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Research on internal secular evolution is now a major industry, but work on environmental secular evolution still is a series of important but disconnected cottage industries. We need to make the subject an integral part of our standard picture of galaxy evolution. This section reviews environmental secular evolution, following Kormendy & Bender (2012).

Our theme is that dwarf spheroidal (dSph) galaxies such as Draco and UMi and higher-luminosity Sph galaxies such as NGC 205 are transformed, "red and dead" spiral and irregular galaxies and that many S0 galaxies similarly are transformed earlier-type spirals. That is, Sph galaxies are bulgeless S0s. The easiest way to introduce this theme is using Fig. 51. This is one of the best-known extragalactic images, but it is not widely realized that it includes an easy way to form a mental picture of the difference between elliptical and spheroidal galaxies. In doing so, it speaks directly to the fundamental question: What is an elliptical galaxy (Fig. 52)?

Figure 51

Figure 51. M 31 (Sb, center), M 32 (E, lower companion) and NGC 205 (Sph, upper companion) from the Digital Sky Survey via

7.1. What is (and what is not) an elliptical galaxy?

In Fig. 51, M 31 is an Sb spiral with a classical bulge; B / T = 0.34 ± 0.03 (Kormendy et al. 2010). Absent the disk, the bulge is indistinguishable from a smallish elliptical. M 32 is one of the tinest true ellipticals, with a V-band absolute magnitude of MV ≃ -16.7 (Kormendy et al. 2009). It is small and dense and commonly called a "compact elliptical" (cE). But compactness is not a disease; it is mandated by the physics that makes the Fundamental Plane (Figs. 57, 68). In fact, M 32 is an entirely normal example of a tiny elliptical (Kormendy et al. 2009). In contrast, NGC 205 is the most luminous example in the Local Group of a galaxy that satisfies the morphological definition of an elliptical but that differs quantitatively from ellipticals (as a result, it is typed "E5 pec"). NGC 205 has the same luminosity as M 32, MV ≃ -16.6 (Mateo 1998). It looks different because it is larger, lower in surface brightness and shallower in surface brightness gradient. Measured quantitatively, these differences put NGC 205 near the bright end of a sequence of elliptical-looking galaxies that is disjoint from – in fact, almost perpendicular to – the sequence of ellipticals and classical bulges in Figs. 43, 57, 6869 and 71. This means that NGC 205 is not an elliptical.

Finding gas and young stars in it supports this conclusion. We call such objects "spheroidal galaxies" (Sphs), adapting a name ("dwarf spheroidal") that is in common use for smaller examples. The fact that NGC 205 has surface brightnesses similar to those of the disk of M 31 is not an accident. A variety of evidence leads to the conclusion that Sph galaxies are defunct late-type galaxies whereas classical bulges and ellipticals are the remnants of major galaxy mergers. This story is the subject of the present section.

Recall (Section 3.4) how classical morphologists attach no interpretation to descriptions, whereas physical morphologists try to construct a system in which classification bins uniquely separate objects that have different origin and evolution. I emphasized there that, even though classical morphologists try to avoid interpretation, they nevertheless makes choices about which features to view as important and which to view as secondary. Figure 52 illustrates how this results in a problem for classifying elliptical galaxies. In its isophote shape, Leo I resembles the elliptical galaxy M 87. However, in its surface brightness, it resembles the irregular galaxies Leo A and Gr 8. Hubble classification is based mainly on isophote shape, so it has been common to call galaxies like Leo I and NGC 205 "dwarf ellipticals" (e. g., Sandage 1961). But there has never been any guarantee that structural morphology identifies physically different kinds of objects. Figure 53 makes this point concrete.

Figure 52

Figure 52. What is an elliptical galaxy? Morphologically, the dwarf galaxy Leo I (top-middle panel) resembles the dwarf irregulars Leo A and GR 8 in its low surface brightness and shallow brightness gradient. But it resembles the giant elliptical M 87 in having elliptical isophotes and no cold gas. Since only the latter characteristics morphologically define ellipticals, Leo I is often called a "dwarf elliptical". However, purely morphological criteria prove unable to distinguish objects that have different formation histories. Leo I turns out to be related to dI galaxies, not to ellipticals. So I do not call it a dwarf elliptical; rather, I call it a dwarf spheroidal (dSph) galaxy.

Who does not belong in Fig. 53? The answer is of course well known (Fig. 54). Dolphins (Fig. 53, top right) are mammals, even though they are morphologically similar to sharks (Fig. 53, top left). To make a living, both need to be well streamlined, strong swimmers. Convergent evolution made them that way. In contrast, a leafy seadragon (Fig. 53, bottom right: is a kind of seahorse whose main need is good camouflage to avoid predators. So, even though it is a fish, its morphology has evolved to be very different from that of a shark. A "Hubble classification" of sea animals that was superficially based on visible structural characteristics could mistakenly combine sharks and dolphins into the same or closely related classification bins and could miss the more subtle (but more important) differences that distinguish sharks and sea dragons from dolphins and cows. Which parameters best distinguish the physical differences that are most important to us is not necessarily obvious without detailed study.

Figure 53

Figure 53. The danger of classifying using only morphology. Who does not belong?

Figure 54

Figure 54. Dolphins are Mammals. Convergent evolution happens. It happens to galaxies as well as to creatures on Earth, and elliptical and spheroidal galaxies prove to be examples. They look morphologically similar but have different formation histories. I warmly thank Douglas Martin ( for permission to use this figure.

7.2. The E – Sph dichotomy

Why did we ever think that Leo I and NGC 205 are ellipticals? The answer is that research on galaxies began with descriptive classical morphology (e. g., Hubble 1936; de Vaucouleurs 1959; Sandage 1961), and then the above galaxies satisfy the definition of an elliptical. However, we will see in Fig. 59 that Sandage et al. (1985b) had no trouble in distinguishing between E and dE galaxies of the same luminosity. If this sounds surpassingly strange to you, you have the right reaction. I will come back to this point below.

Astronomers are conservative people – this is often healthy – and most people clung to the idea that galaxies like Leo I and NGC 205 are ellipticals even after hints to the contrary started to appear. Figure 55 shows an example. Ellipticals (filled circles) have higher surface brightness at lower galaxy luminosities, whereas "dwarf ellipticals" (open circles and crosses) have lower surface brightnesses at lower luminosities. M 32 is consistent with the extrapolation of the E sequence. However, at that time, we thought that M 32 is compact because it has been tidally truncated by M 31 (King 1962; Faber 1973). Bingelli et al. (1984) therefore concluded that E and dE galaxies form a continuous but not monotonic sequence in surface brightness as a function of luminosity. Meanwhile, one could wonder whether the two sequences in Fig. 55 already hint at different formation physics.

Figure 55

Figure 55. Parameter correlations for elliptical and "dwarf elliptical" galaxies from Bingelli et al. (1984). These authors suggested that giant and dwarf ellipticals form a continuous but not monotonic sequence in mean surface brightness as a function of absolute magnitude MBT and that M 32 – which deviates prominently from this sequence – is pathological.

Wirth & Gallagher (1984) were the first to suggest that M 32-like compact ellipticals and not the more diffuse galaxies like Draco and Leo I and NGC 205 form the faint end of the luminosity sequence of elliptical galaxies. This was based on a successful search for relatively isolated dwarf compact ellipticals which resemble M 32. The new compact ellipticals and the well known ones that are companions to larger galaxies were found to lie along the extrapolation to lower luminosity of the correlations for normal ellipticals of parameters such as effective radius and velocity dispersion. With respect to this family of normal ellipticals, "the diffuse ellipticals are a distinct structural family of spheroids whose properties begin to diverge from those of the classical ellipticals at an absolute magnitude of MB ~ -18. At MV = -15, these two families differ in mean surface brightness by nearly two orders of magnitude. The key point to note for this discussion is that, in the range -18 ltapprox MB ltapprox -15, both structural classes of elliptical galaxies coexist" (Wirth & Gallagher 1984). This implies that the luminosity functions of elliptical and spheroidal galaxies differ as shown in Fig. 56.

Figure 56

Figure 56. Luminosity functions of (top) normal elliptical galaxies roughly from M 32 to M 87 and (bottom) spheroidal galaxies roughly from Draco and UMi to galaxies such as NGC 205 (Wirth & Gallagher 1984). At that time, "spheroidals" were commonly called "dwarf ellipticals". This figure then shows that the smallest non-dwarf ellipticals have lower luminosity than the biggest dwarf ellipticals.

The Wirth & Gallagher (1984) paper was largely based on four newly found, free-flying compact ellipticals. The competing idea (Faber 1973) that compact ellipticals are tidally truncated was largely based on three galaxies, M 32, NGC 4486B and NGC 5846A; then the diffuse dwarfs would be the faint extension of the E sequence. With both conclusions based on small numbers of galaxies, it was not clear which picture is correct. The rest of this section reviews the now very strong evidence that Wirth & Gallagher (1984) were presciently close to correct in almost every detail, including Fig. 56.

As a graduate student at Caltech in the early 1970s, I was brought up on the picture that ellipticals form a continuous, non-monotonic sequence in their structural parameters from the brightest to the faintest galaxies known. Then, in the 1980s, I gained access to two important technical advances. The first was CCD detectors that are linear in sensitivity over large dynamic ranges. The second was the Canada-France-Hawaii telescope (CFHT), which had the best "seeing" then available on any optical telescope. These allowed me to study the central structure of galaxies in unprecedented detail. The results revolutionized my picture of ellipticals. They confirmed and extended Wirth & Gallagher (1984), whose ideas I was not aware of until the end of my work. The story is instructive for students, so I describe it here in detail, abstracted from a popular article in Stardate magazine (Kormendy 2008b).

