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 | m_{n} – m_{T}| 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 | M_{T} | M_{S}
-------------+-----------+----------------------
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 = M_{S} – M_{T}
+-----------+----------------------
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.