Enhancing gravitational-wave burst detection confidence in expanded detector networks with the BayesWave pipeline

The global gravitational-wave detector network achieves higher detection rates, better parameter estimates, and more accurate sky localisation, as the number of detectors, $\mathcal{I}$ increases. This paper quantifies network performance as a function of $\mathcal{I}$ for BayesWave, a source-agnostic, wavelet-based, Bayesian algorithm which distinguishes between true astrophysical signals and instrumental glitches. Detection confidence is quantified using the signal-to-glitch Bayes factor, $\mathcal{B}_{\mathcal{S},\mathcal{G}}$. An analytic scaling is derived for $\mathcal{B}_{\mathcal{S},\mathcal{G}}$ versus $\mathcal{I}$, the number of wavelets, and the network signal-to-noise ratio, SNR$_\text{net}$, which is confirmed empirically via injections into detector noise of the Hanford-Livingston (HL), Hanford-Livingston-Virgo (HLV), and Hanford-Livingston-KAGRA-Virgo (HLKV) networks at projected sensitivities for the fourth observing run (O4). The empirical and analytic scalings are consistent; $\mathcal{B}_{\mathcal{S},\mathcal{G}}$ increases with $\mathcal{I}$. The accuracy of waveform reconstruction is quantified using the overlap between injected and recovered waveform, $\mathcal{O}_\text{net}$. The HLV and HLKV network recovers $87\%$ and $86\%$ of the injected waveforms with $\mathcal{O}_\text{net}>0.8$ respectively, compared to $81\%$ with the HL network. The accuracy of BayesWave sky localisation is $\approx 10$ times better for the HLV network than the HL network, as measured by the search area, $\mathcal{A}$, and the sky areas contained within $50\%$ and $90\%$ confidence intervals. Marginal improvement in sky localisation is also observed with the addition of KAGRA.