A star begins life with a large proportion of short-lived atoms, and
so at first generates energy furiously. As it ages, the shortest
lived atoms disappear first, and in so doing reduce the average
energy-generation of the star per ton so that, as a star’s weight
decreases, so also must its rate of generation of energy per ton.
Finally all the atoms with much energy-generating capacity have
disappeared, and the star is left, a shrunken and diminished mass of
atoms which have very little capacity for generating radiation.
To put the same thing in another way, the rate at which a star
generates energy per ton is proportional to the death-rate in its
population of atoms. To say that Sirius generates 16 times as much
energy per ton as the sun is only another way of saying that the
average atom in Sirius has only a sixteenth of the expectation of life
of the solar atoms; their death-rate is 16 times as high. As those
types of atoms which have the highest death-rate gradually die off in
any star, the average death-rate of the population decreases, or, in
other words, as a star ages its capacity for energy-generation per ton
decreases.
This agrees with the findings of observational astronomy. The most
massive stars not only generate more energy than less massive stars,
as is in any case to be expected; they also generate enormously
more energy per ton. This is illustrated by the following list of
main-sequence stars:
+-----------------+-----------------+--------------------+
| Star | Weight |Generation of energy|
| |(in terms of sun)| (ergs per gramme) |
+-----------------+-----------------+--------------------+
|Pearce’s Star _A_| 36·3 | 15,000 |
|_V_ Puppis _A_ | 19·2 | 1,000 |
|Sirius _A_ | 2·45 | 29 |
|Sun | 1·00 | 1·90 |
|ε Eridani | (0·45) | 0·26 |
|Kruger 60 _B_ | 0·20 | 0·021 |
+-----------------+-----------------+--------------------+
Seares’ diagram of stellar weights (p. 282) shews that this is a
general property of the stars. To repeat our former metaphor, the
stars squander their substance lavishly in their youth, while they
have plenty left to spend, but parsimony comes over them with old age.
Theoretical considerations have now given us an explanation of this
phenomenon.
Public-domain text, read in full here on John Shaqi.
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