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

Abstract

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 ⩽ 16M ⊙ and the effective spins of −0.9 ⩽ χ eff ⩽ 0.9 and calculate the measurement errors of the mass and the spin parameters using 104 Monte-Carlo samples randomly distributed in our mass and spin parameter space. We find that for the same sources ET can achieve ∼ 14 times better signal-to-noise ratio than aLIGO and the error ratios (σ λ,ET/σ λ,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 2M ⊙ 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 Λ ~ can also be significantly reduced by ET, with the error ratio of 3.6%–6.1%. We investigate the effect of prior information by applying the Gaussian prior on the coalescence phase ϕ c to the Fisher matrix and find that the error of the intrinsic parameters can be reduced to ∼ 70 % of the original priorless error ( σ λ priorless ) if the standard deviation of the prior is similar to σ ϕ c priorless .