Energy Production in Stars

It is shown that the most important source of energy in ordinary stars is the reactions of carbon and nitrogen with protons. These reactions form a cycle in which the original nucleus is reproduced, viz. ${\mathrm{C}}^{12}$+H=${\mathrm{N}}^{13}$, ${\mathrm{N}}^{13}={\mathrm{C}}^{13}+{\epsilon }^{+}$, ${\mathrm{C}}^{13}$+H=${\mathrm{N}}^{14}$, ${\mathrm{N}}^{14}$+H=${\mathrm{O}}^{15}$, ${\mathrm{O}}^{15}={\mathrm{N}}^{15}+{\epsilon }^{+}$, ${\mathrm{N}}^{15}$+H=${\mathrm{C}}^{12}$ +${\mathrm{He}}^4$. Thus carbon and nitrogen merely serve as catalysts for the combination of four protons (and two electrons) into an $\alpha$-particle (§7).

The carbon-nitrogen reactions are unique in their cyclical character (§8). For all nuclei lighter than carbon, reaction with protons will lead to the emission of an $\alpha$-particle so that the original nucleus is permanently destroyed. For all nuclei heavier than fluorine, only radiative capture of the protons occurs, also destroying the original nucleus. Oxygen and fluorine reactions mostly lead back to nitrogen. Besides, these heavier nuclei react much more slowly than C and N and are therefore unimportant for the energy production.

The agreement of the carbon-nitrogen reactions with observational data (§7, 9) is excellent. In order to give the correct energy evolution in the sun, the central temperature of the sun would have to be 18.5 million degrees while integration of the Eddington equations gives 19. For the brilliant star Y Cygni the corresponding figures are 30 and 32. This good agreement holds for all bright stars of the main sequence, but, of course, not for giants.

For fainter stars, with lower central temperatures, the reaction $\mathrm{H}+\mathrm{H}=\mathrm{D}+{\epsilon }^{+}$ and the reactions following it, are believed to be mainly responsible for the energy production. (§10)

It is shown further (§5-6) that no elements heavier than ${\mathrm{He}}^4$ can be built up in ordinary stars. This is due to the fact, mentioned above, that all elements up to boron are disintegrated by proton bombardment ($\alpha$-emission!) rather than built up (by radiative capture). The instability of ${\mathrm{Be}}^8$ reduces the formation of heavier elements still further. The production of neutrons in stars is likewise negligible. The heavier elements found in stars must therefore have existed already when the star was formed.

Finally, the suggested mechanism of energy production is used to draw conclusions about astrophysical problems, such as the mass-luminosity relation (§10), the stability against temperature changes (§11), and stellar evolution (§12).