The Gravitational Wave Background from Cosmological Compact Binaries

TL;DR

This study uses population synthesis (via the BSE code) to predict the extragalactic gravitational-wave background from cosmological compact binaries in the LISA band (0.1–10 mHz), focusing on binaries descended from low- to intermediate-mass stars and calibrating against Galactic double degenerates. The analysis shows the background is dominated by double white dwarf systems, with a robust spectral shape largely independent of population-model details, and an amplitude at 1 mHz in the range 1×10^-12 to 6×10^-12. By exploring a suite of evolutionary and cosmological scenarios, the work provides quantitative constraints on the background amplitude, highlights the relative contributions of WD–WD, interacting WD–WD, and WD–nHe systems, and assesses implications for LISA design and for disentangling primordial gravitational-wave signals from astrophysical foregrounds. Overall, the results demonstrate that the extragalactic binary background constitutes a predictable, model-bounded foreground in the LISA band, tightly linked to the cosmic star-formation history and binary-evolution physics, and it informs both detector requirements and foreground subtraction strategies.

Abstract

We use a population synthesis approach to characterise, as a function of cosmic time, the extragalactic close binary population descended from stars of low to intermediate initial mass. The unresolved gravitational wave (GW) background due to these systems is calculated for the 0.1-10 mHz frequency band of the planned Laser Interferometer Space Antenna (LISA). This background is found to be dominated by emission from close white dwarf-white dwarf pairs. The spectral shape can be understood in terms of some simple analytic arguments. To quantify the astrophysical uncertainties, we construct a range of evolutionary models which produce populations consistent with Galactic observations of close WD-WD binaries. The models differ in binary evolution prescriptions as well as initial parameter distributions and cosmic star formation histories. We compare the resulting background spectra, whose shapes are found to be insensitive to the model chosen, and different to those found recently by Schneider et al. (2001). From this set of models, we constrain the amplitude of the extragalactic background to be 1E-12 < Omega(1 mHz) < 6E-12, in terms of Omega(f), the fraction of closure density received in gravitational waves in the logarithmic frequency interval around f.

Figures (17)

• Figure 1: Gravitational wave spectrum arising from constant WD--WD formation rate, at times 2, 5, 10, 100 and 1000 Gyr, increasing in the direction of the arrow shown.
• Figure 2: Gravitational wave spectrum arising from a burst of WD--WD formation between 0 and 1 Gyr. Curves plotted are spectra at times 2, 5, 10, 100 and 1000 Gyr, increasing in the direction of the arrow shown.
• Figure 3: Two possible cosmic star formation histories, plotted as a function of redshift $z$ and parametrized according to the smooth curve fits given in col01. Dashed line: no extinction correction made, used in Model J. Solid line: extinction corrected with $E(B-V)=0.15$, used in all other Models. The time integral of each rate is fixed using the appropriate $\Omega_{*,\rm{tot}}$ derived from col01. Curves shown are for the KTG IMF.
• Figure 4: The GW background for our fiducial Model A, in terms of the three quantities described in section \ref{['sec:quantities']}. Solid line: WD--WD pairs; dotted line: nHe--WD pairs; dashed line: MS--MS binaries, and dot-dash line: WD--MS binaries. The total signal (the sum of the four parts) is given by the thick solid line. Only $n=2$ harmonics of the orbital frequency are plotted (see section \ref{['sec:ecc_test']}).
• Figure 5: Comparison of spectral shapes for all Models. Curves are the same as in Fig. \ref{['fig:basic']}, but all quantities are plotted as solid lines. Only $n=2$ harmonics of the orbital frequency are plotted (see section \ref{['sec:ecc_test']}).