The parallelism of the two curves representing formulae [(2)] and [(6)] indicates that the regular extra-galactic nebulae, when reduced to the standard type, are similar objects. The mean surface brightness is constant, and the luminosity of the nucleus, as measured by Hopmann, is a constant fraction, about one-fourth, of the total luminosity of the nebulae. If there is a considerable range in absolute magnitude and hence in actual dimensions, the smaller nebulae must be faithful miniatures of the larger ones.
ABSOLUTE MAGNITUDES OF EXTRA-GALACTIC NEBULAE
Reliable values of distances, and hence of absolute magnitudes, are restricted to a very few of the brightest nebulae. These are derived from a study of individual stars involved in the nebulae, among which certain types have been identified whose absolute magnitudes in the galactic system are well known. The method assumes that the stars involved in the nebulae are directly comparable with the stars in our own system, and this is supported by the consistency of the results derived from the several different types which have been identified.
TABLE XIV
| Type | mn – mT | Number | |
|---|---|---|---|
| E0–E3 | 1.64 | (9) | |
| E4–E7 | 1.43 | (7) | |
| Sa–SBa | 0.97 | (5) | 1.27 when N.G.C. 5866 is omitted |
| Sb–SBb | 1.70 | (11) | |
| Sc–SBc | 1.76 | (5) | 1.19 when N.G.C. 5194 is omitted |
| Unweighted mean | 1.50 | (37) | 1.45 (35) |
| Weighted mean | 1.55 | (37) | 1.52 (35) |
TABLE XV
Absolute Magnitudes of Nebulae
| System | MT | MS |
|---|---|---|
| Galaxy | –5.5 | |
| M 31 | –17.1 | 6.5 |
| LMC | 17.0 | 8.0 |
| SMC | 16.0 | 5.5 |
| M 33 | 15.1 | 6.5 |
| N.G.C. 6822 | 13.7 | 5.8 |
| M 101 | 13.5 | –6.3 |
| M 32 | –13.3 | |
| –6.3 | ||
| –9.0 = MS – MT | ||
| Means | –15.1 | –15.3 |
| Adopted | –15.2 |
In [Table XV] are listed absolute magnitudes of the entire system and of the brightest stars involved, for the galaxy and the seven nebulae whose distances are known. The data for the Magellanic Clouds are taken from Shapley’s investigations. The absolute magnitudes of the remaining nebulae were derived from Holetschek’s apparent magnitudes and the distances as determined at Mount Wilson, where the stellar magnitudes were also determined. M 32 is generally assumed to be associated with the great spiral M 31, because the radial velocities are nearly equal and are unique in that they are the only large negative velocities that have been found among the extra-galactic nebulae. M 101 has been added to the list on rather weak evidence. The brightest stars involved are slightly brighter than apparent magnitude 17.0, and several variables have been found with magnitudes at maxima fainter than 19.0. Sufficient observations have not yet been accumulated to determine the light-curves of the variables, but from analogy with the other nebulae they are presumed to be Cepheids. On this assumption, both the star counts and the variables lead to a distance of the order of 1.7 times the distance of M 33. The inclusion of M 101 does not change the mean magnitude of the brightest stars involved, but reduces the mean magnitude of the nebulae by 0.2.
The range in the stars involved is about 2.5 mag., and in the total luminosities of the nebulae, about 3.8 mag. This latter is consistent with the scatter in the diagram exhibiting the relation between total luminosities and diameters. The associated objects, M 31 and 32, represent the extreme limits among the known systems, and the mean of these two is very close to the mean of them all.