My CFHT surface photometry showed an unexpected result (Fig. 57). Ellipticals define the sequence of red points: less luminous ones are smaller and higher in surface brightness from M 87 to M 32. This much was expected; for bright galaxies, it is the correlation shown by the filled circles in Fig. 55. Importantly, the high-resolution CFHT photometry helps to fill in the gap between M 32 and the other ellipticals. This makes M 32 look less peculiar. The surprise was the behavior of the "dwarf ellipticals", shown in Fig. 57 by yellow points. Using near-central parameters rather than parameters measured within the effective radii re as in Fig. 55, it is clear that dwarf ellipticals do not satisfy the correlations for elliptical galaxies. Less luminous dwarf ellipticals are lower – not higher – in surface brightness. A gap has appeared between ordinary and dwarf ellipticals. Wirth & Gallagher's (1984) conclusions are confirmed with a much larger sample.

Figure 57

Figure 57. Kormendy (1985, 1987) showed with much larger samples that E and Sph galaxies form disjoint sequences in parameter space (cf. Wirth & Gallagher 1984). Sphs (yellow) are not faint ellipticals (red). Instead, their parameter correlations are almost identical to those of dwarf spiral and irregular galaxies (blue). This figure shows approximate central surface brightness and King (1966) core radius, both corrected as well as possible for PSF blurring, versus B-band absolute magnitude.

Size and density are diagnostic of galaxy formation, so I realized at this point that dwarf ellipticals are not ellipticals at all. As one point after another got plotted and intermediate cases failed to show up, my previous picture of elliptical galaxies fell apart. Kuhn (1970) captures exactly what happens in a scientist's mind when his understanding of a subject falls apart. Quoting Kormendy (2008b): "The first reaction was consternation. What have I screwed up? I checked my data reduction. I considered whether my galaxy sample could be biased. Nothing seemed wrong. Better data just led in an unexpected direction. I had to accept the new result: dwarf ellipticals are not ellipticals. But then we should not call them "dwarf ellipticals". The smallest such companions to our Milky Way had sometimes been called dwarf spheroidals. So, to minimize the departure from tradition, I called all such objects "spheroidals". The biggest ones in Virgo are only as luminous as an average elliptical, but they are giant spheroidals."

"If spheroidals are not ellipticals, what are they? Kuhn describes what happens next. Deprived of the guidance of any previous understanding of a subject, a scientist in the midst of a scientific revolution does not know what to do next. In turmoil and in desperation, wild ideas get tried out, most of them wrong. I plotted in my diagrams all the other kinds of stellar systems that I knew about. I plotted globular clusters of stars [green points], spiral galaxy disks [two large blue plus signs, each an average for several galaxies from Freeman 1970], and irregular galaxies [blue plus signs]. The globulars were unconnected with ellipticals and spheroidals. But the irregulars and spirals were a surprise. They showed exactly the same correlations as the spheroidals. Aha! A new picture was emerging. Maybe spheroidals are related to spirals and irregulars. They have almost the same structure. They don't contain gas and young stars, which are common in spirals and irregulars. And they have smoother structure. But I realized that, if the gas were removed or converted into stars, dynamical evolution of the now-gasless spheroidal would smooth out its formerly patchy structure within a few galactic rotations. We knew that the dwarf spheroidal companions of the Milky Way had varied star formation histories. A few contain only old stars, as ellipticals do, but most experienced several bursts of star formation, and the most recent burst was a few billion or even as little as a few hundred million years ago. What are galaxies that have not yet had their last burst of star formation and that therefore still must contain gas? This is not a controversial question [Kormendy & Bender 1994]. They are irregulars. I realized: if we looked at the Milky Way's dwarf spheroidals when the Universe was half of its present age, about half of them would still be irregulars. Irregulars have been turning into Sphs gradually over most of the history of the Universe. In the Virgo cluster, lots of processes can make this happen. The most obvious is ram-pressure stripping: as an irregular galaxy falls into Virgo for the first time, it rams into the million-degree gas that fills the cluster, and its cold gas gets swept away. It started to look like no accident that the irregulars in Virgo live around the outside of the cluster, while the center is inhabited by spheroidals [Binggeli et al. 1987]."

"Within a few days, I had a new picture. Spheroidals are defunct spiral and irregular galaxies converted by their environment to look like ellipticals. This helped our picture of galaxy formation, because we already knew that ellipticals form by galaxy mergers, whereas, quoting Tremaine (1981), `Dwarf elliptical satellite galaxies cannot form by mergers with other satellites since their relative velocities are too high.' We were in trouble when we had to find a single formation process that could explain NGC 4472, one of the biggest galaxies in the nearby Universe, and dwarf spheroidals that are a million times less luminous and that look like fragile, gossamer clouds of stars [Fig. 58 here]. But they look like the smallest irregulars, minus gas and young stars [Fig. 52 here]. So this problem was solved. I reported these results [at a workshop in Rehovot, Israel], and they were well received." The result that E and Sph galaxies are different is called the E – Sph dichotomy.

Figure 58

Figure 58. Luminosity sequence of dSph satellites of our Galaxy. Fornax, Sculptor and Draco have absolute magnitudes of MV = -13.2, -11.1 and -8.8, respectively (Mateo 1998), and correspondingly decreasing surface brightnesses (see Fig. 57). Draco is the cloud of faint stars in the right panel; the bright stars with the instrumentally-produced red halos are foreground stars in our Galaxy. Contrast M 87 in Fig. 52. Could M 87 and Draco really have similar formation histories, with different results only because changing the mass tweaks the formation physics? The results reviewed here imply that the answer is "no". We now believe that M 87 is a remnant of the dynamical violence of galaxy mergers, whereas Draco formed quescently as a dwarf irregular that lost its gas long ago. From Kormendy (2008b).

7.3. Mixed reactions to the E – Sph dichotomy

Scientific research is a quintessentially human enterprise, as reactions to the above result illustrate:

The essential theoretical understanding of why Sph and S+Im galaxies have lower stellar densities at lower galaxy masses followed immediately. Dekel & Silk (1986) "suggest that both the dI's and the dE's [here: dSphs] have lost most of their mass in [supernova-driven] winds after the first burst of star formation, and that this process determined their final structural relations. The dI's somehow managed to retain a small fraction of their original gas, while the dE's either have lost all of their gas at the first burst of star formation or passed through a dI stage before they lost the rest of the gas and turned dE." Our story here adds detail on dI → dSph transformation processes but otherwise is based on exactly the above picture.

Reactions among observers have been more mixed. The reasons are many and revealing and occasionally entertaining; they range from innate conservatism to specific scientific arguments to turf wars. I will concentrate on the part of this history that is most instructive for students.

I already noted that many astronomers are conservative: they do not easily discard a picture that they believed in for many years. This is healthy – imagine what would happen if we chased, willy-nilly, after every outrageous idea that got proposed. It is prudent to treat new ideas with respect, but in a mature subject, it is uncommon for a long-held, well-supported picture to be completely wrong. The situation is more tricky when subjects are young and not yet well developed. This proved to be such a case. Nevertheless, it is understandable that people who had long been involved in research on dwarf galaxies reacted to the above developments with some ambivalence. In particular, the group of Sandage, Binggeli, Tammann and Tarenghi wrote a series of papers on the Virgo cluster in the mid-1980s, some before and some after the Wirth & Gallagher (1984) and Kormendy (1985, 1987) papers. Struggles with the new ideas were evident in some of the later papers. The nature of these struggles reveals how seeds of the new ideas could have been recognized in the older results. I belabor this point because the conceptual blindness that results when we embrace a paradigm of how nature works always threatens our ability to see something new. As you do your research, it is healthy to be careful and conservative but also prudent to ask yourself: Am I missing something because of paradigm-induced conceptual blindness? Kuhn (1970) provides a perceptive discussion of this subject.

Figure 55 already illustrated how one hint – the opposite slopes of the surface-brightness–luminosity correlations – was contained in previous work.

Figure 59 is a better illustration (Sandage et al. 1985b). It shows with data on Virgo galaxies the result that is shown schematically in Fig. 56. The luminosity function of ellipticals is bounded at high and low L. M 32 has normal properties for its low luminosity, but such tiny ellipticals are rare. In contrast, spheroidal galaxies (which Sandage et al. 1985b call "dEs") never are very bright, but they get rapidly more common at lower luminosities until they are lost in the detection noise. The steep faint-end slope of the luminosity function had been recognized for a long time (Zwicky 1942, 1951, 1957) and is built into the well known Schechter (1976) analytic luminosity function. But, to the best of my knowledge, Sandage et al. (1985a, b) and Binggeli et al. (1988) were the first to measure luminosity functions separately for different morphological types of galaxies and to show that only Sph galaxies have luminosity functions that continue to rise with decreasing luminosity to the detection limit of the data. This is the solid result in Fig. 59. Here is the incongruity:

Figure 59

Figure 59. Luminosity functions of elliptical and spheroidal galaxies in the Virgo cluster. This figure is adapted from Sandage et al. (1985b), who used the traditional name "dE" for spheroidals. I have updated the Hubble constant from H0 = 50 to 70 km s-1 Mpc-1. Magnitudes are in B band. From Kormendy & Bender (2012).

Sandage et al. (1985b) distinguish between elliptical and dwarf elliptical galaxies of the same luminosity. Quoting Kormendy & Bender (2012): "A dwarf version of a creature is one that, when mature, is smaller than the normal sizes of non-dwarf versions of that creature. ... And yet, [Fig. 59] invites us to imagine that the smallest non-dwarf ellipticals are 20 times less luminous than the brightest `dwarf ellipticals'."

