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Dynamic stability of compact stars. Properties of the neutron star crust .

Dynamic stability of compact stars. Properties of the neutron star crust. G.S.Bisnovatyi-Kogan Space Research Institute RAN, Moscow Joint Institute of Nuclear Researches, Dubna. 1. History 2. Stability criteria 3. Critical states of stars: loss of dynamic stability

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Dynamic stability of compact stars. Properties of the neutron star crust .

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  1. Dynamic stability of compact stars. Properties of the neutron star crust. G.S.Bisnovatyi-Kogan Space Research Institute RAN, Moscow Joint Institute of Nuclear Researches, Dubna 1. History 2. Stability criteria 3. Critical states of stars: loss of dynamic stability 4. Quark stars: can they exist? 5. Non-equilibrium layer in the neutron star crust 6. Neutron star cooling, glitches, and explosions 7. Non-equilibrium matter heating in weak interactions Dubna, August 22, 2006

  2. Chandrasekhar, 1931, ApJ, 74, 81 Yerevan03

  3. L.D.Landau, Phys. Zeit. Sov., 1932, 1, 285 On the theory of stars. Molecular weight=2, M=1.4 Solar masses (accepted value). Neuron discovery (Chadwick, 24 Feb. 1932, letter to Bohr), “Landau improvised the concept of neutron stars” in discussion with Bohr W.Baade and F.Zwicky, Phys.Rev., 1934, 45, 138 (Jan. 15) Hund (1936), Landau (1937), Gamow (1937): stability of neutron state of matter at high densities.

  4. J.Oppenheimer and G.Volkoff, Phys. Rev., 1939, 55, 374 On Massive Neutron Cores First calculations of neutron star equilibrium in GR. Oppenheimer-Volkov equilibrium equation in GR, spherical symmetry:

  5. Ideal Fermi gas of neutrons

  6. MASS - Total Radius

  7. J.A. Wheeler, 1958. Paper read at Solway Conference

  8. A.G.V. Cameron, 1959, ApJ, 130, 884 Equation of state of nonideal matter

  9. Cameron, 1959

  10. Correct neutron star models at large densities: Relativistic Oscillations of M(rho) V.A.Ambartsumian and G.S.Saakian, 1961, Astron.Zh., 38, 1016; G.S.Saakian, Yu.L.Vartanian, 1964, Astron.Zh., 41, 193. At incresing density each extremum add one unstable mode: N.A. Dmitriyev and S.A. Kholin, “Features of static solutions of the gravity equations” Problems of cosmogony (1963), 9, 254-262 (in Russian); Harrison, K. Thorne, Vacano, J.A.Wheeler, 1965, Gravitational Theory and Gravitational Collapse.

  11. Criteria of hydrodynamic stability • Finding of proper frequencies from perturbation equations • 2. Variational principle (Chandrasekhar, 1964) • 3. Static criteria of stability • Ya.B. Zeldovich,Problems of cosmogony (1963), 9, 157-175 (in Russian). New unstable mode appears or disappears in the extremum.

  12. Point of loss of stability is after the maximum of the curve (A) of rigidly rotating stars (intersection of the curve D) Thermodynamic stability, in presence of transport properties, corresponds to mass maximum of rigidly rotating star, t(th) >> t(dyn).

  13. Static criteria with account of phase transition: G.S.Bisnovatyi-Kogan, S.I. Blinnikov, E.E.Shnol, 1975, Astron.Zh. 52, 920.Stability of stars in presence of a phase transition.

  14. 4. Energetic method. Static criteria is hard to apply for complicated equation of state, and entropy distribution over the star. Energetic method follows from the exact variation principle for linear trial function: Ya.B. Zeldovich and I.D. Novikov (1965), UFN, 86, 447. Relativistic Astrophysics II. – For isentropic stars. G.S.Bisnovatyi-Kogan (1966), Astron. Zh. 43, 89. Critical mass of hot isothermal white dwarf with the inclusion of general relativistic effects.- Equations for equilibrium and stability for arbitrary distribution of parameters over the star.

