Binary neutron star (NS) mergers are strong gravitational-wave (GW) sources and the leading candidates to interpret short-duration gamma-ray bursts (SGRBs). Under the assumptions that SGRBs are produced by double neutron star mergers and that the x-ray plateau followed by a steep decay as observed in SGRB x-ray light curves marks the collapse of a supramassive neutron star to a black hole (BH), we use the statistical observational properties of Swift SGRBs and the mass distribution of Galactic double neutron star systems to place constraints on the neutron star equation of state (EoS) and the properties of the post-merger product. We show that current observations already impose the following interesting constraints. (1) A neutron star EoS with a maximum mass close to a parametrization of $M_{\max }=2.37M_{\odot }(1+1.58\times {10}^{-10}{P}^{-2.84})$ is favored. (2) The fractions for the several outcomes of NS-NS mergers are as follows: $\sim 40\%$ prompt BHs, $\sim 30\%$ supramassive NSs that collapse to BHs in a range of delay time scales, and $\sim 30\%$ stable NSs that never collapse. (3) The initial spin of the newly born supramassive NSs should be near the breakup limit ($P_i\sim 1\mathrm{ms}$), which is consistent with the merger scenario. (4) The surface magnetic field of the merger products is typically $\sim {10}^{15}\mathrm{G}$. (5) The ellipticity of the supramassive NSs is $\epsilon \sim (0.004-0.007)$, so that strong GW radiation is released after the merger. (6) Even though the initial spin energy of the merger product is similar, the final energy output of the merger product that goes into the electromagnetic channel varies in a wide range from several ${10}^{49}$ to several ${10}^{52}\mathrm{erg}$, since a good fraction of the spin energy is either released in the form of GWs or falls into the black hole as the supramassive NS collapses.

Fast radio bursts (FRBs), bright transients with millisecond durations at ∼GHz and typical redshifts probably >0.8, are likely to be gravitationally lensed by intervening galaxies. Since the time delay between images of strongly lensed FRB can be measured to extremely high precision because of the large ratio ∼10⁹ between the typical galaxy-lensing delay time $$\sim{\cal O}$$~ O (10 days) and the width of bursts $$\sim{\cal O}$$~ O (ms), we propose strongly lensed FRBs as precision probes of the universe. We show that, within the flat ΛCDM model, the Hubble constant H₀ can be constrained with a ~0.91% uncertainty from 10 such systems probably observed with the square kilometer array (SKA) in <30 years. More importantly, the cosmic curvature can be model independently constrained to a precision of ∼0.076. This constraint can directly test the validity of the cosmological principle and break the intractable degeneracy between the cosmic curvature and dark energy.

Due to the limited sensitivity of the current gravitational wave (GW) detectors, the central remnant of the binary neutron star (NS) merger associated with GW170817 remains an open question. In view of the relatively large total mass, it is generally proposed that the merger of GW170817 would lead to a short-lived hypermassive NS or directly produce a black hole (BH). There is no clear evidence to support or rule out a long-lived NS as the merger remnant. Here, we utilize the GW and electromagnetic (EM) signals to comprehensively investigate the parameter space that allows a long-lived NS to survive as the merger remnant of GW170817. We find that for some stiff equations of state, the merger of GW170817 could, in principle, lead to a massive NS, which has a millisecond spin period. The post-merger GW signal could hardly constrain the ellipticity of the NS. If the ellipticity reaches 10⁻³, in order to be compatible with the multi-band EM observations, the dipole magnetic field of the NS (B _p ) is constrained to the magnetar level of ∼10¹⁴ G. If the ellipticity is smaller than 10⁻⁴, B _p is constrained to the level of ∼10⁹–10¹¹ G. These conclusions weakly depend on the adoption of the NS equation of state.

GRB 080503 is a short gamma-ray burst (GRB) detected by Swift and has been classified as a GRB originating from a compact star merger. The soft extended emission and the simultaneous late re-brightening in both the X-ray and optical afterglow light curves raise interesting questions regarding its physical origin. We show that the broadband data of GRB 080503 can be well explained within the framework of the double neutron star merger model, provided that the merger remnant is a rapidly rotating massive neutron star with an extremely high magnetic field (i.e., a millisecond magnetar). We show that the late optical re-brightening is consistent with the emission from a magnetar-powered “merger-nova.” This adds one more case to the growing sample of merger-novae associated with short GRBs. The soft extended emission and the late X-ray excess emission are well connected through a magnetar dipole spin-down luminosity evolution function, suggesting that direct magnetic dissipation is the mechanism to produce these X-rays. The X-ray emission initially leaks from a hole in the merger ejecta pierced by the short GRB jet. The hole subsequently closes after the magnetar spins down and the magnetic pressure drops below ram pressure. The X-ray photons are then trapped behind the merger-nova ejecta until the ejecta becomes optically thin at a later time. This explains the essentially simultaneous re-brightening in both the optical and X-ray light curves. Within this model, future gravitational-wave sources could be associated with a bright X-ray counterpart along with the merger-nova, even if the short GRB jet beams away from Earth.

The merger of a double neutron star (NS–NS) binary may result in a rapidly rotating massive NS with an extremely strong magnetic field (i.e., a millisecond magnetar). In this case, the magnetic spin-down of the NS remnant provides an additional source of sustained energy injection, which would continuously power the merger ejecta. The thermal emission from the merger ejecta would give rise to a bright optical “magnetar-powered merger-nova.” In this work, we carry out a complete search for magnetar-powered merger-nova from a Swift short gamma-ray burst sample. We focus on short GRBs with extended emission or internal plateau, which may signify the presence of magnetars as the central engine. We eventually find three candidates of magnetar-powered merger-nova from the late observations of GRB 050724, GRB 070714B, and GRB 061006. With standard parameter values, the magnetar remnant scenario could well interpret the multi-band data of all three bursts, including the extended emission and their late chromatic features in the optical and X-ray data. The peak luminosities of these merger-novae reach several times , more than one order of magnitude brighter than the traditional “kilo-novae” with peak luminosity of . Intense, multi-color, late-time observations of short GRBs are encouraged to identify more merger-novae in the future.