Sandage and collaborators recognized and struggled with this incongruity. Quoting Sandage & Binggeli (1984): "The distinction between E and dE types is made on morphological grounds alone, using surface brightness as the criterion. Normal E galaxies have a steep radial profle (generally following an r1/4 law) with high central brightness. The typical dE has a nearly flat radial profile, following either a King (1966) model with a small concentration index or equally well an exponential law. The morphological transition from E to dE is roughly at MB ≃ -18, but there is overlap." Recognition of this difference dates back at least to Baade (1944): "NGC 147 and NGC 185 are elliptical nebulae of very low luminosity. In structure, they deviate considerably from what is considered the typical E-type nebula. In both objects the density gradient is abnormally low." Binggeli et al. (1985) also recognized the quantitative similarity beween spheroidals and irregulars; their Virgo "membership criteria applied are: (1) dE and Im members have low surface brightness. ...". Soon afterward, Sandage et al. (1985b) admit that "We are not certain if this [E – dE dichotomy] is totally a tautology due merely to the arbitrary classification criteria that separate E from dE types ... or if the faint cutoff in the [E luminosity function] has physical meaning related to the properties of E and dE types. In the first case, the problem would be only one of definition. In the second, the fundamental difference in the forms of the luminosity functions of E and dE types ... would suggest that two separate physical families may, in fact, exist with no continuity between them (cf. Kormendy 1985 for a similar conclusion)." Revising a long-held picture can be uncomfortable.

Within a few more years, Binggeli et al. (1988) recognized that "The distinction [between] Es and dEs must almost certainly mean that the two classes are of different origin (Kormendy 1985, Dekel & Silk 1986). This is also supported by the fact that the luminosity functions of Virgo Es and dEs [are different]." And Binggeli & Cameron (1991) concluded that "there are no true intermediate types between E and dE. The [E – dE] dichotomy is model-independent" (emphasis in the original).

But psychology did not lose its hold on people. Binggeli changed his mind: in a section entitled "The E–dE dichotomy and how it disappears", Jerjen & Binggeli (1997) emphasize the observation that, in a plot of brightness profile Sérsic index versus MBT, E and dE galaxies show a continuous correlation. They conclude that compact ellipticals like M 32 and its analogs in Virgo are "special" and that dEs form the extension of the ellipticals to low L. However, this is not the only relevant correlation. The observations which suggest the dichotomy had not disappeared. And the fact that one can find parameters of galaxies that are insensitive to the differences between two types does not prove that the two types are the same. Many parameters are continuous between ellipticals and spheroidals. E. g., the content of heavy elements is not only a continuous function of luminosity for ellipticals and spheroidals, it is essentially the same continuous function for spirals and irregulars, too (e. g., Mateo 1998). If we looked only at element abundances, we would be blind to all structural differences encoded in Hubble types.

More recent criticisms of the E – Sph dichotomy are reviewed in Kormendy et al. (2009) and in Kormendy & Bender (2012). The arguments involve technical details such as sample size and profile analysis techniques. These are of less immediate interest, and any discussion of them quickly gets long. I therefore refer readers to the above papers for our answers to the criticisms. A few are relevant here and will be discussed below. But the best way to address uncertainty about the E – Sph dichotomy is to observe larger samples of galaxies and to address more general scientific questions, as follows.

7.4. Confirming the E–Sph dichotomy with large galaxy samples

Kormendy et al. (2009: KFCB) extend the sample size of the parameter correlations in Fig. 57 by measuring brightness profiles for all known ellipticals in the Virgo cluster and combining these with data on ~ 275 Sph galaxies. Examples are shown in Fig. 60. Data from many sources were combined to construct composite profiles over large dynamic ranges. Sérsic functions fit most of the galaxy light to remarkable precision: over the fit ranges (vertical dashes in Fig. 60), the average RMS deviation = 0.040 mag arcsec-2 for the whole KFCB sample. Kormendy (2009) further added ellipticals from Bender et al. (1992) and Sphs from Chiboucas et al. (2009). The updated Fig. 57 is shown in Fig. 61.

Figure 60

Figure 60. Surface brightness profiles of 3 galaxies from KFCB. NGC 4486 (M 87) is an elliptical galaxy with a central "core"; i. e., central "missing light" with respect to the inward extrapolation of the outer Sérsic function fit (black curve). NGC 4458 is an elliptical galaxy with central "extra light" above the inward extrapolation of the outer Sérsic fit. VCC 1185 is a Sph galaxy with a nuclear star cluster (type Sph,N) in addition to its Sérsic-function main body. This figure illustrates the robust profiles that are derived by using many images that provide data in overlapping ranges of radii (e. g.,HST data near the center; large-field CFHT data at large r).

Figure 61 strongly confirms the dichotomy between E and Sph galaxies as found in Kormendy (1985, 1987), Binggeli & Cameron (1991) and Bender et al. (1992, 1993). Note that the Sph sequence approaches the E sequence near its middle, not near its faint end.

Figure 61

Figure 61. Global parameter correlations from KFCB and Kormendy (2009) with Sph galaxies in the Local and M 81 groups updated from Kormendy & Bender (2012). This figure shows 90 ellipticals and 295 spheroidals. One elliptical plots in the Sph sequence when effective parameters are used; difficult cases such as this one were classified in KFCB using parameters measured at the radius that contains 10% of the total light. Reason: the E – Sph dichotomy is most pronounced when near-central parameters are used (contrast Fig. 57 with this figure).

The small-re, bright-μe end of the sequence of ellipticals is defined in part by galaxies like M 32 that are sometimes called "compact ellipticals". As noted above, compact ellipticals are not a special class. They are continuously connected to brighter ellipticals in essentially all parameters. Moreover, M 32 is no longer unique, as it appeared to be in Fig. 57. We now know of a number of M 32 analogs (Binggeli et al. 1985; Lauer et al. 1995; Faber et al. 1997; KFCB). Figure 61 illustrates and KFCB reviews evidence that M 32 is normal for its low L. However, it is often suggested that these galaxies are compact only because they have been tidally stripped by much larger companions (e. g., Faber 1973; Ferrarese et al. 2006; Bekki et al. 2001; Chen et al. 2010). Kormendy & Bender (2012) review why it is not plausible that this is the explanation for why small Es are compact. This issue is important, so I enumerate the arguments here:

  1. Compact ellipticals are not always companions of brighter galaxies (Wirth & Gallagher 1984). Some are so isolated that no tidal encounter with a big galaxy is likely ever to have happened (e. g., VCC 1871: Kormendy & Bender 2012).

  2. Compact Es do not have small Sérsic indices suggestive of tidal truncation. In fact, they have the same range of Sérsic indices n ~ 2 to 3.5 as isolated coreless ellipticals. For example, M 32 has n ≃ 2.9, larger than the median value for coreless ellipticals. Numerical simulations show that major mergers of gas-poor galaxies like the ones in the nearby Universe make remnants that have exactly the above range of Sérsic indices (Hopkins et al. 2009a).

  3. Many Sph galaxies also are companions of bright galaxies, but we do not argue that they have been truncated amd thereby made abnormally compact. An example is NGC 205, which is shown by the open square at MVT = -16.6 in Fig. 61. It is much fluffier than M 32.

  4. Figure 68 below will show that the compact end of the E sequence is also defined by tiny bulges. Classical bulges and ellipticals have closely similar parameter correlations. Most classical bulges that appear in our correlation diagrams do not have bright companion galaxies.

  5. In Fig. 61, the ellipticals from M 32 to cD galaxies define projections of the "fundamental plane" correlations (Djorgovski & Davis 1987; Faber et al. 1987; Djorgovski et al. 1988; Bender et al. 1992). Its interpretation is well known: galaxy parameters are controlled by the Virial theorem modified by small nonhomologies. N-body simulations of major galaxy mergers reproduce the E-galaxy fundamental plane, not the Sph parameter sequence that is almost perpendicular to it (Robertson et al. 2006; Hopkins et al. 2008, 2009b).

Kormendy and Bender conclude: "some compact Es may have been pruned slightly, but tidal truncation is not the reason why the E sequence extends to the left of where it is approached by the Sph sequence in [Fig. 61]."

7.4.1. Classical bulges and ellipticals satisfy the same fundamental plane parameter correlations. I. Bulge-disk decomposition

Point (d) above anticipates the result of this subsection: classical bulges are essentially indistinguishable from elliptical galaxies of the same luminosity. This in turn was further anticipated when I defined classical bulges to be elliptical galaxies that happen to live in the middle of a disk. Here, the time has come to ante up the evidence by adding classical bulges to Fig. 61.

Figure 62 emphasizes the most important requirement for this analysis. For each disk galaxy, it is necessary to decompose the observed brightness distribution into (pseudo)bulge and disk parts. This is a fundamental part of the classification of the central component as classical or pseudo. It provides separately the parameters of the bulge and the disk, both of which we need. For some applications, a kinematic decomposition is also needed.

Figure 62

Figure 62. (left) Sombrero Galaxy and (right) NGC 4762, the second-brightest S0 galaxy in the Virgo cluster. These galaxies illustrate why bulge-disk decomposition is necessary. NGC 4594 is an Sa galaxy with B / T = 0.93 ± 0.02 (Kormendy 2011b). Without photometric decomposition, we measure essentially only the bulge. We learn nothing about the disk. If an S0 version of this galaxy (e. g., NGC 3115) were viewed face-on, it would be difficult even to discover the disk (Hamabe 1982). In contrast, NGC 4762 is an edge-on S0 with a tiny bulge; B / T = 0.13 ± 0.02 (Fig. 63). Without photometric decomposition, we measure essentially only the disk. We learn nothing about the bulge.

