Likelihood of white dwarf binaries to dominate the astrophysical gravitational wave background in the mHz band

¹ Institute of Astronomy, KU Leuven, Celestijnenlaan 200D, 3001 Leuven, Belgium
² Department of Astrophysics/IMAPP, Radboud University PO Box 9010 6500 GL Nijmegen, The Netherlands
³ DAMTP, Centre for Mathematical Sciences, University of Cambridge, Wilberforce Road, Cambridge CB3 0WA, UK
e-mail: ss3033@cam.ac.uk
⁴ SRON, Netherlands Institute for Space Research, Niels Bohrweg 4, 2333 CA Leiden, The Netherlands

Received: 30 October 2023
Accepted: 8 December 2023

Abstract

Context. The astrophysical gravitational wave background (AGWB) is a collective signal of astrophysical gravitational wave sources dominated by compact binaries. One key science goal of current and future gravitational wave detectors is to obtain its measurement.

Aims. We aim to determine the population of compact binaries dominating the AGWB in the mHz band. We revisit and update an earlier work by Farmer & Phinney (2003, MNRAS, 346, 1197) to model the astrophysical gravitational wave background sourced by extragalactic white dwarf binaries in the mHz frequency band.

Methods. We calculated the signal using a single-metallicity model for the white dwarf population in the Universe using the global star formation history.

Results. We estimate the white dwarf AGWB amplitude to be ∼60% higher than the earlier estimate. We also find that the overall shape of the white dwarf AGWB shows a good fit with a broken power law combined with an exponential cut-off.

Conclusions. We compare our results to present-day best estimates for the background due to black hole and neutron star binaries, finding that the white dwarf component is likely to dominate in the mHz band. We provide an order-of-magnitude estimate that explains this hierarchy and we comment on the implications for future missions that aim to detect the AGWB. We also note that the black hole AGWB may only be detectable at high frequency. We outline several improvements that can be made to our estimate, however, these points are unlikely to change our main conclusion, which posits that the white dwarf AGWB dominates the mHz band.