34
The Light from the Stars [ch. ii
There appears to be a slight excess of stars of absolute magnitudes between
8 and 12, but our list is certainly deficient in stars fainter than twelfth mag
nitude (cf. fig. 1, p. 8), and if all stars were included the excess would probably
be in the faintest stars of all. Our sun is well up in the list, being fourth out
of twenty-three.
This distribution fails to represent that in the universe as a whole because
the number of stars under discussion is so small as to contain no stars of very
high luminosity. By counting the stars to far greater distances, Kapteyn and
Seares have obtained results summarised in the following table:
Table V. The Luminosity-Function ( Kapteyn-Seares).
Abs. Mag.
Luminosity
No. of stars
per magnitude
-5
10,000
1
-2-5
1000
90
0
100
3,300
2-5
10
42,000
200,000
5
1
7'5
o-i
350,000
10
0 01
500,000
12-5
0 001
600,000
The last column gives the relative number of stars per unit absolute
magnitude which have the absolute magnitude shewn in the first column, or
the luminosity, in terms of the sun as unity, shewn in the second column.
Between absolute magnitudes 4 and 12 the stars are again found to be fairly
evenly distributed, although the excess of faint stars which we suspected in
the smaller sample is now quite noticeable. But the table further shews the
existence, in quite small numbers, of stars of very high luminosity, their
numbers falling off steadily and very rapidly for absolute magnitudes less than
about 5, i.e. for stars appreciably more luminous than the sun.
The last column of Table IV gives the masses of the stars when these are
known from direct observation. The mass of the sun is calculated from the
circumstance that its gravitational attraction just suffices to keep the earth
in its orbit. In the same way the masses of the two components of a binary
system can be calculated from the fact that the gravitational attraction of
each just retains the other in its orbit. There is no other means of calculating
the masses of stars by direct observation, so that no masses are entered except
for the components of binary systems. We shall, however, find later that
purely physical considerations make it possible to calculate the masses of
single stars with fair accuracy from their luminosities and the temperatures
of their surfaces.