Impact of site-dependent noise configurations on Einstein Telescope science at low frequency

The gist The achievable low-frequency sensitivity can have a significant impact on ET science, and preserving the best possible sensitivity below approximately 10 Hz is essential for realizing the distinctive scientific potential of ET.

Detector Networks and Noise Configurations

The study investigates how site-dependent Newtonian noise configurations affect the scientific performance of the Einstein Telescope (ET) by comparing baseline triangular and 2L detector geometries under three representative site-dependent noise scenarios from the Euregio Meuse-Rhine region, Lausitz, and Sardinia The differences among the adopted sensitivities are concentrated mainly below 10 Hz and therefore have the greatest impact on science cases that rely on the early inspiral of light objects, or on massive systems whose characteristic frequencies lie in the low-frequency band Within the configurations considered here, a 2L network in which at least one of the two L-shaped interferometers attains a noise level comparable to that assumed for the Sardinian site generally provides better performance than the triangular configurations.

Impact on Scientific Science Cases

The paper quantifies these effects for four representative ET science cases, including (1) detection and parameter estimation of intermediate-mass black-hole binaries, (2) post-Newtonian tests of General Relativity based on the early inspiral, (3) black-hole ringdown spectroscopy with massive remnants, and (4) early-warning and sky-localization capabilities for binary neutron star mergers. Using Bayesian parameter estimation, the findings indicate that improved low-frequency sensitivity can significantly enhance ET’s scientific performance across all four cases. For intermediate-mass or high-redshift BH binaries, the improved low-frequency sensitivity associated with the Sardinia site leads to an SNR enhancement reaching approximately a factor of 2 in the most favorable part of the mass range.

Performance Comparison Across Geometries and Sites

The comparison between 10-km triangular and 15-km 2L layouts cannot be made independently of the low-frequency sensitivity actually achievable at the selected sites. The “2L LF Lausitz” configuration shows that the advantage associated with the longer arms can be substantially reduced when the sensitivity below approximately 10 Hz diminishes. For binary NS early-warning and sky-localization, the nominal 2L network provides the longest warning time over the full range of thresholds considered, although at lower thresholds – 23.

Constraints on General Relativity Tests

In parametrized tests of GR, the comparison among detector configurations confirms that preserving the best possible low-frequency sensitivity produces the largest scientific gain for negative-PN tests. The relative separation among the configurations is largest for most negative PN orders, for which most of the constraining power comes from the lowest-frequency portion of the signal.

Black Hole Spectroscopy and Binary Neutron Stars

For black hole spectroscopy of intermediate-mass remnants, the Sardinia triangle provides substantially tighter constraints on the frequency and damping time of the subdominant mode than the TERZ and Lausitz triangles when source-frame masses are large. For binary NS mergers, sensitivity at a few Hz determines how early a source can be identified and how long Earth rotation can modulate the detector response before merger. The Sardinia triangle and the site-dependent 2L network provide warning times of several hours, approximately twice those obtained for the TERZ and Lausitz triangles over a broad range of detection thresholds.

Conclusion on Site Selection

The results support one robust conclusion: preserving the best possible sensitivity below approximately 10 Hz is essential for realizing the distinctive scientific potential of ET. The advantage of longer arms or of a particular detector geometry cannot be assessed independently of the noise that can realistically be achieved at the selected sites. Continued site characterization, realistic end-to-end noise simulations, and science studies including correlated and non-Gaussian noise will therefore be crucial for translating the ET design choices into a reliable assessment of its ultimate scientific performance.

How it works

The strain-noise amplitude spectral densities (ASDs) adopted in this work are constructed by removing the nominal low-frequency Newtonian noise contribution from the reference ET noise budget and replacing it with the local seismic body-wave Newtonian-noise estimate. The Newtonian noise strain ASD is estimated as ehNN(f) = 4π/3Gρ02√2Lxe(f)(2πf)2. This estimate assumes a spherical cavern in an infinite homogeneous medium, an isotropic body-wave field, one third of the body-wave contribution arising from compressional waves, negligible surface-wave contributions at the detector depth, and uncorrelated Newtonian noise between the test masses.

Detector Geometries and Coordinates

The analysis considers two detector geometries: a triangular configuration consisting of three nested 60◦ interferometers with 10 km arms at a single site, and a 2L configuration consisting of two geographically separated 90◦ interferometers with 15 km arms. The geographical locations and detector orientations used in the analysis are shown in Fig. 2. For each candidate site, a representative triangular configuration is constructed using the site-specific noise curves.

Methods for Parameter Estimation

The Bayesian inference framework adopted involves estimating the posterior probability distribution p(θ s) of a set of source parameters θ conditioned on the observed strain data s(t) = h(t, θ) + n(t). The likelihood factorizes into contributions from individual instruments via L(s θ) ∝ exp −1/2 X k∈detectors hk(θ) − sk hk(θ) − sk k, where Sn,k(f) is the one-sided noise power spectral density of the k-th detector. The prior π(θ) encodes the information available about the source parameters before analyzing the data.

