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
