Validating Prior-informed Fisher-matrix Analyses against GWTC Data

Next-generation gravitational-wave detectors, such as the Einstein Telescope (ET), are expected to observe a few 100,000 signals each year. This will require efficient analysis tools and computational resources well beyond the needs of current detectors. Such resources are not presently available to the science community. Therefore, to investigate ET observational capabilities and science cases, Fisher-matrix methods are used to predict how precisely parameters like mass, spin, source distance or sky location can be estimated from ET data. The approach is based on a Gaussian approximation of the likelihood function. However, the reliability of error estimates obtained from Fisher-matrix methods remains an open question. In this article, we present a Fisher-matrix analysis of signals of the Gravitational Wave Transient Catalog (GWTC). We compare parameter-estimation errors obtained using the Fisher matrix code GWFish with the errors from the marginal distributions of the Virgo/LIGO posterior analysis. In order to understand the impact of prior distributions on the results, we implemented a Gaussian likelihood sampling algorithm with priors in GWFish. To ensure a fair comparison of the methods, the GWFish analyses presented in this article use the same priors and the same instrument-noise spectra as the Virgo/LIGO posterior analyses. Our findings imply that Fisher-matrix methods, especially if augmented with the use of priors, are a valid tool for ET science-case studies.