Comparing next-generation detector configurations for high-redshift gravitational wave sources with neural posterior estimation

TL;DR

The paper investigates how seven next-generation gravitational-wave detector configurations impact parameter estimation for massive, high-redshift BBHs using neural posterior estimation with Dingo-IS. It demonstrates that Dingo-IS reproduces standard Bayesian posteriors with substantially lower compute time and validates its ability to reveal multimodal sky and distance posteriors in complex ET configurations. The results show a nuanced trade-off: two misaligned ET detectors (2L MisA) excel in sky localization and localization volume, while a triangular ET ($\Delta$) provides superior luminosity-distance precision; adding CE and/or LIGO detectors further enhances localization by reducing sky-mode degeneracies. These findings inform design decisions for XG GW networks, highlighting the value of optimized baselines and polarization measurements, and confirm the viability of fast likelihood-free inference for large-scale GW data analysis. The work advances practical decision-making for detector configuration by linking geometry to parameter-estimation performance, with implications for cosmology and multi-messenger astronomy.

Abstract

The coming decade will be crucial for determining the final design and configuration of a global network of next-generation (XG) gravitational-wave (GW) detectors, including the Einstein Telescope (ET) and Cosmic Explorer (CE). In this study and for the first time, we assess the performance of various network configurations using neural posterior estimation (NPE) implemented in Dingo-IS-a method based on normalizing flows and importance sampling that enables fast and accurate inference. We focus on a specific science case involving short-duration, massive and high-redshift binary black hole (BBH) mergers with detector-frame chirp masses $M_{\mathrm{d}} > 100$ M$_\odot$. These systems encompass early-Universe stellar and primordial black holes, as well as intermediate-mass black-hole binaries, for which XG observatories are expected to deliver major discoveries. Validation against standard Bayesian inference demonstrates that NPE robustly reproduces complex and disconnected posterior structures across all network configurations. For a network of two misaligned L-shaped ET detectors (2L MisA), the posterior distributions on luminosity distance can become multimodal and degenerate with the sky position, leading to less precise distance estimates compared to the triangular ET configuration. However, the number of sky-location multimodalities is substantially lower than the eight expected with the triangular ET, resulting in improved sky and volume localization. Adding CE to the network further reduces sky-position degeneracies, and the better performance of the 2L MisA configuration over the triangle remains evident.

Figures (12)

• Figure 1: Top panel: Injections as function of sample efficiency ($\epsilon$, $x$-axis) and optimal SNR ($\rho$, $y$-axis) for each detector configuration (color-coded). Filled markers indicate injections with sample efficiencies $> 1\%$. Percentages in parentheses denote the fraction of sources with sample efficiency above $1\%$, while the horizontal colored lines indicate the median $\rho$ for sources exceeding this threshold. Bottom panel: Injections as function of detector-frame chirp mass ($x$-axis) and luminosity distance (left $y$-axis), with corresponding redshifts (right $y$-axis). Colored markers indicate events with sample efficiency greater than $1\%$ in all considered detector configurations. See Section \ref{['sec:high_eff']} for details.
• Figure 2: Top panel: Marginalized one-dimensional posterior distributions for the luminosity distance, recovered with Dingo-IS for an event observed with the $\Delta$ (dark blue) and 2L MisA (light blue) configurations. The results are compared with Bilby (orange). The vertical line marks the injected luminosity distance. The remaining parameters are shown in Appendix \ref{['app:bilby']}. Middle panel: Posterior samples obtained with Dingo-IS in the $\Delta$ configuration for right ascension (ra) and declination (dec), color-coded by luminosity distance. The red cross marks the injected sky position. We also report the sky-localization area ($\Delta \Omega_{90\%}$) and comoving-volume localization ($\Delta V^c_{90\%}$) errors. Bottom panel: Same as the middle panel, but for the 2L MisA configuration. See Section \ref{['sec:single']} for details.
• Figure 3: Cumulative distributions of events as a function of the information gain (top-left panel, see also Section \ref{['sec:metrics']}), the relative variations in luminosity distance (top-right panel, $\Delta D_{\mathrm{L}}/D^{\mathrm{inj}}_{\mathrm{L}}$), sky (bottom-left panel, $\Delta \Omega_{90\%}$, see also Table \ref{['tab:sky']}), and comoving volume localization (bottom-right panel, $V^{c}_{90\%}$) for all considered XG detector configurations (color-coded). See Section \ref{['sec:pe_perfom']} for details and Appendix \ref{['app:results']} for the remaining parameters.
• Figure 4: Percentage of sky maps ($y$-axis) with $\Delta \Omega_{90\%} \leq 100$ deg$^2$ exhibiting one to eight or more disconnected modes (color-coded), for all detector configurations ($x$-axis). See Section \ref{['sec:pe_perfom']} for details.
• Figure 5: Amplitude spectral densities (ASDs) adopted in this work for different XG detectors. See Section \ref{['sec:detectors']} and Appendix \ref{['app:detectors']} for details.