Annu. Rev. Astron. Astrophys. 1984. 22: 185-222 Copyright © 1984 by Annual Reviews. All rights reserved

4.2 Three Classes of Models

The models that are reviewed here fall roughly into three classes. In the first type, similar initial conditions are assumed for all galaxies, regardless of their future destiny as cluster or field galaxies. This is the case, for example, in the hierarchical clustering model (Peebles 1974a, b, 1980) with a perturbation spectrum that is nearly white and randomly phased, because in this model the fluctuations that become galaxies reached the nonlinear growth phase long before the cluster-size perturbations. In this sense, galaxies could not ``know'' their future environments. The aim is to reproduce all the morphological variation with fairly late evolution (after clusters became important); for example, S0s might be produced from stripping and ellipticals from merging an initial population of spiral galaxies.

In the second class, later evolution is retained as the primary modifier of galaxy type, in particular through the truncation of disk development, but initial conditions or very early evolution are added to account for the prominence of bulge-dominated galaxies in regions of high galaxy density. This might be accomplished, for example, by dropping the condition of random phasing, so that galaxies with higher central concentration were destined to inhabit regions of high galaxy density (Dressler 1980b), or by including mergers in the early evolution of clusters (the small group phase) to build up a population of more massive spheroids.

If these types of models are unable to explain the morphological data described above (along with the more detailed constraints that will undoubtedly be forthcoming), there is still the possibility that initial conditions were primarily responsible for galaxy morphology. The challenge with this third class of models is to understand how galaxies ``knew'' at the time of their formation about their eventual environments. Recent cosmological models may provide a solution to this problem.

CLASS 1: LATE EVOLUTION Models that explain the existence of S0 galaxies as ``normal spirals'' that have lost their gas as a result of environmental influences attempt to explain variation in morphological types by recent environment alone. Spitzer & Baade (1951) originally proposed that spiral galaxies in dense clusters might strip gas from each other in direct collisions, but today ram-pressure stripping (Gunn & Gott 1972) and gas evaporation (Cowie & Songaila 1977) by a hot (T ~ 10<sup>7-8</sup> K) intracluster gas are considered to be more important. Strong evidence that this is not the primary mechanism for the production of S0 galaxies is presented by Dressler (1980b), who points out that most (~ 80%) S0s are found in low-density environments (the outskirts of clusters and in the field), where these processes are ineffective. It seems extravagant to propose a different production mechanism for the remaining fraction, which are indistinguishable from their field counterparts in properties like D / B, color, luminosity function, kinematics, and surface density. Detailed comparisons of spirals and S0s by Burstein (1979), Dressler (1980b), and Gisler (1980) confirm that field and cluster S0s have D / B ~ 1, much lower than the value (D / B ~ 3-10) typical of most present-day spirals, as noted by Faber & Gallagher (1976) and Sandage & Visvanathan (1978). In addition, Burstein (1979) has demonstrated that S0s have a ``thick disk'' component not found in spirals. This component has a larger scale height and decreases more slowly with radius than the thin disk. In this latter respect, thick disks are more like the bars and lenses described by Kormendy (1982). These structural differences are further evidence that most S0s have not descended from late-type spiral galaxies.

This is not to say that gas ablation is unimportant in the evolution of spiral galaxies. Although there is still disagreement over the ease with which gas can be removed from a spiral (cf. Gisler 1979, 1980, Kent 1980, Nulsen 1982), there is now observational evidence that such processes could be responsible for the some of the ``anemic'' spirals (van den Bergh 1976) in clusters (Strom & Strom 1979, Wilkerson 1980, Sullivan et al. 1981). These observations show a tendency for spirals in the intermediate-density environments (there are very few spirals in the densest environments) to be gas poor by factors of 2-3 relative to their field counterparts at the same Hubble type. These data have been compiled from HI measurements (Bothun et al. 1982, Giovanelli et al. 1981, and references therein) and from optical measurements of integrated H flux (Kennicutt 1983). Gas depletion, whether by ablation or exhaustion by star formation (accelerated by interactions with neighboring galaxies, for example), looks to be a rather slow process, since the relationships among galaxy gas fraction, color, and star formation rate are maintained as the gas is removed (Bothun 1982, Kennicutt 1983).

