Correlations Of Astrophysical Phenomena In Black Hole Systems Of Different Scales

Recently, some observations indicate that lots of high-energy radiation properties of black holes (BHs) in X-ray binaries and active galactic nuclei (AGN) are similar, such as jets, X-ray quasi-periodic oscillations (QPOs), the high emissivity index, Fe Kαlines, etc, though the masses in these objects span, at least, six orders of magnitude. Studying the similarities and correlations among the different phenomena benefits us to understand the essential of these BH systems of different scales. Correlation between 3:2 QPO pairs and jets of two scales of BH systems is discussed in this thesis based on the coexistence of the Blandford-Znajek (BZ) and magnetic coupling (MC) process model (CEBZMC). The main results are summarized as follows.Firstly, we introduce two mechanisms of extracting BH rotating energy through magnetic field: BZ and MC process. The unified analytical expressions for the BZ and MC powers and torques are derived based on an improved equivalent circuit. A mapping relation between the angular coordinate on the BH horizon and the radial coordinate on the accretion disc is established and then the condition for coexistence of BZ and MC process is discussed. In addition, we discuss the screw instability of magnetic field, and find that the state of CEBZMC always accompanies the screw instability.Secondly, a double-hotspots-model for 3:2 QPO pairs is introduced based on CEBZMC. The hotspot in the inner region of the disc is produced by energy transferred from a spinning BH with non-axisymmetric magnetic field. The outer hotspot is produced due to the screw instability of the magnetic field on the disc. The Keplerian orbit frequency of inner and outer hotspot correspond to the upper and lower frequency of QPO pairs respectively. We fit the 3:2 QPO pairs of several BH X-ray binaries and the galactic center BH, and explain the correlation between their 3:2 QPO pair and the jet. A new idea for interpreting the critical line of CEBZMC as the jet line in the state transition of BH X-ray binaries is proposed. And we discuss the state transition due to the fluctuations of the number densities of the accreting plasma from a companion star.Finally, we briefly discuss the high emissivity index, Fe Kαlines and X-ray QPOs in BHs of AGN and stellar-mass BHs and the correlations among them. The similar phenomena in the BH systems of masses varying in a large scales imply that they arise from the same physical origin, accreting BHs.