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Abstract

The Laser Interferometer Space Antenna (LISA) will detect and characterize




$\sim10^4$ Galactic Binaries consisting predominantly of two White Dwarfs (WD).




An interesting prospect within this population is a third object--another WD




star, a Circumbinary Exoplanet (CBP), or a Brown Dwarf (BD)--in orbit about the




inner WD pair. We present the first fully Bayesian detection and posterior




analysis of sub-stellar objects with LISA, focusing on the characterization of




CBPs. We used an optimistic astrophysically motivated catalogue of these CBP




third-body sources, including their orbital eccentricity around the inner




binary for the first time. We examined Bayesian Evidence computations for




detectability, as well as the effects on the posterior distributions for both




the inner binary parameters and the third-body parameters. We find that the




posterior behavior bifurcates based on whether the third-body period is above




or below half the observation time. Additionally, we find that undetectable




third-body sources can bias the inner binary parameters whether or not the




correct template is used. We used the information retrieved from the study of




the CBP population to make an initial conservative prediction for the number of




detectable BD systems in the original catalogue. We end with commentary on the




predicted qualitative effects on LISA global fitting and Galactic Binary




population analysis. The procedure used in this work is generic and can be




directly applied to other astrophysical effects expected within the Galactic




Binary population.