我们联合约束的亮度函数（LF）和黑洞质量函数（BHMF）的宽线类星体的前向贝叶斯模型在类星体的质量-光度平面，基于一个均匀的样本约58,000 SDSS DR 7类星体在z ~ 0.3-5。我们考虑到样品通量限制的选择效应;更重要的是，我们处理真实BH质量和基于FWHM的单历元维里质量估计之间的统计分散，以及这些质量估计的潜在亮度依赖性偏差。LF被严格限制在由SDSS采样的区域中，并且当外推到~ 3个星等时做出合理的预测。在LF型号中可以看到缩小尺寸。另一方面，我们发现在z>~0.7时难以将BHMF限制在几个因子内（具有基于MgII和CIV的维里BH质量）。这主要是由这些质量估计的未知亮度依赖的偏差及其与其他模型参数的简并性驱动的，其次是由SDSS类星体仅在高红移处对活动BH种群的尖端进行采样的事实驱动的。然而，最有可能的模型有利于一个积极的亮度依赖的偏差镁II和可能的CIV，这样在固定的真实BH质量，具有高于平均亮度的对象有高估的FWHM为基础的维里质量。有初步的证据表明，缩小也体现在活动的BHMF，和BH质量密度在宽线类星体的总BH质量密度在任何时候都贡献了微不足道的金额。在我们的模型的不确定性，我们没有发现一个强大的BH质量依赖的平均爱丁顿比，但有证据表明，平均爱丁顿比（在固定BH质量）增加与红移。
英文摘要：
We jointly constrain the luminosity function (LF) and black hole mass function (BHMF) of broad-line quasars with forward Bayesian modeling in the quasar mass-luminosity plane, based on a homogeneous sample of ~ 58,000 SDSS DR7 quasars at z ~ 0.3-5. We take into account the selection effect of the sample flux limit; more importantly, we deal with the statistical scatter between true BH masses and FWHM-based single-epoch virial mass estimates, as well as potential luminosity-dependent biases of these mass estimates. The LF is tightly constrained in the regime sampled by SDSS, and makes reasonable predictions when extrapolated to ~ 3 magnitudes fainter. Downsizing is seen in the model LF. On the other hand, we find it difficult to constrain the BHMF to within a factor of a few at z>~0.7 (with MgII and CIV-based virial BH masses). This is mainly driven by the unknown luminosity-dependent bias of these mass estimators and its degeneracy with other model parameters, and secondly driven by the fact that SDSS quasars only sample the tip of the active BH population at high redshift. Nevertheless, the most likely models favor a positive luminosity-dependent bias for MgII and possibly for CIV, such that at fixed true BH mass, objects with higher-than-average luminosities have over-estimated FWHM-based virial masses. There is tentative evidence that downsizing also manifests itself in the active BHMF, and the BH mass density in broad-line quasars contributes an insignificant amount to the total BH mass density at all times. Within our model uncertainties, we do not find a strong BH mass dependence of the mean Eddington ratio; but there is evidence that the mean Eddington ratio (at fixed BH mass) increases with redshift.
Zooming into the broad line region of the gravitationally lensed quasar Q2237+0305 = the Einstein Cross: III. Determination of the size and structure of the CIV and CIII] emitting regions using microlensing
A SPectroscopic survey of biased halos In the Reionization Era (ASPIRE): A First Look at the Rest-frame Optical Spectra of $z > 6.5$ Quasars Using JWST
