Milky Way galaxy-analogs and isolated galaxies with bars: environmental density in the Local Volume

The environmental density of galaxies within the cosmic web constrains their 3D locations in filaments, voids, groups, and clusters. It traces the distribution of baryons and the influence of dark-matter halos on galaxy evolution, and helps diagnose external processes such as supernova and AGN feedback, tidal interactions, ram-pressure stripping, and large-scale flows. We focus on isolated barred galaxies, the parent population that includes Milky Way analogs. To measure local environmental density and verify isolation (|Delta v| <= 500 km s^-1), we built a Python pipeline that works in two redshift regimes: low (z0 < 0.02) and high (z0 >= 0.02). Densities were estimated with k-nearest neighbors and Voronoi tessellations and classified as void (Sigma < 0.05), filament (0.05 <= Sigma < 0.5), group (0.5 <= Sigma < 2.0), and cluster (Sigma >= 2.0). Our northern-sky sample contains 311 isolated barred galaxies from 2MIG plus Milky Way analog systems (z < 0.07). We find 157 void, 84 filament, 27 group, and 11 cluster galaxies; 30 have no detected neighbors. Sixty-seven lie in extremely low-density regions (Sigma_3D < 0.01 gal Mpc^-3), and 22 have the nearest companion beyond 5 Mpc, indicating residence in extended voids. The Milky Way (Sigma_5NN ~ 0.13 gal Mpc^-3, R ~ 2.1 Mpc) and its close analog NGC 3521 both lie in filamentary environments at the edge of a nearby void. For z > 0.02 we identify three additional Milky Way analog candidates from the density metrics: CGCG 208-043 (3D Voronoi) and NGC 5231 and CGCG 047-026 (5th-nearest neighbor). These results show that local environmental density is an effective, physically motivated criterion for selecting Milky Way analogs.