354 
THE OUTSIDE OF A STAR 
It has sometimes been urged against pressure broadening that we do not 
get anything like so much broadening in a vacuum tube when the pressure 
is equal to that now assigned to the reversing layer of a star. For example, 
the Balmer series is quite sharp in a vacuum tube at a pressure of 10 -4 
atmospheres. But this comparison overlooks the great difference due to 
the ionisation of stellar material. The ion or electron is the centre of a 
disturbing field of far wider extent than the neutral atom’s field which 
can scarcely come into play except at collision; and the broadening effect 
is of a much higher order of magnitude. Although ions and free electrons 
are produced in a vacuum tube, their abundance is insignificant compared 
with photospheric conditions. 
As an example we consider the H p line of hydrogen which corresponds 
to a transition between a 4-quantum and a 2-quantum orbit. In the 
4-quantum orbit the period is 0-97.10~ 14 sec. The average duration of the 
4-quantum state is about 10~ 8 sec. or 10 6 periods. Hence we should expect 
the quantisation in this state to be sharp to about 1 part in a million. 
Roughly speaking the purity of the H p line emitted or absorbed by un 
disturbed atoms should correspond to the purity of the spectrum from a 
grating with a million lines. This can be modified by the disturbance of 
other atoms or electrons in two ways: (1) the average duration of the 
excited state may be shortened by frequent collisions, (2) general irregular 
disturbance may shorten the stretches over which the phase of the 
periodicity is approximately preserved—just as the resolving power of 
the grating is impaired (1) by reducing the number of lines, (2) by ir 
regularity of ruling. Numerical calculation seems to indicate that in 
photospheric conditions the process (2) is the more important. The problem 
has been discussed by Russell and Stewart*. 
Let a be the total number of electrons and (singly charged) ions per 
cu. cm., and let r 0 be a length such that |7ror 0 3 = 1. Then if we draw a 
sphere of radius r 0 round a given atom this sphere will on the average 
contain one disturbing charge. The more distant charges will by their 
imperfect symmetry also produce disturbing fields, but the order of 
magnitude of the resultant field will be not very different from that due 
to the nearest charge. 
For singly ionised material at 10,000° and 10~ 4 atmospheres pressure, 
we have CT =7-4.10 13 , r 0 = 1-48.10“ 5 cm. 
The field due to a charge e at distance r 0 is 
2T8 electrostatic units. 
Since the nearest charge is within r 0 the average disturbing field will be 
larger. Russell and Stewart calculate the average to be 2-7 times larger 
* Astrophys. Journ. 59, p. 197 (1924).