Photometric decomposition is the crucial requirement that allows us to ask whether classical bulges satisfy the parameter correlations for ellipticals. Absent such a decomposition, even the distinction between ellipticals and spheroidals is blurred. This is part of the reason why Ferrarese et al. (2006); Chen et al. (2010), and Glass et al. (2011) do not see the E – Sph dichotomy. If bulges and disks are combined in various proportions and then measured as one-component galaxies, it is inevitable that the resulting parameters will be intermediate between those of bulges and disks and that including them will blur the distinction between the bulge and Sph ≈ disk sequences in Fig. 61 (see Figs. 76 and 77 in KFCB and Figs. 63 and 64 here).

The need for bulge-disk decomposition can best be understood using an analogy. Imagine studying a population of people, horses and people who ride on horses. Knowing nothing about them, one might measure parameters and plot parameter correlations (linear size, mass, ...) to look for different physical populations and regularities within each population that might drive interpretation. We need to be careful, because some parameters (volume mass density within this analogy; mass-to-light ratio for galaxies) prove to be insensitive to structural differences. Still, careful parameter study is promising. But the biggest people are bigger than the smallest horses. If random people are paired with random horses and the resulting population of people+horses, together with some pure people and some pure horses, are analyzed as one-component systems, it is inevitable that a complete continuity will be found between people and horses. But it would be wrong to conclude that people are the same as horses. Rather, if one decomposes people and horses when they occur together and measures their parameters separately, it will be found that some parameter correlations clearly separate people of various sizes from horses of various sizes, even though their size distributions overlap. Further study will also show that certain special parameters (semi-trivially: number of arms versus number of legs in this analogy; near-central parameters in the cases of galaxies) are especially helpful in distinguishing the physically different populations that are under study. The one elliptical galaxy (red point) that lies within the sequence of Sphs (green points) in some panels of Fig. 61 was classified using central parameters (Fig. 34 in KFCB).

It feels strange to "beat this dead horse" (I'm sorry – I could not resist): the need for component decomposition has been understood for more than 30 years. It quickly became standard analysis (Kormendy 1977a; Burstein 1979; Kent 1985). It is still so now (Peng et al. 2002; Knapen et al. 2003; de Souza et al. 2004; Laurikainen et al. 2004, 2005, 2007; Courteau et al. 2007; Méndez-Abreu et al. 2008; Weinzirl et al. 2009). The structure (this section) and formation physics (Section 8) of bulges and disks are very different, and it blurs our vision of both to analyze them as single-component systems.

7.4.2. Small-bulge S0 galaxies and the transition from S0 to Sph galaxies

Kormendy & Bender (2012: KB2012) collect bulge and disk parameters from a variety of sources for or do photometry and bulge-disk decomposition of all S0 galaxies from the HST ACS Virgo Cluster survey (Côté et al. 2004; Ferrarese et al. 2006). This section reviews the results. Classical bulges are added to the parameter correlation diagrams in Fig. 68. But another and – it will turn out – especially interesting result will be to extend the Sph sequence to higher luminosities. Kormendy & Bender (2012) conclude that Sph galaxies and S0 disks (but not bulges) are continuous in their parameter correlations. That is, Sph galaxies are bulgeless S0s.

Three galaxies serve here to illustrate the transition from S0 galaxies with large classical bulges and flat disks to Sph galaxies with no bulges and with structure that can be vertically disky or thick. We start with NGC 4762. Figure 62 shows that it differs from our canonical picture of Hubble classification (Sandage 1961) in which S0 galaxies are transition objects between elliptical and Sa galaxies. The bulge-to-total luminosity ratio B / T is a classification parameter; B / T ≡ 1 for ellipticals, and B / T is intended to decrease along the sequence E – S0 – Sa – Sb – Sc. With some noise, this is observed (Simien & de Vaucouleurs 1986). But Sidney van den Bergh (1976) already recognized that some S0 galaxies such as NGC 4762 have small bulges and, except for their cold gas content and spiral structure, are more similar in their overall structure to Sbc galaxies than they are to Sa galaxies. As an alternative to the Hubble (1936) "tuning-fork diagram", he proposed a "parallel sequence classification" in which S0 galaxies form a sequence S0a – S0b – S0c with decreasing B / T that parallels the sequence Sa – Sb – Sc of spiral galaxies with similar, decreasing B / T ratios. Van den Bergh suggested that late-type S0 galaxies with small bulges are defunct late-type spiral galaxies that were transformed by environmental processes such as ram-pressure stripping of cold gas by hot gas in clusters. The KB2012 bulge-disk decompositions of NGC 4762 and similar galaxies quantitatively confirm van den Bergh's picture, as follows.

The brightness profile of NGC 4762 measured along the major axis of the disk is shown in Fig. 63 (left). It shows a central bright and relatively round bulge and, at larger radii, three shelves in a very flat edge-on disk. The inner shelf is somewhat subtle, but the steep decrease in surface brightness between the middle and outer shelves is obvious in Fig. 62. What is this complicated structure? This may seem like a tricky problem, but in fact, it is easy. Relatively face-on galaxies that have two or three shelves in their brightness distributions are very common. The ones with two shelves are the oval-disk galaxies discussed in Section 3.3. To get a third shelf, it is just necessary to add an early-type bar – these have shallow radial brightness gradients interior to a sharp outer end. Now, the bar normally fills its attendant lens in one dimension (Section 4.3.4 and Fig. 17). But consider a non-edge-on SB(lens)0 galaxy such as NGC 2859 (Fig. 9) or NGC 2950 (Fig. 17) in which the bar has a skew orientation (not along either the apparent major or apparent minor axis). If we rotated either of these galaxies about a horizontal line through the center in the corresponding figure until the galaxy was seen edge-on, its disk would show three shelves in its major-axis profile. Exterior to the bulge, the innermost shelf would be the bar, the next would be the lens, and the third would be the outer disk. This is how Kormendy & Bender interpret Fig. 63 (left). Thus NGC 4762 is an edge-on SB(lens)0 galaxy. Bars and lenses have shallow brightness gradients at small r, so profile decomposition is easy. The bulge Sérsic index n = 2.29 ± 0.05 and round shape identify it as classical. Importantly, B / T = 0.13 ± 0.02 is very small. So Kormendy & Bender (2012) classify NGC 4762 as SB(lens)0bc. Note in Fig. 63 (right) how measuring NGC 4762 as a single-component system (green point with brown center) mixes parameters of the classical bulge (brown point) and disk (green cross). Only after bulge-disk decomposition do we see that the tiny classical bulge of NGC 4762 helps to define the compact extension of the E – bulge parameter sequence.

Figure 63

Figure 63.(left) Ellipticity and surface brightness along the major axis of NGC 4762 measured by fitting elliptses to the isophotes in the ACS and SDSS g-band images. The dashed curves show a decomposition of the profile inside the fit range (vertical dashes). The bulge, bar, lens and disk are represented by Sérsic functions with indices n given in the figure. Their sum (solid curve) fits the data with an RMS of 0.033 V mag arcsec-2. (right) Parameter correlations showing the results of the bulge-disk decomposition. The green filled circles with the brown centers show the total parameters measured by Ferrarese et al. (2006) for the bulge and disk together. They are connected by straight lines to the parameters of the bulge (dark brown filled circles) and disk (dark green crosses). From KB2012.

NGC 4452 is closely similar to NGC 4762 but is even more extreme. Figure 64 (left) shows that it, too, is an edge-on SB(lens)0 galaxy. The decomposition robustly shows that NGC 4452 has only a very tiny pseudobulge with n ≃ 1.06 ± 0.14 (recall classification criterion (6) in Section 5.3) and PB/T = 0.017 ± 0.004. This is an SB(lens)0c galaxy.

Figure 64

Figure 64. (top left) SB(lens)0 galaxy NGC 4452. The tiny pseudobulge is almost invisible. The inner disk is edge-on and very flat; it again consists of two shelves in surface brightness. Including the outer, thicker disk, these three shelves are signatures of a bar, lens and disk. (bottom left) Ellipticity є and surface brightness μV along the major axis of NGC 4452. The five dashed curves show a decomposition of the profile inside the fit range (vertical dashes). The nucleus, bulge, bar, lens and disk are represented by Sérsic functions with indices n given in the figure. Their sum (solid curve) fits the data with RMS = 0.044 V mag arcsec-2. (bottom right) Parameter correlations showing the results of the bulge-disk decomposition. The green filled circles with the blue centers show the total parameters measured by Ferrarese et al. (2006) for the bulge and disk together. These points are connected by straight lines to the parameters of the pseudobulge (blue filled circles) and disk (dark green crosses). From KB2012.

The parameter correlations in Figs. 63 and 64 serve to emphasize how bulge-disk decomposition improves our understanding of the E sequence. The small black filled dots show the parameters measured by Ferrarese et al. (2006) for the ACS Virgo cluster survey S0s. They do not violate the E sequence. But they do combine bulge and disk properties into one set of parameters, so they fail to show something that is very important. In each of these two galaxies, the bulge is tiny, comparable in luminosity to the smallest ellipticals. The classical bulge of NGC 4762 helps to define the extension of the E sequence toward objects that are more compact than any spheroidal. Even the tiny pseudobulge of NGC 4452 lies near the compact end of the E+bulge sequence (cf. Figs. 42 and 43, which show other, similarly compact and tiny pseudobulges). Figures 68 and 69 will summarize the parameter correlations for classical bulges and S0 disks, respectively. Here, I want to emphasize two things. First, there exist S0 galaxies with classical-bulge-to-total luminosity ratios B / T that range from almost 1 to essentially zero. The pseudobulge in NGC 4452 is so small that one cannot hide a significant classical bulge in that galaxy. Second, both NGC 4762 and NGC 4552 have vertically thickened and warped outer disks. Both galaxies have nearby companions. Kormendy & Bender (2012) interpret these results as indicating that the outer disks are tidally warped and being heated dynamically in the vertical direction. They present evidence that many other S0 and Sph galaxies in the Virgo cluster are dynamically heated, too. Thus NGC 4762 and NGC 4552 are "missing links" that have some properties of S0 galaxies and some properties of the brightest Sph galaxies.