Gas ``deficiencies'' of spirals are >modest (factors of 2-3) in intermediate-density environments, where S0s are quite common. Since S0s are deficient in gas by factors of 100 or more compared with spirals, this is further evidence that this type of environmental influence does not explain the existence of most S0 galaxies. Only in the Coma cluster has a deficiency of order 10 been found, and Bothun (1981) claims that in this one case there is a population of small-bulge S0s in the very core, possibly the true remains of stripped spirals. It is doubtful that a spiral could survive in such an environment; thus the rarity of small-bulge, gasless systems is probably a sign that (a) few large D / B spirals have plunged into these conditions up to the present-epoch or (b) disk formation is slowest for these systems, so that their development will be inhibited by the cluster virialization (see below). On the other hand, ablation may be very important for gas removal from relatively gas-poor systems like S0s and ellipticals (Gisler 1978, Fabian et al. 1980, Nulsen 1982).

Toomre & Toomre's (1972) suggestion that ellipticals form by mergers of disk galaxies is another attempt at a class 1 model. This idea has been more fully developed by Roos (1981), who attempts to build both ellipticals and the bulges of disk galaxies from mergers of what are initially purely disk systems. The attractions and problems of such merger models are briefly discussed in the next section.

CLASS 2: LATE EVOLUTION PLUS INITIAL CONDITIONS Kent (1981) has provided a prescription for altering disk luminosity as a function of density that can reproduce the fractional increase in elliptical and S0 galaxies in dense environments as found by Dressler (1980b). Dressler pointed out that a ``fading'' of disks of 1.5-2.0 magnitudes (this could be dimming due to changes in the stellar population or to prevented formation) could account for the difference between the distributions of bulge luminosity for spirals and S0s. Kent develops this idea and shows that if this fading is a particular function of the local galaxy density, the morphology-density relation is reproduced as well. This is a class 2 model, since Kent requires an ad hoc ``initial condition'' that large-bulge systems preferentially ``become'' S0s, while small-bulge systems remain spirals. Kent's model is very successful in reproducing the morphology-density relation, and the identification of the critical parameter as the virialization time at a given density is particularly attractive. It fails only for the reason that Dressler rejected the 2-magnitude fading: the LF (luminosity function) of the ``faded'' galaxies should be quite different from the LF of the galaxies that have finished building their disks (the low-density clusters or field). Kent notes this problem, but he points out correctly that Dressler's data suffer from incompleteness just fainter than M and thus cannot be used to rule out the single power-law LF he adopts. (A single power law has no characteristic magnitude, of course, so ``before'' and ``after'' LFs are indistinguishable.) However, comparisons of spiral and S0 LFs that do not suffer the incompleteness problem (Tammann et al. 1979, Thompson & Gregory 1980) also show little or no difference in M. This issue is discussed in more detail below.

Larson et al. (1980; hereinafter LTC) concentrate their efforts on a different aspect of the same scheme by suggesting a mechanism for the ``fading.'' Their calculations indicate that gas exhaustion times for spirals are short, typically a few billion years; therefore, they suggest that spirals must be refueled by infall from tenuous gas envelopes. These envelopes would be easily ``stripped'' by tidal encounters, so a morphology-density relation is expected. This mechanism should still be effective in lower-density regions (while those that remove gas directly from the disks are not). Furthermore, star formation would continue for a few billion years in these ``stripped spirals,'' and this might explain the ``survival'' of blue galaxies observed by Butcher & Oemler in dense, high-redshift clusters (see Section 5).

