发表机构
European Space Agency (ESA), European Space Research and Technology Centre (ESTEC); INAF - Osservatorio Astrofisico di Arcetri; INAF - Istituto di Astrofisica Spaziale e Fisica Cosmica di Milano; Scuola Normale Superiore; Dipartimento di Fisica e Astronomia, Università degli Studi di Firenze; Scuola Superiore Meridionale; Istituto Nazionale di Fisica Nucleare, sez. di Napoli（欧洲空间局（ESA），欧洲空间研究与技术中心（ESTEC）; 意大利国家天体物理研究所 - 阿切特里天文台; 意大利国家天体物理研究所 - 米兰空间天体物理学与宇宙物理学研究所; 比萨高等师范学院; 佛罗伦萨大学物理与天文系; 南方高等学院; 意大利国家核物理研究所，那不勒斯分部）
机构由 AI 辅助整理，请以论文原文为准。AI 中文总结
通过利用XMM-Newton多历元观测的类星体X射线变异性，绕开黑洞质量不确定性，恢复了Γ-λ_Edd关系，发现其斜率较平缓，且爱丁顿比差异不足以解释光子指数多样性。
AI 中文摘要
我们利用SDSS DR16Q星表与4XMM-DR14偶然发现星表的交叉匹配作为母样本，测量了未遮蔽的1型类星体中X射线光子指数Γ与爱丁顿比λ_Edd之间的关系。在清理样本中潜在的观测偏差后，我们获得7835个天体，比文献中大多数先前分析的样本大一个数量级。使用单历元维里黑洞质量，对Γ对logλ_Edd进行单一回归，得到的斜率取决于质量指标（Hβ、MgII、CIV）和热光度修正，且通常较平缓。我们将此解释为回归稀释：维里质量的系统不确定性远大于SDSS类星体中λ_Edd的固有弥散。因此，我们引入一种不同的方法，将黑洞质量从问题中移除。对于被XMM-Newton在多个历元观测到的类星体，每个天体的质量是固定的，其X射线光度的变化追踪其吸积状态的变化。我们拟合每个天体（样本N=893）的Γ-log(L_2keV)关系，并组合每个天体的后验分布。这恢复了种群的平均响应a_X=0.35±0.03，当仅使用光子指数精确测量的历元时，该响应陡增至约0.43。转换为爱丁顿比，这对应于a_λ≈0.20-0.25，取决于热光度修正的选择和L_X-L_UV斜率。因此，Γ-λ_Edd关系确实存在，但只能通过利用单个源的变异性来揭示，这消除了黑洞质量的影响。此外，其平缓性意味着，目前测量的爱丁顿比差异本身无法解释未遮蔽类星体中观测到的光子指数的多样性。
英文摘要
We measure the relation between the X-ray photon index $Γ$ and the Eddington ratio $λ_{Edd}$ in unobscured type-1 quasars, using as parent sample the cross-match of the SDSS DR16Q catalogue with the 4XMM-DR14 serendipitous catalogue. After cleaning the sample of potential observational biases, we obtain 7835 objects, one order of magnitude larger than most previous analyses in the literature. A single regression of $Γ$ against $\logλ_{Edd}$, with single-epoch virial black-hole masses, returns slopes that depend on the mass indicator (H$β$, MgII, CIV) and on the bolometric correction, and that are generally flat. We interpret this as regression dilution: the systematic uncertainty on virial masses is much larger than the intrinsic spread of $λ_{Edd}$ in SDSS quasars. We therefore introduce a different approach, which removes the black-hole mass from the problem. For quasars observed by XMM-Newton at multiple epochs, the mass of each object is fixed, and changes in its X-ray luminosity trace changes in its accretion state. We fit the $Γ$-$\log(L_{2keV})$ relation of each object (for a sample of N=893) and combine the per-object posteriors. This recovers the mean response of the population $a_X = 0.35\pm0.03$, which steepens to $\approx0.43$ when only epochs with precisely measured photon indices are used. Translated to the Eddington ratio, this corresponds to $a_λ\approx0.20$-0.25, depending on the choice of bolometric correction and on the LX-LUV slope. The $Γ$--$λ_{Edd}$ relation therefore exists, but it can be uncovered only by exploiting the variability of individual sources, which removes the black-hole mass from the problem. Moreover, its shallowness implies that the differences in Eddington ratio, as currently measured, cannot by themselves account for the variety of photon indices observed among unobscured quasars.
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