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A non-zero mutual information between morphology of a galaxy and itslarge-scale environment is known to exist in SDSS upto a few tens of Mpc. It isimportant to test the statistical significance of these mutual information ifany. We propose three different methods to test the statistical significance ofthese non-zero mutual information and apply them to SDSS and Millennium Runsimulation. We randomize the morphological information of SDSS galaxies withoutaffecting their spatial distribution and compare the mutual information in theoriginal and randomized datasets. We also divide the galaxy distribution intosmaller subcubes and randomly shuffle them many times keeping the morphologicalinformation of galaxies intact. We compare the mutual information in theoriginal SDSS data and its shuffled realizations for different shufflinglengths. Using a t-test, we find that a small but statistically significant (at99.9% confidence level) mutual information between morphology and environmentexists upto the entire length scale probed. We also conduct another experimentusing mock datasets from a semi-analytic galaxy catalogue where we assignmorphology to galaxies in a controlled manner based on the density at theirlocations. The experiment clearly demonstrate that mutual information caneffectively capture the physical correlations between morphology andenvironment. Our analysis suggests that physical association between morphologyand environment may extend to much larger length scales than currently believedand the information theoretic framework presented here, can serve as asensitive and useful probe of the assembly bias and large-scale environmentaldependence of galaxy properties.

A study on the statistical significance of mutual information between morphology of a galaxy and its large-scale environment