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between these three parameters of elliptical galaxies define what has come to be known as the “fundamental plane” (Kormendy and Djorgovski 1989). The plane tells us that larger E galaxies tend to have lower average surface brightness than smaller E galaxies, and that more luminous E galaxies have higher central velocity dispersion than do lower luminosity E galaxies.
1.4. Spiral galaxies
The spiral structure of galaxies was discovered more than 170 years ago. The subtle patterns were first detected in 1845 with the world’s largest telescope at the time, the “Leviathan of Parsonstown” located in central Ireland. William Parsons, the Third Earl of Rosse, visually saw the spiral arms of the “Whirlpool Galaxy” M51 with his newly built 72-inch speculum metal reflector. In the parlance of 19th Century astronomy, M51 was called a “nebula”, not a galaxy, although the general view at the time was that most or all nebulae were distant systems of stars like the Milky Way (“Island Universe” hypothesis). Parsons built the Leviathan partly to test this idea. The discovery of spiral structure added mystique to the nebulae, and led to alternative ideas as to what the nebulae actually were. It would be nearly a century after Parsons’ discovery that any serious understanding of the nature of spiral structure would be achieved (section 1.11).
Spiral galaxies are generally two-component systems consisting of a bulge and a disk. Although at one time bulges were thought to be generally less flattened components than disks, it is now clear that bulges include a mix of dissimilar structures, such as spheroidal “classical” bulges, highly flattened “pseudobulges” (Kormendy and Kennicutt 2004) and “boxy/peanut” bulges, the latter thought to be due to edge-on views of bars (e.g. Lutticke and Dettmar 1999).
The classification of spirals is generally based on a rough correlation between the degree of central concentration and the character of the spiral arms. Hubble had noticed that galaxies with tightly wrapped, relatively smooth arms tended to have bright central bulges, while galaxies having open, relatively patchy spiral arms tended to have very small bulges. Hubble (1926) called the former cases Sa galaxies and the latter cases Sc galaxies, with Sb galaxies being intermediate between the two types. This observation set the stage for galaxy classification for nearly a century. However, the correlation works best for non-barred galaxies. It is poorer for barred galaxies that, even in cases with smooth, tightly wrapped arms, can have very small bulges. An example is NGC 3351, type SBb, which has a very small bulge in the center of a bright nuclear ring (Buta et al. 2007). Because of such inconsistencies, Sandage (1961) advocated basing spiral stage classifications (i.e. Sa, Sb, etc.) mainly on the appearance of the spiral arms.
Figure 1.9 shows a full CVRHS stage sequence for non-barred galaxies from stage S0° to stage Sm, that is, from the intermediate S0 stage (Figure 1.3) to the latest stage on the spiral sequence. The spiral sequence begins with the stage S0/a, which is considered to be a transition type between S0s and spiral galaxies. Type S0/a is a legitimate type in the sense that it is easily recognized and the continuity that de Vaucouleurs envisioned seems well represented by the type. Nevertheless, this apparent continuity does not necessarily imply that all S0s are correctly placed in the Hubble (1936) “tuning fork”. The stage generally begins with pseudorings made of tightly wrapped spiral structure as in NGC 809. In the CVRHS classification, stage S0/a is closer to S0 than to Sa, while S0/a is closer to Sa than to S0.
The sequence for non-barred galaxies in Figure 1.9 shows the rough correlation between central concentration and stage. Bulges are most prominent at stages Sbc and earlier, and are least prominent at stages Sc and later. The sequence shows well how arms are smooth at stage Sa and knotty, well-resolved, more open features at stage Sc. Intermediate stages are as well defined as regular stages: Sab galaxies often resemble Sa galaxies but with a greater degree of resolution into star-forming regions; Sbc galaxies typically have the bulge of an Sb galaxy in a disk with Sc arms; Scd is recognized as an Sc galaxy with only a trace of central concentration; and Sdm galaxies are typically bulge-less asymmetric systems with an offset bar and one spiral arm longer than the other. Similar underline stages (e.g. Sab. Scd) are used throughout the CVRHS sequence (de Vaucouleurs 1963).
Figure 1.10 shows the same kind of stage sequence for barred galaxies. Initially, Hubble (1926) believed that non-barred galaxies were the “normal” form of spirals, with perhaps maybe 20% of the spirals being barred. He nevertheless envisioned barred spirals as falling on a sequence parallel to that of non-barred spirals. In the Hubble Atlas of Galaxies, Sandage (1961) smoothly connects non-barred and barred S0s with the non-barred and barred spiral prongs, respectively, which is also true for the VRHS and the CVRHS systems. The same kinds of types are recognizable among barred spirals as among non-barred spirals. However, Figure 1.10 shows the small bulge effect in early-type barred spirals, an example being NGC 5610 whose smooth arms wrap into an outer pseudoring but whose bulge is no more prominent than that in an Sc galaxy.
Figure 1.9. A sequence of stages for non-barred galaxies in the VRHS/CVRHS system
The bars of spiral galaxies: As already noted in section 1.2, the CVRHS classification of bars utilizes five categories, SA, SAB, SAB, SAB and SB (de Vaucouleurs 1963), in a sequence of increasing visual bar strength (Figure 1.11). The classification is based on the length, contrast and axis ratio of the bar or bar-like feature. Although leading dust lanes are not a classification criterion for bars, such lanes are often seen in barred spirals of types S0/a to Sbc and could impact the apparent bar strength. Based on CVRHS classifications, the bar fraction is about 50% for SAB, SAB and SB cases, but increases to 67% if SAB is included (Buta et al. 2015; Buta 2019). The cosmological significance of the bar fraction is discussed by Sheth et al. (2008).
Figure 1.10. A sequence of stages for barred galaxies in the VRHS/CVRHS system
There are additional aspects of bars recognized in CVRHS classifications. Most bars are regular bars, the kinds of features seen in classic barred spirals like NGC 1300 or NGC 1365. Others are “ansae-type” bars, where the bar appears to have “handles” or enhanced spots at the ends (Martinez-Valpuesta et al. 2007). Several examples are shown in Figure 1.12, which are classified using the symbols SBa or SABa. In some cases, the appearance of ansae-type bars suggests a regular bar in the process of actual dissolution. On the other hand, Athanassoula et al. (2016) have recently used numerical simulations to show that ansae could form in the disk-shaped remnant of the merger of two spiral galaxies. Another aspect of bar classification comes from box/peanut bulge galaxies. A box/peanut bulge galaxy is generally an edge-on disk-shaped galaxy where the bulge has boxy isophotes and has the look of an “X” pattern crossing the center. One of these is shown in Figure 1.12 and several others are shown in Figure 1.13 (bottom row). The appearance of a boxy/peanut bulge can depend on whether the bar is viewed end-on or broadside-on. The X is believed to be