Impact of the Einstein Telescope's duty cycle on the estimation of binary black holes parameters

Author(s)

Negri, Luca, Ng, Thomas C.K., Wouters, Thibeau, Kuhlbusch, Tim J., Narola, Harsh, Chan, Robin, Doney, Kailib Ryan, Cireddu, Francesco, Wong, Isaac C.F., Gittins, Fabian, Pang, Peter T.H., Samajdar, Anuradha, Stahl, Achim, Janquart, Justin, Van Den Broeck, Chris, Li, Tjonnie G.F.

Abstract

The geometry of the Einstein Telescope, the proposed next-generation European gravitational-wave observatory, is yet to be finalized. Two competing designs are under consideration: a nested triangular configuration (ET-Δ) and two separated L-shaped detectors (ET-2L). Extensive prior comparisons of ET designs established the scientific landscape using the Fisher-information-matrix formalism and identified that duty-cycle-induced single-detector operation is precisely the regime where this approximation becomes less reliable, underscoring the need for a refined, principled treatment of the duty cycle. In this manuscript, we build on that foundation by revisiting the comparison with full Bayesian parameter estimation of gravitational-wave signals from binary black-hole mergers, projected onto a simulated Einstein Telescope that incorporates a refined duty cycle modelled via continuous-time Markov chains and testing different detector maintenance strategies. We find that the redundancy inherent in the ET-Δ design enables it to maintain at least two operational detectors for the majority of the observing time, whereas the ET-2L configuration is often limited to a single detector. Crucially, we show that, during partial network operation, ET-Δ often outperforms ET-2L, and that the increased multi-detector uptime translates into tighter constraints on the luminosity distance and source-frame component masses. Notably, this remains true even when gravitational-wave events have a lower signal-to-noise ratio in ET-Δ than in ET-2L.

Figures

Caption

Fractions of time spent by ET-2L and ET-$\Delta$ in specific detector configurations as a function of the uptime of a single detector. Both coincident and rotating maintenance strategies are considered for ET-$\Delta$. Maintenance time is always set to 10\%. ET-$\Delta$ with rotating maintenance allows for both the highest chance of having at least 2 detectors online and the lowest chance of no detectors observing. Assuming single detector uptimes comparable with the O3 average of 76\% , these percentages are 85\% and 3\% respectively.

Caption

Posterior distributions of the source-frame component masses $m_1^\text{source}$ and $m_2^\text{source}$, the luminosity distance $d_{L}$ and the sky position, comparing 2V online (from the ET-$\Delta$ configuration) against 1L online (in the ET-2L design). 90\% credible intervals are drawn. Although the 1L online configuration yields a higher SNR than the 2V online configuration, the most astrophysically relevant parameters are better constrained by the 2V due to an improved measurement of the luminosity distance.

Caption

Ratio of the $90\%$ highest density interval widths of the posteriors for source-frame masses plotted against SNR ratio between ET-$\Delta$ with $2$V online and ET-2L with $1$L online. Independent of SNR ratio, ET-2V outperforms ET-1L in 99.6\% of instances. ET-2V posteriors are on average 0.6 times as wide as ET-1L. Even if ET-1L imposes better constraints on the detector frame masses, this advantage is lost when looking at source frame masses, due to the improved accuracy in measuring redshift for ET-2V.

Caption

The efficiency of different \ac{ET} designs, defined by the duty-cycle-weighted uncertainty ratio (see Eq.~\ref{eq:efficiency}), as a function of the fractional uptime of a single detector, for luminosity distance and source-frame masses, both the rotational (rot) and coincident (coinc) maintenance schedules regarding for ET-$\Delta$. The uptimes of Hanford in O4a, Virgo in O2, and the overall O3 average offer a pessimistic, realistic, and optimistic projection, respectively. ET-$\Delta$ effciency is improved by implementing a rotating maintenance scheme, which was not explored in previous works. The configuration measures, on average, tighter confidence intervals than ET-2L for most of the parameter space explored , being outperformed only when ET-2L reaches average uptimes not yet achieved by any interferometer operational today.

Caption

\red{Comparison of the predicted duty cycle from our model, considering 70\% of uptime of interferometers, with 10\% of correlated maintenance and the rest of the downtime due to uncorrelated causes. Our model is able to predict up to a few percentage points LIGO O4a data. The discrepancies can be attributed to correlated unlocks of non-co-located detectors, like the ones due to strong earthquakes, which are not considered in our model.}

Caption

Comparison of results between GWfish and dynesty on the same injection for an ET 2V network and SNR of 28. While the width of the chirp mass posterior aligns with the nested sampling estimate, FIM fails to capture the complex correlation structure between the inclination angle and the luminosity distance, which leads to an overall overestimation of the latter.

Caption

All cornerplots overlayed for the 5 different configurations for the signal in Figure~\ref{fig: example single injection 2V vs 1L}. It is evident how the ET-2L posteriors widen as soon as 1 \red{detector} is lost, for source masses and distance, while for ET-$\Delta$, the posteriors with one detector offline are similar to the full configuration.

Caption

Full cornerplot for the signal in Figure~\ref{fig: example single injection 2V vs 1L}. While some intrinsic parameters are better constrained by ET-1L due to the higher SNR, other extrinsic parameters are better constrained by the ET-$2$V due to the better measurement of the polarization of the \ac{GW} signal.