Prototype stochastic gravitational wave background recovery in the LISA global fit residual

The Laser Interferometer Space Antenna (LISA) mission poses a difficult parameter estimation challenge: the sources will be so dense in both time and frequency that they all must be fit simultaneously in a `global fit'. Successful tests of global fit efforts on synthetic datasets have been recently reported, recovering extragalactic black hole mergers and galactic binaries, including the GLASS pipeline in Littenberg and Cornish [Prototype global analysis of LISA data with multiple source types, Phys. Rev. D 107, 063004 (2023).]. Injected stochastic sources, however, have so far been absent in these datasets. In this work we report our development of a stochastic search pipeline ready for inclusion in future tests of the global fit, capable of detecting or placing limits on a wide variety of possible cosmologically- and astrophysically-inspired stochastic backgrounds (SGWBs). The code uses short-time Fourier transforms to allow for inference despite the nonstationarity of the noise. We quote results using both purely synthetic confusion noise and two GLASS residuals, and quantify the impact of the residuals' non-Gaussianity on injected signal recovery and on setting upper limits. We find that, if not properly mitigated, non-Gaussianities can preclude setting accurate SGWB upper limits and lead to false detections. We also stress that the narrow-band non-Gaussianities we find do not affect all sources equally, and many narrower-band, cosmologically-inspired SGWBs are more sensitive to non-Gaussianity than others.