We investigate the accretion process in high-luminosity AGNs (HLAGNs) in the scenario of the disk evaporation model. Based on this model, the thin disk can extend down to the innermost stable circular orbit (ISCO) at accretion rates higher than $0.02
dot{M}_{rm Edd}$; while the corona is weak since part of the coronal gas is cooled by strong inverse Compton scattering of the disk photons. This implies that the corona cannot produce as strong X-ray radiation as observed in HLAGNs with large Eddington ratio. In addition to the viscous heating, other heating to the corona is necessary to interpret HLAGN. In this paper, we assume that a part of accretion energy released in the disk is transported into the corona, heating up the electrons and thereby radiated away. We for the first time, compute the corona structure with additional heating, taking fully into account the mass supply to the corona and find that the corona could indeed survive at higher accretion rates and its radiation power increases. The spectra composed of bremsstrahlung and Compton radiation are also calculated. Our calculations show that the Compton dominated spectrum becomes harder with the increase of energy fraction ($f$) liberating in the corona, and the photon index for hard X-ray($2-10 rm keV$) is $2.2 < Gamma < 2.7 $. We discuss possible heating mechanisms for the corona. Combining the energy fraction transported to the corona with the accretion rate by magnetic heating, we find that the hard X-ray spectrum becomes steeper at larger accretion rate and the bolometric correction factor ($L_{rm bol}/L_{rm 2-10keV}$) increases with increasing accretion rate for $f<8/35$, which is roughly consistent with the observational results.
We compile a blue AGN sample from SDSS and investigate the ratio of hard X-ray to bolometric luminosity in dependence on Eddington ratio and black hole mass. Our sample comprises 240 radio-quiet Seyfert 1 galaxies and QSOs. We find that the fraction
of hard X-ray luminosity (log$(L_{rm 2-10 kev}/L_{rm bol})$) decreases with the increase of Eddington ratio. We also find that the fraction of hard X-ray luminosity is independent on the black hole mass for the radio-quiet AGNs. The relation of log$(L_{rm 2-10 kev}/L_{rm bol})$ decreasing with increasing Eddington ratio indicates that X-ray bolometric correction is not a constant, from a larger sample supporting the results of Vasudevan & Fabian (2007). We interpret our results by the disk corona evaporation/condensation model (Meyer et al. cite{me200}; Liu et al. 2002a; Liu et al. 2007). In the frame of this model, the Compton cooling becomes efficient in cooling of the corona at high accretion rate (in units of Eddington rate), leading to condensation of corona gas to the disk. Consequently, the relative strength of corona to the disk becomes weaker at higher Eddington ratio. Therefore, the fraction of hard X-ray emission to disk emission and hence to the bolometric emission is smaller at higher Eddington ratio. The independence of the fraction of hard X-ray luminosity on the mass of the black hole can also be explained by the disk corona model since the corona structure and luminosity (in units of Eddington luminosity) are independent on the mass of black holes.
