Analyzing the cosmic architecture in the vicinity of Grand-design and Flocculent spiral galaxies with Local Geometric Index

We explore the environment of 351 grand-design and 541 flocculent spiral galaxies recently identified employing convolutional neural networks from the $17^{th}$ data release of Sloan Digital Sky Survey. We introduce a novel estimator called the Local Geometric Index to quantify the morphology of the local environment of these 892 spirals. Based on the local geometric index of the galaxies, we identify their local environments to be voids, sheets, filaments or clusters. We find that grand-designs are mostly located in dense environments like clusters and filaments ($\sim 76\%$), whereas a reasonable fraction of the flocculents lie in sparse environments like voids and sheets ($\sim 45\%$). A $p$-value $<$ $10 ^{-10}$ from a Kolmogorov-Smirnov test indicates that our results are statistically significant at $99.9\%$ confidence level. Further, we note that dense environments with large tidal flows are dominated by the grand-designs. Metal-poor environments, such as sheets and voids, with a high abundance of gas clouds, on the other hand, are mostly populated by the flocculents.