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 $\alpha$, 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 $\alpha$. We therefore conclude that LISA may be able to diagnose the CE efficiency, which is currently poorly constrained.