Long-duration gamma-ray bursts (LGRBs) and ultra-LGRBs (ULGRBs) originate from collapsars, in the center of which a newborn rotating stellar-mass black hole (BH) surrounded by a massive accretion disk may form. In the scenario of BH hyperaccretion inflow-outflow model and BlandfordZnajek (BZ) mechanism to trigger gamma-ray bursts (GRBs), the real accretion rate to power a BZ jet is far lower than the mass supply rate from the progenitor star. The characteristics of the progenitor stars can be constrained by GRB luminosity observations, and the results exceed usual expectations.LGRBs lasting from several seconds to tens of seconds in the rest frame may originate from solar-metallicity (Z ∼ 1 Z ⊙ , where Z and Z ⊙ are the metallicities of progenitor stars and the Sun), massive (M 34 M ⊙ , where M and M ⊙ are the masses of progenitor stars and the Sun) stars or some zero-metallicity (Z ∼ 0) stars. A fraction of low-metallicity (Z 10 −2 Z ⊙ ) stars, including Population III stars, can produce ULGRBs such as GRB 111209A. The fraction of LGRBs lasting less than tens of seconds in the rest frame is more than 40%, which cannot conform to the fraction of the demanded type of progenitor star. It possibly implies that the activity timescale of central engine may be much longer than the observed timescale of prompt emission phase, as indicated by X-ray late-time activities. Alternatively, LGRBs and ULGRBs may be powered by a millisecond magnetar central engine.

Active galactic nuclei (AGNs) have long been observed to "twinkle" (i.e., their brightness varies with time) on timescales from days to years in the UV/optical bands. Such AGN UV/optical variability is essential for probing the physics of supermassive black holes (SMBHs), the accretion disk, and the broad-line region. Here we show that the temperature fluctuations of an AGN accretion disk, which is magnetically coupled with the corona, can account for observed high-quality AGN optical light curves. We calculate the temperature fluctuations by considering the gas physics of the accreted matter near the SMBH. We find that the resulting simulated AGN UV/optical light curves share the same statistical properties as the observed ones as long as the dimensionless viscosity parameter α, which is widely believed to be controlled by magnetohydrodynamic (MHD) turbulence in the accretion disk, is about 0.01-0.2. Moreover, our model can simultaneously explain the larger-thanexpected accretion disk sizes and the dependence of UV/optical variability upon wavelength for NGC 5548. Our model also has the potential to explain some other observational facts of AGN UV/optical variability, including the timescale-dependent bluer-when-brighter color variability and the dependence of UV/optical variability on AGN luminosity and black hole mass. Our results also demonstrate a promising way to infer the black-hole mass, the accretion rate, and the radiative efficiency, thereby facilitating understanding of the gas physics and MHD turbulence near the SMBH and its cosmic mass growth history by fitting the AGN UV/optical light curves in the era of time-domain astronomy.