Submillimeter Detectability of Gravitational-Wave Counterparts from Neutron-Star Mergers with the Xue-shan-mu-chang 15-meter Telescope

Abstract

Submillimeter (sub-mm) follow-up of binary neutron star (BNS) mergers provides unique constraints on the early-time energetics and environments of relativistic outflows, capturing the spectral evolution at epochs where centimeter-band emission is often still optically thick or yet to peak. However, the practical scientific yield depends on instrument-specific thresholds, the observing cadence, and the distinct temporal contributions from isotropic ejecta versus beamed relativistic jets. With the upcoming Xue-shan-mu-chang 15-meter SubMillimeter Telescope (XSMT), facility-specific forecasts are needed to test for sustained engine energy injection, as expected for a long-lived magnetar remnant rather than a promptly formed black hole. We present a unified numerical framework that couples engine-driven ejecta dynamics to non-thermal synchrotron emission, accounting for synchrotron self-absorption and deep-Newtonian effects. Adopting fixed 5$\sigma$ (1 h) point-source thresholds of 1.5/2.9/10.2 mJy at 230/345/460 GHz, we construct parameter-space detectability maps and estimate event rates based on current BNS merger-rate priors. For a fiducial local event at 40 Mpc, we find that a magnetar-boosted ejecta afterglow peaks on timescales of weeks to months and remains detectable long enough to allow delayed follow-up, with an expected all-sky rate of $\dot N_{\rm ej} \approx 0.05$--1.7 yr$^{-1}$ at 230 GHz for $f_{\rm mag}=1$; this rate is an upper limit and scales linearly with the long-lived magnetar fraction. Conversely, while relativistic jets produce intense early-time signals, their detection is constrained by narrow beaming and fleeting visibility. Our framework provides a quantitative basis for prioritizing gravitational-wave triggers and maximizing the scientific yield of XSMT in the multi-messenger era.