**3.4.2. Disk Properties. I. Freeman's (1970) Study**

Freeman's (1970) classic study of the photometry of 36 spiral and S0 galaxies provides the basic results which are the starting point for any discussion of disk structure. (1) Disk profiles were found to be exponential (see also de Vaucouleurs 1959b),

(8) |

where *I*_{0}^{D} is the extrapolated central
surface brightness and *r*_{0} is the
scale length. The reason is basically unknown, although an exponential
is a possible (but not necessary) result of the collapse of a uniformly
rotating, constant-density sphere
(Mestel 1963;
Freeman 1970;
Gunn 1981).
(2) Sometimes the exponential has an inner cutoff; i.e., it
does not extend all the way to the center ("Type II profile"). (3) The
scale length is
2 *r*_{0}
10 kpc in S0-bc galaxies
but always less than
5 kpc in Sc-Im galaxies (*H*_{0} = 50 km s^{-1}
Mpc^{-1}). (4) The most
surprising result was that the extrapolated central disk brightness,
corrected for inclination and Galactic absorption, is constant at
*B*(0)_{c} = 21.65 ± 0.30 B sag arcsec^{-2} in
28 of the 36 galaxies. Except
for one dwarf irregular, all of the other disks are brighter. Discussion
of these results and of their implications is given in
Freeman (1970,
1975b,
1976,
1978,
1979).

Recent work discussed below weakens conclusions (1) and (4), although both remain useful approximations. Despite this, the above paper is fundamental, because it began work on many of the basic questions of disk structure.