TABLE VIII
| Type | C | Δ log d |
|---|---|---|
| E0 | 10.30 | +0.54 |
| 1 | 10.65 | .47 |
| 2 | 11.00 | .40 |
| 3 | 11.35 | .33 |
| 4 | 11.70 | .26 |
| 5 | 12.05 | .19 |
| 6 | 12.40 | .12 |
| 7 | 12.75 | +0.05 |
| Sa | 13.31 | –0.06 |
| Sb | 13.90 | .18 |
| Sc | 14.45 | .29 |
| SBa | 13.00 | .00 |
| SBb | 13.16 | .03 |
| SBc | 14.41 | .28 |
| Irr | 13.68 | –0.14 |
Fig. 7.—Relation between luminosity and diameter among extra-galactic nebulae. The nebulae have been reduced to a standard type, S0, which, being the mean of E7, Sa, and SBa, represents a hypothetical transition point between elliptical nebulae and spirals. The Magellanic Clouds have been included in order to strengthen the brighter end of the plot.
SIGNIFICANCE OF THE LUMINOSITY RELATION
The correlations thus far derived are between total luminosities and maximum diameters. In the most general sense, therefore, they express laws of mean surface brightness. The value, K = 5.0, in [formula (1)] indicates that the surface brightness is constant for each separate type. The variations in C indicate a progressive diminution in the surface brightness from class to class throughout the entire sequence. The consistency of the results amply justifies the sequence as a basis of classification, since a progression in physical dimensions is indicated, which accompanies the progression in structural form. Although the correlations do not necessarily establish any generic relation among the observed classes, they support in a very evident manner the hypothesis that the various stages in the sequence represent different phases of a single fundamental type of astronomical body. Moreover, the quantitative variation in C is consistent with this interpretation, as is apparent from the following considerations.
TABLE IX
Residuals in mT + 5 log d as a Function of Orientation
| Type | Round | Elliptical | Edge-On | |
|---|---|---|---|---|
| Sa | –0.02 (13) | –0.27 (13) | +0.57 (23) | |
| Sb | .77 (24) | .0 (35) | 1.71 (11) | |
| Sc | –0.08 (35) | –0.13 (57) | +0.66 (22) | |
| All S | –0.26 (72) | –0.11 (105) | +0.83 (56) | |
| SBa | 0.0 (10) | –0.30 (7) | +0.31 (8) | |
| SBb | – .16 (10) | + .07 (6) | ||
| SBc | +0.19 (9) | –0.50 (4) | +0.32 (2) | |
| All SB | +0.01 (29) | +0.21 (17) | +0.31 (10) | |
| All spirals | –0.22 (101) | –0.13 (122) | +0.73 (66) | |
Among the elliptical nebulae it is observed that the nuclei are sharp and distinct and that the color distribution is uniform over the images. This indicates that there is no appreciable absorption, either general or selective, and hence that the luminosity of the projected image represents the total luminosity of the nebula, regardless of the orientation. If the observed classes were pure, that is, if the apparent ellipticities were the actual ellipticities, [formula (1)] could be written
| (3) |