DOI: 10.5281/zenodo.13850415
title: Parameter estimation catalogs for binary neutron star mergers detected with next-generation gravitational wave detectors

description: Next-generation gravitational wave (GW) observatories, such as the Einstein Telescope (ET) and the Cosmic Explorer, will provide access to the population of binary neutron star (BNS) mergers throughout cosmic history and yield precise parameter estimates. Here, we publish the results of a comprehensive study evaluating BNS merger detection prospects using the ET alone or in a network of current or next-generation detectors up to redshift equal to 1. We publicly release all the parameter estimation for 10 years of observations of BNSs in the form of catalogs. These catalogs are made available to the community for multi-messenger studies, multi-probe cosmology, and nuclear study to constrain the neutron star (NS) equation of state (EOS). They can be used to focus on specific events (for example golden events with high signal-to-noise ratio) or for statistical studies on the BNS populations. 

Our simulations assessed the perspectives for detecting the optical emission of BNS mergers in the era of next-generation detectors, considering how uncertainties in BNS population properties, NS mass distribution, and the EOS might affect the detection rate and parameter estimation. The study is published in Loffredo, Hazra, Dupletsa, Branchesi et al. 2024 arXiv:2411.02342 (submitted to A&A).


BNS merger rate

As shown in Santoliquido et al. (2021), the common envelope ejection efficiency parameter, α, determines one of the main sources of uncertainty for the number of BNS mergers per year. In order to evaluate the impact of the uncertainties of the BNS merger rate normalization on our results, we generate two catalogues of BNS mergers assuming α to be either 0.5 or 1.0. 

NS mass distribution

We draw the component masses of the NS binaries, M_1 and M_2, from two different mass distributions: Gaussian anduniform mass distributions. The Gaussian distribution is centred at 1.33 M⊙ with a standard deviation of 0.09 M⊙. The uniform mass distribution ranges in [1.1 M⊙, M_max], where M_max depends on the selected EOS.

Equation of state (EOS)

Since the NS EOS affects both the GW and EM signals expected from BNS mergers, we considertwo different EOSs, namely the APR4 and BLh microscopic EOSs.

Detector configuration

Given the two values of α (0.5 and 1.0), the two mass distributions (uniform and Gaussian), and the two EOSs (BLh and APR4), we have a total of 8 different population sets, which constitute our injections for the gravitational signal analysis. For each of these datasets, we consider the following GW detector configurations:



ET in its triangular design of 10 km arms, located in Sardinia, alone and operating together with (ET_delta_10_cryo):



the current ground-based network LIGO-Hanford, LIGO-Livingston, Virgo, KAGRA, LIGO-India (LVKI) 

one L-shaped CE with 40 km arms, located in the USA (1CE)

2 CEs, both with 40 km arms, one in the USA and one in Australia (2CE)



ET in its 2L-shaped interferometer configuration of 15 km arms misaligned at 45 deg (one located in Sardinia and the other in the Netherlands); we consider the same networks as above, using the 2L-configuration instead of the triangular one (ET_2L_15_cryo_45deg). 


We thus have eight different detector networks giving a total of 64 simulations available in this repository. 

Catalog description

The parameter estimation of the injected GW signals by the various detector networks is obtained through the Fisher matrix software GWFish (Dupletsa et al. 2023). The Fisher analysis method approximates the likelihood with a multivariate Gaussian distribution. All the parameters [M_1, M_2, dL, ι, RA, DEC, Ψ, phase, tc, Λ_1, Λ_2] are considered for the Fisher matrix derivation. The uncertainties on parameters coming from the covariance matrix (the inverse of the Fisher matrix) are given at 1σ. We implement a duty cycle of 85% for each of the L-shaped detectors, and for each of the three nested detectors composing the triangle. 



Signals_{BNS_merger_rate}_{EOS}_{NS_mass_distribution}_{Detector_configuration}.txt  contains the parameters describing a GW event and the corresponding network signal-to-noise ratio (SNR)



mass_1: primary mass of the binary in [Msol] (in detector frame) (M_1)

mass_2: secondary mass of the binary in [Msol] (in detector frame) (M_2)

luminosity_distance: the luminosity distance of the merger in [Mpc]

dec: declination angle in [rad]. It varies in  [−𝜋/2,+𝜋/2]

ra: right ascension in [rad]. It varies in  [0,2/𝑝𝑖]

theta_jn: the angle between the line of observation and the total angular momentum (orbital, spin and GR corrections) of the binary [rad] (it reduces to the so-called inclination angle or iota if the spin component is absent); it ranges in  [0,𝜋]

psi: the polarization angle in [rad]; it ranges in  [0,𝜋]

geocent_time: merger time as GPS time in [s]

phase: the initial phase of the merger in [rad]; it ranges in  [0,2𝜋]

redshift: the redshift of the merger

lambda_1: dimensionless tidal polarizabilty of primary component

lambda_2: dimensionless tidal polarizabilty of secondary component

network_SNR: network SNR for a the given event



Errors_{BNS_merger_rate}_{EOS}_{NS_mass_distribution}_{Detector_configuration}.txt contains the 



parameter errors for each event. The first column is network_SNR, the following columns repeat the injected parameters as above and the relative errors err_{parameter}. The last column is the error on sky localisation (err_sky_location) at 90% credible interval. 




Further details 

Further details on the assumptions we made to produce these catalogs can be found in Loffredo et al. 2024, while further details on GWFish can be found on this tutorial. We also provide the jupyter notebook paper_plots.ipynb, to reproduce Figs. 10, 11, 13, D.1, D.5, D.6.  
description: GWFish is publicly available at https://github.com/janosch314/GWFish: the version used in this work is the commit cf26d3c in the main branch.