Analysis of Science Cases

The paper performs controlled comparisons among selected triangular and 2L configurations, using Bayesian inference to estimate measurement errors on waveform parameters for intermediate-mass BH binaries, parametrized tests of GR based on the early inspiral, black hole spectroscopy, and binary NS early warning. The results are interpreted primarily as relative measures of the sensitivity of each scientific observable to the assumed low-frequency noise rather than as exhaustive forecasts of ET performance.

Results for Intermediate-Mass Binaries

At larger masses, an increasing fraction of the signal shifts into the low-frequency band, and the improved low-frequency sensitivity associated with the Sardinia site leads to an SNR enhancement reaching approximately a factor of 2 in the most favorable part of the mass range. The “2L LF Lausitz” configuration shows that the advantage associated with the longer arms can be substantially reduced when the sensitivity below approximately 10 Hz diminishes.

Results for Parametrized Tests of GR

The most prominent feature in constraints on parametrized deviations in the inspiral phase is the strong dependence of the constraints on PN order, with negative-PN corrections being constrained much more tightly than non-negative-PN terms. The relative separation among the configurations is largest for most negative PN orders, for which most of the constraining power comes from the lowest-frequency portion of the signal.

Results for Black Hole Spectroscopy

For sufficiently massive remnants, the frequencies of the dominant and subdominant QNMs shift toward the low-frequency edge of the detector band, where site-dependent noise becomes increasingly important. In this regime, the Sardinia triangle provides substantially tighter constraints on the frequency and damping time of the subdominant mode than the TERZ and Lausitz triangles.

Results for Binary Neutron Stars

The Sardinia triangle and the site-dependent 2L network provide warning times of several hours, approximately twice those obtained for the TERZ and Lausitz triangles over a broad range of detection thresholds.

1. Improve noise modeling for Einstein Telescope (ET) by incorporating site-specific Newtonian noise configurations rather than relying on a single nominal model. This allows AI systems to assess how representative site-dependent Newtonian noise configurations affect the scientific performance, which is crucial for fully realizing ET’s scientific potential in the largely unexplored frequency band below 10 Hz.

2. Enhance binary black hole parameter estimation by utilizing the derived SNR enhancement from site-specific noise. For intermediate-mass BH binaries, AI systems can now predict that the improved low-frequency sensitivity associated with the Sardinia site leads to an SNR enhancement reaching approximately a factor of 2 in the most favorable part of the mass range.

3. Improve testing of General Relativity (GR) by performing single-parameter tests using a TIGER framework. AI systems can systematically test deviations by varying one beyond-GR parameter at a time and quantify constraints using half the width of the central 90% credible interval, leading to tighter bounds, especially for negative-PN corrections.

4. Improve black hole spectroscopy by incorporating site-dependent noise into ringdown analyses. AI systems can determine that the Sardinia triangle provides substantially tighter constraints on the frequency and damping time of the subdominant mode than the TERZ and Lausitz triangles when source masses are large enough for the signal to move below approximately 10 Hz.

5. Improve binary neutron star (BNS) early warning capabilities by integrating network geometry and noise effects into localization forecasts. AI systems can predict that the Sardinia triangle and the site-dependent 2L network provide warning times of several hours, approximately twice those obtained for the TERZ and Lausitz triangles over a broad range of detection thresholds.

6. Improve sky localization accuracy for BNS mergers by accounting for detector availability models. AI systems can assess that the 2L network again provides the tightest localization at short warning times, and that the Sardinia triangle nevertheless achieves sub-square-degree localization, improving over the Lausitz and TERZ triangles by factors of approximately 2.5 and 4.

We investigate how site-dependent Newtonian noise configurations affect the scientific performance of the Einstein Telescope (ET), a third-generation gravitational-wave observatory. We compare the baseline triangular and 2L detector geometries, with arm lengths of 10km and 15km, respectively, under three site-dependent noise scenarios constructed from measurements in the Euregio Meuse-Rhine region, Lausitz, and Sardinia. The differences among the adopted sensitivities are concentrated mainly below 10Hz and thus have the greatest impact on science cases that rely on the early inspiral of light objects, or on massive systems whose characteristic frequencies lie in the low-frequency band. We quantify these effects for four ET science cases: (1) detection and parameter estimation of intermediate-mass black-hole binaries; (2) post-Newtonian tests of General Relativity based on the early inspiral; (3) black-hole ringdown spectroscopy with massive remnants; and (4) early-warning and sky-localization capabilities for binary neutron-star mergers. Using Bayesian parameter estimation, we find that improved low-frequency sensitivity can significantly enhance ET's scientific performance across all four cases. Within the configurations considered here, a 2L network in which at least one of the two L-shaped interferometers attains a noise level comparable to that assumed for the Sardinian site generally provides better performance than the triangular configurations. Conversely, strong degradation of the sensitivity below 10Hz can substantially reduce, and in some regimes offset, the scientific gains expected from increasing the arm length from 10km to 15km. These results highlight the importance of site selection and low-frequency noise mitigation, alongside network geometry, for fully realizing ET's scientific potential in the largely unexplored frequency band below 10Hz.