Analyzing the cosmic web environment in the vicinity of grand-design and flocculent spirals with local geometric index

We explore the environment of a combined set of $367$ grand-design and $619$ flocculent spiral galaxies. We introduce a novel estimator called the $\mathit{\text{local}}\mathit{\text{geometric}}\mathit{\text{index}}$ to quantify the morphology of the local environment of these $986$ spirals. The local geometric index allows us to classify the environment of galaxies into voids, sheets, filaments, and clusters. We find that grand-designs are mostly located in dense environments like clusters and filaments ($\sim 78\mathrm{\%}$), whereas the fraction of the flocculents lying in sparse environments like voids and sheets is significantly higher ($>10\mathrm{\%}$) than that of the grand-designs. A $p$-value $<$ ${10}^{-3}$ from a Kolmogorov-Smirnov test indicates that our results are statistically significant at $99.9\mathrm{\%}$ confidence level. Further, we note that dense environments with large tidal flows are dominated by the grand-designs. On the other hand, low-density environments such as sheets and voids favor the growth of flocculents.