Aims. An extreme Kerr black hole (BH) surrounded by a precessing disk is invoked to explain the light curves of gamma-ray bursts (GRBs) based on the coexistence of the Blandford-Znajek (BZ) and the magnetic coupling (MC) processes. Methods. The overall shape of the light curves and the duration of GRBs are interpreted by the evolution of the half-opening angle of the magnetic flux on the BH horizon, and the complex temporal structures are modulated by the precession and nutation of the jet powered by the BZ process. Results. The time profile of the emission exhibits a fast rise and a slow decay due to the effect of the evolution of the half-opening angle. The light curves of several GRBs are well fitted by this model with only six free parameters.

The continued observations of Sw J1644+57 in X-ray and radio bands accumulated a rich data set to study the relativistic jet launched in this tidal disruption event. The X-ray light curve of Sw J1644+57 from 5-30 days presents two kinds of quasi-periodic variations: a 200 second quasi-periodic oscillation (QPO) and a 2.7-day quasi-periodic variation. The latter has been interpreted by a precessing jet launched near the Bardeen-Petterson radius of a warped disk. Here we suggest that the ∼ 200s QPO could be associated with a second, narrower jet sweeping the observer line-of-sight periodically, which is launched from a spinning black hole in the misaligned direction with respect to the black hole's angular momentum. In addition, we show that this two-component jet model can interpret the radio light curve of the event, especially the re-brightening feature starting ∼ 100 days after the trigger. From the data we infer that inner jet may have a Lorentz factor of Γ j ∼ 5.5 and a kinetic energy of E k,iso ∼ 3.0 × 10 52 erg, while the outer jet may have a Lorentz factor of Γ j ∼ 2.5 and a kinetic energy of E k,iso ∼ 3.0 × 10 53 erg.

The universal radio-X-ray correlation (F R ∝ F b X , b ∼ 0.5 − 0.7) has been found for a sample of black-hole X-ray binaries (BHBs) in their low/hard states, which can roughly be explained by the coupled model of jet and radiatively inefficient advection dominated accretion flow. However, more and more 'outliers' were found in last few years, which evidently deviate from the universal radio-X-ray correlation and usually show a much steeper correlation with an index of ∼ 1.4. Based on simple physical assumptions, the radiatively efficient accretion flows are speculated to exist in these 'outliers'. In this work, we test this issue by modelling the 'outliers' track based on the radiatively efficient disc-corona model and the hybrid jet model. We find that our model predicts a steeper radio-X-ray correlation with slopes 1.2 for the typical viscosity parameter of α ∼ 0.05 − 0.2. In particular, the slope is ∼ 1.4 for the case of α ∼ 0.1, which is consistent with the observational results of H1743−322 very well. Our results suggest that the 'outliers' track may be regulated by the disc-corona model.

We argue, following our earlier works (the ''CEBZMC model ''), that the phenomenon of twin-peak highfrequency quasi-periodic oscillations (QPOs) observed in black hole X-ray binaries is caused by magnetic coupling ( MC) between the accretion disk and the black hole ( BH ). Due to MC, two bright spots occur at separate radial locations r in and r out at the disk surface, energized by a kind of Blandford-Znajek mechanism (BZ ). We assume, following the Kluzniak-Abramowicz QPO resonance model, that the Keplerian frequencies at these two locations are in the 3:2 ratio. With this assumption, we estimate the BH spins in several sources, including GRO J1655À40, GRS 1915+105, XTE J1550À564, H1743-322, and Sgr A Ã . We give an interpretation of the ''jet line'' in the hardness-intensity plane, discussing the parameter space consisting of the BH spin and the power-law index for the variation of the large-scale magnetic field in the disk. Furthermore, we propose a new scenario for the spectral state transitions in BH X-ray binaries based on fluctuations in the densities of the accreting plasma from a companion star.

A model for 3:2 high-frequency quasi-periodic oscillations (HFQPOs) with 3:2 pairs observed in four black hole X-ray binaries (BHXBs) is proposed by invoking the epicyclic resonances with the magnetic connection (MC) between a spinning black hole (BH) with a relativistic accretion disc. It turns out that the MC can be worked out due to Poynting-Robertson cosmic battery (PRCB), and the 3:2 HFQPO pairs associated with the steep power-law states can be fitted in this model. Furthermore, the severe damping problem in the epicyclic resonance model can be overcome by transferring energy from the BH to the inner disc via the MC process for emitting X-rays with sufficient amplitude and coherence to produce the HFQPOs. In addition, we discuss the important role of the magnetic field in state transition of BHXBs.