The Impact of Spin in Compact Binary Foreground Subtraction for Estimating the Residual Stochastic Gravitational-wave Background in Ground-based Detectors

Stochastic gravitational-wave (GW) background (SGWB) contains information about the early Universe and astrophysical processes. The recent evidence of SGWB by pulsar timing arrays in the nanohertz band is a breakthrough in the GW astronomy. For ground-based GW detectors, while in data analysis, the SGWB can be masked by loud GW events from compact binary coalescences (CBCs). Assuming a next-generation ground-based GW detector network, we investigate the potential for detecting the astrophysical and cosmological SGWB with non-CBC origins by subtracting recovered foreground signals of loud CBC events. The Fisher Information Matrix (FIM) method is adopted for quick calculation. As an extension of the studies by Sachdev {\it et al.} (2020) and Zhou {\it et al.} (2023), two more essential features are considered. Firstly, we incorporate non-zero aligned or anti-aligned spin parameters in our waveform model. Because of the inclusion of spins, we obtain significantly more pessimistic results than the previous work, where the residual energy density of foreground is even larger than the original CBC foreground. For the most extreme case, we observe that the subtraction results are approximately 10 times worse for binary black hole events and 20 times worse for binary neutron star events than the scenarios without accounting for spins. The degeneracy between the spin parameters and the symmetric mass ratio is strong in the parameter estimation process, and it contributes most to the imperfect foreground subtraction. Secondly, in this work, extreme CBC events with condition numbers of FIMs $c_{\rm{\Gamma}}>10^{15}$ are preserved. The impacts of these extreme events on foreground subtraction are discussed. Our results have important implications for assessing the detectability of SGWB from non-CBC origins for ground-based GW detectors.