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We have seen that galaxy morphology includes a bewildering array of complex structures, and that the evolutionary path that any galaxy took to reach its current morphological state is not obvious. Nevertheless, some reasonable judgments can be made. This section summarizes some aspects of morphology that are well understood, and others that are still largely uncertain.

Galaxy formation: The best current theory of galaxy formation is the Λ Cold Dark Matter model (White and Rees 1978). In this model, galaxy clusters begin as tiny fluctuations in the temperature of the cosmic microwave background radiation that are expanded during the inflationary period to much larger sizes. The fluctuations become “seeds” of cold dark matter within which baryonic matter collects. The formation of collapsing proto-galactic clouds is enhanced by the extra gravity of the dark matter. Whether a galaxy becomes a disk galaxy or a non-disk galaxy depends on how much angular momentum the collapsing cloud has from tidally induced torques due to neighboring clouds (Ryden 1988) and on how effectively it converts its baryonic material into stars. If this conversion is largely complete within a billion or so years after collapse, then the object could become an elliptical galaxy. If instead the rate of conversion is slower, the proto-galactic cloud may have time to form a disk. Multiple mergers of small objects with this disk-shaped object could lead to the build up of what is generally known as a “classical bulge”. This formation scenario is not expected to form a bulge-less, pure disk galaxy, and it is also well-established that some ellipticals have likely formed from mergers of disk-shaped galaxies (Schweizer 1982).

Figure 1.27. Images of four relatively isolated grand-design spirals (Buta et al. 2019)

Although the “formative” phase of a galaxy never really ends (i.e. a galaxy may continue to accrete material long after the formation period largely ended, just as planets still accrete interplanetary debris even now), at some point the accretion rate slows down and galactic changes occur very much more slowly. This is the time when secular evolution takes over as the dominant mechanism of change (Kormendy and Kennicutt 2004). Secular evolution can be driven entirely by internal processes or by external processes. The idea is that the formative phase of galaxy evolution is fairly rapid compared to secular evolution. To interpret the morphology of some nearby galaxies, we should appeal to secular evolutionary processes.

The origin of S0 galaxies: Dressler (1980) describes the morphology-density relation in rich galaxy clusters, where the most common types of galaxies found are E and S0. This relation, which was first described by Hubble and Humason (1935), led to the general idea, originally proposed by Spitzer and Baade (1951), and elaborated upon by van den Bergh (1976), that S0 galaxies are former spirals that have been stripped of their interstellar gas and dust. The stripping shut down (“quenched”) star formation and essentially “killed” the spiral arms. In this scenario, as already noted in section 1.5, S0s cannot be transition stages between ellipticals and spirals, but must form a sequence of decreasing bulge to total luminosity ratio parallel to spirals. This idea is strongly supported by kinematic studies of early-type galaxies (Cappellari et al. 2011), photometric studies of dE and dS0 galaxies (Kormendy and Bender 2012) and by multicomponent analysis of a large sample of S0s (Laurikainen et al. 2011).

Table 1.1. Comparison of classifications

Galaxy1	CVRHS type2	Willett et al. 2013 Type 3
NGC 5057	(RL)SA(l)0+	E(r)r
NGC 6116	SA(s)a	Sb2m
UGC 10258	(R′)SA(s)ab	Sb2t
NGC 2649	SA(rs)bc	Sc2t
CGCG 62-1	SA(rs)bc	Sc2l
CGCG 91-20	SA(s)bc	Sc2t
CGCG 210-9	SA(s)bc	Sc2t
UGC 4549	SA(rs)cd	Sc?t
IC 2604	SA(s)d	Sc3m
iUGC 9243	SA(s)dm	Sc?m
NGC 4260	SBx(rs)a	SBc2t
NGC 5610	(R′)SB(s)ab	SBc2m
UGC 6854	SB(s)c pec	SBc2m(i)
NGC 5964	SB(s)cd	SBc2m
NGC 5112	SB(s)d	SBc?m
UGC 9215	SB(s)dm	Sd?l(i)

Recent studies of S0 bulges (e.g. Laurikainen et al. 2013; Gao et al. 2018) have shown that while pseudobulges are present in the class, most S0 bulges are classical in nature. As noted by Gao et al. (2018), this strongly rules out any connection between S0s and later-type spiral galaxies (whose bulges are often pseudobulges).

