We investigate whether the hard X-ray photon index (${\Gamma}$) versus accretion rate correlation 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, including 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 ${\Gamma}$ values. We find a statistically significant ($R_{\rm S}=0.43$, $p=7.75\times{10}^{-3}$) correlation between ${\Gamma}$ and $\dot{\mathscr{M}}$ for the super-Eddington subsample. The ${\Gamma}$-$\dot{\mathscr{M}}$ 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 ${\rm \Gamma}=(0.34\pm0.11){\rm log}{\dot{\mathscr{M}}}+(1.71\pm0.17)$ and ${\rm \Gamma}=(0.09\pm0.04){\rm log}{\dot{\mathscr{M}}}+(1.93\pm0.04)$ for the super- and sub-Eddington subsamples, respectively. The ${\Gamma}$-$\dot{\mathscr{M}}$ 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 ${\Gamma}$-$\dot{\mathscr{M}}$ 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.

中文翻译：

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超爱丁顿吸积类星体硬X射线光子指数与吸积率的关系

我们研究了超爱丁顿吸积类星体的硬 X 射线光子指数 (${\Gamma}$) 与吸积率的相关性是否与亚爱丁顿吸积类星体的不同。我们从斯隆数字巡天数据第 14 版类星体目录中构建了 113 个明亮类星体样本，其中 38 个类星体作为超爱丁顿子样本，75 个类星体作为子爱丁顿子样本。我们使用基于 ${\rm H\beta}$ 线的简单时代维里质量公式推导出黑洞质量，并使用标准薄盘模型推导出无量纲吸积率 ($\dot{\mathscr{ M}}$) 用于我们的示例。这些类星体的 X 射线数据是从钱德拉和 XMM-牛顿档案收集的。我们使用单一幂律模型拟合硬 X 射线光谱以获得 ${\Gamma}$ 值。我们发现 ${\Gamma}$ 和 $\dot{\mathscr{M 之间存在统计显着性（$R_{\rm S}=0.43$, $p=7.75\times{10}^{-3}$）相关性}}$ 用于超级爱丁顿子样本。子爱丁顿子样本的 ${\Gamma}$-$\dot{\mathscr{M}}$ 相关性也很显着，但较弱（$R_{\rm S}=0.30$, $p=9.98\times {10}^{-3}$）。线性回归分析表明 ${\rm \Gamma}=(0.34\pm0.11){\rm log}{\dot{\mathscr{M}}}+(1.71\pm0.17)$ 和 ${\rm \Gamma}=(0.09\pm0.04){\rm log}{\dot{\mathscr{M}}}+(1.93\pm0.04)$ 分别用于超爱丁顿子样本和子爱丁顿子样本。两个子样本的 ${\Gamma}$-$\dot{\mathscr{M}}$ 相关性不同，表明这两种系统中的磁盘-电晕连接不同。