Annu. Rev. Astron. Astrophys. 1984. 22: 185-222
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3.3 Optical Observations Relevant to Merging, Accretion, and Tidal Stripping

ARE cD GALAXIES BUILT FROM HOMOLOGOUS MERGERS? Ostriker & Hausman (1977) and Hausman & Ostriker (1978; hereinafter HO) have proposed that mergers and accretion build giant galaxies with radial profiles that scale simply as R propto M. This assumption allows them to predict the surface brightnesses and metric magnitudes of cD galaxies as a function of their total luminosities. This approach has been sharply criticized by Schweizer (1981), who claims that both N-body simulations (White 1978, Duncan et al. 1983, Farouki et al. 1983) and observations show that mergers are not homologous, but that rather they build cores with higher central concentrations than the progenitors. Because the observational data are extensive and varied, only a subset can be examined here. It is sufficient to show, however, that although the specific question of whether giant ellipticals and cDs have small core radii is unresolved, as Schweizer (1979) might like to put it, the available observations are roughly consistent with homologous growth for cD galaxies.

Schweizer is correct in pointing out that if all giant ellipticals have Rcore ~ 100 pc, like NGC 1316, then few galaxies for which it has been claimed that core radii have been measured have actually been measured. Several overenthusiastic observers, including Dressler, have misinterpreted data like Oemler's (1976) as indicating large core radii for cD galaxies, when the true core radii may well have been hidden by the atmospheric seeing disk (as Schweizer notes). He is probably also correct in stating that Hoessel's (1980) analysis of 108 first-ranked cluster galaxies includes a large number, perhaps a majority, of cases whose Hubble core radii are only artifacts of the seeing. In some cases, however, the cores have radii of several kiloparsecs and are well resolved.

All of this is probably irrelevant, however, since it is the large-scale structure that is indicative of whether the cannibalism model adequately describes the evolution of cD galaxies. Hoessel (1980) and Schneider et al. (1983) were really after the logarithmic intensity gradient alpha = d (ln L) / d (ln r) at r = 16 kpc. The latter study included a better (double-Gaussian) seeing model and fit the galaxies to both a t modified Hubble law and a de Vaucouleurs profile that has no core. These new data show that it is possible to measure alpha quite accurately for galaxies with z leq 0.2, since the radius at which alpha is being measured is an order of magnitude larger than the seeing. Schneider (private communication) has repeated observations of 41 galaxies in a variety of seeing conditions, and his data show that alpha changes by an order of 10% over a range of seeing of a factor of two, again indicating that these measurements are basically unaffected by seeing. The core radii that are derived when a Hubble law is fit may be artifacts of the technique, but only Space Telescope observations will tell if the core radii are actually much smaller.

In the samples of Hoessel and Schneider et al., alpha increases with absolute magnitude in a way that is roughly consistent with the HO models of homologous growth. Morbey & Morris (1983) reach the same conclusion independently for another sample of cD galaxies. Thuan & Romanishin (1981) and Morbey & Morris (1983) both find that giant cDs have much lower surface brightnesses within their effective radii, again in agreement with the HO model.

Since it is clear that cDs do seem to mimic the model of homologous growth on the large scale, it is worthwhile to reconsider Schweizer's comments about core radii and central surface brightnesses. Although the N-body models consistently predict higher central surface brightness as evolution proceeds, these simulations have a small number of particles (~ 1000), and it is possible that two-body relaxation effects dominate in the central regions and render these models inappropriate. On the observational side, it is relatively easy to find examples of giant galaxies whose central surface brightness is low. For example, despite Schweizer's early report to the contrary, four of the five cases studied by Kron & Albert (1982) have lower central surface hrightness than other bright ellipticals in the clusters. A2029, A2218, and A1413 are additional excellent examples of cDs whose central surface brightness is very low. The lower surface brightnesses of these archetype cDs are striking, and comparisons with puny galaxies like NGC 1316 are, therefore, very misleading. Though there may be good counterexamples (A2634, A2670), the general rule seems clear: the most luminous cD galaxies have low central surface brightnesses. This is again consistent with the homologous merger picture. The exceptions might be due to the remnants of a captured galaxy.

