348
THE OUTSIDE OF A STAR
The number of atoms in a state to absorb a given line varies with
temperature and density. Fowler and Milne take as their two variables
the temperature T and the electron pressure P e ; the latter is presumably
about half the total gas pressure since we may expect about 1 free electron
per atom in photospheric conditions*. Keeping P e fixed we can trace how
the proportion of atoms in the required state changes with T, and deter
mine the temperature for which it is a maximum. If P e is rightly chosen
this should be the temperature at which the line reaches maximum in
tensity, and the spectral class of observed maximum intensity can thus
be correlated with temperature. Conversely if we know the temperatures
of the different spectral classes we can determine the value of P e for the
reversing layer.
The formulae for determining the number of atoms in a given state of
ionisation when the electron density is given have been developed in § 47;
the proportion of these in any given excited state is also known by Boltz
mann’s formula. By differentiating with respect to T the temperature of
maximum abundance of the given state can be found. We do not give the
formulae here explicitly, since for practical computation simplifications
appropriate to the particular conditions considered are introduced, and
we are not here concerned with the technique of practical computation^.
The following examples are taken from Fowler and Milne’s calculations—
(1) H. Balmer Series. Maximum in type A 0 = 10,500° on temperature
scale usually adopted. Temperatures of maximum abundance of hydrogen
atoms in a state to absorb the Balmer series are—
P e = 1-3.10- 4 atmos., T = 10,000°,
P e = 7-2.10- 4 , T= 11,000,
P e = 3-1.10- 3 , T = 12,000.
(2) Mg + . A4481. Maximum in type A 0 = 10,500°—
P e = 0-8.10~ 4 , T = 10,000,
P e = 5-2.10~ 4 , T = 11,000,
P e =M.10~ 3 , T = 12,000.
(3) Mg. A5711, 5528, 4703, 4352. Maximum “between sun and sun
spot” = 5500°—
P e = 2-4.10- 5 , T = 5,000,
P e =l-6.10- 4 , T = 5,500,
P e = 7-8.10“ 4 , T= 6,000.
(4) Ca + . H and K lines. Maximum in type K 0 = 4300°—
P e = 9*9.10~ 7 , T = 5,000,
P e = 5-0.10~ 5 , T = 6,000.
* Some elements will not be ionised, others may be doubly ionised.
f Reference may be made to Fowler and Milne, Monthly Notices, 83, pp. 408—410.
