How much a galaxy knows about its large-scale environment?: An information theoretic perspective

The small-scale environment characterized by the local density is known to play a crucial role in deciding the galaxy properties but the role of large-scale environment on galaxy formation and evolution still remain a less clear issue. We propose an information theoretic framework to investigate the influence of large-scale environment on galaxy properties and apply it to the data from the Galaxy Zoo project that provides the visual morphological classifications of ∼1 million galaxies from the Sloan Digital Sky Survey. We find a non-zero mutual information between morphology and environment that decreases with increasing length-scales but persists throughout the entire length-scales probed. We estimate the conditional mutual information and the interaction information between morphology and environment by conditioning the environment on different length-scales and find a synergic interaction between them that operates up to at least a length-scales of ∼30 h^-1 Mpc. Our analysis indicates that these interactions largely arise due to the mutual information shared between the environments on different length-scales.