NGC 4638 is even more spectacularly an S0 – Sph transition object. Figure 65 shows (bottom) the large-scale structure and (top) an embedded, edge-on disk and bulge in an enlargement from HST images. When we wrote KB2012, this structure was, to our knowledge, unique. Figure 65 (bottom) suggests that NGC 4638 is an edge-on S0 whose bulge happens to be very boxy. This would be interesting but not unique; boxy bulges are discussed in Section 5.2.9. But already in the bottom panel of Fig. 65, the structure looks suspiciously unusual: the brightness gradient in the boxy structure is very shallow, like that in its companion, the normal Sph,N galaxy NGC 4637. The top panel of Fig. 65 shows an almost-round, small bulge in NGC 4638 with a normal, steep brightness gradient. To our surprise, the brightness profile robustly shows (Fig. 66) that the outer boxy structure has a Sérsic brightness profile with n = 1.11 ± 0.12 characteristic of the main body of a Sph galaxy. This profile is not concave-upward, as it would be if the bulge and the boxy structure where part of the same component with n ≫ 4.

Figure 65

Figure 65. (top) Color image of NGC 4638 = VCC 1938 made from the HST ACS g, mean of g and z, and z images. This image shows the edge-on disk and central bulge. Brightness is proportional to the square root of intensity, so the brightness gradient in the bulge is much steeper than that in the boxy halo. The very red foreground star near the NE side of the disk is also evident in the bottom image. (bottom) Color image of NGC 4638 = VCC 1938 from WIKISKY. The brightness "stretch" emphasizes faint features, i. e., the extremely boxy, low-surface-brightness halo in which the S0 disk and bulge are embedded. The elongated dwarf to the west of NGC 4638 is the Sph,N galaxy NGC 4637. Like many other spheroidals, NGC 4637 is flatter than any elliptical. Note also that VCC 2048 (not illustrated) is another "missing link" galaxy with both S0 and Sph properties: like NGC 4637, it is flatter than any elliptical; its main body is clearly a Sph, but it contains an embedded, tiny S0 disk (see KB2012, from which the above images are taken).

Figure 66

Figure 66. Ellipticity є and surface brightness μV along the major axis of NGC 4638 as measured on the HST ACS and SDSS g images. Dashed curves show a three-Sérsic-function decomposition of the profile inside the fit range (vertical dashes). The bulge is small, but it is classical. The disk has a Gaussian profile, as do many other S0s discussed in KB2012. Remarkably, the outer, boxy halo is clearly distinct from the bulge and disk and has a Sérsic index n = 1.11 ± 0.12. The sum of the components (solid curve) fits the data with an RMS of 0.054 V mag arcsec-2. From KB2012.

Kormendy & Bender (2012) therefore conclude that NGC 4638 contains three structural components, and edge-on S0 galaxy that consists of an n = 3.6 ± 1.4 classical bulge plus an n = 0.5 ± 0.1 Gaussian disk embedded in a normal Sph galaxy with n = 1.11 ± 0.12. I. e., NGC 4638 has the properties of both an S0 and a Sph galaxy. VCC 2048 is similar (Fig. 65 caption).

It is instructive to compare the parameters of the three components of NGC 4638 with their counterparts in pure S0 and Sph galaxies (Fig. 67). The classical bulge helps to define the compact end of the normal E – Sph parameter sequence. It is within a factor or ~ 2 as compact as M 32. The disk proves to have the highest effective brightness of any S0 disk shown in Fig. 69. The reasons are (1) that it is edge-on, so the path length through it is large, and (2) that its profile is Gaussian rather than exponential; the strong outer truncation results in small re and hence bright μe. The boxy component is consistent with the extrapolation of the Sph sequence; it is the brightest Sph galaxy known in the Virgo cluster.

Figure 67

Figure 67. Parameter relations showing results of the bulge-disk-Sph decomposition of NGC 4638. The green circles with the brown centers show the total parameters measured by Ferrarese et al. (2006) for all components together. These points are connected by lines to the parameters of the classical bulge (brown circles), the disk (green crosses), and the Sph halo (green square). From KB2012.

NGC 4638 lives in a high-density part of the Virgo cluster where strong dynamical heating is plausible. Kormendy & Bender interpret the boxy Sph part of the galaxy as the dynamically heated remnant of the outer disk. Because these stars are no longer part of a disk, the disk that remains has a strongly truncated, i. e., Gaussian profile.

KB2012 discusses additional evidence that higher-luminosity Sphs are, by and large, more disky. This is consistent with the suggestion that dynamical heating is one of the S → Sph transformation processes and that this heating has the smallest effect on the biggest, most robust galaxies.

7.4.3. Interim summary and road map

In Section 7.4.2, our discussion of the E – Sph dichotomy branched out in a new direction – the close relationship between Sphs and S0 galaxy disks. Section 7.5 pursues this. Meanwhile, it is useful to summarize where we are.

Section 7 is about environmental secular evolution. The "bottom line" will be that a variety of environmental processes appear to have transformed some intermediate-Hubble-type spiral galaxies into S0s and some late-type spiral and Magellanic irregular (Im) galaxies into Sphs. Sph galaxies will prove to be bulgeless S0s. "Missing link" galaxies that have some S0 and some Sph properties are the new subject that entered the above discussion.

Recall that we were in the process of investigating the E – Sph dichotomy. That is, even though they look similar, elliptical and spheroidal galaxies have quantitatively different structural parameters and parameter correlations. This imples that they have different formation histories – histories that we are in the process of deciphering. I reviewed the history of the above discovery, concentrating on how improved measurements and enlarged galaxy samples have strengthened the evidence for the dichotomy. Originally not recognized (Fig. 55), it was first found using small galaxy samples (Fig. 57) and since has been confirmed using 90 ellipticals and 295 spheroidals (Fig. 61). Our next aim has been to add classical bulges, to increase the sample size and to further show that tiny ellipticals are not compact because they are tidally stripped. This led us into a discussion of bulge-disk decomposition and a description of three example galaxies, two of which have classical bulges that are substantially as compact as the smallest ellipticals. In our standard picture of bulge formation by major mergers, these bulges would have formed before their attendant disks. It is implausible that such bulges are compact because they were tidally stripped.

The bulge parameters measured and collected in KB2012 now allow us to "pay the piper" in confirming our definition of bulges as (essentially) ellipticals that live in the middle of a disk. This is the subject of Section 7.4.4. I then return to Sph and S0 galaxies in Section 7.5.

7.4.4. Classical bulges and ellipticals satisfy the same fundamental plane parameter correlations. II. Results

Figure 68 shows the parameter correlations from Fig. 61 with 57 bulges added. Of these, 35 are known to be classical via their parameters and the discussion in the source papers (see the key). I also add 22 bulges from Baggett et al. (1998); they are shown with open circles, because we cannot be certain that they are classical. I examined all of these galaxies and ensured as well as possible (using Section 5.3) that their bulges are classical.

Figure 68

Figure 68. Global parameter correlations from KFCB, from Kormendy (2009), and from Fig. 61 here including the sample of bulges from KB2012. All ACS VCS S0s are included, three as Sphs and 23 as bulges. For simplicity, points in further figures encode bulge type but not the source of the data.

Figure 68 confirms the assumptions that underlie our definition of classical bulges: they satisfy the same parameter correlations as do ellipticals. Given the uncertainties in bulge-disk decomposition, there is no evidence that the scatter for classical bulges is different from that for ellipticals. This is an update of a result that has been found previously, e. g., by Fisher & Drory (2008, 2010: Fig. 41 here). Pseudobulges can satisfy these relations, but they have much larger scatter, and they fade out by becoming low in surface brightness, not by becoming compact (Figs. 42 and 43).

7.5. Sph galaxies are bulgeless S0 galaxies

Figure 69 shows Fig. 68 with the disks of S0 galaxies added. Kormendy & Bender (2012) conclude that spheroidals are continuous in their parameter correlations with the disks (but not the bulges) of S0 galaxies. People call a galaxy an S0 if it has smooth, nearly elliptical isophotes and two components, a bulge and a disk. If it has no bulge and only one, shallow-surface-brightness-gradient component, we give it a different name – a spheroidal.

Figure 69

Figure 69. Parameter correlations for ellipticals, bulges and Sphs with disks of 126 S0s added (green points outlined in black). Bulges and disks of S0 galaxies are plotted separately. The middle panel shows the Freeman (1970) result that disks of big galaxies tend to have the same central surface brightness μ0 = μe - 1.822 mag arcsec-2 for an exponential. We conclude that Sphs are continuous with the disks but not the bulges of S0 galaxies. Updated from KB2012.

That bulges disappear where Fig. 69 suggests is shown in Fig. 70. Rotation curve decompositions confirm what our experience tells us: bulges disappear at Vcirc ~ 100 km s-1 or MV, disk ~ -18 (Tully & Fisher 1977). There is noise; e. g., M 33 has MV, disk = -19.0 and Vcirc ≃ 135 ± 10 km s-1 (Corbelli 2003) and no bulge (Kormendy & McClure 1993). But of course, we also expect that disks fade when they are transformed from S+Im to S0. Figure 70 is an important observational "target" for future work: the formation physics that underlies it is largely unknown. But there is ample evidence that bulges disappear approximately where the Sph and S0 disk sequences meet in Fig. 69. This is enough to explain the different names.

