3.4.4. Disk Properties. II. The Shape of the Radial Profile
There is now considerable evidence that exponential profiles are a good approximation in some galaxies but a very poor one in others (Fig. 27). It is difficult to reliably estimate the prevalence of non-exponential disks, because published photometric samples may not be representative. Boroson's (1981) sample favors galaxies with strong bulges. Of his 26 objects, 35% have exponential disks (NGC 488, 628, 2268, 2336, 2681, 2841, 2967, 3147, 6340), 38% do not (NGC 1058, 2775, 3368, 3642, 4378, 4725, 4736, 4941, 5194, 7217) and the other 27% are indeterminate, usually because the bulge contributes too much light (Fig. 27). Many of the non-exponential disks are oval; recall from section 2.5.1 that such disks consist of nested ovals of nearly constant surface brightness, each much fainter than the one interior to it. Some profiles are clearly not measuring the mass distribution of the disk, because star formation is producing local variations in mass-to-light ratio. For example, Talbot, Jensen and Dufour (1979) have shown that the brightness profile of M83 is non-exponential because of the contribution of young stars (i.e., pixels with B - V < 0.40). A profile constructed using only the reddest pixels (B - V > 0.65) is exponential. Boroson (1981) also notes galaxies in which departures from exponentials are produced by star formation. Nevertheless, it is clear that many non-exponential profiles are still non-exponential in the near-infrared. This is especially true of oval galaxies; compare NGC 1097, 3504 and 5248 in Sandage (1961) and in Elmegreen (1981). Finally, there are galaxies which are found to have non-exponential disks only when the light of the bulge is removed from the data (Kormendy 1977b, 1980). Evidently non-exponential disks are very common.
Figure 27. Average brightness profiles (plus signs) of selected galaxies from Boroson (1981). Where the profile can be decomposed, the lines show the final r1/4-law and exponential fits, and their sum. Otherwise only the bulge fit is shown. NGC 488 and 2841 have well-defined exponential disks. In NGG 2855 we cannot tell conclusively whether the disk is exponential because the bulge contributes too much light. The other three galaxies have non-exponential disks. The profiles of NGC 4736 and 4941 show the successive shelves of prototypical oval galaxies (see section 2.5.1 and Sandage 1961).
Even disks which appear to be exponential have outer cutoffs at low light levels (van der Kruit and Searle 1980, 1981a, b, 1982a; Jensen and Thuan 1982). Figures 28 and 29 show two examples. All seven galaxies studied by van der Kruit and Searle have such cutoffs. They occur at an average radius of <rmax / r0> = 4.7 ± 0.3 (dispersion / 71/2). The surface brightness at the edge, corrected to face-on inclination, is typically 27.3 J mag arcsec-2. The reason for the outer cutoffs is not known. It is possible (1) that the disk is not yet completely formed at these radii, (2) that star formation ceases beyond rmax because the primordial gas disk is stable (van der Kruit and Searle 1981a) or (3) that the disk becomes non-self-gravitating and begins to flare in thickness (Gunn 1981). The last hypothesis should be testable with further photometry of edge-on galaxies. It is certainly true that mass-to-light ratios have typically grown to large values at rmax = 4.7r0 (section 4.1).
As van der Kruit and Searle (1981a) emphasize, "the exponential surface brightness distribution is no fundamental law of nature but simply a rough generalization; individual galaxies often depart from this distribution quite severely."