Annu. Rev. Astron. Astrophys. 1989. 27: 235-277
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7. BRIGHTNESS PROFILES AND TIDAL EFFECTS

The shapes of galaxy brightness profiles and their dependence on luminosity contain information about galaxy formation. Systematic trends with environment tell us about tidal effects. And the functional form of the profile determines the best way to derive size and density scale parameters (Section 8).

Studies of profile shapes are affected by a variety of problems, some of which are worse for CCDs than for photographic observations. (a) Some data are not accurate at large radii. CCDs have a reputation for omnipotence that does not apply to measurements of galaxy halos. CCDs are small, so sky estimates are often uncertain (Capaccioli 1987). Observers know this, but poor sky subtraction nevertheless plagues even the best CCD photometry of halos. Capaccioli et al. (1988) and Peletier et al. (1988a) cite examples; errors of 0.2-0.5 mag arcsec-2 are common. (b) Most CCD data reach out to only a few de Vaucouleurs (1948) effective radii re; the systematic departures from r1/4 laws that are discussed below begin at about these radii. (c) Seeing is a problem, especially for low-luminosity galaxies. These have such tiny cores that seeing can completely change their brightness profiles. For example, if M32 were in the Virgo cluster, we would know nothing about its inner power-law profile Tonry 1984b, 1987). No one has studied enough nearby cases; for example, Schombert's (1986, 1987) low-luminosity galaxies are in the Coma cluster. (d) Tidal effects modify outer profiles upward or downward (Section 7.2). (e) Some "ellipticals" are misclassified SOs. (f) Finally, many ellipticals contain unrecognized dust (Section 4.1).

7.1. Do Elliptical Galaxies Have r1/4 -Law Brightness Profiles?

De Vaucouleurs' (1948, 1953) r1/4 law fits bright elliptical galaxies reasonably well except where tidal effects are important. We do not attach physical significance to this choice of function, although Binney (1982c) and Bertin & Stiavelli (1984, 1989) find reasonable distribution functions whose density profiles are similar to it. The r1/4 law is a convenient parameterization that extracts all of the scaling information that we are entitled to derive, given the similarity of profiles to power laws (Kormendy 1980, K82). But how well does it work?

No definitive study has been published. Based on large photometric surveys, Michard (1985), Djorgovski et al. (1985), Djorgovski (1985), Schombert (1986, 1987), Kodaira et al. (1986), Jedrzejewski (1987b), Capaccioli et al. (1988), and de Carvalho & da Costa (1988) conclude that ellipticals have a wide variety of profile shapes. A corollary is that fitting functions with two scale parameters but no shape parameter are not particularly useful. However, these conclusions are undermined by the problems discussed above.

Much of what we know about galaxy halos still comes from photographic data. These show that profiles of isolated ellipticals vary with luminosity (e.g. Kormendy 1980, Michard 1985, Schombert 1986, 1987), although with significant scatter. The r1/4 law fits best near MB = -21. Even at this luminosity, profiles are slightly concave upward when plotted against r1/4, typical deviations are ± 0.1-0.2 mag arcsec-2 over gtapprox 6 mag arcsec-2 (Kormendy 1977b, Capaccioli 1985). Galaxies much brighter than MB = -21 have more light at large radii than the extrapolation of r1/4 laws fitted further in, and fainter galaxies have less.

We believe that a good approach for future investigation of profile shapes is one suggested by Schombert (1986, 1987). For each luminosity, bin, Schombert constructs template profiles by averaging many observed profiles. Two further improvements are needed. First, total luminosities should be used. Schombert's 16-kpc metric absolute magnitudes measure different fractions of the total light in giant and dwarf galaxies: They are total magnitudes for dwarfs but contain only ~ 50% of the luminosity of first-ranked galaxies (see Figure 8 in Schombert 1986). Second, we need to use isolated galaxies to minimize tidal effects. The resulting templates can then be compared with profiles of galaxies that have companions to study tidal effects.

It remains true that characteristic sizes and densities are well measured using two-parameter fitting functions. These are basically equivalent. None has a special physical interpretation, but among formulas explored so far, the r1/4 law is most convenient and fits best. Profile fits can be improved by adding a third parameter, but then the parameters are too coupled to be useful. All this has been reviewed by Kormendy (1980, K82) and Capaccioli (1988b). Parameters can also be derived without using fitting functions. For example, the actual half-light radius and surface brightness can be used. Or scale radii can be derived using dimensionless monotonic functions like Petrosian's (1976) eta function, i.e. the ratio of the surface brightness at a given radius to the mean surface brightness within that radius.

7.2. Tidal Effects

Tidal effects are reviewed in K82. In the cores of rich clusters, galaxies are observed to have abnormally small sizes (Strom & Strom 1978, and subsequent papers; see K82). This is particularly true of faint ellipticals, which moreover have outer cutoffs in their profiles (see also Schombert 1986, 1987). These observations are convincingly interpreted as truncation by the mean gravitational field of the cluster, especially during virialization (Merritt 1984, and references therein).

Whether small galaxies are truncated by large ones is less clear. Suggestions that M32 (King 1962) and NGC 4486B (Rood 1965, Kormendy 1977a) are truncated conflict with recent photometry [see Nieto & Prugniel (1987a, b) and N88 for reviews]. On the other hand, King & Kiser (1973) find that NGC 5846A has an outer Cutoff. Examples of both "truncated" and untruncated small companions are given by Prugniel et al (1987, 1988). Some photometry is uncertain because the galaxies are embedded in the halos of companions (N88). Also, some close pairs must be optical doubles. Thus the implications of these observations are unclear.

Despite possible truncation, it is clear that ellipticals like M32 are not dwarfs only because of tidal effects. They are genuinely the low-L end of the luminosity function of elliptical galaxies (Section 8.1; see also Nieto & Prugniel 1987a, b, N88).

Encounters between ellipticals of nearly the same mass cannot by symmetry produce truncation if the total mass lost to the system is small (Aguilar & White 1985, and references therein). Kormendy (1977b, 1982a) concluded that ellipticals with companions of comparable sizes have distended outer profiles, and he interpreted this as tidal stretching or heating. The effect needs checking: Schombert (1988) and de Carvalho & da Costa (1988) did not see it in their samples. However, distension is seen in N-body simulations. Aguilar & White (1986) find that encounters produce transient tidal waves in the density distribution. An encounter heats each galaxy. Strong encounters steepen the profiles (i.e. make the galaxies smaller) because mass is lost; weak encounters make the profiles shallower. In either case, the final profile is set up first at small radii. As time passes, the transition between the old and new profile moves outward until only the final profile is left. An r1/4 -law profile shape is approximately preserved; there is no truncation.

Azimuthal distortions produced by tides are also observed (K82, Djorgovski 1985, Borne & Hoessel 1988, Borne 1988, Borne et al. 1988, Porter 1988, Davoust & Prugniel 1988, Prugniel et al. 1988, Lauer 1988a). As Borne notes, these are clear evidence for tidal friction in action.

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