Rest-frame Optical Spectroscopy of $z \sim 2$ Quasars with Steep Hard X-ray Spectral Shapes: X-ray Selection of Super-Eddington Accretion and Verification

Abstract: Super-Eddington accretion is a crucial phase in the growth of supermassive black holes. However, identifying super-Eddington accreting quasars observationally is challenging due to uncertain black-hole mass estimates and other complications. The Eddington ratio parameter does not represent accurately the accretion rate in the super-Eddington regime. On the other hand, super-Eddington accreting quasars appear to show large hard X-ray (rest-frame > 2 keV) power-law photon indices, and they also exhibit distinct optical spectral features including weak [O III] $\lambda 5007$ emission and strong Fe II emission. We test steep X-ray photon-index selection of super-Eddington accreting quasars by obtaining Palomar 200-inch Hale Telescope near-infrared spectra for a pilot sample of nine $\Gamma=2.0-2.6$ quasars at $z\approx1.4-2.5$. We derive H$\beta$-based single-epoch virial black-hole masses (median value $\rm 4.3 \times 10^{8}~M_{\odot}$) and Eddington ratios (median value 0.6). The Eddington ratio distribution is consistent with that of the comparison sample, which is a flux-limited sample of quasars at $z\approx1.5-3.5$ with near-infrared spectroscopy. But our super-Eddington candidates do show statistically weaker [O III] emission ($P_{\rm null}=0.0075$) and marginally stronger Fe II emission ($P_{\rm null}=0.06$). We also find one candidate with broad (width of 1960 km/s) and blueshifted (690 km/s) [O III] $\lambda 4959$ and [O III] $\lambda 5007$ lines, which probably originate from a strong [O III] outflow driven by super-Eddington accretion. Overall, the steep X-ray photon-index selection of super-Eddington accreting quasars appears promising. But a larger sample is needed to assess further the reliability of the selection.