The correlations between galaxy properties in different environments of the cosmic web

Abstract: We study the correlations between $(u-r)$ colour, stellar mass, specific star formation rate (sSFR) and metallicity of galaxies in different geometric environments of the cosmic web using a volume limited sample from the SDSS. The geometric environment at the location of each galaxy is determined using the eigenvalues of the tidal tensor in three dimensions. We use the Pearson correlation coefficient (PCC) and the normalized mutual information (NMI) to quantify the correlations between these galaxy properties in sheets, filaments and clusters after matching the stellar mass distributions of the galaxies in these environments. A two-tailed t-test assesses the statistical significance of the observed differences between these relations in different geometric environments. The null hypothesis can be rejected at $>99.99\%$ significance level in most of the cases, suggesting that the scaling relations between the observable galaxy properties are susceptible to the geometric environments of the cosmic web.