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

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