Detectability and resolvability of quasinormal modes with space-based gravitational wave detectors

The detection of quasinormal modes during the ringdown phase is a crucial method for testing the no-hair theorem. In this paper, the detectabilities and resolvabilities of multiple quasinormal modes using space-based gravitational wave detectors have been analyzed. The results indicate that TianQin and LISA have the potential to detect and resolve a series of modes, including six fundamental modes, one overtone, and two nonlinear second-order modes. Furthermore, the analysis of systematic errors in the waveform suggests that even modes such as $(l,m,n)=(3,3,1)$ and (4, 3, 0), which are unlikely to be directly detected and resolved, need to be taken into account in the ringdown waveform templates.