宇宙学背景下的Eddington-Malmquist偏差
Eddington-Malmquist bias in a cosmological context
摘要：
1914年，爱丁顿推导出了一个公式，用于计算“在太空中”和“从天空中”收集的恒星的平均绝对星等之间的差异。Malmquist（1920）在欧几里得空间中导出了这种差异的一般关系。在这里，我们研究宇宙学中的这种统计偏差，澄清和扩展以前的工作。我们推导出Malmquist关系的一般宇宙学框架内，包括弗里德曼的模型，类似的方式Malmquist表明，在1936年，他的公式也是有效的存在灭绝的欧几里得空间。我们还讨论了一些概念方面，解释范围广泛的偏见关系。内禀差<M>_m-M_0 = - sigma_M^2 dlna（m）/dm的Malmquist公式也适用于在膨胀的弗里德曼宇宙中进行的观测。当a（m）是指观测到的视星等分布（未校正K效应或z相关消光）时，这对热辐射和有限波段星等也是适用的。
英文摘要：
In 1914, Eddington derived a formula for the difference between the mean absolute magnitudes of stars "in space" or gathered "from the sky". Malmquist (1920) derived a general relation for this difference in Euclidean space. Here we study this statistical bias in cosmology, clarifying and expanding previous work. We derived the Malmquist relation within a general cosmological framework, including Friedmann's model, analogously to the way Malmquist showed in 1936 that his formula is also valid in the presence of extinction in Euclidean space. We also discuss some conceptual aspects that explain the wide scope of the bias relation. The Malmquist formula for the intrinsic difference <M>_m - M_0 = - sigma_M^2 dlna(m)/dm is also valid for observations made in an expanding Friedmann universe. This is holds true for bolometric and finite-band magnitudes when a(m) refers to the distribution of observed (uncorrected for K-effect or z-dependent extinction) apparent magnitudes.
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