Assessing the Impact of Instrumental Requirements on the Scientific Performance of the Einstein Telescope

Abstract

We investigate the relationship between instrumental requirements and the scientific performance of the Einstein Telescope (ET), a third-generation (3G) gravitational-wave (GW) observatory. Different technical design choices result in distinct noise budgets, ultimately shaping the detector's scientific capabilities. To systematically assess and compare their impact, we define a comprehensive set of performance metrics spanning compact binary coalescence (CBC) detection and parameter estimation, as well as other sources, including stochastic GW backgrounds, isolated spinning neutron stars, and core-collapse supernovae (CCSNe). We build a comparative reference framework that links degradations in specific noise contributions and frequency bands to losses in scientific capabilities. We consider a representative selection of technical parameters, such as coating and suspension temperatures, the filter cavity length in the low-frequency instrument, and the beam size in the high-frequency instrument. We evaluate how sensitivity variations across specific frequency bands affect different scientific objectives. We quantify how the sensitivity below 30 Hz impacts the detectability of massive and/or high-redshift sources and the reconstruction of long-duration CBC signals, affecting early warning and sky localization for binary neutron stars (BNSs). Sensitivity in the 30-450 Hz range governs most CBC parameter-estimation metrics, while high-frequency sensitivity above ~450 Hz predominantly impacts BNS post-merger studies and CCSN detectability, with modest effects on detection rates. Even with the most significant degradations considered, the ET science case remains robust overall. Our results provide a comprehensive benchmark linking scientific objectives to instrumental requirements, particularly important as the final design and infrastructure of 3G observatories are being defined.