2.1.1. Luminosity Fractions

We consider first the luminosity fractions f in equation (2). In Table 1 we show the bulge fraction of galaxies in luminosity, = L_bulge / (L_bulge + L_disk), for each morphological type, from the bulge-disk decomposition of Kent (1985) based on his accurate Gunn r band CCD photometry. We take the median of the distribution presented by Kent. The bulge fraction in r band is converted into that in the B band using the color transformation law B - r = 1.19 for elliptical galaxies and bulges (Fukugita, Shimasaku & Ichikawa 1995). The values of thus obtained in the B band are consistent with the result of Whitmore and Kirshner (1981), although the latter sample is not as large as that of Kent and the decomposition, based on photography, may be less accurate. The bulge fraction is well correlated with the morphology (Morgan 1962; Dressler 1980; Meisels & Ostriker 1984; Kent 1985), but the morphologies at given bulge fraction overlap neighboring classes.

TABLE 1.
Galaxy Parameters

Parameter	E	S0	Sab	Sbc	Scd	Irr
Bulge fraction (r)............	1	0.75	0.40	0.24	0.10	0
Bulge fraction (B)...........	1	0.64	0.33	0.16	0.061	0
Morphology fraction µ(B)....	0.11	0.21	0.28	0.29	0.045	0.061
HI typical mass (109 M)...	0	0.64	2.5	4.0	2.9	1.8
H2 / HI...........................	...	2.5	1.0	0.63	0.25	0.06

Row (3) in Table 1 is our adopted distribution of morphologies, expressed as the fraction µ_t of the mean luminosity density contributed by galaxies of morphological type t. Postman & Geller (1985) give E:S0S+Irr=0.12:0.23:0.65. This ratio is consistent with the Tinsley mix (Tinsley 1980), which subdivides the spiral fraction into further subclasses, while E and S0 are not separated. The luminosity fractions in equation (2) are obtained by combining the two results:

(3)

The sum in the second expression is from SOs through spirals. Because the mass in S0 discs is so small we make little error in treating the disks of spirals and S0s as the same population. The separation into each morphological type is ambiguous, and the classification depends much on the author. To model such error, we recalculate the fractions f after reclassifying 1/3 of the galaxies in each type systematically to the neighboring later type, or else to the neighboring earlier type. This produces the range (0.324-0.459):(0.599-0.499): (0.076-0.041). When we use a morphological fraction or a bulge-to-disk ratio taken from other authors, we find the luminosity fractions f fall within this range in most cases. In particular these estimates, when translated into the V pass band, agree with the survey of Schechter and Dressler (1987). This spread of values of the µ_t is taken into account in our assignment of errors in estimates of the mean mass density.