Although gas envelopes of the type required have yet to be observed (Sancisi 1981, 1983, and references therein), the LTC model, like Kent's, has attractive aspects, and it is the first to make detailed predictions that can be checked by observations. Like Kent's model, however, it cannot easily explain the similarity of spiral and S0 LFs. LTC brushed this problem aside by noting that spheroids in dense environments appear to be more luminous to begin with (for example, there are all those ellipticals), so it seems reasonable that the S0s will come preferentially from large-bulge spirals.

Comparing luminosity functions to test disk truncation and initial conditions The evidence that brighter spheroids, in addition to fainter disks, are necessary to explain the morphology-density relation rests on a comparison of LFs in high- and low-density regions. This comparison is a decisive test of whether initial conditions or very early evolution must be invoked in addition to (or in place of) later evolutionary processes like disk truncation. At present, this LF comparison is suggestive, though perhaps not compelling. In Dressler's (1980a) data, for example, Hercules (Abell 2151) has a 55% spiral population and a <D / B> = 3.70 (weighted by luminosity and averaged over all types) comparable to a value of <D / B> ~ 5 for a volume-limited sample of the Revised Shapley-Ames Catalog (Sandage & Tammann 1981). Coma (A1656) has a 12% spiral population in Dressler's sample and <D / B> = 1.18. A ``fading'' of the disks by a factor of 3.14 (1.25 magnitudes) is therefore required to bring Hercules to the same <D / B > as Coma. In this sample, D/B is not a strong function of luminosity near M, so this 1.25-magnitude disk fading will result in a change M = 0.85. ⁽²⁾

Schechter's (1976) analysis of Oemler's (1974) data gives M (Coma) -M(Hercules) = 0.26, considerably smaller than the value predicted in the disk-fading model. Indeed, for the average of Oemler's four ``spiral-rich'' clusters compared with the five ``cD'' clusters (lowest proportion of spirals), M = -0.21, which goes in the wrong sense for the disk-fading model. An even larger value of M ~ 1.2 magnitudes is to be expected in comparing a ``faded field'' population (<D / B> ~ 5) with the population of the Coma core (<D / B> ~ 0.8), but, in fact, there is no significant difference in M for any region of Coma compared with the field.

If these data are corroborated by better-quality photometric observations, then the inference will be clear: a brightening of spheroids by factors of 2-3 in dense regions is needed to compensate for the lower luminosities of disks and thus leave the LF basically unchanged. It is perhaps encouraging that early attempts to model cluster evolution (Miller 1983, Malumuth & Richstone 1984) do show an approximate balance between the opposing effects of mergers and tidal stripping.

In summary, it is difficult to account for the data on morphological types, D / B, and LFs as a function of environment without appealing to both disk truncation and larger spheroidal components in dense regions. Since a disk luminosity function for the Coma cluster would include few luminous systems like those found in the low-density field, it seems reasonable to conclude that a disk truncation mechanism is at work. Furthermore, as pointed out by Ostriker (1977), the mass of intracluster gas in Coma is roughly what would remain if disks of the size found in field spirals were prevented from forming. (This implies, moreover, that the fraction of mass in ``left over'' gas will be found to be a function of spiral fraction, and that little residual gas should be found in the field.) By implication, the spheroidal LF, like the disk LF, must also be different in clusters than in the field (since the spheroidal + bulge = total LFs are so similar).

Building up spheroids by mergers Is there a way to account for the larger bulges in dense environments, short of appealing to initial conditions? Mergers may provide a method of producing ellipticals from spiral galaxies (Toomre & Toomre 1972, Toomre 1977, White 1978, 1979, Fall 1979), and perhaps bulges of disk galaxies are ``built up'' by some kind of merger as well (Roos 1981). It is too early to tell if mergers can account for the observed parameters of ellipticals, but some of the attractive aspects, as well as some of the difficulties, are mentioned here. A comprehensive review can be found in White (1982). Fall & Efstathiou (1980) have shown that the dissipation of gas in large halos can reasonably account for the properties of disk galaxies, but Fall (1983) argues that it is difficult to produce the more slowly rotating ellipticals in a similar manner. Ellipticals have low values of the dimensionless spin parameter that range from ~ 0.07 for the most luminous systems to 0.2-0.3 for the flattened, low-luminosity galaxies (Davies et al. 1983). Simulations by Efstathiou & Jones (1979) and Aarseth & Fall (1980) show that low values of result from mergers of galaxies bound on highly eccentric orbits. (These simulations refer to the nonluminous halos; it is unknown if the more concentrated luminous matter would also acquire the low- values typical of ellipticals.) It is particularly attractive to identify the brightest systems with multiple mergers, since the average surface brightness of elliptical galaxies falls with increasing luminosity M < -21 (Binggeli et al. 1984) and the frequency of ellipticals flattened by anisotropic velocity fields is rising (Davies et al. 1983).