Perhaps the best piece of evidence that the merger process is responsible for building the insides of cD galaxies is the observation that a large fraction (25-50%) of such objects have multiple nuclei (Matthews et al. 1964, Hoessel 1980, Schneider et al. 1983). This high frequency cannot be dominated by projection effects (Schneider et al.), so the conclusion that at least some galaxies are being consumed by the cD seems unavoidable. Schneider et al. point out that the frequency of multiple nuclei for the second- and third-ranked cluster galaxies is an order of magnitude less. This datum seems to confirm the special place of the cD in the bottom of the cluster potential well and its unique evolution compared with other bright galaxies in the cluster.

If none of this evidence is compelling for the case that cD galaxies grow by ``cannibalism,'' it is sufficient to say that most optical observations now available are consistent with the general features of this model.

ARE THE TIME SCALES FOR DYNAMICAL FRICTION CORRECT? Rood & Leir (1979) have pointed out that the brightest galaxies in Bautz-Morgan (1970; hereinafter BM) type I and II clusters (one or two dominant galaxies, respectively) are multiple systems about 25% of the time, and that this is much higher than the frequency in BM III clusters (no dominant galaxy). They and Tremaine (1981) agree that the relevant time scale for coalescence of these systems (as indicated by N-body simulations) is 1 or 2 orbital periods. Assuming these binary galaxies have circular orbits with typical separations of 40 kpc and relative velocities of order 500 km s-1, this time scale is several times 108 yr. Tremaine uses this time scale, a frequency of occurrence of 25%, and a cluster age of order 5 x 109 yr to conclude that there are several such short-lived binaries in the lifetime of each cluster. Rood & Leir (1979) reject this idea on the grounds that it would result in very dissimilar brightnesses for the two components, but one could imagine that each galaxy is the result of a previous coalescence. However, unless orbital angular momentum can be dumped into the outer envelope, mergers from bound circular orbits would result in rapidly rotating, bright ellipticals (White 1979) and none are observed (Davies et al. 1983). The time scale for orbital decay could also be several times longer if (a) the pairs seen are actually on highly eccentric orbits whose semimajor axes are larger than the projected separation implies (this also mitigates the rotation problem), and/or (b) the mass of each component is much less than the 1013 Msun value used by Rood & Leir (i.e. the visible galaxies are moving in a common envelope formed from their dark halos).

This possible discrepancy is reminiscent of similar discussions about cD galaxies and the frequency of their multiple nuclei, which are typically 10 kpc from the cD center. Hoessel (1980) and Schneider et al. (1983) have argued that the frequency of multiple nuclei is consistent with the expected time scale for dynamical friction of 109 yr. (The victims are low mass.) On the other hand, Blandford & Smarr (1984) claim that a much larger central mass than a cD galaxy (a black pit) is needed to hold these victims on their spiraling orbits. Furthermore, a smaller core radius and a larger orbital velocity will result in a longer infall time, consistent with the high frequency of occurrence of multiple nuclei. Tonry's (1984b) simulations imply, however, that black pits may not be necessary if the galaxies are infalling on highly elliptical orbits.

Such simulations and observations suggest that there is much to be learned about the processes that go under the label ``dynamical friction,'' and, therefore, discrepancies between "predicted" and ``observed'' time scales of less than an order of magnitude should be viewed with interest, but not despair.

OTHER OBSERVATIONS RELEVANT TO CANNIBALISM Many other optical observations are useful for testing the cannibalism model. Quintana & Lawrie (1982) review the evidence that cDs are at the kinematical centers of their clusters, and Beers & Geller's (1983) study indicates that D and cD galaxies are usually found at local density maxima.

