Parameter estimation bias from overlapping binary black hole events in second generation interferometers

Since the initial detection of gravitational waves in 2015, over 50 candidate events have been reported by the LIGO-Virgo-KAGRA collaboration. As the current generation of detectors move toward their design sensitivity, the rate of these detections will increase. The next generation of detectors are likely to have high enough sensitivities that multiple merging binaries will be visible at the same time. In this paper we show that this is likely to happen before the end of the decade, during observations by the LIGO-Voyager detector. We investigate the situation of overlapping binary black hole (BBH) mergers in these detectors. We find that current parameter estimation techniques are capable of distinguishing the louder of two merging BBH events, without significant bias, when their merger times are not less than $\sim 0.1$ seconds apart or when the ratio of the signal-to-noise ratios of the systems is uneven. This region of overlapping parameter space is dependent upon the sky locations of the signals and the relation of those locations to the light travel time between detectors. We also find that, if two signals are highly overlapping, then the recovered set of parameters often show strong evidence of precession. Finally, we show that bias can occur even when the signal causing the bias is below the detection threshold.

Figure 1

Distribution of primary mass, red, secondary mass, blue, for BNS mergers.

Figure 2

Probability distribution for the likely number of BNS, blue, and BBH, red, mergers, that overlap that each event of that type in Einstein Telescope. The likely number of BBH events overlapping each BNS event is also presented in the green curve.

Figure 3

Recovered chirp mass posterior distributions. Posteriors labeled Signal A and Signal B are for data with a single signal injected at SNR 30. Signal B is injected with a relative merger time of $+0.025$ seconds and a chirp mass of $26.6{\mathrm{M}}_{\odot }$. The next five posteriors have the two signals injected with the same properties but with the SNR of Signal B varying from 5 to 30. Signal A is kept with an SNR of 30 in all runs. The two horizontal lines in blue and red show the injected values of the chirp mass for Signal A and Signal B respectively.

Figure 4

Recovered chirp mass posteriors. Posteriors labeled Signal A and Signal B are for data with a single signal injected at SNR 30. Signal B is injected with SNR 30 and a chirp mass of $24.1{\mathrm{M}}_{\odot }$. The next seven posteriors have the two signals injected with the same properties but with the relative merger time of the secondary varying. The two horizontal lines in blue and red show the injected values of the chirp mass for Signal A and Signal B respectively.

Figure 5

Recovered chirp mass posteriors. All runs are identical with Signal B of chirp mass $27.6{\mathrm{M}}_{\odot }$, relative merger time of $-0.025$ seconds and SNR 30. The overlapping signal posteriors differ due to the initial phase of Signal B, which was selected at random from a uniform distribution. The two horizontal lines in blue and red show the injected values of the chirp mass for Signal A and Signal B respectively.

Figure 6

A plot of posteriors for recovered mass ratio. Here Signal B has chirp mass $26.6{\mathrm{M}}_{\odot }$ relative merger time of $+0.025$ seconds compared to Signal A. The numerically labeled posteriors are at different injected SNRs of Signal B. Signal A has SNR 30 throughout. The two horizontal lines in blue and red show the injected values of the mass ratio for Signal A and Signal B respectively.

Figure 7

A plot of posteriors for recovered ${\chi }_p$. Here Signal B has chirp mass $26.6{\mathrm{M}}_{\odot }$ relative merger time of $+0.025$ seconds compared to Signal A. The numerically labeled posteriors are at different injected SNRs of Signal B. Signal A has SNR 30 throughout. The two horizontal lines in blue and red show the injected values of ${\chi }_p$ for Signal A and Signal B respectively.

Figure 8

Recovered Mass ratio posteriors for Signal B overlapping either 0.025 seconds before or after Signal A at a variety of initial phases, injected into a LIGO-Virgo network. Signal B was injected with an SNR of 25. The sky locations of the two systems of Signal A and Signal B were selected to maximize the travel time between the LIGO: Hanford and Virgo detectors. Stated relative merger times apply to the Hanford detector. The two horizontal lines in blue and red show the injected values of the mass ratio for Signal A and Signal B respectively.

Figure 9

Recovered luminosity distance posteriors for Signal B overlapping either 0.025 seconds before or after Signal A at a variety of initial phases, injected into a LIGO-Virgo network. Signal B was injected with an SNR of 25. The sky locations of the two systems of Signal A and Signal B were selected to maximize the travel time between the LIGO: Hanford and Virgo detectors. Stated relative merger times apply to the Hanford detector. The two horizontal lines in blue and red show the injected values of the luminosity distance for Signal A and Signal B respectively. The final horizontal line shows the injected luminosity distance for Signal B in the combined runs at the lower SNR.

Figure 10

Recovered mass ratio posteriors for Signal B overlapping either 0.025 seconds before or after Signal A at a variety of initial phases, injected into a LIGO-Virgo network. Signal B was injected with an SNR of 25. The sky locations of the two events are identical creating identical arrival times at all three detectors. The two horizontal lines in blue and red show the injected values of the mass ratio for Signal A and Signal B respectively.

Figure 11

Recovered luminosity distance posteriors for Signal B overlapping either 0.025 seconds before or after Signal A at a variety of initial phases, injected into a LIGO-Virgo network. Signal B was injected with an SNR of 25. The sky locations of the two events are identical creating identical arrival times at all three detectors. The two horizontal lines in blue and red show the injected values of the luminosity distance for Signal A and Signal B respectively. The final horizontal line, purple, shows the injected luminosity distance for Signal B in the combined runs at the lower SNR.

Figure 12

Recovered chirp mass posteriors for Signal B overlapping either 0.025 seconds after Signal A at a variety of different SNRs, injected into a LIGO-Virgo network. The values given for each posterior are the SNR of Signal B in the LIGO: Hanford detector. Signal A was injected with an SNR of 8. The two horizontal lines in blue and red show the injected values of the chirp mass for Signal A and Signal B respectively.

Figure 13

Recovered mass ratio posteriors for Signal B overlapping either 0.025 seconds before or after Signal A at a variety of initial phases, injected into a LIGO-Voyager network. These plots are for the equivalent runs in the aLIGO network, given in Fig. 10. The two horizontal lines in blue and red show the injected values of the mass ratio for Signal A and Signal B respectively.

Figure 14

Recovered luminosity distance posteriors for Signal B overlapping either 0.025 seconds before or after Signal A at a variety of initial phases, injected into a LIGO-Voyager network.These plots are for the equivalent runs in the aLIGO network, given in Fig. 11. The two horizontal lines in blue and red show the injected values of the luminosity distance for Signal A and Signal B respectively.