Observations show that the accretion flows in low-luminosity active galactic nuclei (LLAGNs) probably have a two-component structure with an inner ADAF and an outer truncated accretion disk. As shown by Taam et al. (2012), the truncation radius as a
function of mass accretion rate is strongly affected by including the magnetic field within the framework of disk evaporation model, i.e., an increase of the magnetic field results in a smaller truncation radius of the accretion disk. In this work, we calculate the emergent spectrum of an inner ADAF + an outer truncated accretion disk around a supermassive black hole based on the prediction by Taam et al. (2012). It is found that an increase of the magnetic field from $beta=0.8$ to $beta=0.5$ (with magnetic pressure $p_{rm m}=B^2/{8pi}=(1-beta)p_{rm tot}$, $p_{rm tot}=p_{rm gas}+p_{rm m}$) results in an increase of $sim 8.7$ times of the luminosity from the truncated accretion disk. We found that the equipartition of gas pressure to magnetic pressure, i.e., $beta=0.5$, failed to explain the observed anti-correlation between $L_{rm 2-10 keV}/L_{rm Edd}$ and the bolometric correction $kappa_{rm 2-10 keV}$ (with $kappa_{rm 2-10 keV} = L_{rm bol}/L_{rm 2-10 keV}$). The emergent spectra for larger value $beta=0.8$ or $beta=0.95$ can well explain the observed $L_{rm 2-10 keV}/L_{rm Edd}$-$kappa_{rm 2-10 keV}$ correlation. We argue that in the disk evaporation model, the electrons in the corona are assumed to be heated only by a transfer of energy from the ions to electrons via Coulomb collisions, which is reasonable for the accretion with a lower mass accretion rate. Coulomb heating is the dominated heating mechanism for the electrons only if the magnetic field is strongly sub-equipartition, which is roughly consistent with observations.
Recent observations reveal that a cool disk may survive in the innermost stable circular orbit (ISCO) for some black hole X-ray binaries in the canonical low/hard state. The spectrum is characterized by a power law with a photon index $Gamma sim 1.5-
2.1$ in the range of 2-10 keV and a weak disk component with temperature of $sim 0.2$ keV. In this work, We revisit the formation of such a cool, optically thick, geometrically thin disk in the most inner region of black hole X-ray binaries at the low/hard state within the context of disk accretion fed by condensation of hot corona. By taking into account the cooling process associated with both Compton and conductive processes in a corona, and the irradiation of the hot corona to the disk, we calculate the structure of the corona. For viscosity parameter $alpha=0.2$, its found that the inner disk can exist for accretion rate ranging from $dot M sim 0.006-0.03 dot M_{rm Edd}$, over which the electron temperatures of the corona are in the range of $1-5times 10^9 rm K$ producing the hard X-ray emission. We calculate the emergent spectra of the inner disk and corona for different mass accretion rates. The effect of viscosity parameter $alpha$ and albedo $a$ ($a$ is defined as the energy ratio of reflected radiation from the surface of the thin disk to incident radiation upon it from the corona) to the emergent spectra are also presented. Our model is used to explain the recent observations of GX 339-4 and Cyg X-1, in which the thin disk may exist at ISCO region in the low/hard state at luminosity around a few percent of $L_{rm Edd}$. Its found that the observed maximal effective temperature of the thermal component and the hard X-ray photon index $Gamma$ can be matched well by our model.
