Improvement of the parameter measurement accuracy by the third-generation gravitational wave detector Einstein Telescope

TL;DR

This paper demonstrates that the third-generation Einstein Telescope significantly improves gravitational wave source parameter measurement accuracy compared to Advanced LIGO, especially for low-mass binaries, by employing Fisher matrix analysis and Monte Carlo simulations.

Contribution

It provides a detailed comparison of parameter estimation errors between ET and aLIGO, highlighting the substantial improvements in measurement precision for various binary systems.

Findings

ET achieves ~14 times better SNR than aLIGO for the same sources.

Error ratios for mass and spin parameters are below 7% for black hole binaries.

Measurement errors for neutron star parameters, including tidal deformability, are reduced to below 1.5%.

Abstract

The Einstein Telescope (ET) has been proposed as one of the third-generation gravitational wave (GW) detectors. The sensitivity of ET would be a factor of 10 better than the second-generation GW detector, Advanced LIGO (aLIGO); thus, the GW source parameters could be measured with much better accuracy. In this work, we show how the precision in parameter estimation can be improved between aLIGO and ET by comparing the measurement errors. We apply the TaylorF2 waveform model defined in the frequency domain to the Fisher matrix method which is a semi-analytic approach for estimating GW parameter measurement errors. We adopt as our sources low-mass binary black holes with the total masses of $M\leq 16 M_{\odot} $ and the effective spins of $-0.9 \leq \chi_{\rm eff} \leq 0.9$ and calculate the measurement errors of the mass and the spin parameters using $10^4$ Monte-Carlo samples randomly distributed in our mass and spin parameter space. We find that for the same sources ET can achieve $\sim 14$ times better signal-to-noise ratio than aLIGO and the error ratios ($\sigma_{\lambda, \rm ET}/\sigma_{\lambda, \rm aLIGO}$) for the chirp-mass, symmetric mass ratio, and effective spin parameters can be lower than $7\%$ for all binaries. We also consider the equal-mass binary neutron stars with the component masses of 1, 1.4, and 2 $M_{\odot}$ and find that the error ratios for the mass and the spin parameters can be lower than $1.5 \%$. In particular, the measurement error of the tidal deformability $\tilde{\Lambda}$ can also be significantly reduced by ET, with the error ratio of $3.6 - 6.1 \%$.