3.4.5. Disk Properties. III. Characteristic Parameters
The only disks whose parameters we can discuss with reasonable accuracy are those which are exponential. This means that discussions of disk parameters are potentially biased and certainly incomplete. The most useful parameter for disk galaxies is probably the bulge-to-disk ratio; this is reviewed in section 2.3 and in Kormendy (1980). Here I will focus on the recent discussion of Freeman's (1970) observation that most disks have a "magic" central surf ace brightness, B(0)c = 21.65 ± 0.30 B mag arcsec-2.
Two kinds of reservations have been expressed about the above result. Disney (1976) and Allen and Shu (1979) have pointed out that selection effects prevent us from finding disks which are much fainter than the night sky. The apparent scarcity of bright disks is real, but very faint disks could exist in large numbers and remain undiscovered. Second, Kormendy (1977b) has argued that the small dispersion in B(0)c values results partly because the parameters measured by Freeman were not corrected for bulge light. The value of B(0)c derived can then be much too bright (see NGC 2855 in Fig. 27). Kormendy (1977b, Fig. 9) modeled the resulting errors by fitting exponentials to composite profiles consisting of exponential disks added to r1/4-law bulges, each with a wide range of parameters. This shows that a disk with B(0)c >> 21.65 B mag arcsec-2 will hardly affect the composite profile. Nevertheless, the central surface brightness of the fitted exponential will be near the canonical value (see also Hamabe et al. 1979a; Phillips and Disney 1982). Even an elliptical fitted with an exponential will yield B(0)c very close to the magic value (see also Freeman 1970). A population of faint disks in S0-b galaxies would be measured quite incorrectly.
Of course, not all galaxies are affected by either of these arguments. For example, many late-type galaxies have no bulge at all and still have surface brightness scales near 21.65 mag arcsec-2. Essentially, the point of the above arguments, and of more extensive recent photometry, is that the dispersion in B(0)c values is larger than we believed. Examples of faint disks have been discussed by Kormendy (1977b) and by Romanishin, Strom and Strom (1982: NGC 5963, B(0)c = 23.4 mag arcsec-2). Both Burstein (1979c) and Boroson (1981) find a broad distribution of B(0)c values between 20 and 23 B mag arcsec-2. Finally, Bosma and Freeman (see Freeman 1979) have investigated the constancy of B(0)c by comparing the sizes of galaxies on sky surveys of different limiting surface brightnesses µ1 and µ2 (the Palomar Observatory Sky Survey and the ES0/SRC IIIa-J Survey). An exponential with a central brightness µ0 will have sizes in these surveys in the ratio r2 / r1 = (µ2 - µ0) / (µ1 - µ0). The predictions are: r2 / r1 = 1.33 if µ0 = 21.6 mag arcsec-2 and r2 / r1 = 1.50 if µ0 = 22.6 mag arcsec-2. The observed average value is <r2 / r1> = 1.3, with a dispersion of 0.2, and with 15% of the galaxies having larger values indicative of much fainter disks. Thus we appear to be converging on the view that disks have B(0)c values not very different from 21.65 mag arcsec-2, but that the dispersion is not surprisingly small.
There are preliminary indications (Boroson 1981; Hamabe 1982) that B(0)c correlates with the scale length r0 in a way reminiscent of the Be - log re relation (Fig. 13). Larger disks have fainter characteristic brightnesses. There is a clear separation of spiral and S0 galaxies, with spirals being larger and fainter. This difference is enhanced when B(0)c values for spirals are corrected for the presence of young stars (Boroson 1981). Disks studied to date have absolute magnitudes in the range -17 MB -21. The faint end of the distribution may be controlled by selection effects. Based on the large difference between spiral and S0 disk parameters, Boroson (1981) argues that the data are more consistent with intrinsic-formation theories than with the view that S0 galaxies are spirals stripped of their gas. However, the robustness of the B(0)c - r0 correlation needs to be verified with additional photometry and with further studies of profile decomposition.