Detection of the stochastic gravitational wave background with the space-based gravitational-wave detector network

The stochastic gravitational wave background (SGWB) is one of the main detection targets for future millihertz space-based gravitational-wave observatories such as the laser interferometer space antenna (LISA), TianQin, and Taiji. For a single LISA-like detector, a null-channel method was developed to identify the SGWB by integrating data from the A and E channels with a noise-only T channel. However, the noise monitoring channel will not be available if one of the laser interferometer arms fails. By combining these detectors, it will be possible to build detector networks to search for SGWB via cross-correlation analysis. In this work, we developed a Bayesian data analysis method based on time delay interferometry (TDI) Michelson-type channel. We then investigate the detectability of the TianQin-LISA detector network for various isotropic SGWB. Assuming a three-month observation, the TianQin-LISA detector network could be able to confidently detect SGWB with energy density as low as ${\Omega }_{PL}=6.0\times {10}^{-13}$, ${\Omega }_{Flat}=2.0\times {10}^{-12}$ and ${\Omega }_{SP}=1.2\times {10}^{-12}$ for power-law, flat and single-peak models, respectively.