Recovering Injected Astrophysics from the LISA Galactic Double White Dwarf Binaries

We present the successful recovery of common envelope ejection efficiency assumed in a simulated population of double white dwarf binaries like those which may be observed by the future LISA mission. We simulate the formation of double white dwarf 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 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, fGW > 5mHz), in their gravitational wave frequency (fGW) 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 double white dwarf 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.