The Internal Temperature of White Dwarf Stars.

Abstract

view Abstract Citations (33) References Co-Reads Similar Papers Volume Content Graphics Metrics Export Citation NASA/ADS The Internal Temperature of White Dwarf Stars. Marshak, R. E. Abstract The state of matter in the interior of a white dwarf star is investigated in detail. The main part of this paper is concerned with the calculation of the temperature distribution i~i the interibr. For this purpose accurate expressions for the radiative and conductive opacity are derived, both for the nondegenerate envelope and the degenerate core of the stars. It is shown that the energy transport is chiefly by radiation in the envelope and by electronic conduction in the core. Furthermore, the free electron density is investi- gated, and it is found that in the transition region between degeneracy and nonde- generacy the atoms are only partially ionized, whereas both in the envelope and in the core the ionization is almost complete (in the envelope, temperature ionization; in the core, pressure ionization). Quantitative calculations are performed for the two well-known white dwarfs, Sirius B and 4o Eridani B; of the two the observational material is better for Sirius B, so that most attention is paid to this star. The extension of the nondegenerate envelope and the internal temperature are calculated for several widely different assumptions regard- ing the chemical composition of the star as well as possible errors in the observed luminosity L and the radius R. The depth/i of the envelope of Sirius B is about 6 * cm, when the observed values of R, L and mass M are used and the star is assumed to consist exclusively of "Russell mixture." For a pure helium star h is even smaller, and, if the theoretical value for the radius is assumed, h is only 8 106 cm. Thus, the envelope constitutes only a very small fraction of the total radius of the star (~ io9 cm). The central temperature T~ of Sirius B is 15,000,0000 for pure Russell mixture and is almost independent of the assumed radius; moreover, the degenerate core is practical- ly isothermal. At this temperature and at the high densities of ~ to 3 io7 gm/cm3 which prevail in the core, nuclear reactions between protons and other nuclei would go at a very rapid rate. Since the observed luminosity is very small, we must conclude that no appreciable number of protons is present inside of white dwarfs. If Sirius B contains carbon and nitrogen in the same abundance as do main-sequence stars, the hydrogen * The major part of this work was done while the author was President White Fel- low at Cornell TJniversity; preliminary results were reported with H. A. Bethe to the American Physical Society (cf. Phys. Rev., 55, 68i, 1939, and 57, 69, 1940). 32 Publication: The Astrophysical Journal Pub Date: November 1940 DOI: 10.1086/144225 Bibcode: 1940ApJ....92..321M full text sources ADS |