On the detection of the electromagnetic counterparts from lensed gravitational wave events by binary neutron star mergers


 Future ground-based gravitational wave (GW) detectors, i.e. Einstein telescope (ET) and Cosmic Explorer (CE), are expected to detect a significant number of lensed binary neutron star (BNS) mergers, which may provide a unique tool to probe cosmology. In this paper, we investigate the detectability of the optical/infrared electromagnetic (EM) counterparts (kilonovae/afterglows) from these lensed BNS mergers by future GW detectors and EM telescopes using simple kilonova, afterglow, and lens models. ET and CE are expected to detect $\sim 5.32^{+26.1}_{-5.10}$ and $67.3^{+332}_{-64.7}$ lensed BNS mergers per year. We find that the EM counterparts associated with all these mergers will be detectable by an all sky-survey in the H-band with the limiting magnitude $m_{\textrm {lim}}\gtrsim 27$, while the detectable fraction is $\lesssim 0.4{{\%}}$ in the g-/z-band if with $m_{\textrm {lim}}\lesssim 24$. Generally it is more efficient to search the lensed EM counterparts by adopting the infrared bands than the optical/UV bands with the same $m_{\textrm {lim}}$. Future telescopes like Vera C. Rubin Observatory, China Space Station Telescope, and Euclid can hardly detect the EM counterparts of even one lensed BNS merger. Roman Space Telescope (RST) and James Webb Space Telescope (JWST) have the capability to detect about a few or more such events per year. Moreover, the time delays and separations between the lensed image pairs are typically in the ranges from minutes to months and from 0.1 to 1 arcsec, suggesting that both the GW and EM images of most lensed BNS mergers can be well resolved by not only CE/ET in the time domain but also RST/JWST spatially.