Some of the early objections to making ellipticals from basically stellar mergers (see, for example, Ostriker 1980) appear to have weakened. Numerical simulations (e.g. White 1978, Farouki et al. 1983) indicate that central densities can grow as mergers proceed (nonhomology), and central velocity dispersions may also rise. Both are necessary if ellipticals are to be produced. A study by Dressler & Lake (1984) of about 15 disturbed systems from the Arp (1966) and Arp & Madore (1984) catalogs of peculiar galaxies confirms that the central velocity dispersions are in reasonable accord with the Faber-Jackson relation (1976) for ellipticals, i.e. these probable mergers already match ellipticals in the L- diagram. Schweizer (1982, 1983) has presented empirical evidence that mergers of field galaxies are common and may result in elliptical galaxies. For example, he claims that the luminosity profile of the highly interactive NGC 7252 system will eventually match the R^1/4 form of typical of ellipticals. The shells and plumes around many ellipticals (Arp 1966, Malin & Carter 1980) may be further evidence that ``field ellipticals'' (those in low-density regions) are in environments that favor mergers, since such features may result from the infall of disk galaxies (Quinn 1983).

The objection that ellipticals are common in rich clusters, where the high relative velocities suppress mergers, is probably negated by the likelihood that the merging occurred when the cluster was a collection of small groups (see, for example, Geller & Beers 1982) in which the velocity dispersions were much lower. This could also explain the existence of field ellipticals as the remnants of mergers of compact groups of galaxies (Carnevali et al. 1981). (In general, it is likely that the evolution of the different morphological types must have begun at a time when the density contrast from the field to the clusters was much smaller than it is today, since morphology is a very slow function of local density.)

Nevertheless, serious problems remain for the theory. Harris (1981) claims that a difference in globular cluster frequency per unit luminosity for spirals compared with ellipticals may be evidence against a merger origin for ellipticals. Sandage (1983) points to a continuity of properties from dwarf ellipticals to luminous systems (a factor of 10⁴ in luminosity) as an argument against mergers, since it is unlikely that the dwarf ellipticals were also made by mergers. The observational data on color (abundance) gradients are still sparse, and the extent to which such gradients would be erased by merging is unclear (White 1980, Villumsen 1982); however, the general trend of redder colors and higher metallicities for brighter systems (Faber 1973, Sandage & Visvanathan 1978) must certainly be explained.

Are mergers responsible for building the bulges of disk galaxies as well? Bulges and low-luminosity ellipticals are isotropic rotators; therefore, they could have developed along the lines of the classical collapse models (Eggen et al. 1962, Larson 1976, Gott & Thuan 1976). In this simple picture, mergers are perhaps responsible only for the ``giants,'' the most massive ellipticals, which are slowly rotating and have low surface brightnesses. But if mergers are to help account for all large spheroids in dense regions, then they must produce some larger-bulge disk galaxies as well. This raises a number of additional problems, such as explaining why disk systems held on to some of their gas while the ellipticals did not. If the gas that formed the disk fell in well after the merger that produced the bulge, can the angular momenta of disk and bulge be expected to align as well as they do (see Gerhard 1981)? Why are even the most luminous bulges flattened by rotation (Kormendy & Illingworth 1982, Dressler & Sandage 1983), while the most luminous ellipticals are not? In the case of our own Galaxy, it has been proposed that gas lost from a spheroid that formed prior to the disk explains otherwise puzzling features of the chemical enrichment history (Ostriker & Thuan 1975). Are these data consistent with a model where disks formed first, and bulges followed afterward from mergers or accretion? A merger model that can explain all of these observations, together with a limitation on disk building as a function of density, can probably account for all basic properties of the morphological types, and the morphology-density relation as well.

