  A long-standing question in active galactic nucleus (AGN) research is how the
corona is heated up to produce X-ray radiation much stronger than that arising
from the viscous heating within the corona. In this paper, we carry out
detailed investigations of magnetic-reconnection heating to the corona,
specifically, studying how the disc and corona are self-consistently coupled
with the magnetic field, and how the emergent spectra depend on the fundamental
parameters of AGN. It is shown that diverse spectral shapes and luminosities
over a broad bandpass from optical to X-ray can be produced from the coupled
disc and corona within a limited range of the black hole mass, accretion rate
and magnetic field strength. The relative strength of X-ray emission with
respect to optical/ultraviolet (UV) depends on the strength of the magnetic
field in the disc, which, together with accretion rate, determines the fraction
of accretion energy transported and released in the corona. This refined
disc-corona model is then applied to reproduce the broad-band spectral energy
distributions (SEDs) of a sample of 20 bright local AGNs observed
simultaneously in X-ray and optical/UV. We find that, in general, the overall
observed broad-band SEDs can be reasonably reproduced, except for rather hard
X-ray spectral shapes in some objects. The radiation pressure-dominant region,
as previously predicted for the standard accretion disc in AGN, disappears for
strong X-ray sources, revealing that AGN accretion discs are indeed commonly
stable as observed. Our study suggests the disc-corona coupling model involving
magnetic fields to be a promising approach for understanding the broad-band
spectra of bright AGNs.
