A Revised Parallel-Sequence Morphological Classification of Galaxies:   Structure and Formation of S0 and Spheroidal Galaxies
  We update van den Bergh's parallel sequence galaxy classification in which S0 galaxies form a sequence S0a-S0b-S0c that parallels the sequence Sa-Sb-Sc of spiral galaxies. The ratio B/T of bulge to total light defines the position of a galaxy in each sequence. Our classification makes one improvement. We extend the S0a-S0b-S0c sequence to spheroidal ("Sph'") galaxies that are positioned in parallel to irregular galaxies in a similarly extended Sa-Sb-Sc-Im sequence. This provides a natural "home" for spheroidals, which previously were omitted from galaxy classifications. To motivate our juxtaposition of Sph and irregular galaxies, we present photometry and bulge-disk decompositions of Virgo S0s, including late-type S0s that bridge the gap between S0b and Sph galaxies. NGC 4762 is a SB0bc with B/T = 0.13. NGC 4452 is a SB0c galaxy with an even tinier pseudobulge. VCC 2048 and NGC 4638 have properties of both S0cs and Sphs. We update the structural parameter correlations Sphs, irregulars, bulges, and disks. We show that spheroidals of increasing luminosity form a continuous sequence with the disks (but not bulges) of S0c-S0b-S0a galaxies. Remarkably, the Sph--S0-disk sequence is almost identical to that of irregular galaxies and spiral galaxy disks. We review published observations for galaxy transformation processes, particularly ram-pressure stripping of cold gas. We suggest that Sph galaxies are transformed, "red and dead" Scd--Im galaxies in the same way that many S0 galaxies are transformed, red and dead Sa-Sc spiral galaxies 
John Kormendy and Ralf Bender
astro-ph.CO