Foreground cleaning and template-free stochastic background extraction for LISA

Based on the rate of resolved stellar origin black hole and neutron star mergers measured by LIGO and Virgo, it is expected that these detectors will also observe an unresolved Stochastic Gravitational Wave Background (SGWB) by the time they reach design sensitivity. A background from the same class of sources also exists in the LISA band, which will be observable by LISA with signal-to-noise ratio (SNR) ~ 121. Unlike the stochastic signal from Galactic white dwarf binaries, for which a partial subtraction is expected to be possible by exploiting its yearly modulation (induced by the motion of the LISA constellation), the background from unresolved stellar origin black hole and neutron star binaries acts as a foreground for other stochastic signals of cosmological or astrophysical origin, which may also be present in the LISA band. Here, we employ a principal component analysis to model and extract an additional hypothetical SGWB in the LISA band, without making any a priori assumptions on its spectral shape. At the same time, we account for the presence of the foreground from stellar origin black holes and neutron stars, as well as for possible uncertainties in the LISA noise calibration. We find that our technique leads to a linear problem and is therefore suitable for fast and reliable extraction of SGWBs with SNR up to ten times weaker than the foreground from black holes and neutron stars, quite independently of the SGWB spectral shape.