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Taking into account the energy and angular momentum transferred from a rotating black hole (BH) to the inner accretion disk by the magnetic connection (MC) process, we simulate the x-ray spectra from the disk-corona system with two different magnetic configurations using the Monte Carlo method. The results show that the MC process reduces the ratio of the power dissipated in the corona to the total and softens the spectrum. The influence of the MC process is stronger with a higher BH spin, a larger accretion rate, and a larger and more centralized magnetic flux threading the disk. The comparison of the model spectra with the observational data suggests that large-scale magnetic fields accumulating in the inner disk could be a candidate explanation for the hard-to-soft state evolutions in BH binaries.

A constraint to black hole (BH) accretion has previously been derived for the inner edge fixed at the innermost stable circular orbit (ISCO) and the innermost bound circular orbit (IBCO). This constraint is referred to as the mass-radius (MR) relation in this study, and the validity of the MR relation is discussed for different cases. It is shown that the product of the BH mass and the inner edge radius decreases monotonically in the accretion process for the inner edge located between IBCO and ISCO. In addition, we discuss the validity of the MR relation by considering the magnetic coupling (MC) effects of a Kerr BH with its surrounding disc. Although theoretically the product of the BH mass and the radius of ISCO increases (decreases) with time for a BH spin greater (less) than some critical value in the MC process, this relation is approximately valid for an Eddington accretion rate persisting for a rather long time, such as more than 106 years. Finally, we discuss the possible application of the MR relation to astrophysics.