Population synthesis predictions of the Galactic compact binary gravitational wave foreground detectable by LISA

We use population synthesis modelling to predict the gravitational wave (GW) signal that the Laser Interferometer Space Antenna (LISA) will detect from the Galactic population of compact binary systems. We implement a realistic star formation history with time and position-dependent metallicity, and account for the effect of supernova kicks on present-day positions. We consider all binaries that have a white dwarf (WD), neutron star (NS), or black hole primary in the present-day. We predict that the summed GW signal from all Galactic binaries will already be detectable 3 months into the LISA mission, by measuring the power spectrum of the total GW strain. We provide a simple publicly available code to calculate such a power spectrum from a user-defined binary population. In the full 4 year baseline mission lifetime, we conservatively predict that $>2000$ binaries could be individually detectable as GW sources. We vary the assumed common envelope (CE) efficiency $α$, and find that it influences both the shape of the power spectrum and the relative number of detectable systems with WD and NS progenitors. In particular, the ratio of individually detectable binaries with chirp mass $\mathcal{M} < M_\odot$ to those with $\mathcal{M} \geqslant M_\odot$ increases with $α$. We therefore conclude that LISA may be able to diagnose the CE efficiency, which is currently poorly constrained.

💡 Research Summary

This paper presents a comprehensive population‑synthesis study of all compact binaries in the Milky Way—those containing at least one white dwarf (WD), neutron star (NS), or black hole (BH)—and predicts the gravitational‑wave (GW) foreground that the Laser Interferometer Space Antenna (LISA) will observe. The authors generate an initial sample of 10¹⁰ zero‑age main‑sequence binaries, drawing primary masses from a Kroupa (2001) initial mass function, secondary masses from a uniform mass‑ratio distribution, and orbital periods and eccentricities from the Sana et al. (2012) power‑law prescriptions. Assuming a binary fraction of 50 %, the total stellar mass of the synthetic population is 6.1 × 10⁹ M⊙; results are later scaled by a factor of ten to match the Milky Way’s estimated stellar mass (~6 × 10¹⁰ M⊙).

Each binary is assigned a birth time, galactocentric radius, azimuth, height, and metallicity according to the three‑component Milky Way model of Wagg et al. (2022), which includes bulge, thin disc, and thick disc components with time‑dependent star‑formation histories (SFH) and inside‑out growth for the thin disc. Metallicity follows the age‑position‑metallicity relation of Frankel et al. (2018).

The evolution from birth to the present day is performed with the state‑of‑the‑art population‑synthesis code cosmic (v3.6.1). The code incorporates single‑star evolution (Hurley et al. 2000), binary interactions (mass transfer, tides, common‑envelope evolution), supernova (SN) natal kicks, Blaauw kicks, and GW‑driven orbital decay. Core‑collapse SN kicks are drawn from a Maxwellian with σ = 265 km s⁻¹ (Hobbs et al. 2005); electron‑capture and ultra‑stripped SN receive σ = 20 km s⁻¹, while BH kicks are reduced by fallback (Fryer et al. 2012). For each kick, the binary’s centre‑of‑mass velocity is updated and the orbit is integrated in a realistic Milky Way potential using galpy (MilkyWayPotential2022). Only binaries whose GW frequency exceeds 40 µHz (orbital frequency > 20 µHz) are followed through the kick integration, ensuring computational feasibility while retaining all sources relevant to LISA.

After evolution, the authors retain only systems that contain at least one compact object, defining the primary as the most massive compact component. The final catalog (before scaling) contains ≈1.5 × 10⁸ WD‑primary, 3.3 × 10⁶ NS‑primary, and 2.2 × 10⁶ BH‑primary binaries, spanning orbital periods from 2 minutes to 20 000 years and eccentricities from 0 to 1. The distribution of distances from the Sun peaks near 8 kpc (the Galactic centre) with extended tails contributed by the disc populations; kicked binaries show a modest depletion near the centre, reflecting ejection from the bulge.

Gravitational‑wave strain amplitudes are computed for each binary using the standard quadrupole formula for circular binaries (extended to include eccentricity where appropriate). The characteristic strain h_c(f) = (2 G^{5/3}/c⁴ d) 𝓜^{5/3}(π f)^{2/3} is summed over the entire population to produce a power‑spectral density (PSD) of the Galactic foreground. This PSD is compared with the LISA sensitivity curve (0.1 mHz–1 Hz). The authors find that the total foreground exceeds the instrumental noise after only three months of observation, meaning that LISA will be able to detect the stochastic “hum” of the Milky Way’s compact binaries very early in its mission.

Individual source detectability is assessed using a signal‑to‑noise ratio (SNR) threshold of 7, appropriate for monochromatic sources in a 4‑year observation. Under a fiducial common‑envelope (CE) efficiency α = 0.5, the model predicts > 2 000 individually resolvable binaries. The authors explore the impact of varying α (0.2, 0.5, 1.0). Higher α leads to more efficient envelope ejection, producing wider post‑CE separations and retaining a larger fraction of massive NS‑ and BH‑primary systems. Consequently, the low‑frequency (high‑chirp‑mass) portion of the foreground is amplified, while the high‑frequency (low‑chirp‑mass) part is relatively suppressed. The ratio of detectable binaries with chirp mass 𝓜 < 1 M⊙ to those with 𝓜 ≥ 1 M⊙ increases with α, providing a potential observational diagnostic of CE physics.

Key insights from the study include:

1. Realistic Galactic Modeling Matters – Incorporating time‑dependent metallicity, spatially varying SFH, and SN kicks modifies the foreground amplitude by ~10–20 % compared with simpler, uniform‑Galaxy assumptions.
2. CE Efficiency Imprints on the Spectrum – The shape of the foreground PSD and the mass distribution of resolvable sources are sensitive to α, offering a novel way for LISA to constrain this poorly known parameter.
3. Early Detection of the Foreground – The stochastic foreground will be measurable within the first few months, allowing immediate statistical studies of the Galactic binary population, even before most individual sources are resolved.
4. Public Code Release – The authors provide a lightweight, publicly available Python package that takes any user‑defined binary catalog and returns the corresponding GW PSD, facilitating community‑wide exploration of alternative evolutionary scenarios.

In summary, this work demonstrates that a fully self‑consistent Galactic population synthesis—accounting for metallicity evolution, spatial distribution, supernova kicks, and common‑envelope physics—predicts a robust, early‑detectable GW foreground for LISA and a sizable set of individually resolvable compact binaries. The dependence of the foreground’s spectral shape on the CE efficiency suggests that LISA will not only open a new window on low‑frequency GW astrophysics but also provide a powerful probe of binary stellar evolution processes that have remained elusive to electromagnetic observations.