3.3.5. Tidal Effects
I would like next to discuss the outer parts of E and cD galaxies, where the profiles depart from standard fitting functions. In this section I review tidal effects; this will be brief since the situation is unchanged from Kormendy (1980). The next section discusses cD halos. Both sections exploit the fact that systematic departures from fitting functions or from profiles of normal galaxies can teach us about environmental effects even in the absence of dynamical models for the template profiles.
The effect of the tidal force due to a perturber is to "heat" the halo of the victim (see White 1982 for a review). Stars at large radii in the victim's halo have orbital periods which are comparable to the encounter time scale. Therefore, they see a gravitational potential that changes strongly but not periodically during an orbit, resulting in violent relaxation (Lynden-Bell 1967). Individual stars gain energy at the expense of the galactic orbit. The halo expands and the two galaxies become more tightly bound on the way to a possible merger. This process has been interpreted as being responsible for a number of observed features of galaxy halos, which suggest that tidal effects produce different results in different environments.
Observational indications are that mild encounters produce a distension of the victim's envelope (Fig. 14). Galaxies with close companions are seen to have extra light at large radii above the extrapolation of an r1/4 law fitted to the inner parts. This was interpreted by Kormendy (1977c) as a combination of reversible tidal stretching and the above tidal heating. A similar effect is seen in Oemler's (1976) photometry of galaxies which are far from the center of the Coma cluster (Kormendy 1980). Further investigation of this effect is needed. The tidal interpretation requires verification: many n-body models demonstrate that tidal distension can be important, but it is not clear whether other processes are also involved. One aspect of the tidal interpretation is difficult to understand. As Figure 14 shows, the tidal halos (if such they are) typically begin at r ~ re (re1/4 = 1.78 in the figure). At such small radii, plausible orbital periods are much shorter than the encounter time scale. The energy of an orbit is then adiabatically invariant (Binney 1982a; White 1982). It is difficult to understand how tidal effects can be this strong.
Figure 14. Brightness profiles of the King (1978) ellipticals (thin solid lines) and of NGC 3379 (dots) scaled to have a common de Vaucouleurs law (dashed lines) with re = 10 kpc and Be = 23 B mag arcsec-2. The galaxies have been divided into tidal groups (Section 3.3.1) and separated by 3 mag arcsec-2 intervals. Isolated (T1) galaxies are better described by a single r1/4 law than (T3) galaxies with companions. The fact that elliptical-galaxy profiles do not all have the same shape was also noted by King (1978). This figure is taken from Kormendy (1977c, 1980).
The more widely known effect of tides is to truncate the halo. This seems to occur when the encounters are more violent, i.e., when the victim is much less massive than the perturber, or when it is located near the center of a rich cluster. Tidal truncation of small objects by large ones has been discussed by King (1962), who derived an expression for the limiting radius and later an approximate dynamical model (King 1966). Examples include the truncation of globular clusters and dwarf ellipticals by the Galaxy (King 1962, 1966; Hodge and Michie 1969), and tidal limiting of small ellipticals by larger companions (M32, King 1962; NGC 4486B, Rood 1965; NGC 5846A, King and Kiser 1973). Further support for this picture is provided by Faber's (1973a) result that the latter three objects have unusually high mean surface brightnesses (because they lack halos) and high metallicities characteristic of more luminous galaxies.
Tidal effects are even stronger in rich clusters. This has been convincingly demonstrated by Strom and Strom (1978a, b, c, 1979a, b), who measured brightness distributions of ~ 600 galaxies in eight rich clusters. Five of the clusters were spiral-poor, three were spiral rich. In all of the spiral-poor clusters ellipticals were found to be smaller at a given MV if they were located near the center of the cluster. Even in the outer parts of these clusters galaxies are smaller than in spiral-rich clusters. The Stroms interpreted this effect to be a result of tidal stripping, although they realized that differences in galaxy formation might also be involved. These results are confirmed by Kormendy's (1980) reanalysis of Oemler's (1976) photometry in the Coma cluster. Near the cluster center profiles of small and moderate-size ellipticals are truncated compared to r1/4 laws. This is not seen in galaxies within 1-2 mag of brightest cluster galaxies, nor is it seen at large radii in the cluster. In agreement with the Stroms, the natural interpretation seems to be that tidal heating in such environments is so strong that the halos acquire positive energy and escape. This effect is more important for fainter galaxies than for brighter ones. It is possible that the brightest galaxies gain rather than lose material. This may be the reason for the occasional presence of more than one cD-like galaxy in a cluster (there are 2-3 in Coma, Oemler 1976). Such a situation should not last long because the most massive galaxies preferentially merge (see White 1982). Further discussion of tidal effects is given in Kormendy (1980).