156-158]
Gaseous Stars
173
Emission
where
f(M)=(4nr<r)l
18-3 M(T e R)* 1*
\c (\ c +1)_
(158-4).
This would give the relation between a star’s mass, bolometric luminosity
and effective temperature if the gas-laws were obeyed.
We could of course exhibit the relation in a diagram of the type shewn
in fig. 12, in which log# and log T e are taken as ordinate and abscissa re
spectively. The lines of constant mass would have equations of the type
E oo Tr,
and so would be a series of straight parallel slant lines.
Fig. 15. Effective temperature (or spectral type) as a function of mass and luminosity.
It will, however, be more convenient to exhibit the relation in a different
form. Equation (158-3) shews that a star of any given mass M and any given
bolometric luminosity E can always find a value of T e such that it will be in
equilibrium provided the gas-laws are obeyed throughout its mass. Thus we
may think of a gaseous star’s effective temperature T e as being determined
by its mass M and its bolometric luminosity, or total rate of generation of
energy E, and we may exhibit the values of T e in a diagram in which E and M
are taken as ordinate and abscissa, as in fig. 15.