Related to this topic are studies by Dressler (1979) of the cD in A2029 and by Carter et al. (1981) of the dumbbell galaxy IC 2082, which show that the velocity dispersions of these galaxies rise with increasing radius, in contrast with the steady or declining velocity dispersions in normal ellipticals (Illingworth 1983). Dressler (1979) interprets this rise in velocity dispersion as the gravitational effect of the cluster's dark matter on the stars in the cD's envelope. Thus the rise in velocity dispersion is, in itself, neither evidence for nor against the cannibalism model, save that it requires the galaxies in question to lie at the true centers of their clusters. Dressler's model for the cD in A2029 includes a normal bright elliptical centered in the cluster potential, but it also requires a component of intermediate M / L and velocity dispersion to supply the additional light at R ~ 100 kpc that distinguishes this cD. This extra component is suggestive of the cannibalism model. since it can be attributed to the remains of accreted galaxies.

McGlynn & Ostriker (1980) show that the relaxation time is a function of Bautz-Morgan type (BM I clusters have shorter times), as is expected with the cannibalism model, but the dependence is weak.

van den Bergh (1983) has argued that the number of globular clusters per unit luminosity is very high in M87 (Virgo) and NGC 3311 (Hydra), so that it is unlikely that these central galaxies are ``star piles'' made from more normal galaxies. Unfortunately, no data are available on the globular cluster frequency in the truly outstanding cD galaxies, and it is for these examples that the cannibalism model is most appealing. Van den Bergh also cites the fact that cDs are often quite elongated and aligned with flattened clusters (see references above) as evidence that the formation of the cD and its cluster were simultaneous (see also Carter & Metcalfe 1980, Adams et al. 1980). On the other hand, Binney (1977) has pointed out that a strong anisotropy in the velocity field of the cluster will result in an anisotropic stellar envelope in the cD as the victims are cannibalized.

Lugger (1984) has presented the most extensive data on colors of the nuclei of bright ellipticals and cDs, from which she concludes that there is a monotonic reddening with increasing luminosity (cf. Thuan & Romanishin 1981). This is in contradiction with the HO prediction that the cDs should break from this relation and be about 0.m1 bluer in U - B than an extrapolation from the lower luminosity ellipticals.

Reliable measurements of color gradients are only available for a small sample of elliptical and cD galaxies (Strom & Strom 1978a, Gallagher et al. 1980, Wirth & Shaw 1983). At present, there are insufficient data to make a meaningful comparison, as well as uncertainty in the models as to what extent the color gradients will be erased in the merging process (e.g. HO, White 1980).

EVOLUTION OF THE LUMINOSITY FUNCTION The luminosity function (LF) specifies the number distribution as a function of absolute magnitude for a volume-limited sample of galaxies. Abell (1962) showed that there is remarkably little variation of the shape and characteristic luminosity of the LF from cluster to cluster, consistent with a ``universal'' function that he characterized as two power laws. Subsequent studies by Bautz & Abell (1973) and Oemler (1974) supported this claim of universality, and luminosity functions for the field (Felten 1977, Kirshner et al. 1979) and small groups (Turner & Gott 1976) showed that variations in luminosity functions are small even in very different environments. These LFs all show a characteristic luminosity Lstar that varies by less than factors of 2-3 (Austin et al. 1975, Schechter 1976). Brighter than Lstar, the numbers of galaxies fall rapidly with increasing magnitude; fainter than Lstar, the counts level off.

This result is quite remarkable. It means that the processes that determined the luminosities of galaxies were either very insensitive to local conditions such as density, temperature, and turbulence (angular momentum), or that these conditions varied little from protocluster to protofield regions of space. Furthermore, it implies that the evolution of the distribution, in dense regions for example, is not substantial.

