The bulk Lorentz factor of the gamma-ray burst (GRB) ejecta (Γ 0 ) is a key parameter to understand the GRB physics. Liang et al. have discovered a correlation between Γ 0 and isotropic γ-ray energy: Γ 0 ∝ E 0.25 γ,iso,52 . By including more GRBs with updated data and more methods to derive Γ 0 , we confirm this correlation and obtain Γ 0 ≃ 91E 0.29 γ,iso,52 . Evaluating the mean isotropic γ-ray luminosities L γ,iso of the GRBs in the same sample, we discover an even tighter correlation Γ 0 ≃ 249L 0.30 γ,iso,52 . We propose an interpretation to this later correlation. Invoking a neutrino-cooled hyperaccretion disk around a stellar mass black hole as the central engine of GRBs, we derive jet luminosity powered by neutrino annihilation and baryon loading from a neutrino-driven wind. Applying beaming correction, we finally derive Γ 0 ∝ L 0.22 γ,iso , which is consistent with the data. This suggests that the central engine of long GRBs is likely a stellar mass black hole surrounded by a hyper-accreting disk.

Gamma-ray bursts are most luminous explosions in the universe. Their ejecta are believed to move towards Earth with a relativistic speed. The interaction between this "relativistic jet" and a circumburst medium drives a pair of (forward and reverse) shocks. The electrons accelerated in these shocks radiate synchrotron emission to power the broad-band afterglow of GRBs. The external shock theory is an elegant theory, since it invokes a limit number of model parameters, and has well predicted spectral and temporal properties. On the other hand, depending on many factors (e.g. the energy content, ambient density profile, collimation of the ejecta, forward vs. reverse shock dynamics, and synchrotron spectral regimes), there is a wide variety of the models. These models have distinct predictions on the afterglow decaying indices, the spectral indices, and the relations between them (the so-called "closure relations"), which have been widely used to interpret the rich multiwavelength afterglow observations. This review article provides a complete reference of all the analytical synchrotron external shock afterglow models by deriving the temporal and spectral indices of all the models in all spectral regimes, including some regimes that have not been published before. The review article is designated to serve as a useful tool for afterglow observers to quickly identify relevant models to interpret their data. The limitations of the analytical models are reviewed, with a list of situations summarized when numerical treatments are needed.

Recent observations and theoretical work on gamma-ray bursts (GRBs) favor the central engine model of a Kerr black hole (BH) surrounded by a magnetized neutrino-dominated accretion flow (NDAF). The magnetic coupling between the BH and disk through a large-scale closed magnetic field exerts a torque on the disk, and transports the rotational energy from the BH to the disk. We investigate the properties of the NDAF with this magnetic torque. For a rapid spinning BH, the magnetic torque transfers enormous rotational energy from BH into the inner disk. There are two consequences: (i) the luminosity of neutrino annihilation is greatly augmented; (ii) the disk becomes thermally and viscously unstable in the inner region, and behaves S-Shape of the surface density versus accretion rate.It turns out that magnetically torqued NDAF can be invoked to interpret the variability of gamma-ray luminosity. In addition, we discuss the possibility of restarting the central engine to produce the X-ray flares with required energy.Subject headings: accretion, accretion disk-black hole physics -magnetic fieldsgamma rays: bursts -neutrinos Recently, the magnetic coupling (MC) between the central spinning BH and their surrounding accretion disk has been paid much attention (e.g. Blandford 1999;van Putten 1999;Li & Paczynski 2000;Li 2002;Wang et al. 2002). As a variant of the BZ process, the MC process exerts a torque on the disk, and transports the rotational energy from the BH to the disk. The effects of MC torque has been discussed in some disk models, for example, Lai (1998) and Lee (1999) in a neutron star with slim disk, Li (2002), Wang et al. (2002Wang et al. ( , 2003, Kluzniak and Rappaport (2007) in a compact object with thin disk, Ye et al. (2007) and Ma et al. (2007) in a BH with advection-dominated accretion flow (ADAF). It is found, the disk properties are greatly changed and its luminosity is augmented significantly due to the rotational energy of BH extracted in the MC process. Therefore, it is attractive for us to investigate the effects of MC torque on NDAF. To highlight the effects of MC torque, we ignore other MHD process, such as BZ and BP mechanism, and we refer to this model as MCNDAF.This paper is organized as follows. In Sect. 2 we describe the MCNDAF model, which is a relativistic steady state thin disk. The effects of MHD stress are described by the dimensionless parameter α. The main equations are based on DPN02 and NPK01.Recently, GLL06, Chen & Beloborodov (2006) and Shibata et al. (2006Shibata et al. ( , 2007 argued that the general relativistic (GR) effects are important for NDAF, so we introduce GR correction factors to the equations. The MC torque appears in the angular momentum equation.

Fast radio bursts (FRBs) are radio bursts characterized by millisecond durations, high Galactic latitude positions, and high dispersion measures. Very recently, the cosmological origin of FRB 150418 has been confirmed by Keane et al. (2016), and FRBs are now strong competitors as cosmological probes. The simple sharp feature of the FRB signal is ideal for them to probe some of the fundamental laws of physics. Here we show that by analyzing the delay time between different frequencies, the FRB data can place stringent upper limits on the rest mass of the photon. For FRB 150418 at z = 0.492, one can potentially reach m γ ≤ 5.2 × 10 −47 g, which is 10 20 times smaller than the rest mass of electron, and is about 10 3 times smaller than that obtained using other astrophysical sources with the same method.

Long-duration γ-ray bursts (GRBs) at z < 1 are in most cases found to be accompanied by bright, broad-lined Type Ic supernovae (SNe Ic-BL). The highestenergy GRBs are mostly located at higher redshifts, where the associated SNe are hard to detect observationally. Here we present early and late observations of