How many extra-Galactic stellar-mass binary black holes will be detected by space gravitational-wave interferometers?

On the basis of GWTC-3, we discuss the detection prospect of extra-Galactic binary black holes (BBHs) by space gravitational-wave interferometers. In particular, targeting BBHs with component masses around 5-100$M_\odot$, we directly incorporate the chirp mass distribution of the 62 BBHs detected at high significance. We find that, due to the reduction of both the comoving merger rate and a weighted average of chirp masses, the expected detection numbers are generally much smaller than the results obtained by the same authors immediately after the report of GW150914. For LISA, the total BBH detections are estimated to be $N_{\rm tot}\sim 2 (T/4{\rm yr})^{3/2}(\rho_{\rm thr}/10)^{-3}$, dominated by nearly monochromatic BBHs ($\rho_{\rm thr}$: the detection threshold, $T$: the observational period). TianQin will have a total detection number $N_{\rm tot}$ similar to LISA. Meanwhile, TianQin has potential to find $N_{\rm mer}\sim0.6 (T/4{\rm yr})^{7/4}(\rho_{\rm thr}/10)^{-3}$ BBHs that merge in the observational period. This number for merging BBHs is 4-5 times larger than that of LISA, because of the difference between the optimal bands. We also investigate prospects for joint operations of multiple detectors, finding that concurrent observations will be more advantageous than sequential ones.