Revealing the origin of supermassive black holes with Taiji-TianQin network

The origin of supermassive black holes (SMBHs) is a pivotal problem in modern cosmology. This work explores the potential of the Taiji-TianQin space-borne gravitational-wave (GW) detector network to identify the formation channels of massive black hole binaries (MBHBs) at high redshifts ($z~\gtrsim~10$). The network substantially improves detection capability, boosting the signal-to-noise ratio by a factor of 2.2-3.0 (1.06-1.14) relative to TianQin (Taiji) alone. It increases the detection rate of MBHBs formed from light seeds (LS) by more than 2.2 times and achieves over 96% detection efficiency for those originating from heavy seeds (HS). Furthermore, the network enables component mass estimation with relative uncertainties as low as $\sim~10^{-4}$ at the $2\sigma$ level. These improvements facilitate the assembly of a well-constrained population sample, allowing robust measurement of the fractional contributions from different formation pathways. The network achieves high precision in distinguishing between LS and HS origins (7.4% relative uncertainty at $2\sigma$) and offers moderate discrimination between delay and no-delay channels in HS-origin binaries (24%). However, classification remains challenging for delay versus no-delay scenarios in LS-origin systems (58%) due to significant population overlap. In conclusion, the Taiji-TianQin network will serve as a powerful tool for unveiling the origins of SMBHs through GW population studies.