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

TL;DR

Using population synthesis with a realistic Milky Way SFH, metallicity, and natal kicks, the paper predicts the LISA Galactic compact-binary foreground from WD/NS/BH populations. It evolves ~10^{10} ZAMS binaries with COSMIC, assigns birth times and metallicities in a three-component Milky Way, and computes the total GW PSD including eccentric-harmonic emission, then explores CE efficiency by varying $\alpha$ from $0.2$ to $5$. The results show the total signal is detectable within ~3 months and that the PSD shape and the number of individually detectable binaries depend on $\alpha$, offering a potential diagnostic of CE physics; NS/WD detection ratios and chirp-mass distributions further sharpen constraints. A public Python tool is provided to compute the PSD for user-defined populations, enabling rapid exploration and early science with LISA.

Abstract

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.

Figures (10)

• Figure 1: Properties of the generated compact binary population. (a) Orbital period distribution within LISA's band, split into primary type (i.e. WD, NS, or BH) and accreting ($\dot{m}\neq 0$) NS-WD systems. The majority of the population (not plotted) lies outside LISA's band towards $10^{-10}~\mathrm{Hz}$. (b) Eccentricity distribution, split by primary type, compared with the input model from 2012Sci...337..444S. Given there are nearly $5\times 10^6$ circular binaries, their peak at $e=0$ has been truncated for visibility. (c) Star formation history of the full compact binary population compared with the theoretical SFH from Wagg+2022, showing fewer compact binaries from very old and very recent times relative to the model.
• Figure 2: (a) Distance distribution (from Earth) of the generated compact binary population, showing a peak near $8~\mathrm{kpc}$ at the Galactic bulge. Kicked binaries show a deficit near the Galactic centre, as some systems are ejected to larger distances. (b) Height above the Galactic plane, $|z|$, for the population pre-kick and post-kick. Both follow an effective scale height of $z_d \approx 0.8~\mathrm{kpc}$ at low $|z|$, but post-kick systems develop a high-$|z|$ tail extending beyond $10~\mathrm{kpc}$. (c) Sky map of the compact binaries in Galactic coordinates, showing the concentration of sources in the bulge near the Galactic centre (star) and a disc-like structure.
• Figure 3: Number density of GW signals from binaries per unit log-frequency-log-power area, projected against LISA's sensitivity curve. The right panels split the population by primary type (i.e. WD, NS, or BH), showing most BH-primary systems lie well below the curve. WD-primary binaries roughy divide into two groups: lower-frequency eccentric systems and higher-frequency circular systems. A detectable subset of NS-primary binaries clusters near $10^{-3}~\mathrm{Hz}$.
• Figure 4: (Left) PSD as a function of GW frequency for compact object binaries, with the full contribution from eccentric harmonics included. The raw, noisy signal is smoothed through geometric re-binning ($c_0=1.3$), shown with $1\sigma$ error bars. A detectable signal is clearly above the LISA noise curve. (Right) Comparison of GW PSDs split by primary type (WD, NS, or BH). BH systems dominate at low frequencies, whereas WD and NS systems govern the detectable higher frequencies within LISA's band.
• Figure 5: The LISA-detected binary signal, obtained by summing simulated instrumental noise and the total binary signal, then subtracting the theoretical noise, for different mission observation times. Even after just 3 months, the signal is already strong, and remains so because individually detectable binaries are not subtracted here.