White dwarfs with rapid rotation

A new analytical approach for calculation of white dwarfs characteristics that accounts for two important competing factors — axial rotation and Coulomb interparticle interactions, is proposed.  The feature of our approach is simultaneous usage of differential and integral forms of equilibrium equation.  In dimensionless form the differential equilibrium equation is strongly nonlinear inhomogeneous equation of the second order in partial derivatives with two dimensionless parameters — the relativistic parameter in stellar center $x_0$ and dimensionless angular velocity $\Omega$.  In inner stellar region, rotation is taken into account as perturbation in the linear approximation for $\Omega^2$.  In stellar periphery rotation is considered as the main factor.  Usage of the integral equation provides correct calculations of integration constants.  Dwarf's mass, moment of inertia relative to the axis of rotation, equatorial and polar radii, equatorial gravity in the following parameter space $1\leq x_0\leq24$, $0\leq\Omega<\Omega_{\rm max}(x_0)$ have been calculated based on the solutions of equilibrium equation.  For the first time it was calculated the total energy of dwarf as function of these parameters.  By the extrapolation, it was calculated the maximal values $\Omega_{\rm max}(x_0)$, as well as the observed angular velocity $\omega_{\rm max}(x_0)$.  The considered model is generalized by taking into account Coulomb interparticle interactions.  Also, we provide the examples of application of obtained results.  It was shown that the characteristics of observed massive dwarfs do not contradict the calculated values for the model with consideration of solid body rotation and Coulomb interparticle interactions.

white dwarfs
axial rotation
Coulomb interparticle interactions
mechanical equilibrium equation
обернена задача
  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. Fowler R. H.  On dense matter.  Monthly Notices of the Royal Astronomical Society. 87 (2), 114–122 (1926).
  3. Chandrasekhar S.  The Maximum Mass of Ideal White Dwarfs.  Astrophysical Journal. 74, 81–82 (1931).
  4. Vavrukh M. V., Smerechynskyi S. V.  Hot degenerate dwarfs in a two-phase model.  Astronomy Reports. 57, 913–983 (2013).
  5. Pelisoli I., Marsh T. R., Dhillon V. S., Breedt E., Brown A. J., Dyer M. J., Green M. J., Kerry P;, Littlefair S. P., Parsons S. G., Sahman D. I., Wild J. F.  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).
  6. Lopes de Oliveira R., Bruch A., Rodrigues C. V., Oliveira A. S., Mukai K.  CTCV J2056-3014: An X-Ray-faint Intermediate Polar Harboring an Extremely Fast-spinning White Dwarf.  The Astrophysical Journal Letters. 898 (2), L40 (2020).
  7. Ashley R. P., Marsh T. R., Breedt E., Gänsicke B. T., Pala A. F., Toloza O., Chote P., Thorstensen J. R., Burleigh M. R.  V1460 Her: a fast spinning white dwarf accreting from an evolved donor star.  Monthly Notices of the Royal Astronomical Society. 499 (1), 149–160 (2020).
  8. James R. A.  The Structure and Stability of Rotating Gas Masses.  Astrophysical Journal. 140, 552–582 (1964).
  9. Tassoul J.-L.  Theory of Rotating Stars. (PSA-1), Vol. 1.  Princeton University Press (2016).
  10. Shapiro S. L. Teukolsky S. A.  Black Holes, White Dwarfs, and Neutron Stars: The Physics of Compact Objects.  Wiley, New York (1983).
  11. Vavrukh M. V., Kostrobij P. P., Markovych B. M.  Reference system approach in the theory of many-electrons systems.  Rastr-7, Lviv (2017), (in Ukrainian).
  12. Vavrukh M. V., Dzikovskyi D. V.  Method of integral equations in the polytropic theory of stars with axial rotation.  II. Polytrope with indices $n>1$.  Mathematical Modeling and Computing. 8 (3), 474–485 (2021).
  13. Monaghan J. J., Roxburgh I. W.  The Structure of Rapidly Rotating Polytropes.  Monthly Notices of the Royal Astronomical Society. 131 (1), 13–22 (1965).
  14. Vavrukh M. V., Tyshko N. L., Dzikovskyi D. V.  New approach in the theory of stellar equilibrium with axial rotation.  Journal of Physical Studies. 24 (3), 3902-1–3902-20 (2020).
  15. Vavrukh M. V., Dzikovskyi D. V.  Exact solution for the rotating polytropes with index unity, its approximations and some applications.  Contrib. Astron. Obs. Skalnaté Pleso. 50 (4), 748–771 (2020).
  16. Vavrukh M., Krokhmalskii T.  Reference System Approach in the Electron Liquid Theory. I. General Relations.  Physica Status Solidi (b). 168 (2), 519–532 (1991).
  17. Vavrukh M. V., Krokhmalskii T. E.  Reference System Approach in the Electron Liquid Theory. ІІ. Ground State Characteristics in the Medium Density Region. Physica Status Solidi (b). 169 (2), 451–462 (1992).
  18. Vavrukh M., Dzikovskyi D., Solovyan V., Tyshko N.  Correlation functions of the degenerate relativistic electron gas with high density.  Mathematical Modeling and Computing. 3 (1), 97–110 (2016).
  19. Pines D., Nozières P.  The Theory of Quantum Liquids: Normal Fermi Liquids. CRC Press (1966).
  20. Fuchs K.  A quantum mechanical investigation of the cohesive forces of metallic copper.  Proceedings of the Royal Society of London. Series A – Mathematical and Physical Sciences. 151 (874), 585–602 (1935).
  21. Carr W. J.  Energy, Specific Heat, and Magnetic Properties of the Low-Density Electron Gas.  Physical Review. 122 (5), 1437–1446 (1961).
  22. Vavrukh M. V., Smerechynskyi S. V., Tyshko N. L.  New models in the theory of white dwarfs structure. Rastr-7, Lviv (2018).
  23. Ceperley D. M., Alder B. J.  Ground State of the Electron Gas by a Stochastic Method.  Physical Review Letters. 45 (7), 566–569 (1980).
  24. Salpeter E. E.  Energy and Pressure of a Zero-Temperature Plasma.  Astrophysical Journal. 134, 669–682 (1961).
  25. Davydov A. C.  Quantum mechanics.  Nauka, Moscow (1973).
  26. Bond H. E., Schaefer G. H., Gilliland R. L., Holberg J. B., Mason B. D., Lindenblad I. W., Seitz-McLeese M., David A. W., Demarque Pi., Spada F., Young P. A., Barstow M. A., Burleigh M. R., Gudehus D.  The Sirius System and Its Astrophysical Puzzles: Hubble Space Telescope and Ground-based Astrometry.  The Astrophysical Journal. 840 (2), 70 (2017).
  27. Kong D., Zhang K., Schubert G.  An exact solution for arbitrarily rotating gaseous polytropes with index unity.  Monthly Notices of the Royal Astronomical Society. 448 (1), 456–463 (2015).
  28. Knopik J., Mach P., Odrzywołek A.  The shape of a rapidly rotating polytrope with index unity.  Monthly Notices of the Royal Astronomical Society. 467 (4), 4965–4969 (2017).
  29. Tricomi F. G.  Integral Equations. Dover Publications (1985).