  15. Equilibrium equation: Condition of loss of stability: G.S.Bisnovatyi-Kogan and Ya.M.Kazhdan (1966), Astron.Zh.43, 761 Critical parameters of stars.- Dynamic instability of presupernovae

  16. g/cm^3 neutronization Iron dissociation Stability of hot neutron stars: G.S.Bisnovatyi-Kogan (1968), Astrofizika, 4, 221. The mass limit of hot superdense stable configurations Pair creation GR Mass of the hot “neutron” star does not exceed 70 Solar mass.

  17. Energetic method for rapidly rotating relativistic stars (isentropic supermassive stars) Two GR correction terms (Rg/R):Yu.L.Vartanian (1972), Diss. For nonrotating stars. Two GR corrections for rigidly rotating stars with arbitrary angular velocity.

  18. J. Drake et al., astro-ph/02-04-159 The conclusion is not reliable: effective temperature may be lower than spectral value, what leads to larger radius.

  19. Astro-ph/0305-249

  20. Astro-ph/02-09-257

  21. Neutron star crust

  22. Compression of cold matter during accretion

  23. Cooling of hot dense matter (new born neutron star)

  24. Nonequilibrium layer of maximal mass =2 10^29 g=10^-4 M Sun

  25. Progress of Theoretical PhysicsVol. 62 No. 4 pp. 957-968 (1979) Nuclear Compositions in the Inner Crust of Neutron Stars Katsuhiko Sato Department of Physics, Kyoto University, Kyoto 606 (Received February 26, 1979) It is likely that matter in a neutron star crust is compressed by accreting matter and/or by the slowingdown of its rotation after the freezing of thermonuclear equilibrium. The change of nuclear compositions, which takes place during the compression, has been investigated. If the initial species of nuclei is 56Fe, the charge and the mass number of nuclei decrease as a result of repeated electron caputures and successive neutron emissions in the initial stage of compression. The nuclear charge and mass are then doubled by pycnonuclear reactions. The final values of the charge numbers of the nuclei in the inner crust at densities ρ< 1013.7g/cm3 are less than 25, which are about one third of those for the conventional cold catalyzed matter. This result reduces the shear modulus of the crust to one half of the conventional value which makes the magnitude of star quakes weaker.

  26. The Astrophysical Journal, 501:L89–L93, 1998 July 1 GRAVITATIONAL RADIATION AND ROTATION OF ACCRETING NEUTRON STARS Lars Bildsten

  27. Fig.1.—Density, pressure, and nuclear abundance in the Ca^56 electron capturelayer for a R =10 km,M =1.4 M Sun. NS accreting at d M/dt =210^-9 M Sun/yr. These are plotted as a function of increasing depth into the star; deeper regions are to the right. For a fixed value of ft, the hottercrustsdeplete sooner. The curves are, from left to right, for T 5 6, 4, and 2.

  28. ---------------------------------------------------------------------------------------------------------------------------------------------------------- ------------------------------------------------------------------------

  29. Progress of Theoretical Physics, Vol. 44 No. 3 pp. 829-830 Effect of Electron Capture on the Temperature in Dense Stars Kiyoshi Nakazawa, Tadayuki Murai,* Reiun Hoshi and Chushiro Hayashi Department of Physics, Kyoto University, Kyoto *Department of Physics, Nagoya University, Nagoya (Received July 6, 1970) Matter is always heated during collapse

  30. 3.70 MeV, 1.61 MeV

  31. Urca shell – layer inside the star, where e(Fermi)=delta Tsuruta S., Cameron A. G. W., 1970, Ap&SS, 7, 374 Convection around Urca shell leads to additional cooling of the star due to Urca neutrino emission. Nonequilibrium heating may lead to opposite result: additional heating instead of cooling Paczynski B., 1972, Astrophys. Lett., 11, 47 Paczynski B., 1974, Astrophys. Lett., 15, 147

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