Impact of cosmic web on galaxy properties and their correlations: Insights from Principal Component Analysis

We use Principal Component Analysis (PCA) to analyse a volume-limited sample from the SDSS and explore how cosmic web environments affect the interrelations between various galaxy properties, such as $(u-r)$ colour, stellar mass, specific star formation rate, metallicity, morphology, and $D4000$. Our analysis reveals that the first three principal components (PC1, PC2 and PC3) account for approximately $\sim 85\text{\%}$ of the data variance. We classify galaxies into different cosmic web environments based on the eigenvalues of the deformation tensor and compare PC1, PC2, PC3 across these environments, ensuring a mass-matched sample of equal size for each environment. PC1 is dominated by colour, sSFR, D4000, and morphology. It displays clear bimodality across all cosmic web environments, with sheets and clusters showing distinct preferences for negative and positive PC1 values, respectively. This variation reflects the strong role of environmental processes in regulating star formation. PC2 and PC3, respectively show positively and negatively skewed unimodal distributions in all environments. PC2 is primarily influenced by metallicity whereas PC3 is dominated by stellar mass. It indicates that metallicity evolves gradually and is less sensitive to environmental extremes, highlighting the importance of internal, secular processes. PC3 likely captures residual variation in stellar mass within the two main galaxy populations (star-forming and quiescent) separated by PC1. A Kolmogorov–Smirnov (KS) test confirms that the distributions of PC1, PC2 and PC3 differ significantly across environments, with a confidence level exceeding 99.99%. Furthermore, we calculate the normalized mutual information (NMI) between the principal components and individual galaxy properties within different cosmic web environments. A two-tailed t-test reveals that for each relationship and each pair of environments, the null hypothesis is rejected with a confidence level $>99.99\text{\%}$. Our analysis confirms that cosmic web environments play a significant role in shaping the correlations between galaxy properties.