2025ApJ...986...28Z

X-ray transients (XTs) driven by newborn magnetars from mergers of neutron star binaries (NSBs) have occasionally been detected in the narrow-field Chandra Deep Field-South (CDF-S) survey and the Swift/X-Ray Telescope observations of short gamma-ray bursts. Quantifying their event rate density (ERD) and luminosity function (LF) is critical for understanding NSB coalescence and magnetar formation. Utilizing population synthesis calculations incorporating various equations of state (EoSs), we derive a local ERD of ∼300 Gpc^–3 yr^–1 and a redshift-dependent ERD profile peaking at z = 1.81 followed by a rapid decline beyond z ∼ 4. Constructing an XT sample based on CDF-S and Swift observations, we characterize the LF by a single power-law function at L ≤ 4.75 × 10⁴⁶ erg s^–1 with a slope of -1.03, followed by a broken power-law function in which the break luminosity is L_b = 4.38 × 10⁴⁷ erg s^–1 and the slopes are -0.28 and -1.66. Based on the ERD and the LF, we estimate that the Einstein Probe (EP) detection rate is ∼31 yr^–1, adopting a conservative threshold flux of 10^–9 erg s^–1, a luminosity range of L ∈ [2 × 10⁴⁴, 2 × 10⁴⁹] erg s^–1, and a correction for the jet opening angle of ∼16^∘. This detection rate is consistent with the EP observations during its first year of operation. It is important to note that our estimation is subject to uncertainties arising from the LF derivation. Future EP observations of these XT events will be crucial in reducing these uncertainties.