GWFish: A simulation software to evaluate parameter-estimation capabilities of gravitational-wave detector networks

Abstract

An important step in the planning of future gravitational-wave (GW) detectors and of the networks they will form is the estimation of their detection and parameter-estimation capabilities, which is the basis of science-case studies. Several future GW detectors have been proposed or are under development, which might also operate and observe in parallel. These detectors include terrestrial, lunar, and space-borne detectors. In this paper, we present gwfish a , a new software to simulate GW detector networks and to calculate measurement uncertainties based on the Fisher-matrix approximation. gwfish models the impact of detector motion on PE and makes it possible to analyze multiband scenarios, i.e., observation of a GW signal by different detectors in different frequency bands. We showcase a few examples for the Einstein Telescope (ET) including the sky-localization of binary neutron stars, and ET's capability to measure the polarization of GWs.

GWFAST: A Fisher Information Matrix Python Code for Third-generation Gravitational-wave Detectors

“…We further compared the predictions for the S/Ns and measurement errors obtained using GWFAST on some of the loudest and best localized events detected during the second and third observing runs of the LVK collaboration with the actual results obtained from a full Bayesian parameter estimation, obtaining good agreement. GWFAST has been used to produce the results in the companion paper , where we also discuss its comparison with other existing codes and results (Borhanian 2021;Harms et al 2022;Pieroni et al 2022), showing their excellent agreement. Due to its structure and to the use of AD, GWFAST is also suitable for extensions of the FIM approximation (Vallisneri 2011;Sellentin et al 2014;Wang et al 2022).…”

“…Note that all of the functions described here assume that the input FIM is an array of matrices in the last dimension, as described in Section 3.2 The conditioning of the FIM can be checked in GWFAST via the function CheckFisher, which returns the eigenvalues, eigenvectors, and condition number of the matrix. The inversion of the FIM to yield the covariance is done with the function CovMatr, as: By default, each row and column is normalized to the square root of the diagonal of the FIM before inversion, so that the resulting matrix has adimensional entries with ones on the diagonal and the remaining elements in the interval [−1, 1] (Harms et al 2022). 17 The inverse transformation is applied after inversion to yield the inverse of the original matrix.…”

“…The value of the threshold λ can be specified with the argument svals_thresh, which is set by default to 10 15 ; ′svd_reg′: the SVD of the FIM is used to invert the matrix, and eigenvalues smaller than the threshold specified by the argument svals_thresh are not included in the inversion. This ensures that the error on poorly constrained parameters is not propagated to the other ones (Harms et al 2022). However, it might result in underestimating the uncertainty for parameters whose eigenvalues are excluded, and the effect should be carefully checked.…”

Adding gamma-ray polarimetry to the multi-messenger era

“…After this, the LIGO detectors are expected to undergo major upgrades to reach the so-called Voyager stage, with a sensitivity about two times better than the Advanced+ design (Adhikari et al 2020). The next step are then thirdgeneration detectors, namely Einstein Telescope (ET) in Europe (Punturo et al 2010;Hild et al 2011) and Cosmic Explorer (CE) in the U.S. (Reitze et al 2019;Evans et al 2021), which are expected to start their operations in the middle of the next decade.…”

“…Other publicly available softwares that implement the Fisher matrix formalism for GW detector networks are GWBENCH(Borhanian 2021) and GWFISH(Harms et al 2022) [see alsoChan et al (2018);Pieroni et al (2022)]; all these have been shown to be in good agreement among them and with GWFAST(Iacovelli et al 2022a). 7 The sensitivity curves are available at https://dcc.ligo.org/LIGO-T2000012/public,Abbott et al (2020b).8 The sensitivity curves are available at https://dcc.ligo.org/LIGO-T1500293/public.…”