RELATION BETWEEN LUMINOSITIES AND DIAMETERS
Among the nebulae of each separate type are found linear correlations between total magnitudes and logarithms of diameters. These are shown in [Figures 2–5] for the beginning, middle, and end of the sequence of types and also for the irregular nebulae. In Figures [2] and [3] adjacent types have been grouped in order to increase the material, and in [Figure 5] the Magellanic Clouds have been added to increase the range.
The correlations can be expressed in the form
| (1) |
where K is constant from type to type, but C varies progressively throughout the sequence. The value of K cannot be accurately determined from the scattered data for any particular type, but, within the limits of uncertainty, it approximates the round number 5.0, the value which is represented by the lines in [Figures 2–5].
When K is known, the value of C can be computed from the mean magnitude and the logarithm of the diameter for each type. This amounts to reading from the curves the magnitudes corresponding to a diameter of one minute of arc, but avoids the uncertainty of establishing the curves where the data are limited.
TABLE IV
Irregular Nebulae
| N.G.C. | mT | log d |
|---|---|---|
| 2968 | 12.6 | +0.08 |
| 3034* | 9.0 | .85 |
| 3077 | 11.4 | .48 |
| 3729 | 11.8 | .17 |
| 4214* | 11.3 | .90 |
| 4449* | 9.5 | .65 |
| 4618 | 12.3 | +0.40 |
| 4656§ | 11.5 | +1.30 |
| 4753 | 11.4 | +0.43 |
| 5144 | 12.8 | – .30 |
| 5363 | 11.1 | +0.20 |
| Mean | 11.34 | +0.469 |
NOTES TO TABLES I–IV
* Magnitude from Hopmann.
† N.G.C. 524 and 3998 are late elliptical nebulae in which the equatorial planes are perpendicular to the line of sight. They might be included with the E6 or E7 nebulae.
§ Absorption very conspicuous.
‡ N.G.C. 3607, 4459, and 5485 appear to be elliptical nebulae with narrow bands of absorption between the nuclei and the peripheries.
The progressive change in the value of C throughout the sequence may be expressed as a variation either in the magnitude for a given diameter or in the diameter for a given magnitude. Both effects are listed in [Table VII] and are illustrated in [Figure 6], in which magnitudes and diameters thus found are plotted against types. With the exception of the later elliptical nebulae, for which the data are wholly inadequate for reliable determinations, the points fall on smooth curves. In the region of the earlier elliptical nebulae, the curves should be somewhat steeper in order to allow for objects of greater ellipticities which are probably included.