The VRHS actually anticipates a strong relation between S0s and spirals. This is because in the VRHS, inner and outer varieties are carried across the spiral sequence into the S0 domain. The S0 stage sequence, S0⁻, S0° and S0⁺, is not the same as the spiral sequence, but is based on the appearance of decaying patterns, often in the form of rings and lenses, and sometimes as extremely subtle spiral patterns. This suggests a link between S0s and some galaxies that once were spirals. The main problem is that the S0 stage sequence and the spiral stage sequence are not compatible and cannot be considered “parallel”.

The sophistication of modern numerical simulations has led to an alternative idea for the origin of some S0s. Rather than simply being stripped spirals, many could be the result of mergers of spirals. This is shown by Eliche-Moral et al. (2018), who compare detailed images of S0 galaxies with the results of the GalMer n-body merger simulations (Chilingarian et al. 2010). Eliche-Moral et al. (2018) argue that GalMer major mergers show features that are commonly seen in S0 galaxies, such as ovals and lenses, and also predict a very low bar fraction for S0s. That S0s do indeed have fewer strong bars than spirals was shown by Buta et al. (2010) based on the relative bar torque parameter Qg.

The origin of spiral structure: The most popular idea, known as “density wave” theory, views spiral structure as a rotating pattern through which a galaxy’s stars and interstellar gas clouds must pass (Lin and Shu 1964; Toomre 1977; for a more recent review, see Dobbs and Baba 2014). The arms are not material objects, always made of the same stars, but are waves of density where stars and gas clouds experience a temporary “slowdown”. It is thought that gas compression in the arms could lead to the enhanced star formation often seen in spiral arms.

Spiral patterns can be leading or trailing in their sense of winding. A leading spiral opens into the direction of rotation, while a trailing spiral opens opposite the direction of rotation. Studies of extinction in tilted spirals shows that trailing arms are the rule (e.g. de Vaucouleurs 1958); leading spirals are very rare but do exist (e.g. Buta et al. 2004). A mechanism in density wave theory known as “swing amplification” was identified by Toomre (1981) as a possible way of explaining the long-lived nature of some spirals. The idea uses a combination of differential rotation, epicyclic theory and self-gravity to “swing” a weak leading spiral instability into a much stronger trailing spiral, and explains the preponderance of trailing spiral patterns.

Although density wave theory could account for the velocity perturbations across spiral arms (e.g. Visser 1980), and also could be used to determine spiral pattern speeds (Roberts et al. 1975), the theory left open the question of the origin of spiral structure and the impact of a spiral on the evolution of a galaxy. Attention turned to a search for driving mechanisms, which led to a focus on bars and companions. Bars especially became primary features for affecting the secular evolution of galaxies, because a bar can drive gas into the center of a galaxy and build up what is known as a “pseudobulge”, or bulge made of disk material. Based on passive orbit studies, it was concluded that secular evolution primarily affects the interstellar gas distribution, and likely can only change a galaxy of intermediate type by at most one Hubble stage interval (e.g. stage Sbc to Sb) during a Hubble time.

Kormendy (1979) and Kormendy and Norman (1979) brought attention to the role of bars in driving galactic secular evolution. Kormendy and Norman (1979) identified bars as the likely driving mechanism for what they referred to as “global” spiral patterns, i.e. well-defined spirals that extend across an entire galactic disk. If not a bar, then the perturbing effects of a close companion may also drive a density wave spiral. However, there are relatively isolated non-barred galaxies with strong global spiral patterns; Figure 1.27 shows four examples from Buta et al. (2019).

Although global spirals are the best-known patterns in galaxies, many galaxies show spiral structure that cannot be called “global”. This is because their patterns are mainly in the form of disconnected pieces or ill-defined spirals, called flocculent (Elmegreen 1981). Such spirals have been interpreted in terms of star-forming complexes sheared by differential rotation into short spiral arcs (Gerola and Seiden 1978). Dobbs et al. (2018) compare numerical simulations with the ill-defined arms of M33, and conclude that the arms form as a result of gravitational instabilities in the stellar and gaseous distributions, coupled with a high amount of stellar feedback.

