The Gravitational Wave Universe Toolbox

II. Constraining the binary black hole population with second and third generation detectors

¹ Department of Astrophysics/IMAPP, Radboud University, PO Box 9010 6500 GL Nijmegen, The Netherlands
e-mail: sxyi@ihep.ac.cn
² Department of Mathematics/IMAPP, Radboud University, PO Box 9010 6500 GL Nijmegen, The Netherlands
³ SRON, Netherlands Institute for Space Research, Sorbonnelaan 2, 3584 CA Utrecht, The Netherlands
⁴ Institute of Astronomy, KU Leuven, Celestijnenlaan 200D, 3001 Leuven, Belgium
⁵ Key Laboratory of Particle Astrophysics, Institute of High Energy Physics, Chinese Academy of Sciences, 19B Yuquan Road, Beijing, 100049 PR China

Received: 17 January 2022
Accepted: 20 April 2022

Abstract

Context: The GW-Universe Toolbox is a software package that simulates observations of the gravitational wave (GW) Universe with different types of GW detectors, including Earth-based and space-borne laser interferometers and pulsar timing arrays. It is accessible as a website, and can also be imported and run locally as a Python package.

Methods: We employ the method used by the GW-Universe Toolbox to generate a synthetic catalogue of detection of stellar-mass binary black hole (BBH) mergers. As an example of its scientific application, we study how GW observations of BBHs can be used to constrain the merger rate as a function of redshift and masses. We study advanced LIGO (aLIGO) and the Einstein Telescope (ET) as two representatives of the second and third generation GW observatories, respectively. We also simulate the observations from a detector that is half as sensitive as the ET at its nominal designed sensitivity, which represents an early phase of the ET. We used two methods to obtain the constraints on the source population properties from the catalogues: the first uses a parameteric differential merger rate model and applies a Bayesian inference on the parameters; the other is non-parameteric and uses weighted Kernel density estimators.

Results: Our results show the overwhelming advantages of the third generation detector over those of the second generation for the study of BBH population properties, especially at redshifts higher than ∼2, where the merger rate is believed to peak. With the simulated aLIGO catalogue, the parameteric Bayesian method can still give some constraints on the merger rate density and mass function beyond its detecting horizon, while the non-parametric method loses the constraining ability completely there. The difference is due to the extra information placed by assuming a specific parameterisation of the population model in the Bayesian method. In the non-parameteric method, no assumption of the general shape of the merger rate density and mass function are placed, not even the assumption of its smoothness. These two methods represent the two extreme situations of general population reconstruction. We also find that, despite the numbers of detected events of the half ET can easily be compatible with full ET after a longer observation duration, and the catalogue from the full ET can still give much better constraints on the population properties due to its smaller uncertainties on the physical parameters of the GW events.