The Theory of Hot White Dwarfs Based on a Two-Component Equation of State

A variant of the theory of hot white dwarfs of small and intermediate masses is proposed using a model with a partially degenerate ideal relativistic electron gas and an ideal classical nuclear gas.  By modeling the radial temperature distribution, a reduced three-parameter equation of state was obtained as a function of matter density.  Based on numerically obtained solutions of the equilibrium equation, the characteristics of white dwarfs were determined as functions of the model parameters.  The inverse problem was solved – the values of the model parameters were calculated for a group of observed white dwarfs with effective temperatures $T_{\rm eff} \leq 8.8\cdot 10^4\,K$.

  1. Adams W. S.  The Spectrum of the Companion of Sirius.  Publications of the Astronomical Society of the Pacific.  27 (161), 236–237 (1915).
  2. Bond H. E., Schaefer G. H., Gilliland R. L., et al.  The Sirius System and Its Astrophysical Puzzles: Hubble Space Telescope and Ground-based Astrometry.  The Astrophysical Journal.  840 (2), 70 (2017).
  3. Pelisoli I., Marsh T. R., Dhillon V. S., et al.  Found: a rapidly spinning white dwarf in LAMOST J024048.51+195226.9.  Monthly Notices of the Royal Astronomical Society: Letters.  509 (1), L31–L36 (2022).
  4. Bédard A., Bergeron P., Brassard P., Fontaine G.  On the Spectral Evolution of Hot White Dwarf Stars. I.~A Detailed Model Atmosphere Analysis of Hot White Dwarfs from SDSS DR12.  The Astrophysical Journal.  901 (2), 93 (2020).
  5. Tremblay P.-E., Bergeron P., Gianninas A.  An Improved Spectroscopic Analysis of DA White Dwarfs from the Sloan Digital Sky Survey Data Release 4.  The Astrophysical Journal.  730 (2), 128 (2011).
  6. Fowler R. H.  On dense matter.  Monthly Notices of the Royal Astronomical Society.  87 (2), 114–122 (1926).
  7. Chandrasekhar S.  The Maximum Mass of Ideal White Dwarfs.  Astrophysical Journal.  74, 81–82 (1931).
  8. Kaplan S. A.  Cooling of white dwarfs.  Astron. Zhurn.  27 (1), 31–33 (1950).
  9. Schatzman E.  Analyse du diagramme de Hertzsprung–Russell dans la région des naines blanches  (complément à la théorie du débit d'énergie des naines blanches).  Annales d'Astrophysique.  10, 19–28 (1947).
  10. Bisnovatyi-Kogan G. S.  The Critical Mass of a Hot Isothermal White Dwarf with General Relativistic Effects Taken into Account.  Soviet Astronomy.  10, 69–74 (1966).
  11. Vavrukh M. V., Smerechynskyi S. V.  A finite temperature Chandrasekhar model: Determining the parameters and calculation of the characteristics of degenerate dwarfs.  Astronomy Reports.  56 (5), 363–378 (2012).
  12. Sommerfeld A.  Zur Elektronentheorie der Metalle auf Grund der Fermischen Statistik.  Zeitschrift für Physik.  47, 1–32 (1928).