3. OBSERVATIONS OF DISKS

The most extensive study of the photometric disk parameters in the optical and near-IR is that of a statistically complete sample of 86 disk dominated galaxies in Roelof de Jong's thesis (1995, 1996a, b, c; de Jong & van der Kruit, 1994). Some of his conclusions are:

• Freeman's law is really an upper limit to the central surface brightness.
  
• The scalelength h_R does not correlate with Hubble type.
  
• In disks fainter regions are generally bluer, probably resulting from a combination of stellar age and metallicity gradients.
  
• Outer regions are on average younger and of lower abundance.

  Richard de Grijs (1997, 1998; de Grijs & van der Kruit, 1996) presented optical and near-IR surface photometry of a sample of 47 edge-on galaxies. The data have recently been re-analysed by Kregel et al. (2001; see also de Grijs et al., 2001) with a new and improved 2-D fitting procedure. Some results (Fig. 4 and 5):

  Figure 4. The radial scalelength hR and vertical scaleheight hz for a sample of 34 edge-on galaxies. Panels (a) and (b) show the distribution (solid line is corrected for sample selection) of hR and the correlation with the rotation velocity. Panels (d) and (e) show the same for hz and (c) and (f) for the ratio hR / hz (after Kregel et al., 2001).

  Figure 5. The relation between the truncation radius Rmax and the radial scalelength hR of the disks in a sample of edge-on galaxies. The righthand panel shows the ratio Rmax / hR as a function of hR and the lines are models based on the formalism of Dalcanton et al., 1997 (from Kregel et al., 2001).

  
  
• Both h_R and h_z correlate in general terms with V_max.
  
• For h_R this is expected from the Tully-Fisher relation.
  
• Our Galaxy would be somewhat unusual if the scalelength h_R is as small as 2 to 2.5 kpc as some recent studies claim (see also van der Kruit, 2000).
  
• The flattening of the sample after volume correction is h_R / h_z = 7.3 ± 2.2. Then

  (21)

  So most galaxies appear not to be "maximum disk". Recall that this result follows directly from the observations using only the rotation curve of the self-gravitating exponential disk, hydrostatic equilibrium and Bottema's (empirical, but explainable) relation (8). Bottema (1993) derived a similar result in the analysis of his sample of galaxies, in which he measured the stellar kinematics and found V^disk_max / V_max = 0.63 ± 0.17.
  

• At least 20 of the spirals show radial truncations.
  
• The ratio of the truncation radius and the scalelength is R_max / h_R = 3.6 ± 0.6.
  
• But large galaxies have smaller values for this ratio than small ones.
  
• For common disks with scalelengths of 5 kpc or less, the ratio is about 4.

The truncation radius in a simple view results from the maximum specific angular momentum of the sphere from which the disk collapsed. Van der Kruit (1987), in the context the Fall & Efstathiou (1980) picture of disk galaxy formation, then predicted a value of 4.5 for the ratio, based on a Peebles (1971) spin parameter = J|E|^1/2 G^-1 M^-5/2 of 0.7. Dalcanton et al. (1997) have extended this to a models with a dispersion in the spin parameter. We have calculated model surface density profiles with their method for M_tot = 10¹⁰ - 10¹³ M and = 0.01 - 0.28. These are the lines in Fig. 5b.

For completeness I mention that in many cases there is a warp in the HI-layer in the outer parts, often starting roughly at the truncation radius. This suggests that the warp material has been accreted subsequent to disk formation.