Nevertheless, the processes of merging, tidal stripping, and accretion discussed above are expected to produce some evolution of the LF, and those early-Universe models in which galaxies form after clusters (within adiabatic perturbations) might be expected to produce some initial variations as a function of environment. Therefore, it is worthwhile to look beyond ``first-order universality'' for second-order differences. A large number of LFs for rich clusters, produced mainly by photographic surface photometry, are now available for such a comparison.

First indications that there are systematic differences from cluster to cluster came from Oemler (1974), who showed what he considered to be weak evidence that the composite LF for ``spiral-rich'' clusters is flatter than those for ``spiral-poor'' or ``cD'' clusters. The latter had a more sudden rise at the bright end and then leveled off fainter than some characteristic magnitude.

Dressler (1978b) applied statistical tests to his sample of 12 very rich clusters to see if such variations were significant. He fit the cluster LFs to a functional form suggested by Schechter (1976), and used Monte Carlo models to test for significant variations of the characteristic magnitude Mstar and the faint-end (power-law) slope alpha. Dressler found three types of variation from the universal form. Statistically significant deviations of Mstar were found in at least two clusters. Several clusters were found to have an unusually flat slope at the faint end, and there was once again marginal evidence that the form itself varies, much like Oemler's comparison of ``spiral-rich,'' ``spiral poor,'' and ``cD'' clusters.

Unfortunately, most of the LFs produced subsequently have not been subjected to these types of statistical tests. Only Schneider (1982) has checked on the universality of Mstar. For his large sample he finds variations in Mstar similar to those found by Dressler, but because the small field size limited his study to ~ 50-100 galaxies per cluster, these variations are not statistically significant.

On the other hand, there is some supporting evidence of variations in faint-end slopes and steepness of the bright end. Among the 8 clusters (plus Virgo) studied by Bucknell et al. (1979), there are clear examples of clusters in which the LF bright end is very steep (A2065, A2670, A2199, and A426), and others where it is much shallower and a distinct ``break'' at Mstar is not obvious (A2151, A2147, and Virgo). Similar steep bright ends have been noted for A1146 (Carter & Godwin 1979), A1413 (Austin & Peach 1974), and A1930 (Austin et al. 1975), while A1367 (Godwin & Peach 1982) has been found to have a flat bright end. The clusters A1656 (Godwin & Peach 1977) and CAO 340-538 (Quintana & Havlen 1979) appear intermediate. These differences in shape may reflect different mixes of morphological types, since the clusters with the steep bright ends are rich in E and S0 galaxies, and the shallower LFs with less obvious breaks are often found in spiral-rich clusters. Thompson & Gregory's (1980) study of the Coma cluster shows that a composite E+S0 LF differs from a spiral LF in just this way. They predict that if the Coma populations are representative, an ensemble of clusters from spiral rich to spiral poor should have sigma(Mstar) ~ 0.m5, which is consistent with both Dressler's and Schneider's results. New luminosity functions for clusters with morphological types like Dressler's (1980a) sample are necessary to test this putative dependence of the LF on cluster population.

The LF bright end is usually very steep in clusters that have a luminous cD galaxy (see, for example, Austin & Peach 1974, Oemler 1974, Dressler 1978b) - that is, there are few other bright galaxies. This could be interpreted as the result of dynamical evolution, where the brightest galaxies have all merged to form the cD. Because of the small-number statistics in each case (only a few bright galaxies are ``missing''), it is difficult to test this suggestion without a much larger sample.

