论文标题
提取辐射效率和QSO质量之间可能的内在关系：最大似然法及其应用于SDSS DR7 QSOS
Extracting the Possible Intrinsic Relation between Radiative Efficiency and Mass of QSOs: a Maximum Likelihood Method and its Application to the SDSS DR7 QSOs
论文作者
论文摘要
QSO的辐射效率及其分布编码有关在宇宙时间内质量和大规模黑洞（MBH）群体演变的丰富信息。在本文中，我们开发了一种最大似然方法，以统计地提取QSO的辐射效率（$ε$）和质量（$ m _ {\ bulter} $）之间的固有关系，从其在亮度（经验估计的病毒）质量平面上的分布中的分布。通过使用模拟样本，我们发现可以对$ε-m _ {\ bullet} $在红移$ z \ z \ Lessim 0.4 $的关系上放在均匀QSO样品中，类似于Sloan Digital Sky调查的样本，以及$ z \ sim \ sim 0.6 $的QSO样本（或$ \ sim 1.0 $ $ \\ sim 1.0 $ $ $ $ $ $ $ $ $ $），幅度更深。将此方法应用于具有$ z \ Lessim 0.7 $的SDSS DR7 QSO，我们发现$ε\ propto m _ {\ bulter}^{0 \ sim 1.1} $（或$ε\ propto m _ {\ bult}^{\ bult}^{ - 1.0 \ sim 0} $ for q s $ s $ s $ collative for q s $ evel $ evel $ evel $ evel $ evel $ ever y y y y y Mass of y Mass of y y Mass of the y Mase or y Mase or y Mores or M.（y Mass）或M。经验质量估计器。这些矛盾的结果可能是由于两个质量估计器中未知的系统错误造成的，从而阻止了使用当前可用的QSO样本对$ε-M _ {\ bullet} $关系的准确约束。我们发现，MBH质量的估计值和Eddington比率分布函数都可以受到$ε-M_ \ bullet $关系的影响，这表明确定这种关系对于理解MBHS的积累和增长历史很重要。将来，如果使用质量估计值的主机银河系污染和系统错误，则可以通过使用比SDS更深的QSO样本来强烈限制固有的$ε-M _ {\ bullet} $关系，可以通过更深的SDS进行QSO样本来严格限制。
Radiative efficiencies of QSOs and its distribution encode rich information on the evolution of both masses and spins of massive black holes (MBHs) across cosmic time. In this paper, we develop a maximum likelihood method to statistically extract the intrinsic relation between radiative efficiency ($ε$) and mass ($M_{\bullet}$) of QSOs from their distribution on the luminosity-(empirically estimated virial) mass plane. By using mock samples, we find that strong constraint can be put on the $ε-M_{\bullet}$ relation at redshift $z\lesssim 0.4$ from uniform QSO samples similar to those in Sloan Digital Sky Survey, and from QSO samples at $z \sim 0.6$ (or $\lesssim 1.0$) if the magnitude limit of the survey can be $\sim 1-2$ (or $2-3$) magnitude deeper. Applying this method to the SDSS DR7 QSOs with $z\lesssim 0.7$, we find $ε\propto M_{\bullet}^{0\sim 1.1}$ (or $ε\propto M_{\bullet}^{-1.0\sim 0}$) correlation for QSOs with the masses obtained according to the H$β$ (or Mg II) empirical mass estimator. These contradictory results may be due to the unknown systematic errors in the two mass estimators, preventing an accurate constraint on the $ε-M_{\bullet}$ relation by using current available QSO samples. We find that both the estimates of MBH mass and Eddington ratio distribution functions can be affected by the $ε-M_\bullet$ relation, suggesting that the determination of this relation is important for understanding the accretion and growth history of MBHs. In future, the intrinsic $ε-M_{\bullet}$ relation is expected to be strongly constrained by using QSO samples obtained from surveys deeper than SDSS if the host galaxy contamination and systematic errors of the mass estimator(s) can be well modeled or removed.
