Detectability of Nearby Binary Neutron Stars with Future sub-mHz Gravitational Wave Missions

Binary neutron stars (BNSs) are one of the most important gravitational wave (GW) sources, which provide key insights to evolution of massive binary stars and nuclear physics. Beyond Laser Interferometer Space Antenna (LISA), Taiji, and Tianqin missions, proposed concepts for next generation space-based GW observatories, including LISAmax, Folkner, and eASTROD, aim to explore the sub-millihertz (mHz) to microhertz ($\mu$ Hz) frequency band. Because the proposed designs substantially suppress low-frequency noise, these detectors are expected to outperform LISA, Taiji, and Tianqin in detecting eccentric Galactic BNS systems. In this paper, we estimate the detectability of nearby inspiraling BNSs using future sub-mHz GW detectors. By utilizing compact binary population synthesis simulations to generate mock BNS samples and estimate their signal-to-noise ratios (SNRs) correspondingly for each GW detector over an observation period of $5-10$\,years, we find that LISAmax may detect $\sim 520-900$ Galactic BNSs, whereas Folkner and eASTROD may detect $\sim 780-1370$ Galactic BNSs. Notably, LISAmax excels in detecting highly eccentric systems $(e>0.90)$ owing to its higher sensitivity at relatively higher sub-mHz frequencies. We further identify seven observed radio BNSs as viable candidates for validation, in particular J0737-3039, which reaches an SNR of $\sim 100$. The expected detection number of LMC inspiraling BNSs is about $\sim 4-18$ for these sub-mHz detectors over an observation period of $5-10$\,years, while detecting inspiraling BNSs in SMC is challenging. This study highlights the significant potential of future sub-mHz GW missions in unraveling BNS formation and evolution physics.