SURVEY OF THE PROBLEM
9
/
nfurcation of
l Shapley on
warf stars of
ree eclipsing
of air. There
sity but is a
higher types
As already
3 giant stars
il differences
fication into
3 method of
t and dwarf
lty; but the
latLockyer,
ddence that
though con-
are greater
ich that the
than under
v in a very
)urse.
nternal dis-
arches. We
r one of the
n be calcu-
(8-1),
! molecular
re only two
differential
conditions :
he pressure
; the layers
es that the
somatically
of the star
• equations
he two in-
any point.
Hence the distribution of pressure, density and temperature is found.
The general scheme of distribution is (in the first approximation) homo
logous from star to star; that is to say, all gaseous stars copy the same
model each on its own appropriate scale of mass, length, temperature, etc.
The heavy work of the solution can be done once for all, and it is then
only a question of adapting it to the scale of the particular star considered.
We do not here enter into details; the problem is fully treated in Chapter iv.
In order to obtain definite numerical values of the temperature inside
a star according to Lane’s theory it was necessary to have the following
data—
M the mass,
R the radius,
/x the mean molecular weight of the material,
y the ratio of specific heats of the material.
The first two define the star under consideration; but we might suppose
that the values of the last two in any star could only be guessed by con
sidering the probable chemical composition of the interior—as to which
we know practically nothing. We shall explain how this difficulty has been
surmounted.
Actually the value of y gave no serious trouble. It cannot exceed f,
the value for a monatomic gas; and it cannot be less than f without
rendering the star unstable—which we know it is not. The difference in
temperature distribution corresponding to the limits f and f is of some
account; but there is no important change in its general character, and
either limit gives an approximation good enough for many purposes. The
constant y, however, no longer concerns us. We shall abandon that part
of Lane’s theory responsible for its introduction, replacing Lane’s hypothesis
of convective equilibrium by radiative equilibrium. In all the earlier
researches it was supposed that heat was carried from the interior to the
surface of the star by convection currents, so that the interior was kept
thoroughly stirred and followed the same law of thermal equilibrium as
the lower part of the earth’s atmosphere. But it appears now that the
heat is transferred by radiation and the temperature distribution is con
trolled by the flow of radiation; convection currents, if they exist, will
strive to establish a different distribution, but the temperature continually
slips back to radiative equilibrium since the transfer by radiation is much
more rapid. Radiative equilibrium was first adopted by R. A. Sampson*
in 1894; but it could not be developed fully without the more recent
progress of thermodynamics. K. Schwarzschildf brought it into promi
nence in a famous paper on the condition of the sun’s atmosphere. Our
task is to apply the same principle to the interior of the sun and stars.
* Memoirs R.A.S., 51, p. 123. f Gottingen Nachrichten, 1906, p. 41.