Gravitational wave peep contributions to background signal confusion noise for LISA

Two-body gravitational interactions will occasionally lead to a stellar-mass compact object entering a very highly eccentric orbit around a massive black hole at the center of a galaxy. Gravitational radiation damping will subsequently result in an extreme mass ratio inspiral. Much of the inspiral time of these events is spent with the compact object on a long-period orbit, with a brief burst of gravitational wave emission at periapsis firmly in the mHz band. Burst orbits have been previously modeled as parabolic, with a focus on extreme examples that could be detectable by space-based gravitational wave detectors. This work focuses on the recurring bursts called ``peeps". Peeps are not likely to be individually resolvable; however, it is also important to consider them as possible sources of signal confusion noise because they do generate a signal within the LISA band with every pericenter passage. To account for peeps, we must utilize estimates for EMRI capture parameters along with tracking the massive black hole population out to a redshift of 3 using the Illustris Project. Then, this population is combined with an EMRI formation rate to estimate the number of EMRI events per unit volume for LISA. In this study, we model four different assumptions for the gravitational wave background produced by these highly eccentric peeps. We find that with our two most likely backgrounds, the signal may result in a slight rise of the LISA noise floor (SNR $\sim 0.3-2.4$); however, in two more abundant cases, the background generated by these sources would be detectable on their own and likely obscure many potentially detectable sources (SNR $\sim77-145$).