New Potential Ultra-compact X-ray Binaries for Space-based Gravitational Wave Detectors From Low-Mass Main-Sequence Companion Channel

We investigate the formation and evolution of Ultra-Compact X-ray Binaries (UCXBs) using the COMPAS binary evolution code, starting from the Zero Age Main Sequence (ZAMS). Focusing on the low-mass MS companion channel, we simulate gravitational wave (GW) signals from UCXBs with LEGWORK and evaluate their detectability by space-based observatories such as Taiji and TianQin. By incorporating signal-to-noise ratio (SNR) calculations with a threshold of SNR > 5, we provide a realistic framework to assess the detectability of the GW source. Our analysis suggests that the Milky Way currently hosts 7-32 observable UCXBs from the MS companion channel. Taiji or LISA alone could detect 1-6 sources over an 8-year observation period, while TianQin, due to its high-frequency sensitivity, contributes to detecting systems with extremely short orbital periods and can also detect 1-4 sources. Comparison with sensitivity curves validates UCXBs as detectable GW sources, particularly at greater Galactic distances. This study improves our understanding of the evolution of UCXBs and their role as GW sources. By integrating population synthesis, SNR-based analyses, and observational data, we establish UCXBs as significant targets for GW astronomy, paving the way for future missions and theoretical studies of compact binary systems.