Some large variations have been reported in the faint-end slope of the luminosity function, as described by the power-law slope alpha (Schechter 1976). The typical situation in rich clusters is for the LF to continue to rise fainter than Mstar, with alpha ~ -1.25. This result has been verified to Mv ~ -14 in Virgo by Sandage & Binggeli (1984) and in Coma by Beckman (1983), although the faint-end LF in Coma is rather complex. Certain other rich clusters, however, particularly A2670 (Oemler 1973, Dressler 1978b), A401 (Dressler 1978b), and A1146 (Carter & Godwin 1979), have flat LFs (alpha = 1.0) several magnitudes below Mstar. Such measurements are plagued, unfortunately, by the uncertainties in field and incompleteness corrections, and a thorough study of cluster membership (i.e. redshifts) may be necessary to confirm this effect. Nevertheless, the data are suggestive, particularly in light of simulations by Miller (1983), who shows that tidal stripping can have a severe effect on faint galaxies, resulting in the flattening of the faint-end LF. (These simulations are usually of the mass function, however, so conclusions about the luminosity function include the additional uncertainty of the distribution of light in a galaxy relative to its mass distribution.) It is therefore worth noting that the rich clusters with flat faint-end LFs are dense and have a high degree of symmetry, properties thought to be indicative of clusters whose dynamical evolution is very advanced.

Recently, evidence of even more dramatic variations in the faint-end LF have been reported (Heiligman & Turner 1980, White & Valdes 1980), but these variations are likely to be due to selection effects.

These indications of variation in the ``nearly universal luminosity function'' are suggestive, but not yet compelling. The rapid growth in the technology of digitizing photographic plates and the advent of linear area detectors should result in many new LFs in this decade; these should settle the issue.

EVIDENCE FOR TIDAL STRIPPING Encounters and collisions between galaxies are expected to remove the loosely bound stars in their outer regions (Gallagher & Ostriker 1972, Richstone 1976, Dekel et al. 1980). Unfortunately, the ease with which a galaxy is tidally stripped is not well understood because of the uncertainties in the distribution of dark matter relative to the luminous stars and the orbits of those stars (Miller 1983). A poor knowledge of the velocity dispersions, ages, and mean tidal fields of groups and clusters makes it even more difficult to estimate the amount of tidal damage.

A few observations are available, however, and they tentatively support the standard models quoted above that predict that galaxies in the densest regions of space may have lost up to 50% of their luminosity (and most of their mass). A monumental data set for 400 elliptical galaxies was constructed by Strom & Strom for A1656 (1978a), A1367 and A426 (1978b), and A1228, A2151, and A2199 (1978c) using photographic photometry from Mayall 4-m plates. The primary data compiled are the R26 radii and the Mv magnitudes within R26. Strom & Strom (1978d) conclude that similar log (R26) vs. Mv relations exist for all clusters, but that elliptical galaxies in the denser, spiral-poor clusters are, on average, 10% smaller at a given Mv than those in spiral-rich clusters. There is also a gradient in size within the spiral-poor clusters, such that ellipticals within 0.5 Mpc of the cluster center are about 5% smaller than those farther out. A similar conclusion concerning the size of S0 galaxies in Coma as a function of radial distance is also reported by Strom & Strom (1978e). They also find that at a given central surface brightness (within a 2" aperture), the smaller galaxies are about 0.m5 fainter. Both of these results concerning size and brightness are consistent with the effects of tidal stripping predicted in the studies cited above.

There is, of course, considerable observational and cosmic scatter in these relationships, and the shortcomings of photographic surface photometry add uncertainty to these results. It is disturbing, for example, that two apparently dense (and evolved) clusters, A401 and A2670 (Strom & Strom 1979), have a similar radial dependence of galaxy size, but that the absolute sizes of the ellipticals in these clusters are as large at a given Mv as those in the spiral-rich clusters studied. More data, preferably done with linear area detectors, are necessary before any firm conclusions can be drawn on the sizes of E and S0 galaxies as a function of environment.

Also consistent with the tidal truncation expected from galaxy encounters is the correlation found by Hickson et al. (1977) between the intergalactic spacing in dense groups and the size of the largest galaxy. These data emphasize the importance of reliable measurements of intergalactic light in these systems for use as an unambiguous measure of tidal damage. For example, Rose (1979) used the absence of intergalactic light to argue that the compact appearance of certain groups of galaxies must be temporary, since there is little evidence of tidal debris.

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