376
DIFFUSE MATTER IN SPACE
For temperatures of two or three thousand degrees and atoms ionised
down to 5-10 volts, log vJvq is about 2-3. (The precise value is not of much
importance; it is clear that in any case it is of order unity.) Hence the
electrons preserve more than half their initial energy, and their average
temperature is not much less than their initial temperature which we have
already estimated at 2000° at least.
To sum up—the processes (a) and (c) have negligible effect on the
temperature. The process (6) continually furnishes electrons at high tem
perature ; and although this is appreciably toned down by process ( d) the
order of magnitude is still roughly that of process (6). Diffuse matter in
space will accordingly rise to a temperature of the order 2000°. It is
scarcely necessary to add that this conclusion is entirely provisional as
there may be important gaps in our present knowledge.
Recently I have come to the conclusion that 2000° may be an under
estimate. The following is an attempt to calculate more specifically the
“initial temperature” of the electrons expelled from the atoms. To
simplify the conditions we suppose that the stars are all black bodies with
the same effective temperature T, so that the energy-density of interstellar
radiation between v and v + dv is proportional to
We are thus dealing with evenly diluted radiation. Suppose also that
all the atoms have the same ionisation potential v 0 (in frequency units).
Let the absorption coefficient follow the law
On Kramers’ theory 5 = 0, but we retain 5 as a precaution. By (257-1)
and (257-2) the amount of radiation absorbed between v and v + dv can
be set equal to p f
In our applications hvJRT will be large so that we can replace (e hu l RT - l)
by e hv l RT . Hence (257-3) becomes
kcc v 3-s (v > v 0 )
(257-2).
V s {(¡fiviRT — 1) ’
and the number of quanta absorbed is
Cdv
hv s+1 ( ghv/RT — 1 ) ’
Hence the average quantum absorbed is
hdv
dv
„„ v s (e hv l RT — 1) ' J.„ o v s
yS+l (çhvjRT — j)
(257-3).
(257-4),
