Luminosity distance uncertainties from gravitational wave detections by third generation observatories

TL;DR

This work assesses how third-generation gravitational-wave networks—notably an ET-like triangular topology and a CE-like L-shaped topology—affect luminosity distance uncertainties for EM-bright standard sirens. Using a Bayesian framework and the Cutler–Flanagan parameterization, it quantifies how detector topology, relative orientation, and the inclination distribution influence the $d_L$ precision, showing that networks with two misaligned detectors can substantially reduce degeneracies and approach the lensing-limited precision around $z\gtrsim0.7$. The results demonstrate that, beyond increasing the number of detectors, incorporating knowledge of the source inclination distribution can dramatically improve distance measurements (up to a factor of ~5 under favorable priors), with CE-CE networks sometimes rivaling ET+ET+CE configurations. These findings have important implications for using 3G GW standard sirens to constrain cosmic expansion, highlighting the role of network design and prior information in maximizing cosmological leverage.

Abstract

A new generation of terrestrial gravitational wave detectors is currently being planned for the next decade, and it is expected to detect most of the coalescences of compact objects in the universe with masses up to a thousand times the solar mass. Among the several possible applications of current and future detections, we focus on the impact on the measure of the luminosity distance of the sources, which is an invaluable tool for constraining the cosmic expansion history of the universe. We study two specific detector topologies, triangular and L-shaped, by investigating how topology and relative orientation of up to three detectors can minimize the uncertainty measure of the luminosity distance. While the precision in distance measurement is correlated with several geometric angles determining the source position and orientation, focusing on bright standard sirens and assuming redshift to be measured with high accuracy, we obtain analytic and numerical results for its uncertainty depending on type and number of detectors composing a network, as well as on the inclination angle of the binary plane with respect to the wave propagation direction. We also analyze the best relative location and orientation of two third generation detectors to minimize luminosity distance uncertainty, showing that prior knowledge of the inclination angle distribution plays an important role in precision recovery of luminosity distance, and that a suitably arranged network of detectors can reduce drastically the uncertainty measure, approaching the limit imposed by lensing effects intervening between source and detector at redshift $z \gtrsim 0.7$.

Figures (14)

• Figure 1: Expected redshift distribution of bright standard sirens assuming an electromagnetic counterpart is detected by Theseus Belgacem:2019tbw, compared with observed star formation rate Madau:2014bja.
• Figure 2: (Left) Luminosity distance reach for equal mass, non-spinning system, assuming fundamental $l=m=2$ mode only, for optimally oriented binaries, given the spectral noise density $S_n$Srivastava:2022sltce_official for CE and [ET-D] from etd for ET. The mass and luminosity distance of GW170817 are highlighted, as well as the mass region where BNSs are expected. (Right) Dimensionless noise characteristic strain $h_c$, defined in terms of spectral noise $h_c\equiv \sqrt{f S_n}$ for $L$-shaped CE and triangle-shaped ET.
• Figure 3: Schematic representation of detector geometry and of radiation frame.
• Figure 10: The three inclination angle distributions for $\iota$ used in injections, dubbed "isotropic", "smooth cutoff", "hard cutoff".
• Figure 11: Error in distance determination averaged over source location, as a function of the angular distance between two 3G detectors. Sources are distributed isotropically in the sky before the $SNR_i>8$ cut in each detector. Source inclinations are distributed according to smooth-cutoff function, see Figure \ref{['fig:iotad_net']}, Bayesian prior for $\iota$ at recovery is isotropic. The bottom right plot refers to two ETs, the others to two CEs with sources respectively at $z=0.1,0.55,1$.