferred values of the chirp mass and mass ratio are smaller than 20% of the statistical measurement uncertainties in parameter estimation for 90% of signals in our mock catalog. Meanwhile, the calibration-induced systematics in the inferred sky location of the signal are smaller than $\sim 50\%$ of the statistical uncertainty. We thus conclude that calibration-induced errors at this level are not a significant detriment to accurate parameter estimation.

Figure 1

A schematic representation of the IFO with the subsystems described in the text.

Figure 2

The high-power, zero-detuning noise curve for Advanced LIGO (red continuous line), and the BNS-optimized Advanced Virgo noise curve (blue dashed).

Figure 3

The first CE realization for the amplitude (top) and phase (bottom).

Figure 4

The distribution of ${\Sigma }^{\mathcal{M}}$ for the signal in the BHNS catalog, using the first CE realization. The vertical blue line correspond to a null shift.

Figure 5

The distribution of ${\Sigma }^D$ for the signals in the BHNS catalog, using the first CE realization. The vertical blue line correspond to a null shift.

Figure 6

${\Sigma }^{\mathcal{M}}$ for the signal in the BHNS catalog, using the first CE realization, plotted against the SNR. The fact that the spread does not increase with the SNR implies that the net bias ${\underline{\theta }}_m^{\mathcal{M}}-{\underline{\theta }}_e^{\mathcal{M}}$ decreases with the SNR.

Figure 7

The median of $\Sigma$ averaged among the 10 CE realizations. The lower end of the error bars corresponds to the lowest 5th percentile encountered in the various CE runs, while the upper end corresponds to the highest 95th percentile. We do not show $\psi$ and ${\varphi }_0$ as those parameters are very poorly estimated. The upper panel refers to the BNS catalog, the middle one to the BHNS and the bottom one to the BBH catalog.

Figure 8

The median of $\sigma$ (introduced in the main text) when using the various CE curves (shown in the abscissa label) and the three mass bins (from the top to the bottom: BNS, BHNS, BBH). The error bars show the 5th and 95th percentiles. Note that the ordinate scale varies in the subplots.

Figure 9

The difference in log Bayes factor between the exact run and the average of the runs with calibration errors. The values in the colorbar correspond to the ${\mathrm{BSN}}_e$ produced by the injections. Generally, louder signals are affected by larger shifts.

Figure 10

Mean of ${\Sigma }^{\eta }$ with the various CE realizations for the BHNS catalog.

Figure 11

Mean of ${\Sigma }^{\mathrm{RA}}$ with the various CE realizations for the BHNS catalog.

Figure 12

Mean of ${\Sigma }^D$ with the various CE realizations for the BHNS catalog.

Figure 13

The second CE realization for the amplitude (top) and phase (bottom).

Figure 14

The third CE realization for the amplitude (top) and phase (bottom).

Figure 15

The fourth CE realization for the amplitude (top) and phase (bottom).

Figure 16

The fifth CE realization for the amplitude (top) and phase (bottom).

Figure 17

The sixth CE realization for the amplitude (top) and phase (bottom).

Figure 18

The seventh CE realization for the amplitude (top) and phase (bottom).

Figure 19

The height CE realization for the amplitude (top) and phase (bottom).

Figure 20

The ninth CE realization for the amplitude (top) and phase (bottom).

Figure 21

The tenth CE realization for the amplitude (top) and phase (bottom).