避免分箱光度函数中的虚假中断
Avoiding spurious breaks in binned luminosity functions
摘要：
我们发现，无论是使用Page & Carrera的方法或著名的$1/V_a$方法来构建活动星系核（AGN）的通量有限样本的分箱光度函数（LF）可以产生一个人为的平坦化（或陡峭的情况下，负演化）的分箱LF由样品的通量截止。这种效应对于具有陡峭和强烈演变的母LF的样品更明显，但即使对于非演变的LF也仍然存在。作为真实LF的这种失真的结果，将模型LF拟合到分箱数据可能导致参数估计中的误差，并且甚至可能促使错误地使用破坏的幂律函数。我们计算的预期位置的明显的突破，在分箱的LF。我们表明，这些虚假的突破，在分仓的LF可以避免，如果分仓是在通量-红移平面，而不是通常使用的光度-红移平面。在通量-红移平面中的分箱可以与在亮度-红移平面中的分箱结合使用，以测试分箱的LF中的真实中断，并识别作为分箱偏差的结果的特征。我们说明了这种效果的最典型的形式的光度依赖性和红移的演变，并显示如何所提出的方法有助于解决这个问题。我们也将这种方法应用到MOJAVE活动星系核样本，并表明它消除了一个明显的突破分仓LF。
英文摘要：
We show that using either the method of Page & Carrera or the well-known $1/V_a$ method to construct the binned luminosity function (LF) of a flux limited sample of Active Galactic Nuclei (AGN) can produce an artificial flattening (or steepening in the case of negative evolution) of the binned LF for bins intersected by the flux cutoff of the sample. This effect is more pronounced for samples with steep and strongly evolving parent LFs but is still present even for non-evolving LFs. As a result of this distortion of the true LF, fitting a model LF to binned data may lead to errors in the estimation of the parameters and may even prompt the erroneous use of broken power law functions. We compute the expected positions of apparent breaks in the binned LF. We show that these spurious breaks in the binned LFs can be avoided if the binning is done in the flux--redshift plane instead of the typically used luminosity--redshift plane. Binning in the flux--redshift plane can be used in conjunction with the binning in the luminosity--redshift plane to test for real breaks in the binned LFs and to identify the features that are the result of binning biases. We illustrate this effect for most typical forms of luminosity dependence and redshift evolution and show how the proposed method helps address this problem. We also apply this method to the MOJAVE AGN sample and show that it eliminates an apparent break in the binned LF.
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