Figure 70

Figure 70. Maximum rotation velocity of the bulge Vcirc,bulge (red points) and disk Vcirc,disk (black points) derived in bulge-disk-halo decompositions of the rotation curves of galaxies whose outer, dark matter rotation velocities are Vcirc. Equality of the visible and dark matter rotation velocities is shown by the dotted line. Every red point has a corresponding black point, but many galaxies are bulgeless and then only a disk was included in the decomposition. This figure illustrates the well known rotation curve conspiracy, Vcirc,bulgeVcirc,diskVcirc for the halo (Bahcall & Casertano 1985; van Albada & Sancisi 1986; Sancisi & van Albada 1987). It shows that the conspiracy happens mostly for galaxies with Vcirc ~ 200 km s-1. The lines are least-squares fits with variables symmetrized around 200 km s-1. The bulge correlation is steeper than that for disks; bulges disappear at Vcirc ≃ 104 ± 16 km s-1. From Kormendy & Bender (2011) and Kormendy & Freeman (2013).

Kormendy & Bender (2012) suggest that the kink in the μeMV correlation that happens roughly at the transition from S0 disk to Sph tells us where the correlation turns into a sequence of decreasing baryon retention at lower galaxy luminosity. It is not an accident that this happens roughly where the bulge contribution to the gravitational potential well disappears.

7.6. Spiral and irregular galaxies have the same structural correlations as S0 galaxy disks and Sph galaxies

Kormendy's (1985, 1987) conclusion that Sph galaxies are defunct dS+Im galaxies depended critically on the observation (Fig. 57) that they all have the same structural parameter correlations. That result was based on a small number of galaxies and has never been checked. KB2012 updates and extends this test with 407 galaxies that cover the complete luminosity range from the tiniest dwarf irregulars to the brightest Sc disks. Figure 71 shows that S+Im galaxies do indeed have the same parameter correlations as S0 disks and spheroidals. Therefore they are closely related.

Figure 71

Figure 71. Fig. 69 correlations with disks of Sa – Im galaxies added (blue points for 407 galaxes from 14 sources listed in the keys). When bulge-disk decomposition is needed, the components are plotted separately. From KB2012.

7.7. A revised parallel-sequence classification of galaxies

Figure 72 shows our proposed revision of Sidney van den Bergh's (1976) morphological classification scheme based on the foregoing observations.

Van den Bergh put S0 galaxies in a sequence that parallels the spirals; the classification parameter that determines the stage along either sequence is the (pseudo)bulge-to-total luminosity ratio, (P)B / T. Pseudo and classical bulges are not distinguished; in a classification based on small-scale images, this is the only practical strategy. Only (P)B / T and not parameters such as spiral arm pitch angle determine the stage, so van den Bergh's classification of spirals is not quite the same as Sandage's or de Vaucouleurs's. We do not address this issue. Figure 72 adopts van den Bergh's theme of placing S0s and spirals in parallel sequences based only on (P)B / T.

Figure 72

Figure 72. Revised parallel-sequence morphological classification of galaxies. The E types are from Kormendy & Bender (1996). Transition objects between spirals and S0s (van den Bergh's anemic galaxies) exist but are not illustrated. Bulge-to-total ratios decrease toward the right; Sc and S0c galaxies have tiny or no pseudobulges. Sph and Im galaxies are bulgeless. From KB2012.

Kormendy & Bender extend ven den Bergh's discussion in two ways.

  1. They resolve the uneasy aspect of van den Bergh's paper that he listed no S0c or later-type S0 galaxies. Based on a comparison of (P)B / T ratios of S0s with spirals of known Hubble type, they find several of the "missing" late-type S0s; e. g., the S0bc galaxy NGC 4762; the S0c galaxy NGC 4452 (Section 7.4.2). NGC 4452 is also singled out as an S0c by Cappellari et al. (2011), who independently propose a parallel-sequence classification based on kinematic maps. A few other S0cs are known (Laurikainen et al. 2011; Buta 2012).

  2. They place Sph galaxies in parallel with Im galaxies. They note that, in a more detailed classification that includes Sd and Sm galaxies, some Sphs (e. g., ones with nuclear star clusters) would be placed in parallel with late-type (especially Sm) spirals, and others (e. g., ones without nuclei) would be put in parallel with Ims. Adding Sph galaxies at the late-type end of the S0 sequence for the first time finds a natural home for them in a morphological classification scheme.

It is important to understand which observations lead to Fig. 72 4. They involve quantitative parameter measurements, but they do not involve interpretation. First, the observations that establish E – S0 – Sph continuity:

  1. Galaxies with smooth, nearly elliptical isophotes, little cold gas and little star formation range in bulge-to-total luminosity ratio from B / T = 1 to B / T = 0. Here, the existence of a bulge component and the measurement of B / T are based on quantitative surface photometry, on nonparametric measurements of structural parameters for elliptical and Sph galaxies by integrating the observed isophotes, on parametric (Sérsic-function-based) bulge-disk decomposition for disk galaxies, and on the resulting structural parameter correlations (Figs. 68, 69). When B / T = 1, we call the object an elliptical; when 1 > B / T > 0, we call the central component a bulge and the outer component – if flat 5. – a disk, and when B / T = 0, we call the galaxy a spheroidal.

  2. In the structural correlations between effective radius re, effective brightness μe ≡ μ(re) and total absolute magnitude, Sph galaxies define a sequence that is continuous with the disks but not the bulges of S0 galaxies. There is some overlap in luminosity between Sphs and S0 disks.

  3. NGC 4762, NGC 4452, NGC 4638 and VCC 2048 are galaxies that have both S0 and Sph properties. We know this because all four galaxies are seen edge-on. All contain flat disks. Three contain a tiny (pseudo)bulge (VCC 2048 contains only a nuclear star cluster). The thick outer components of all four galaxies have parameters – including Sérsic indices n ~ 1 – that are indistinguishable from those of Sphs. That is, these galaxies consist of S0 central parts embedded in Sph or Sph-like outer halos. This helps to establish S0 – Sph continuity.

  4. Bigger Sph galaxies tend to be dynamically more S0-disk-like: they have larger ratios of rotation velocity to velocity dispersion (van Zee et al. 2004). Note: at all L, some Sphs rotate slowly (see KB2012 for a review).

These observations justify our conclusion that Sph galaxies are continuous in their properties with S0 disks, which in turn motivates our juxtaposition of Sph galaxies with S0cs. In essence, Sph galaxies are bulgeless S0s.

Observations that suggest parallel sequences of S+Im and S0+Sph galaxies:

  1. For every B / T ratio that is observed in an S0 or Sph galaxy, there are S or Im galaxies that have corresponding, similar B / T ratios. We see a continuous transition from S0 to E as B / T → 0. We do not know whether Sas also have a continuous transition B / T → 0. The Sombrero galaxy (NGC 4594) has one of the largest bulge-to-total ratios known, B / T = 0.93 ± 0.01 (Kormendy & Bender 2013). I know no Sa with larger B / T. Thus it is prudent to retain a classification S0(0) that is intermediate between elliptical and both Sa and S0a.

  2. Except for details such as spiral structure, the global structure of spirals and S0s is similar. For any generic Sa, Sb, or Sc galaxy, there are similar S0a, S0b, or S0c galaxies. In particular, the bulges of spiral and S0 galaxies both satisfy the E parameter correlations. The fractions of classical and pseudo bulges are similar at similar stages along the tuning fork (Kormendy & Kennicutt 2004). And the disks of S+Im galaxies have almost the same parameter correlations as Sph galaxies and S0 disks (Fig. 71).

  3. Some Sph galaxies contain low-contrast spiral structure; therefore they contain embedded disks (Jerjen et al. 2000, 2001; Barazza et al. 2002; De Rijcke et al. 2003; Graham et al. 2003; Ferrarese et al. 2006; Lisker et al. 2006, 2007, 2009).

  4. Many dSph companions of our Galaxy contain intermediate-age stellar populations (Da Costa 1994; Mateo 1998: Fig. 73 here; Tolstoy et al. 2009). Both among the Galaxy's satellites and in the larger HST ACS Nearby Galaxy Treasury Survey (Weisz et al. 2011a, b), dS, dIm and dSph galaxies have similar, heterogeneous star formation histories except that the star formation rate in dSph galaxies is currently zero. This is a matter of definition – if a dwarf contains gas and star formation, it is called dSph/dIm or dIm. The Virgo cluster contains several examples (Ferrarese et al. 2006; KB2012).

    Figure 73

    Figure 73. Star formation histories of dSph and dIm galaxies from Mateo (1998). Relative star formation rates are shown as a function of time since the Big Bang.

  5. Similarly, some spiral galaxies in clusters contain gas only near their centers, and some S0s contain near-central gas and small amounts of star formation. This is discussed in Section 7.9. Here, it again means that some S0 galaxies are less different from some spiral galaxies than optical images would suggest.

  6. Van den Bergh's (1976) "anemic galaxies" are omitted from Fig. 72 for simplicity, but they are galaxies that are intermediate in properties between spiral and S0 galaxies. Their contain only low-amplitude spiral structure star formation. The transition from S to anemic to S0 looks continuous.

