类星体光度函数

The Luminosity Function of Quasars

对前人在类星体光度函数研究中的工作作了详细的介绍。在前人工作的基础上，提出两个新的研究方法和一个新的统计方法。第一为分类研究法。将类星体分作若干子类，每一子类的光度演化形式可以通过相关分析求出，而数密度则可由简单计数求得。第二为平均星等法，定义平均星等Ｍ。研究表明，对于纯密度演化模型，Ｍ与红移ｚ无关；而对于纯光度演化模型，Ｍ与光度演化形式（Ｍｚ－Ｍ）成线性关系。提出的新的统计方法为ｎ／ｎｍａｘ检验法，它是传统的Ｖ／Ｖｍａｘ和Ｖ′／Ｖ′ｍａｘ检验法的推广。与传统方法不同，它能适用于任何光度函数模型。若所采用的光度函数正确，则样品的ｎ／ｎｍａｘ值应均匀分布于数域［０，１］

An entire review of the history and present status of research on the luminosity function of quasars is given in this paper. Based on previous works, two new methods and a new statistical test are proposed. The first is the classification method. In this method, quasars are divided into several subclasses. The luminosity evolution form of each subclass can be determined by correlation analysis and the density law of the subclass can be obtained by simple number-counting. The second is the mean magnitude method. A mean absolute magnitude is defined. The study shows that, in the pure density evolution model, independents redshift z , while in the pure luminosity evolution model, is linearly correlated with the luminosity evolution form (M z-M *) . The new statistical test is the n/n max test. It is a generalization of the V/V max and V′/V′ max tests. Unlike the conventional ones, it could be applied to any luminosity function models. If the adopted luminosity function is correct, the values of the statistic n/n max would be uniformly distributed in the interval.