CLASS 3. INITIAL CONDITIONS The models described above rely on later evolution to produce the range in morphological types and their dependence on present environment. It is also possible that these later influences are minor compared with the role played by initial conditions. The first attempts to identify initial conditions that would lead to different galaxy types identified angular momentum (Sandage et al. 1970) and density (Gott & Thuan 1976) as the variables responsible for the differentiation. The models have grown in complexity in recent years (see, for example, Larson 1976, Rees & Ostriker 1977, Silk 1978, White & Rees 1978, Tinsley & Larson 1979, Ostriker & Cowie 1981, Silk & Norman 1981, Struck-Marcell 1981, Kashlinsky 1982, Faber 1982, and Gunn 1982 if you doubt it), but a dependence of galaxy concentration, and possibly angular momentum, on the amplitude of the initial density perturbation is still generally expected. Observations of present-day galaxies show that more-concentrated systems are dominated by spheroidal components with lower specific angular momenta than their disks. If density perturbations of high amplitude consistently lead to the conversion of most of the available gas into stars before large-scale dissipation forms a global disk, then the basic structures of present-epoch galaxies could be established at very early epochs. Judging from the small fraction of gas in field S0s and early type spirals, it seems possible that the presence of a large spheroidal component alone can induce increased rates of star formation that lead to gas exhaustion, independent of external environment (Roberts et al. 1975). Thus the LTC-type model of truncating the formation of disks may be superfluous, and the fraction of gas ``left over'' in the Coma cluster (roughly twice the luminous matter) may be typical of all environments.

The deficiency in these models that employ only initial conditions is that they provide no obvious explanation for the observed dependence of morphology on later environment. To achieve this, the perturbation that becomes the protogalaxy must be affected by the larger scale perturbation that grows into a group or cluster. In a crude sense, they must form at the same time. For a white noise spectrum, this can be accomplished by abandoning random phasing so that the largest amplitude galaxy perturbations are always found within the largest amplitude cluster perturbations. For the isothermal perturbation model (hierarchical clustering; Peebles 1974a, b, 1980), the same results can be achieved if the initial spectrum contained more power at large scales (pink noise). The adiabatic perturbation models (Doroshkevich et al. 1980, and references therein) have a built-in preferred scale of large mass. These conditions result in earlier growth of the groups and clusters relative to the galaxies; therefore, the final amplitude of a protogalaxy fluctuation will depend on whether it is in a protocluster or protofield region. The recent emphasis on cosmologies with exotic particles that dominate the mass of the Universe has produced several models where these preferred mass scales for galaxies and clusters are expected [see Primack & Blumenthal (1983) for a review], and within these types of models such coupling of galaxies to clusters is likely, if not unavoidable. High-energy physics, then, could supply the extra ingredient that enables the construction of galaxy formation models that rely primarily on initial conditions.

Alternatively, it has been suggested that differences might arise in the angular momentum gained through tidal torques (Peebles 1969) in protocluster and protofield regions (DiFazio & Vagnetti 1979, Shaya & Tully 1984). Large-scale variations in the distribution of angular momentum would provide a correlation with environment for the model of galaxy differentiation first suggested by Sandage et al. (1970).

At present, it might be best to consider these types of models as ``last resorts.'' Our ignorance of initial conditions is greater than our ignorance of later evolutionary effects ; therefore, such models are rather ad hoc and offer few predictions or tests. Until they are able to do so, it seems advisable to embrace this alternative only if the models that stress later external influences fail to explain the data on morphological types and their environments.