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.

A calibration is made for the correlation between the X-ray Variability Amplitude (XVA) and black hole (BH) mass. The correlation for 21 reverberationmapped Active Galactic Nuclei (AGNs) appears very tight, with an intrinsic dispersion of 0.20 dex. The intrinsic dispersion of 0.27 dex can be obtained if BH masses are estimated from the stellar velocity dispersions. We further test the uncertainties of mass estimates from XVAs for objects which have been observed multiple times with good enough data quality. The results show that the XVAs derived from multiple observations change by a factor of 3. This means that BH mass uncertainty from a single observation is slightly worse than either reverberation-mapping or stellar velocity dispersion measurements; however BH mass estimates with X-ray data only can be more accurate if the mean XVA value from more observations is used. With this calibrated relation, the BH mass and accretion rate may be determined for a large sample of AGNs with the planned International X-ray Observatory mission.Proper interpretation of the first AGN X-ray quasi-periodic oscillation (QPO), seen in the Seyfert galaxy RE J1034+396, depends on its BH mass, which is not currently known very well. Applying this relation, the BH mass of RE J1034+396 is found to be 4 +3 −2 × 10 6 M ⊙ . The high end of the mass range follows the relationship between the 2f 0 frequencies of high-frequency QPO and the BH masses derived from the Galactic X-ray binaries.We also calculate the high-frequency constant C = 2.37 M ⊙ Hz −1 from 21 reverberation-mapped AGNs. As suggested by Gierliński et al.,where C M is the high-frequency variability derived from XVA. Given the similar shape of power-law dominated X-ray spectra in ultra-luminous X-ray sources (ULXs) and AGNs, this can be applied to BH mass estimates of ULXs. We discuss the observed QPO frequencies and BH mass estimates in the ULXs M82 X-1 and NGC 5408 X-1 and favor ULXs as intermediate mass BH systems.

Recent observations suggest that in black hole X-ray binaries jet/outflow formation is related to the hot plasma in the vicinity of the black hole, either in the form of an advection-dominated accretion flow at low accretion rates or in a disk corona at high accretion rates. We test the viability of this scenario for supermassive black holes using two samples of active galactic nuclei distinguished by the presence (radio-strong) and absence (radio-weak) of well-collimated, relativistic jets. Each is centered on a narrow range of black hole mass but spans a very broad range of Eddington ratios, effectively simulating, in a statistical manner, the behavior of a single black hole evolving across a wide spread in accretion states. Unlike the relationship between the radio and optical luminosity, which shows an abruptly break between high-and low-luminosity sources at an Eddington ratio of ∼ 1%, the radio emission-a measure of the jet power-varies continuously with the hard X-ray (2-10 keV) luminosity, roughly as L R ∝ L 0.6−0.75 X . This relation, which holds for both radio-weak and radio-strong active galaxies, is similar to the one seen in X-ray binaries. Jet/outflow formation appears to be closely linked to the conditions that give rise to the hot, optically thin coronal emission associated with accretion flows, both in the regime of low and high accretion rates.

We compile 23 Gamma-ray Bursts (GRBs) and 21 blazars with estimated Doppler factors, and the Doppler factors of GRBs are estimated from their Lorentz factors by assuming their jet viewing angles θ → 0 o . Using the conventional assumption that the prompt emission of GRBs is dominated by the synchrotron radiation, we calculate the synchrotron luminosity of GRBs from their total isotropic energy and burst duration. Intriguingly, we discover a uniform correlation between the synchrotron luminosity and Doppler factor, L syn ∝ D 3.1 , for GRBs and blazars, which suggests that they may share some similar jet physics. One possible reason is that GRBs and blazars have, more or less, similar intrinsic synchrotron luminosities and both of them are strongly enhanced by the beaming effect. After Doppler and redshift-correction, we find that the intrinsic peak energy of the GRBs ranges from 0.1 to 3 keV with a typical value of 1 keV. We further correct the beaming effect for the observed luminosity of GRBs and find that there exists a positive correlation between the intrinsic synchrotron luminosity and peak energy for GRBs, which is similar to that of blazars. Our results suggest that both the intrinsic positive correlation and the beaming effect may be responsible for the observed tight correlation between the isotropic energy and the peak energy in GRBs (so called "Amati" relation).

A toy model for gamma-ray burst-supernovae (GRB-SN) is discussed by considering the coexistence of baryon poor outflows from black holes (BHs) and a powerful spin-connection to surrounding disk, giving rise to consistent calorimetry as described by van Putten (2001a) in a variant of the Blandford-Znajek process (BZ, 1977). In this model the half-opening angle of the magnetic flux tube on the horizon is determined by the mapping relation between the angular coordinate on the BH horizon and the radial coordinate on the surrounding accretion disk. The GRB is powered by the baryon poor outflows in the BZ process, and the associated SN is powered by very small fraction of the spin energy transferred from the BH to the disk in the magnetic coupling (MC) process. The timescale of the GRB is fitted by the duration of the open magnetic flux on the horizon. It turns out that the data of several GRB-SNe are well fitted with our model.

We investigate the correlation between 151 MHz radio luminosity, L 151 MHz , and jet power, P jet , for a sample of low-power radio galaxies, of which the jet power is estimated from X-ray cavities. The jet power for a sample of FR I radio galaxies is estimated with the derived empirical correlation. We find that P jet /L Edd is positively correlated with L 2−10 keV X /L Edd for FR Is, where L Edd is the Eddington luminosity and L 2−10 keV X is 2-10 keV X-ray luminosity. We calculate the jet power of a hybrid model, as a variant of Blandford-Znajek model proposed by Meier, based on the global solution of the advection-dominated accretion flow (ADAF) surrounding a Kerr black hole (BH). Our model calculations suggest that the maximal jet power is a function of mass accretion rate and the black hole spin parameter j. The hard X-ray emission is believed to be mainly from the ADAFs in FR Is, and the mass accretion rate is therefore constrained with the X-ray emission in our ADAF model calculations. We find that the dimensionless angular momentum of BH j 0.9 is required in order to reproduce the observed relation of P jet /L Edd − L 2−10 keV X /L Edd for FR Is. Our conclusion will be strengthened if part of the X-ray emission is contributed by the jets. Our results suggest that BHs in FR I radio galaxies are rapidly spinning, which are almost not affected by the uncertainty of the black hole mass estimates.

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.