Abstract:
A non-zero mutual information between morphology of a galaxy and its large-scale environment is known to exist in Sloan
Digital Sky Survey (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 data sets. 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 per cent confidence level) mutual information between
morphology and environment exists upto the entire length-scale probed. We also conduct another experiment using mock data
sets 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 demonstrates 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