Dobbs and Baba (2014) summarize the general view of spiral structure today: “With the possible exception of barred galaxies, spiral arms are transient, recurrent, and initiated by swing-amplified instabilities in the disk”.

The origin of bars in spiral galaxies: The general idea has been that bars form through a natural process known as the “bar instability”. This is the tendency for an initially axisymmetric but cold stellar disk to naturally form a bar (Hohl 1971). Numerical simulations showed that bars develop in systems where the bulk of the kinetic energy is in the form of ordered motions, i.e. in a rotating disk-shaped galaxy (e.g. Miller and Smith 1979).

Gadotti (2004) argues that while this mechanism seems likely for spirals, it may not be the origin of bars in S0 galaxies because these tend to be found in a cluster environment and have a higher relative abundance of classical bulges (as opposed to pseudobulges). The light-deficient regions around some bars suggest a mechanism where a bar forms at the expense of the disk (Gadotti and de Souza 2003a; Kim et al. 2016).

The origin of galactic rings: The general view is that the vast majority of galaxy rings are associated with orbital resonances in galactic disks. A resonance ring is a feature that can, on the basis of morphology and other characteristics, such as star formation, be linked to a specific orbital resonance with a bar, oval or spiral density wave. The idea of a resonance ring first appeared in discussions of density wave theory (for example, Lin 1970), but it was the modeling of barred galaxies that led to a better understanding of these features (Schwarz 1981, 1984).

Resonances occur where m(Ω − Ωp) = nκ, where Ω is the circular angular velocity, Ωp is the pattern speed (uniform angular rotation rate of the spiral pattern), κ is the radial (epicyclic) frequency, and m/n is the number of radial oscillations per single orbit in the reference frame rotating at Ωp. Both Ω and κ are functions of galactocentric radius. The main ring-forming resonances are the outer and inner Lindblad resonances (OLR and ILR, respectively), for which m = 2 n =±1, and the outer and inner 4:1 resonances (O4R and I4R, respectively), for which m = 4 and n =±1. In any normal galaxy, there will likely be two ILRs, with the innermost one called the inner ILR (or IILR) and the outermost one called the outer ILR (or OILR). Another important (but not necessarily ring-forming) resonance is the corotation resonance (CR), where Ωp = Ω. The locations of all of these resonances can be determined by plotting the curves Ω and Ω ± κ/m versus galactocentric radius and reading the radii where these functions equal Ωp.

Support for the resonance idea comes principally from (a) the morphology of galactic rings (Buta and Crocker 1991; Buta 1995b); (2) statistical studies of intrinsic shapes and orientations of galactic rings with respect to bars (Buta 1995b; Comerón et al. 2014); and (3) detailed studies and numerical modeling of individual cases such as NGC 3081 (Buta and Purcell 1998) and NGC 6782 (Lin et al. 2008). Rings are relatively narrow features, most frequently associated with gas. In particular, nuclear rings are often conspicuous sites of star formation. In general, rings form when gas is accumulating in the bar resonance locations, since the gravity torques from the bar are then canceling out. The angular momentum transport is discussed in detail in Buta and Combes (1996).

Figure 1.28 shows three galaxies from the Catalogue of Southern Ringed Galaxies (Buta 1995b) having well-defined outer resonant features. The white circles in the images show the estimated location of the CR in each galaxy based on the “gap method”, a way of determining the radius of the CR using dark gaps lying along the line perpendicular to the bar axis (Buta 2017b). By using this method, and assuming the rotation curves for the galaxies are approximately flat, the schematics show the locations of the other major resonances, I4R, O4R and OLR. The results from these galaxies and 47 others examined by Buta (2017b) provide a consistent picture of systems where rings lie slightly outside the OLR, R₁ and rings lie near but inside the OLR, and inner rings and bars lie close to the I4R. The ILR was once thought to play a major role in nuclear ring formation, but this view was challenged by Regan and Teuben (2004), who argued that the most reliable interpretation of these features is in terms of an orbit transition region inside the bar.

