69, 70]
Pressure of Radiation
75
Before accepting this view of a star’s constitution as complete, a further
complication must be taken into account. We have already noticed that the
presence of radiation results in a pressure J aT 4 , where a = 7'63 x 10 -15 . If T has
the value just calculated for the centre of the sun, namely, 4T x 10 7 degrees,
the corresponding pressure of radiation is found to be 7*2 x 10 1 * dynes, which
is about one-sixth of the total pressure given by the rough calculation of § 66 .
Thus the mechanical effects of the pressure of radiation, while not great,
are just too large to be disregarded entirely. The present writer drew
attention to Emden’s neglect of the pressure of radiation when reviewing his
Gas Kugeln in 1909*, and gave the first reasonably accurate estimate of its
importance in 19l7j\ Eddington had attempted a calculation some months
earlier, but had obtained values which were thousands of times too large
through supposing the stellar matter to consist of unbroken atoms
When the pressure of radiation is taken into account, the total pressure p
inside a star whose material is of mean molecular weight p is given by
P = ~ pT + § aT 4 (70-1),
where the first term on the right represents the usual gas-pressure, which we
shall henceforth denote by p 0 and shall, for the present, suppose to be given
by Boyle’s law, and the second term denotes the pressure of radiation, which
we shall call p R . If the ratio of gas-pressure to pressure of radiation is denoted
by X,
p = P° + P«=(i + l)p°= R ^eT (702),
so that the effect of taking radiation-pressure into account is the same as that
of reducing the molecular weight p by a factor X/(l + X). We may, if we please,
treat the gas as though it had a fictitious molecular weight p given by
/
P =
/jl\
1 + X
(70-3),
and neglect the pressure of radiation entirely. By so doing we should be
treating the pressure of radiation as though it arose from molecules of
molecular weight zero, and on averaging over these fictitious molecules and
the real material molecules of molecular weight g we obtain the average
molecular weight p given by equation (70'3).
The very rough calculation given above has suggested that X is about 5 at
the sun’s centre, so that we could allow for the pressure of radiation by reducing
the effective molecular weight at the sun’s centre by about 17 per cent.
In more massive stars the pressure of radiation assumes greater importance.
To see this let us start from a standard star such as the sun and increase its
* Astrophys. Journ. xxx. (1909), p. 72.
t Bakerian Lecture (1917), Phil. Trans. 218 a, p. 209.
X M.N. Lxxvn. (1917), p. 16.
