The local environment of flat galaxies

The existence of flat or bulgeless galaxies poses a challenge to the hierarchical structure formation scenario advocated by modern cosmology. We determine the geometrical environment of a sample of $315$ flat galaxies from the Revised Flat Galaxy Catalog (RFGC) using `local dimension' $D$, which, on a given length scale, quantifies the dimension of the cosmic structure in which a galaxy is embedded. For galaxies residing in filaments, nodes and sheets, $D \sim 1$, $D \sim 1.5$ and $D \sim 2$ respectively; $D \sim 3$ represents field galaxies. We also determine the local dimensions of a sample of 15,622 non-flat galaxies identified in the Galaxy Zoo project from the Sloan Digital Sky Survey (SDSS). We find that the median values of $D$ for the flat and the non-flat galaxies are $2.2$ and $1.8$ respectively, implying that flat galaxies are located in a relatively sparser environment compared to non-flat galaxies; a Kolmogorov-Smirnov (KS) test indicates that their geometrical environments are different at $>99$\% confidence level. Further, using a group finding algorithm, we study the local environment of a subset of $779$ flat galaxies with major-to-minor axes ratio $a/b >10$ identified as superthin galaxies. We find that the median clusterization index $k_{\rm{min}}$ for superthin flat galaxies $\sim$ $2.3$ while $\sim$ $1.7$ for other flat galaxies, confirming that the superthins reside in an under-dense environment compared to other flat galaxies at $> 98 \%$ confidence level. Our results may therefore have important implications for the formation and evolution models of flat galaxies in the universe.