Ringed galaxies and invariant manifolds: Romero-Gomez et al. (2006) proposed an alternative to the resonance interpretation of galactic rings. In this idea, the R₁, , and subclasses of outer rings and pseudorings in barred galaxies can all be interpreted in terms of invariant manifolds that emanate from the unstable L₁ and L₂ Lagrangian points near the ends of a bar. In this interpretation, rings are not necessarily resonant features, but are features mapped by the manifolds as tube-guided homoclinic, heteroclinic and escaping chaotic orbits. In homoclinic orbits, a spiral emanates from L₁ or L₂ and closes at L₂ or L₁, respectively, after winding 180°; this is a morphology consistent with R₁ and rings. In heteroclinic orbits, a spiral emanates from L₁ or L₂ and closes at L₁ or L₂, respectively, after winding 360°; this is a morphology consistent with the double outer ring/pseudoring morphology . Finally, in an escaping orbit, a spiral emanates from L₁ or L₂ and winds outward, never to intersect the opposing Lagrangian point; these can account for the morphology of outer pseudorings.

Figure 1.28. Three galaxies showing outer resonant subclass features. The white circle in each image is the estimated location of the corotation resonance (CR) based on the gap method of Buta (2017b). The schematics show the locations of other resonances relative to visually mapped ring and pseudoring features, assuming a flat rotation curve. The method assumes that light deficits on the line perpendicular to the bar axis trace the location of unstable Lagrangian points L₄ and L₅ (indicated as L4 and L5 each plot). These points are assumed to trace the location of the CR. The other resonances highlighted are the inner 4:1 resonance (I4R), the outer 4:1 resonance (O4R) and the outer Lindblad resonance (OLR)

The potential-density phase shift and galactic secular evolution: Models of barred galaxies like those of Schwarz (1981, 1984) and Rautiainen and Salo (2000) suggest that rings are products of the evolution of spiral patterns near resonances. That is, a ring begins as a pseudoring and then evolves into a more closed feature. However, very few galaxies show the influence of resonances as strongly as do cases like NGC 3081 or any galaxy showing outer resonant subclass features. This is because the typical inner variety for spirals is (s), the typical nuclear variety is no nuclear feature and the typical outer variety is no outer feature. The question to ask, then, is not why some galaxies have rings, but why so many do not.

The theoretical work of Zhang (2018 and references therein) challenges previous views on galaxy dynamics and provides a real mechanism for the secular evolution of the stellar distribution of a spiral galaxy, not just the interstellar gas distribution. The galaxy-disk mass distribution, contributed mostly by stellar mass, is part of the so-called “basic state” used to calculate spiral density wave perturbations. In addition to the axisymmetric (i.e. azimuthally averaged) mass distribution, determined observationally from disk surface brightness and color, the basic state specification includes also the axisymmetric rotation speed (with contributions from the halo and bulge, in addition to the contribution from the disk) and velocity dispersion, with all three usually specified as a function of galactocentric radius. The key factor for the evolution of the basic-state mass distribution is an azimuthal phase shift (phase offset in angles) between a self-consistent spiral perturbation potential, and the density this potential gives rise to. The spiral can arise as a mode in an initially featureless disk, and if it can achieve a quasi-steady state, angular momentum can be taken away from the inner disk, transferred outward and deposited onto the outer disk, leading to the slow buildup of a central mass concentration and an extended outer disk.

The main departure of Zhang’s work from previous studies of galactic dynamics is the elevated role of collective effects on the dynamical evolution of galaxies. This refers to the correlated small-angle scatterings stars would experience as they move across the spiral density wave crest. The density wave itself was shown in Zhang’s work to be collisionless shocks related to “dissipative structures”. Another important aspect of the work is that the phase shift is not simply an abstract concept from potential theory, but is manifestly measurable from any image which approximates the stellar mass distribution. From such images, one can derive a graph of the phase shift as a function of radius, and in such a graph a single mode appears as a single positive bump followed by a single negative bump (e.g. Buta and Zhang 2009). The point where the phase shift changes from positive to negative is the location of the mode’s CR, which is generally considered the most important resonance for any model pattern in a galaxy. This location is also the divide between radial mass inflow and outflow patterns.