Significant challenges for astrophysical inference with next-generation gravitational-wave observatories

TL;DR

This work demonstrates that next-generation gravitational-wave observatories will observe long, high-SNR binary neutron star signals whose analysis is dramatically complicated by Earth’s rotation and the detectors’ free spectral range. It rigorously evaluates reduced order modeling (ROM) and reduced order quadrature (ROQ) in this context, showing that standard compression strategies fail to deliver unbiased inference once these effects are included, especially when considering sub-16 Hz data essential for precise sky localization. The authors develop a comprehensive ROM framework within the Rombus ecosystem, incorporate time-dependent detector responses, and quantify the memory and SNR limitations that hinder practical inference for the loudest events. A targeted inference test with a GW170817-like signal demonstrates substantial but insufficient speedups, highlighting the need for new approaches such as amortized inference or deeper algorithmic innovations. Overall, the paper maps out the computational bottlenecks, clarifies the limitations of current compression methods, and points toward prospective avenues to enable robust Bayesian inference for long-duration, high-SNR gravitational-wave signals in the next generation of detectors.

Abstract

The next generation of gravitational-wave observatories will achieve unprecedented strain sensitivities with an expanded observing band. They will detect ${\cal O}(10^5)$ binary neutron star (BNS) mergers every year, the loudest of which will be in the band for $\approx 90$ minutes with signal-to-noise ratios $\approx 1500$. Current techniques will not be able to determine the astrophysical parameters of the loudest of next-gen BNS signals. We show that subtleties arising from the rotation of the Earth and the free-spectral range of gravitational-wave interferometers dramatically increases the complexity of next-gen BNS signals compared to the one-minute signals seen by LIGO--Virgo. Various compression methods currently relied upon to speed up the most expensive BNS calculations -- reduced-order quadrature, multi-banding, and relative binning -- will no longer be effective. We carry out reduced-order inference on a simulated next-gen BNS signal taking into account the Earth's rotation and the observatories' free-spectral range. We show that standard data compression techniques become impractical, and the full problem becomes computationally infeasible, when we include data below $\approx 16$Hz -- a part of the observing band that is critical for precise sky localisation. We discuss potential paths towards solving this complex problem.

Figures (7)

• Figure 1: The limitations of inference with data compression strategies. Solid blue shows the SNR of a GW170817-like event as observed by a single Cosmic Explorer. This is contrasted with the dashed black showing the maximum signal-to-noise ratio that that we can currently achieve with reduced order modelling. In the green region above $\unit[16]{Hz}$, the maximum SNR is limited only by double machine precision, which is almost sufficient. In the orange region between $\unit[13-16]{Hz}$, the maximum SNR is limited by our memory limit of $\unit[100]{Gb}$; we can carry out inference, but only by artificially inflating error bars. In the red region below $\unit[13]{Hz}$, the maximum SNR drops below 10, and we are unable to carry out meaningful calculations, even by inflating error bars.
• Figure 2: Relative log likelihood ratio errors for a fixed range in chirp mass $\Delta\mathcal{M}_c$ for a linear reduced order quadrature rule, multibanding, and relative binning. Both relative binning and multibanding ignore the effects due to Earth's rotation and the free spectral range, whereas the reduced order quadrature method includes them. The top panel compares the likelihood acceleration techniques over $50,000$ waveforms from $f_{\min}=\unit[30]{Hz}$ and chirp mass range $\Delta\mathcal{M}_c=6\times10^{-4}$. The bottom panel shows the same comparison with waveforms evaluated from $f_{\min}=\unit[24]{Hz}$ with chirp mass range $\Delta\mathcal{M}_c=9\times10^{-4}$. The peak of the error distributions are indicated in the figure legend, with the associated likelihood speedups listed next to each curve. For relative binning we set the tunable accuracy parameters $\chi, \epsilon$ to $\chi=10, \epsilon=0.1$, and for multi-banding we set the accuracy parameter $L$ to $L=5$. The accuracy of multi-banding and relative binning can be increased by modifying these accuracy parameters, but this has the effect of further slowing inference.
• Figure 3: One- and two- dimensional posterior distributions for the component masses $m_{1,2} [M_{\odot}]$, spin magnitudes $\chi_{1,2}$, and cosine of the spin tilts $\cos\theta_{1,2}$ of a GW170817-like binary neutron star signal injected into a single Cosmic Explorer with SNR=792 and $f_\text{min}=\unit[24]{Hz}$. The true values are indicated in orange.
• Figure 4: One- and two- dimensional posterior distributions for the right ascension $\text{RA} [rad]$ and declination $\text{Dec} [rad]$ of a GW170817-like binary neutron star signal injected into a single Cosmic Explorer with SNR=792 and $f_\text{min}=\unit[24]{Hz}$. The true values are indicated in orange.
• Figure 5: One- and two- dimensional posterior distributions for the tidal deformabilities $\Lambda_{1,2}$ of a GW170817-like binary neutron star signal injected into a single Cosmic Explorer with SNR=792 and $f_\text{min}=\unit[24]{Hz}$. The true values are indicated in orange.