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GRB 170817A, detected by Fermi Gamma-ray Burst Monitor 1.7 s after the merger of a neutron star (NS) binary, provides the first direct evidence for a link between such a merger and a short-duration gamma-ray burst. The X-ray observations after GRB 170817A indicate a possible X-ray flare with a peak luminosity |$L_{\rm peak} \sim 2\times 10^{39}\, {\rm erg\, s}^{-1}$| near day 156. Here we show that this X-ray flare may be understood based on a slim disc around a compact object. On the one hand, there exists the maximal accretion rate |$\dot{M}_{\rm max}$| for the slim disc, above which an optically thick outflow is significant and radiation from the disc is obscured. Based on the energy balance analysis, we find that |$\dot{M}_{\rm max}$| is in the range of |${\sim } 4\dot{M}_{\rm Edd}$| and |${\sim } 21\dot{M}_{\rm Edd}$| when the angular velocity of the slim disc is between |$\rm (1/5)^{1/2}\Omega _K$| and |$\rm \Omega _K$| (where |$\dot{M}_{\rm Edd}$| is the Eddington accretion rate and ΩK is the Keplerian angular velocity). With |$\dot{M}_{\rm max}$|⁠, the slim disc can provide a luminosity ∼ L peak for a compact object of |$2.5 \, \mathrm{M}_{\odot }$|⁠. On the other hand, if the merger of two NSs forms a typical neutrino-dominated accretion disc whose accretion rate |$\dot{M}$| follows a power-law decline with an index −1.8, then the system must pass through the outflow regime and enter the slim disc in ∼11–355 d. These results imply that a post-merger slim accretion disc could account for the observed late-time L peak. [ABSTRACT FROM AUTHOR]

Neutrino-dominated accretion flows (NDAFs) around rotating stellar-mass black holes (BHs) are plausible candidates for the central engines of gamma-ray bursts (GRBs). NDAFs are hyperaccretion disks with accretion rates in the range of around 0.001–10 M ⊙ s − 1 , which have high density and temperature and therefore are extremely optically thick and geometrically slim or even thick. We review the theoretical progresses in studying the properties of NDAFs as well as their applications to the GRB phenomenology. The topics include: the steady radial and vertical structure of NDAFs and the implications for calculating neutrino luminosity and annihilation luminosity, jet power due to neutrino-antineutrino annihilation and Blandford–Znajek mechanism and their dependences on parameters such as BH mass, spin, and accretion rate, time evolution of NDAFs, effect of magnetic fields, applications of NDAF theories to the GRB phenomenology such as lightcurve variability, extended emission, X-ray flares, kilonovae, etc., as well as probing NDAFs using multi-messenger signals such as MeV neutrinos and gravitational waves. [ABSTRACT FROM AUTHOR]