The Astrophysical Gravitational Wave Background in the mHz band is likely dominated by White Dwarf binaries

Abstract

Context. The Astrophysical Gravitational Wave Background (AGWB) is a collective signal of astrophysical gravitational wave sources and is dominated by compact binaries. Its measurement is one of the science goals of current and future gravitational wave detectors. Aims. We aim to determine what population of compact binaries dominates the AGWB in the mHz band. Methods. We revisit and update earlier work by Farmer & Phinney (2003) to model the astrophysical gravitational wave background sourced by extragalactic white dwarf binaries in the mHz frequency band. We calculate the signal using a single-metallicity model for the white dwarf population in the Universe using a global star formation history. Results. We estimate the white dwarf AGWB amplitude to be $\sim$ 60% larger than the earlier estimate and find that the overall shape of the white dwarf AGWB is well fitted by a broken power law combined with an exponential cut-off. Conclusions. We compare the results to the present-day best estimates for the background due to black hole and neutron star binaries, and find that the white dwarf component likely dominates in the mHz band. We provide an order of magnitude estimate that explains this hierarchy, and comment on the implications for future missions that aim to detect the AGWB. The black hole AGWB may only be detectable at high frequency. We outline several improvements that can be made to our estimate, but this is unlikely to change our main conclusion that the white dwarf AGWB dominates in the mHz band.