The jet breaks in the afterglow lightcurves of short gamma-ray bursts (SGRBs), rarely detected so far, are crucial for estimating the half-opening angles of the ejecta (θ j ) and hence the neutron star merger rate. In this work we report the detection of jet decline behaviors in GRB 150424A and GRB 160821B and find θ j ∼ 0.1 rad. Together with five events reported before 2015 and other three "identified" recently (GRB 050709, GRB 060614 and GRB 140903A), we have a sample consisting of nine SGRBs and one long-short GRB with reasonably estimated θ j . In particular, three Swift bursts in the sample have redshifts z ≤ 0.2, with which we estimate the local neutron star merger rate density to be ∼ 1109 +1432 −657 Gpc −3 yr −1 or 162 +140 −83 Gpc −3 yr −1 if the narrowly-beamed GRB 061201 is excluded. Inspired by the typical θ j ∼ 0.1 rad found currently, we further investigate whether the off-beam GRBs (in the uniform jet model) or the off-axis events (in the structured jet model) can significantly enhance the GRB/GW association or not. For the former the enhancement is at most moderate, while for the latter the enhancement can be much greater and a high GRB/GW association probability of ∼ 10% is possible. We also show that the data of GRB 160821B may contain a macronova/kilonova emission component with a temperature of ∼ 3100 K at ∼ 3.6 days after the burst and more data are needed to ultimately clarify.

Very recently the NICER collaboration published the first-ever accurate measurement of mass and radius together for PSR J0030+0451, a nearby isolated quickly rotating neutron star (NS). In this work we set the joint constraints on the equation of state (EoS) and some bulk properties of NSs with the data of PSR J0030+0451, GW170817, and some nuclear experiments. The piecewise polytropic expansion method and the spectral decomposition method have been adopted to parameterize the EoS. The resulting constraints are consistent with each other. Assuming the maximal gravitational mass of nonrotating NS M TOV lies between 2.04M ⊙ and 2.4M ⊙, with the piecewise method the pressure at twice nuclear saturation density is measured to be at the 90% level. For an NS with canonical mass of 1.4M ⊙, we have the moment of inertia , tidal deformability , radius , and binding energy at the 90% level, which are improved in comparison to the constraints with the sole data of GW170817. These conclusions are drawn for the mass/radius measurements of PSR J0030+0451 by Riley et al. For the measurements of Miller et al., the results are rather similar.

On 17 August 2017, a gravitational wave event (GW170817) and an associated short gamma-ray burst (GRB 170817A) from a binary neutron star merger had been detected. The followup optical/infrared observations also identified the macronova/kilonova emission (AT2017gfo). In this work we discuss some implications of the remarkable GW170817/GRB 170817A/AT2017gfo association. We show that the ∼ 1.7s time delay between the gravitational wave (GW) and GRB signals imposes very tight constraint on the superluminal movement of gravitational waves (i.e., the relative departure of GW velocity from the speed of light is ≤ 4.3 × 10 −16 ) or the possible violation of weak equivalence principle (i.e., the difference of the gamma-ray and GW trajectories in the gravitational field of the galaxy and the local universe should be within a factor of ∼ 3.4 × 10 −9 ). The socalled Dark Matter Emulators and a class of contender models for cosmic acceleration ("Covariant Galileon") are ruled out, too. The successful identification of Lanthanide elements in the macronova/kilonova spectrum also excludes the possibility that the progenitors of GRB 170817A are a binary strange star system. The high neutron star merger rate (inferred from both the local sGRB data and the gravitational wave data) together with the significant ejected mass strongly suggest that such mergers are the prime sites of heavy r-process nucleosynthesis.

We present time-resolved spectral analysis of the steep decay segments of 29 bright X-ray flares of gamma-ray bursts (GRBs) observed with the Swift/X-ray telescope, and model their lightcurves and spectral index evolution behaviors with the curvature effect model. Our results show that the observed rapid flux decay and strong spectral index evolution with time can be well fit with this model, and the derived characteristic timescales (t c ) are in the range of 33 ∼ 264 seconds. Using an empirical relation between the peak luminosity and the Lorentz factor derived from the prompt gammarays, we estimate the Lorentz factors of the flares (Γ X ). We obtain Γ X = 17 ∼ 87 with a median value of 52, which is smaller than the initial Lorentz factors of prompt gamma-ray fireballs. With the derived t c and Γ X , we constrain the radiating regions of 13 X-ray flares, yielding R X = (0.2 ∼ 1.1) × 10 16 cm, which are smaller than the radii of the afterglow fireballs at the peak times of the flares. A long evolution feature from prompt gamma-ray phase to the X-ray epoch is found by incorporating our results with a sample of GRBs whose initial Lorentz factors are available in literatures, i.e., Γ ∝ [t p /(1 + z)] −0.69±0.06 . These results may shed lights on the long term evolution of GRB central engines.

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