A non-zero mutual information between morphology of a galaxy and its large-scale environment is known to exist in SDSS upto a few tens of Mpc. It is important to test the statistical significance of these mutual information if any. We propose three different methods to test the statistical significance of these non-zero mutual information and apply them to SDSS and Millennium Run simulation. We randomize the morphological information of SDSS galaxies without affecting their spatial distribution and compare the mutual information in the original and randomized datasets. We also divide the galaxy distribution into smaller subcubes and randomly shuffle them many times keeping the morphological information of galaxies intact. We compare the mutual information in the original SDSS data and its shuffled realizations for different shuffling lengths. Using a t-test, we find that a small but statistically significant (at 99.9% confidence level) mutual information between morphology and environment exists upto the entire length scale probed. We also conduct another experiment using mock datasets from a semi-analytic galaxy catalogue where we assign morphology to galaxies in a controlled manner based on the density at their locations. The experiment clearly demonstrate that mutual information can effectively capture the physical correlations between morphology and environment. Our analysis suggests that physical association between morphology and environment may extend to much larger length scales than currently believed and the information theoretic framework presented here, can serve as a sensitive and useful probe of the assembly bias and large-scale environmental dependence of galaxy properties.

中文翻译：

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星系形态与大尺度环境互信息统计显着性研究

已知在 SDSS 中存在高达几十 Mpc 的星系形态与其大尺度环境之间的非零互信息。如果有的话，测试这些互信息的统计显着性很重要。我们提出了三种不同的方法来测试这些非零互信息的统计显着性，并将它们应用于 SDSS 和 Millennium Run 模拟。我们在不影响空间分布的情况下随机化 SDSS 星系的形态信息，并比较原始和随机数据集中的互信息。我们还将星系分布划分为更小的子立方体，并多次随机打乱它们，保持星系的形态信息完整。我们比较了原始 SDSS 数据中的互信息及其不同混洗长度的混洗实现。使用 t 检验，我们发现形态学和环境之间存在一个很小但具有统计显着性（置信度为 99.9%）的互信息，直至探测到的整个长度尺度。我们还使用来自半解析星系目录的模拟数据集进行了另一项实验，在该实验中，我们根据星系位置的密度以受控方式为星系分配形态。实验清楚地表明互信息可以有效地捕捉形态和环境之间的物理相关性。我们的分析表明，形态和环境之间的物理关联可能会扩展到比目前所认为的更大的长度尺度以及这里提出的信息理论框架，