Unveiling a multi-component stochastic gravitational-wave background with the TianQin + LISA network

Space-borne detectors, including TianQin and Laser Interferometry Space Antenna (LISA), are tasked with simultaneously observing the Galactic foreground, astrophysical and cosmological stochastic gravitational-wave backgrounds (SGWBs). For the first time, we employ a space-borne detector network to identify these SGWBs. Specifically, we develop a tailored likelihood for cross-correlation detection with such networks. Combined with the likelihood, we use the simulated datasets of the TianQin + LISA network to conduct an analysis for model selection and parameter estimation. In our analysis, we adopt an astrophysical background originating from extragalactic white-dwarf binaries, along with a flat cosmological background associated with the early Universe. Our results indicate that, after 4 years of operation, the network could detect a single SGWB from either astrophysical or cosmological origins, with an energy density $\Omega_{\rm ast/cos}$ (10 mHz) on the order of $10^{-12}$, despite the presence of a Galactic foreground. Furthermore, to distinguish the cosmological background from both a Galactic foreground and an extragalactic background produced by white-dwarf binaries, the energy density $\Omega_{\rm cos}$ should reach around $2\times 10^{-11}$.