Impact of the Einstein Telescope’s duty cycle on the estimation of binary black hole parameters

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-$\mathrm{\ensuremath{\Delta}}$) and two separated $\mathsf{L}$-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 modeled via continuous-time Markov chains and testing different detector maintenance strategies. We find that the redundancy inherent in the ET-$\mathrm{\ensuremath{\Delta}}$ 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-$\mathrm{\ensuremath{\Delta}}$ often outperforms ET-2L, and that the increased multidetector 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-$\mathrm{\ensuremath{\Delta}}$ than in ET-2L.