Atomic Synthesis and Stellar Energy

Abstract

view Abstract Citations (18) References Co-Reads Similar Papers Volume Content Graphics Metrics Export Citation NASA/ADS Atomic Synthesis and Stellar Energy Atkinson, R. d'Escourt Abstract A synthesis theory of stellar energy and of the origin of the elements is developed, in which the various chemical elements are built up step by step from lighter ones in stellar interiors, by the successive incorporation of protons and electrons one at a time. The essential feature is that helium, which cannot well be formed in this way, is sup- posed to be produced entirely indirectly, by the spontaneous disintegration of unstable nuclei which must first themselves be formed. A formula for the probability of penetration of nuclei by protons is derived from the wave-mechanics; it is a correction of one previously given, but agrees with that in show- ing that with any approach at all to the observed absolute amounts of the lighter ele- ments very high temperatures in normal stellar interiors are impossible. The model must be approximately that of Eddingion, but with Jeans's modification to take account of Kramers' formula for the absorption coefficient. Russell's value for the hydrogen con- tent reconciles this formula with astrophysical data. The low temperature and the relative amounts of the heavier elements make a second synthesis process for protons unavoidable; this is assumed to exist, and to possess arbitrary but extremely simple properties with no special features at any particular element. The possibility of incorporation of electrons, when "room" has become avail- able, is taken for granted. The elements whose disintegration supplies helium are in all cases either those known (or strongly suspected) to be unstable, or those isotopes, unknown now, whose instability follows from Gamow's theory of mass defects. The rate of formation of helium must be nearly constant, in any one star, throughout most of its lifetime. The law of mass action demands then that all stars, after a marked initial contraction and rebound, should spend the greater part of their lives very slowly expanding. The constancy of the helium supply can be guaranteed, in the main se- quence, if the average life of oxygen, until further synthesis, is about equal to the past lifetime of the star. This leads to central temperatures which can be calculated for the L. sun and estimated for other stars. The figure for the sun is ió,ooo,ooo°, which is in good agreement with that calculated for a polytrope of index about 3 and constitution somewhat over 50 per cent hydrogen. The increase necessary for heavier stars can be covered by a small systematic change in the polytropic index. The main sequence is thus accounted for. The relative proportions of the elements in stars of the main sequence follow from the theory, in excellent qualitative agreement with Russell's figures for the sun. The scarcity of the lightest elements, the principal maximum at a fairly early point, a minimum before the iron group, a maximum in it, a scarcity. of all elements above it, and minor maxima in the barium and lead regions all follow (Fig. 2) without any special assump- tions, from Gamow's theory of nuclear stability, owing to the peculiarities of the Aston mass-defect curve. For the low-density giants some earlier source of helium must be operative. This is taken to be Be8, whose instability was already assumed by F. G. Houtermans and the writer, and has since acquired almost the status of observational fact. It must be long- lived, since it is found on the earth, and this accounts for the Hertzsprung gap and its continuation between the Cepheids and B stars, and for the fact that Be8 cannot supply helium in the main sequence. In giants it can supply enough helium, and even the brightest red supergiants can exist on the He-Li synthesis given by the wave- mechanics alone, with central temperatures as low as 4,000,0000. This figure can be reached on Eddington's theory by a systematic change in the polytropic index which is considerable but not prohibitive. 25 Publication: The Astrophysical Journal Pub Date: May 1931 DOI: 10.1086/143307 Bibcode: 1931ApJ....73..250A full text sources ADS | Related Materials (2) Part 2: 1931ApJ....73..308A Part 3: 1936ApJ....84...73A