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Abstract We present the successful recovery of common-envelope ejection efficiency assumed in a simulated population of double white dwarf (DWD) binaries like those which may be observed by the future Laser Interferometer Space Antenna (LISA) mission. We simulate the formation of DWD binaries by using the COSMIC population synthesis code to sample binary formation conditions such as initial mass function, metallicity of star formation, initial orbital period, and initial eccentricity. These binaries are placed in the m12i synthetic Milky Way–like galaxy, and their signal-to-noise ratio (SNR) for the LISA instrument is estimated, considering a Galactic gravitational-wave foreground informed by the population. Through the use of Fisher estimates, we construct a likelihood function for the measurement error of the LISA-bright DWD binaries (≥20 SNR,f_GW≥ 5 mHz), in their gravitational-wave frequency (f_GW) and chirp mass. By repeating this process for different assumptions of the common-envelope ejection efficiency, we apply Bayesian hierarchical inference to find the best match to an injected astrophysical assumption for a fiducial population model. We conclude that the impact of common-envelope ejection efficiency on the mass-transfer processes involved in DWD formation may be statistically relevant in the future observed LISA population, and that constraints on binary formation may be found by comparing simulated populations to a future observed population. 

ABSTRACT We explore the eccentricity measurement threshold of Laser Interferometer Space Antenna (LISA) for gravitational waves radiated by massive black hole binaries (MBHBs) with redshifted BH masses Mz in the range 104.5–107.5 M⊙ at redshift z = 1. The eccentricity can be an important tracer of the environment where MBHBs evolve to reach the merger phase. To consider LISA’s motion and apply the time delay interferometry, we employ the lisabeta software and produce year-long eccentric waveforms using the inspiral-only post-Newtonian model taylorf2ecc. We study the minimum measurable eccentricity (emin, defined one year before the merger) analytically by computing matches and Fisher matrices, and numerically via Bayesian inference by varying both intrinsic and extrinsic parameters. We find that emin strongly depends on Mz and weakly on mass ratio and extrinsic parameters. Match-based signal-to-noise ratio criterion suggest that LISA will be able to detect emin ∼ 10−2.5 for lighter systems (Mz ≲ 105.5 M⊙) and ∼10−1.5 for heavier MBHBs with a 90 per cent confidence. Bayesian inference with Fisher initialization and a zero noise realization pushes this limit to emin ∼ 10−2.75 for lower-mass binaries, assuming a <50 per cent relative error. Bayesian inference can recover injected eccentricities of 0.1 and 10−2.75 for a 105 M⊙ system with an ∼10−2 per cent and an ∼10 per cent relative errors, respectively. Stringent Bayesian odds criterion ($$\ln {\mathcal {B}}\gt 8$$) provides nearly the same inference. Both analytical and numerical methodologies provide almost consistent results for our systems of interest. LISA will launch in a decade, making this study valuable and timely for unlocking the mysteries of the MBHB evolution.