Thus a substantial collection of morphological and structural parameter observations motivate our suggested parallel-sequence galaxy classification. We revise it to place Sph galaxies at the end of the S0 sequence, juxtaposed with the latest-type spirals and irregulars. It is important to note three things. We do not intend to imply that the luminosity function of galaxies is the same at all stages of the tuning fork. Indeed, we already know that Im and Sph galaxies tend to have lower luminosities than earlier-type S and S0 galaxies. Second, we do not mean to imply that galaxies are equally abundant at every stage of either the S+Im or the S0+Sph sequence. Indeed, it is clear that S0c galaxies are much rarer than Sphs or earlier-type S0s. This provides a hint for interpretation. But it is not a reason to change the classification. And third, we do not intend to fix what isn't broken. Our suggestion of a parallel-sequence classification is not meant to replace Hubble classes. We propose Fig. 72 as a complement to Hubble classification, useful because it encodes a different collection of observations that are relevant to a different collection of questions about formation physics.

7.8. Parallel-sequence classification and bimodality in the galaxy color-magnitude relation

Work on galaxy formation nowadays concentrates on the history of star formation in the Universe and on understanding stellar populations. The iconic observation that current work tries to explain is the color bimodality of galaxies in the color-magnitude relation as revealed by the Sloan Digital Sky Survey (SDSS) at low redshifts (Strateva et al. 2001; Bernardi et al. 2003; Kauffmann et al. 2003a, b; Hogg et al. 2002, 2004; Blanton et al. 2003, 2005; Baldry et al. 2004) and by HST studies of galaxies at high redshifts. Figure 74 shows this result and illustrates how the E – S0 – Sph arm of the parallel-sequence tuning fork relates to it. The bright end of the prominent and thin red sequence consists of ellipticals, S0s, and some early-type spirals. But their luminosity functions are bounded at low L. When the red sequence is extended fainter, it must become dominated by Sphs at MV ≪ -18. The deepest surveys detect this (Blanton et al. 2005; Drory et al. 2009).

Figure 74

Figure 74. Correspondence between our parallel-sequence classification and the color bimodality of galaxies in the SDSS color-magnitude relation. The top panel shows contours of galaxy number density in the correlation between SDSS u - r color and galaxy baryonic mass M / M (Baldry et al. 2004). The narrow "red sequence" of mostly-non-star-forming galaxies and the broader "blue cloud" of star-forming galaxies are well known. The bottom panel shows the morphological types from Fig. 72 that dominate in various parts of the top panel. The rapidly rising luminosity function of spheroidals at the low-mass limit of the diagram may account for the contour in the top panel at (9.0, 2.2). The "take-home point" is that the bright end of the red sequence consists of ellipticals, S0s and early-type spirals, but the faint end is dominated by Sph galaxies. Adapted from KB2012.

7.9. S+Im → S0+Sph galaxy transformation processes

The natural interpretation of the observations discussed in this section is that S0 and Sph galaxies are defunct, "red and dead" versions of spiral and irregular galaxies that have been transformed by physical processes to be discovered. Most of these turn out to be environmentally driven and slow.

The relative ordering and positioning of galaxies in the parallel-sequence classification is justified on purely observational grounds based on choices of which results to use in the classification and which to regard – for present purposes – as secondary. However, it would be disingenuous to pretend that I and many others have not been thinking about the underlying formation and evolution processes for a long time. This is inevitable in a world where no observational curiosity goes uninterpreted for long. In fact, there are many candidate processes. Astronomers frequently argue about which of many compelling theories are correct. My experience is that these arguments go on longest when everybody is correct. This is one of those occasions.

Candidate S+Im → S0+Sph galaxy transformation processes are reviewed in KB2012. Here, I list them briefly including only the most important supporting observations:

  1. The main internal evolution process was already mentioned in Section 7.3. Below a fiducial mass that corresponds to Vcirc ≃ 100 km s-1, i. e., just where bulges disappear (Fig. 70) and therefore galaxy names get changed from S0 to Sph (Fig. 69), supernova-driven winds are expected to expell a larger fraction of a galaxy's baryons from lower-mass objects regardless of whether they now are irregular or spheroidal (e. g., Larson 1974; Saito 1979; Dekel & Silk 1986; Vader 1986; Schaeffer & Silk 1988; see Hensler et al. 2004; Stinson et al. 2007 for two among many more recent discussions). This is why I suggested that the decreasing surface brightnesses of Sph and Im galaxies at lower luminosities (Fig. 71) is a baryon retention sequence.

  2. The most thoroughly studied external transformation process is ram-pressure stripping of cold gas by hot gas in clusters and perhaps groups of galaxies. Suggested by Gunn & Gott (1972), the idea has varied in popularity. It has never gained widespread acceptance, perhaps in part because Dressler (1980) argued that it was not the main cause of the morphology-density relation that spiral galaxies get less abundant whereas S0 galaxies get more abundant at higher galaxy densities in clusters. Dressler argued that this result does not strongly depend on cluster richness. However, examination of his Fig. 8 – 10 (see Fig. 25 in KB2012) shows that the ratio of S0 to S galaxies increases from low-concentration clusters to high-concentration clusters to X-ray-emitting clusters. An alternative hypothesis is that ram-pressure stripping happens more easily in clusters of all richness than simple energy arguments suggest. More recent results bear this out:

  3. Compelling evidence for ongoing ram-pressure stripping is provided by Hα and H i observations of spiral galaxies in the Virgo cluster (Chung et al. 2007; Kenney et al. 2004, 2008). Figure 75 shows some of these results. Many spiral galaxies embedded in the X-ray gas that fills the cluster center show remarkable H i tails. The above authors interpret them as cold gas that trails behind the galaxy after having been stripped from the galaxy by the hot gas in the cluster. The spectacular Hα filaments that point from the tidally disturbed NGC 4438 toward the hot-gas-rich NGC 4406 (top panel in Fig. 75) are similarly interpreted as ram-pressure stripped. Also, many spirals near the center of the cluster are much smaller and more depleted in H i than are galaxies in the cluster outskirts (Cayatte et al. 1990; Chung et al. 2009). Kormendy & Bender (2012) note that "the three most depleted galaxies illustrated in Fig. 8 of Chung et al. (2009) are NGC 4402, NGC 4405 and NGC 4064. They have a mean absolute magnitude MV = -19.4 ± 0.2. Virtually all Sphs are fainter than this. If even the deep gravitational potential wells of still-spiral galaxies suffer H i stripping, then the shallow potential wells of dS+Im galaxies are more likely to be stripped." Substantial additional evidence also suggests that ram-pressure stripping is more effective than we thought (see KB2012 and van Gorkom & Kenney 2013 for reviews).

    Figure 75

    Figure 75. The large panel shows 0.5 – 2.0 keV X-ray brightness contours in the Virgo cluster as measured with ROSAT by Böhringer et al. (1994). Superposed are grayscale images of galaxies with H i tails indicative of ongoing ram-pressure gas stripping (white or black contours). The H i images are from Chung et al. (2007); Kenney et al. (2004); Abramson et al. (2011). The color inset image and large image at top show the Hα emission filaments that extend from NGC 4438 to NGC 4406 (Kenney et al. 2008). Each small inset image shows the galaxy centered on its position in the cluster, but the panels are magnified. This figure is adapted from Fig. 4 in Chung et al. (2007) and is reproduced from KB2012.

    Can ram-pressure stripping still happen in the Local Group's much shallower gravitational potential well? Compelling observations which indirectly suggest that the answer is "yes" are shown in Fig. 76. Close companions of our Galaxy, of M 31, and of other nearby giant galaxies are almost all spheroidals; distant companions are irregulars; Sph/Im transition galaxies tend to live at intermediate distances, and larger irregulars "survive" at closer distances to their giant companions (Einasto et al. 1974; van den Bergh 1994a, b, 2007; Mateo 1998; Skillman et al. 2003; Bouchard et al. 2009; McConnachie 2012). Hints of similar effects in larger satellites are seen in the Zurich Environmental Study (ZENS: Cibinel et al. 2012). Like previous authors, Kormendy & Bender suggest that "ram-pressure stripping can happen even in environments that are gentler than cluster centers. It may be indirect evidence for a pervasive warm-hot intergalactic medium (WHIM: Davé et al. 2001) that is difficult to detect directly but that may be enough to convert dwarf irregulars into spheroidals."

    Figure 76

    Figure 76. From Mateo (2008), the ages of the youngest stellar populations in dwarf galaxy companions versus Galactocentric or M31centric distance R. Except for the Magellanic Clouds, all close companions of our Galaxy and of M 31 are spheroidals. Distant companions are irregulars except for three free-flying dSphs (pink points). The Sph/Im transition galaxies mostly lie at intermediate distances.

    All this evidence suggests that ram-pressure stripping is one of the processes that transforms late-type, gas-rich and star-forming galaxies into red and dead S0 and Sph galaxies.

  4. Galaxy harassment is a dynamical process that should operate wherever objects orbit repeatedly through rapidly varying gravitational potential fields, especially in virialized clusters of galaxies with velocity dispersions that are much larger than the internal velocities of galaxies. It is the cumulative effect of many encounters with other galaxies and with the cluster potential. Simulations show that it strips outer mass, heats disks and promotes gas inflow toward the center that presumably feeds star formation (Moore et el. 1996, 1998; Lake et al. 1998). A variant is tidal stirring of dwarf galaxies on elliptical orbits around our Galaxy or M 31 (Mayer et al. 2001a, b, 2006). Kormendy & Bender concur with the above authors in suggesting that harassment converts late-type disks into spheroidals and more robust, earlier-type spirals into hotter systems that resemble S0s. A benefit of this picture is that inflowing gas can feed star formation; this helps to explain why S0 disks and spheroidals – which must fade substantially after star formations stops – do not have much lower surface brightnesses than current versions of S+Im progenitors (see Ferguson & Binggeli 1994 for a review of this problem). Gravity is not negotiable. Its effects are clean. It is encouraging how many observations can be tied together into a coherent picture if harassment is one of the galaxy transformation processes:

    1. Dynamical heating plausibly explains why faint spheroidals are not flat, why many bright spheroidals contain disks (either observed directly when seen edge-on or inferred from their spiral structure), and why the outer parts of our "rosetta stone" galaxies NGC 4762, NGC 4552, NGC 4638 and VCC 2048 are vertically thick whereas their more robust inner parts are flat.

