The Hubble-Jeans sequence (Jeans 1919, 1928; Hubble 1926, 1936; reviewed in van den Bergh 1997 and Sandage 2004) is not purely a bulge-to-disk (B / D) flux ratio sequence; the pitch angle (e.g., Kennefick 2013; Puerari 2013; Davis 2013) is a primary criteria for determining the Hubble type. Indeed, in the Hubble Atlas of Galaxies, Sandage (1961) made the spiral arms the primary criteria, noting that Sa galaxies can therefore exist with both large and small bulges. There is in fact a range of B / D flux ratios for any given spiral Hubble type (Fig. 5).
Figure 5.Bulge-to-disk flux ratios. Adapted from Graham & Worley (2008). The dashed line corresponds to a bulge-to-total flux ratio of 0.3, and reveals no evidence for a divide which has been advocated by some as delineating pseudobulges from classical bulges. (Note: T=1=Sa, T=2=Sab, T=3=Sb, T=5=Sc, T=7=Sd, etc.)
The range of B / D flux ratios for the lenticular galaxies had led some to propose an S0 sequence of varying B / D flux ratio, running parallel to the spiral sequence (van den Bergh 1976; Cappellari et al. 2011; Kormendy & Bender 2012), but as Fig. 5 shows, the spiral galaxies actually occupy a grid of pitch angle (i.e. roughly galaxy type: Sa, Sb, Sc, Sd) verus B / D ratio. That is, it not simply that the S0 galaxies display a range or sequence of B / D values, every disk galaxy type does. It is therefore suggested here that a grid (of spiral type based on the spiral arms, and the bulge-to-disk flux ratio or bulge magnitude) might be a useful (z = 0) classification scheme, in addition to the Hubble-Jeans sequence and expanding upon the van den Bergh track of just three parallel sequences, referred to as a comb diagram by Cappellari et al. (2011). That is, while this comb diagram focusses on the bulge-to-disk flux ratio and the prominance of the spiral arms (strong for spirals, non-existent for lenticular galaxies, and of intermediate strength for the anemic spirals), there may also be value in a grid which focusses on the bulge-to-disk flux ratio and the extent to which the spiral arms are unwound.
3.1. Bulgeless galaxies
There is some need for qualification when it comes to the term `bulgeless'. The Milky Way has been referred to as a bulgeless galaxy by some who regard it as a pure disk galaxy harboring no `classical' bulge. However, it certainly has a bulge relative to the underlying disk, and Dékány et al. (2013) suggest that it is comprised of both a classical bulge and a pseudobulge. The Scd galaxy NGC 1042 is another example which has recently been heralded as a bulgeless galaxy, and importantly one with an AGN (i.e. a supermassive black hole), but Knapen et al. (2003) have shown that it does actually have a bulge. Similarly, Simmons et al. (2013) call galaxies bulgeless if B / T is small (< ~ 0.05), even though a bulge is often still apparent. There is thus some ambiguity as to what is meant by `bulgeless'. Having noted this, readers are directed to the references in Secrest et al. (2013) for 'bulgeless' galaxies with AGN, some of which may truly be bulgeless.
While IC 5249 has less than 2% of its total light in a bulge component, NGC 300 (Bland-Hawthorn et al. 2005) has no perceivable bulge. There are also examples of apparently bulgeless, super-thin edge-on galaxies (Kautsch 2009), and super-thin disks such as in NGC 891 (see Schechtman-Rook 2013).