High-order 3D Voronoi tessellation for identifying isolated galaxies, pairs and triplets

A geometric method based on the high-order 3D Voronoi tessellation is proposed for identifying single galaxies, pairs and triplets. This approach allows us to select small galaxy groups and isolated galaxies in different environments and to find the isolated systems. The volume-limited sample of galaxies from the Sloan Digital Sky Survey Data Release 5 spectroscopic survey was used. We conclude that in such small groups as pairs and triplets, segregation by luminosity is clearly observed: galaxies in isolated pairs and triplets are on average two times more luminous than isolated galaxies. We consider the dark matter content in different systems. The median values of mass-to-luminosity ratio are  12 M_⊙/L_⊙  for the isolated pairs and  44 M_⊙/L_⊙  for the isolated triplets, and 7 (8)  M_⊙/L_⊙  for the most compact pairs (triplets). We also found that systems in denser environments have greater rms velocity and mass-to-luminosity ratio.