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Zhang (2013) proposed a type of GRB-less X-ray transient associated withdouble neutron star (NS-NS) mergers under the conjecture of a rapidly-spinningmagnetar merger product with the line of sight off the short GRB jet. Weinvestigate possible light curves of these transients by considering differentobserver's viewing angles. We perform Monte Carlo simulations to calculate thepeak luminosity function (LF) and event rate density of these X-ray transients.By considering that a fraction of massive neutron stars may be supra-massiveand later collapse into black holes after spinning down, we investigate how thepredicted LF depends on the equation of state (EoS) of the central object andthe geometry of the system. In general, the LF can be fit by two log-normaldistributions peaking around $10^{46.4}$ and $10^{49.6}$ $\rm erg\,s^{-1}$,corresponding to the trapped and free zones, respectively. For the majority ofthe EoS models, the current non-detection is consistent with having a free zonesolid angle at most a few times of the solid angle of the short GRB jet. Theevent rate density of these X-ray transients is around a few tens of $\rmGpc^{-3}yr^{-1}$ for luminosity above $10^{45}$ $\rm erg\,s^{-1}$. We predictthat future X-ray telescopes (such as Einstein Probe) with sensitivity $\sim10^{-11}$ $\rm erg\,s^{-1}\,cm^{-2}$ would detect as many as several tens ofsuch transients per year per steradian. Within 200 Mpc, the aLIGO average rangefor NS-NS mergers, the estimated event rate of these transients is about 1transient per year all sky.

X-ray counterpart of gravitational waves due to binary neutron star mergers: light curves, luminosity functions, and event rate densities