On the Relation between the Hard X-Ray Photon Index and Accretion Rate for Super-Eddington Accreting Quasars

We investigate whether the correlation between the hard X-ray photon index ( ${\rm{\Gamma }}$ ) and accretion rate for super-Eddington accreting quasars is different from that for sub-Eddington accreting quasars. We construct a sample of 113 bright quasars from the Sloan Digital Sky Survey Data Release 14 quasar catalog, with 38 quasars as the super-Eddington subsample and 75 quasars as the sub-Eddington subsample. We derive black hole masses using a simple-epoch virial mass formula based on the ${\rm{H}}\beta $ lines, and we use the standard thin disk model to derive the dimensionless accretion rates ( $\dot{{\mathscr{M}}}$ ) for our sample. The X-ray data for these quasars are collected from the Chandra and XMM-Newton archives. We fit the hard X-ray spectra using a single power-law model to obtain ${\rm{\Gamma }}$ values. We find a statistically significant ( ${R}_{{\rm{S}}}=0.43$ , $p=7.75\times {10}^{-3}$ ) correlation between ${\rm{\Gamma }}$ and $\dot{{\mathscr{M}}}$ for the super-Eddington subsample. The ${\rm{\Gamma }}$ - $\dot{{\mathscr{M}}}$ correlation for the sub-Eddington subsample is also significant, but weaker ( ${R}_{{\rm{S}}}=0.30$ , $p=9.98\times {10}^{-3}$ ). Linear regression analysis shows that ${\rm{\Gamma }}=(0.34\pm 0.11)\mathrm{log}\dot{{\mathscr{M}}}+(1.71\pm 0.17)$ and ${\rm{\Gamma }}=(0.09\pm 0.04)\mathrm{log}\dot{{\mathscr{M}}}+(1.93\pm 0.04)$ for the super- and sub-Eddington subsamples, respectively. The ${\rm{\Gamma }}$ - $\dot{{\mathscr{M}}}$ correlations of the two subsamples are different, suggesting different disk-corona connections in these two types of systems. We propose one qualitative explanation of the steeper ${\rm{\Gamma }}$ - $\dot{{\mathscr{M}}}$ correlation in the super-Eddington regime that involves larger seed photon fluxes received by the compact coronae from the thick disks in super-Eddington accreting quasars.