    2. Sph and Im galaxies have similar distributions of axial ratios (Ferguson & Sandage 1989; Binggeli & Popescu 1995). The latter authors conclude that "there is no evidence for a difference between the flattening distributions of nucleated dE,N and classical (giant) Es". However, in my experience, many Sph,N galaxies are flatter than any elliptical. NGC 4637 in Fig. 65 and VCC 2048 in Fig. 10 of KB2012 are examples. Ferguson & Sandage note that "The similarity of flattenings of dE (bright, no N) and Im types removes one of the previous objections to the hypothesis that some dwarf ellipticals could be stripped dI's". The exact engineering needs further study, but dynamical heating added to the fact that the smallest galaxies are not flat anyway provides a promising way to explain the flattening observations.

    3. Intracluster light is believed to consist of stars that have been stripped by harassment from individual galaxies. In the Virgo cluster, it is irregular and still in the early stages of formation (Mihos et al. 2005, 2009; Arnaboldi et al. 1996, 2002, 2004; Castro-Rodriguéz et al. 2009; Arnaboldi & Gerhard 2010). In rich clusters, it is widely observed (Thuan & Kormendy 1977; Adami et al. 2005; Krick & Bernstein 2007; Gonzalez et al. 2007; Okamura 2011). When intracluster light is very bright, it is called a "cD halo" (Morgan & Lesh 1965; Oemler 1976; Schombert 1988). These halos are robustly understood to consist of tidally liberated stars and disrupted galaxies (Richstone 1976; Dressler 1979; Kelson et al. 2002). If gravitational harassment can produce all these effects, it is difficult to see how the mere heating of smaller galaxies could be avoided.

    4. Kormendy & Bender (2012) suggest that the "new class of dwarfs that are of huge size (10000 pc in diameter in the extreme) and of very low surface brightness of about 25 B mag arcsec-2 at the center" discovered by Sandage & Binggeli (1984) are "spheroidals that have been harassed almost to death".

    5. Anisotropic dynamical heating is a natural way to try to explain triaxial and slowly rotating Sphs (e. g., Bender & Nieto 1990). This idea is consistent with the observation that the brightest Sphs are in many cases the most disky and rapidly rotating ones. However, unusually violent encounter histories can allow a small number of Sphs to be anisotropic even at the highest masses.

    6. Carefully engineered encounter histories can make Sph galaxies that have kinematically decoupled subsystems, even counterrotation of the harassed outer parts with respect to the inner galaxy (De Rijcke et al. 2004; González-García et al. 2005). Counterrotating systems are seen in VCC 510 (Thomas et al. 2006).

  5. Starvation of continued infall of cold gas from the cosmological structure hierarchy is frequently discussed as an S+Im → S0+Sph transformation process (e. g., Larson et al. 1980; Balogh et al. 2000; Bekki et al. 2002; Boselli et al. 2009). Absent such infall, star formation at currently observed rates generally uses up the available gas in a few Gyr (Larson et al. 1980; Boselli et al. 2009). Given the observation that the center of the Virgo cluster and a fortiori the centers of rich clusters of galaxies are dominated by hot gas (e. g., Fig. 75), it is difficult to see how starvation can be avoided. These are not environments where low-density cold gas can survive to feed continued accretion onto galaxies for billions of years after the cluster acquires a large velocity dispersion.

Thus many processes (1) may explain the growing dark matter dominance (i. e., baryon deficiency) of lower-mass dwarf galaxies and (2) can potentially transfrom S+Im galaxies into S0+Sph galaxies. Kormendy & Bender (2012) emphasize that "the relevant question is not `Which one of these mechanisms is correct?' It is `How can you stop any of them from happening?' It seems likely to us that all of the above processes matter."

In this regard, I conclude by emphasizing the following points.

Most papers (Boselli et al. 2009 is an exception) investigate one process; when they get into trouble explaining some particular observation, they conclude that this process is not the answer. If all above processes happen, then there is more potential to understand all of the diagnostic observations. Theorists like to ask clean questions, investigating one process at a time. There are good reasons for this. But Nature does everything together. Eventually, we will have to do likewise if we expect to understand galaxy evolution. The hellishly complicated interplay of different processes is a feature, not a bug. We cannot avoid this problem forever.

Second, one observation that is frequently cited to disfavor ram-pressure stripping and strangulation is that bulges are systematically bigger in S0s than in spirals (e. g., Dressler 1980). But (i) small pseudobulges in late-type spirals skew the distribution of S-galaxy bulges to smaller luminosities; if such galaxies are transformed before secular evolution has time to make pseudobulges, the result is a Sph, not an S0. Then it will not be counted among the S0s. Also, (ii) the distribution of S0 bulges is skewed toward high luminosity by the frequent misclassification of the highest ellipticals as S0s (KFCB). This happens because their high Sérsic indices n ≫ 4 give them a "core-halo" appearance that persuades classifiers to call them S0s. An example is the elliptical galaxy NGC 4406, which is classified S0 by Sandage & Tammann (1981). Similarly, giant ellipticals are commonly classified S03 when they contain nuclear dust disks; e. g., the elliptical NGC 4459 (KFCB). (iii) When accurate bulge-disk decompositions are carried out, the folklore that S0 galaxies mostly have large bulges is not confirmed. Among S0s discussed in KFCB and in KB2012, about half have (P)B / T < 0.5 and six have (P)B / T ltapprox 1/3, the value for the Sb galaxy M 31. Finally, (iv) the distribution of B / T in the progenitor galaxies of any transformation process is a strong function of environment – bulgeless disks are preferentially made in the field, and merger remnants are preferentially made in clusters such as Virgo (Kormendy et al. 2010). So field spirals do not fairly sample the potential progenitors of S0 galaxies in clusters.

Another observation that is frequently cited to disfavor ram-pressure stripping and strangulation is that S0s have higher surface brightnesses than spirals. Disk fading that follows the shutdown of star formation might lead us to expect the opposite effect. But Fig. 71 shows little sign of such an effect. Note that the surface brightnesses of both S0 and spiral disks are not corrected for inclination, so they are treated in the same way. However, internal absorption is important in spirals and not in S0s. So internal-absorption-corrected surface brightnesses of spiral galaxy disks would be brighter than those of S0 disks. Also, harassment – like any effect that rearranges angular momentum – persuades some gas to fall toward the center and should increase the surface brightness there via star formation.

Finally, Kormendy & Bender (2012) point out that S → S0 transformation does not require the removal of all gas nor the quenching of all star formation. Some S0s still contain gas, especially molecular gas near their centers (e. g., Welch & Sage 2003; Sage & Wrobel 1989; Thronson et al. 1989; Devereux & Young 1991; Young et al. 1995). These S0s form stars. The Virgo spirals whose outer H i distributions are truncated have normal central molecular gas content (Kenney & Young 1986). We do not need to solve the problem of removing all gas from the deepest parts of galaxy potential wells.

It is clear that much work – much complicated work – is still needed on the messy baryonic physics of galaxy evolution. But I am encouraged to think that the still unknown details of the various transformation processes do not threaten our overall picture that at least some S0s and likely all Sph galaxies are defunct spiral and irregular galaxies.

7.10. Environmental secular evolution – "An Idea Whose Time Has Come"

Morphological observations such as those encoded in the parallel-sequence classification of Fig. 72 lead to the robust conclusion that many S0s are closely related to spiral galaxies and that essentially all Sph galaxies are closely related to the latest-type spirals and irregulars. Figure 72 does not directly tell us what that relationship is. However, in recent years, rapidly improving observations of transformation processes in action, including H i and Hα tails, relatively recent star formation in dSph galaxies, vertically thick outer disks in interacting S0s and "rosetta stone" galaxies with both S0 and Sph properties, strongly imply that some or all of a collection of environmental processes transform spiral and irregular galaxies into red and dead S0 and spheroidal galaxies. This happens especially in rich clusters, but small galaxies can suffer transformation even in relatively quiescent environments such as the Local Group. Kormendy & Bender (2012) suggest that "environmental secular evolution is An Idea Whose Time Has Come."

4 Allan Sandage (2004) accused Sidney van den Bergh of hermeneutical circularity in setting up his parallel-sequence classification, which – he thought – involved too much interpretation. A prosaic but sufficient paraphrase is "circular reasoning". The basic idea is this: a morphological classification of galaxies should be set up based only on observations and not on interpretation (see Section 3.4). The aim is that regularities revealed by the classification will later aid interpretation. However, if some interpretation is used in setting up the classification, then the "aid" that the classification can provide is foreordained. This is circular reasoning. In practice, science is not as "black and white" as Sandage suggests. Even the greatest scientists (Sandage explicitly picked Hubble as one of these) set up classifications with future interpretation in mind. They make decisions about which observations to treat as relevant and which ones to treat as secondary. Van den Bergh did this faithfully; Sandage was just uneasy about how important those decisions were. It should be clear from these remarks that I respect both sides of the argument. In the end, further advances reviewed here have, I claim, vindicated van den Bergh's decisions. For a classification to be successful, it must ultimately motivate a clearcut paradigm of interpretation. Van den Bergh's parallel-sequence classification has done this. Back.

5 This is to prevent confusion with cD galaxies, which have cluster-sized debris halos, not disks. Back.

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