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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
Chandrasekhar, 1931, ApJ, 74, 81
Yerevan03
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.
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:
Ideal Fermi gas of neutrons
MASS - Total
Radius
J.A. Wheeler, 1958. Paper read at Solway Conference
A.G.V. Cameron, 1959, ApJ, 130, 884
Equation of state
of nonideal matter
Cameron,
1959
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.
Criteria of hydrodynamic stability
1. 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.
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).
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.
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.
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
g/cm^3
Stability of hot neutron stars:
G.S.Bisnovatyi-Kogan (1968),
Astrofizika, 4, 221.
The mass limit of hot superdense
stable configurations
neutronization
Iron dissociation
Pair creation
GR
Mass of the hot “neutron” star
does not exceed 70 Solar mass.
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.
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.
Astro-ph/0305-249
Astro-ph/02-09-257
Neutron star crust
Compression of cold matter during accretion
Cooling of hot dense matter (new born neutron star)
Nonequilibrium layer of maximal mass
=2 10^29 g=10^-4 M Sun
Progress of Theoretical Physics
Vol. 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.
The Astrophysical Journal, 501:L89–L93, 1998 July 1
GRAVITATIONAL RADIATION AND ROTATION OF
ACCRETING NEUTRON STARS
Lars Bildsten
Fig. 1.—Density, pressure, and nuclear
abundance in the Ca^56 electron capture
layer for a R = 10 km, M = 1.4 M Sun.
NS accreting at d M/dt = 2 10^-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 hotter crusts deplete sooner. The
curves are, from left to right, for T 5 6, 4,
and 2.
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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
3.70 MeV,
1.61 MeV
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
Mon. Not. R. Astron. Soc. 321, 315-326
(2001)
Stellar oscillations and stellar convection in the presence of
an Urca shell
G. S. Bisnovatyi-Kogan
The problem of damping of stellar oscillations in presence of a Urca shell is
solved analytically in a plane symmetrical approximation. Low-amplitude
oscillations are considered. Oscillatory pressure perturbations induce beta
reactions of the electron capture and decay in the thin layer around the Urca
shell, leading to damping of oscillations. Owing to the non-linear dependence of
beta reaction rates on the pulsation amplitude in degeneratematter, even a lowamplitude oscillation damping follows a power law. It is shown that in the
presence of the Urca shell the energy losses owing to neutrino emission and the
entropy increase resulting from non-equilibrium beta reactions are much smaller
than the rate of decrease of the energy of pulsations by the excitation of shortwavelength acoustic waves. The dissipation of the vibrational energy by the last
process is the main source of heating of matter.Convective motion in the
presence of an Urca shell is considered, and equations generalizing the mean
free path model of the convection are derived.
Conclusions.
1. Existence of quark (strange) stars is possible
only
if they are stable: it depends on the equation of
state of quark (strange) matter
2. Until now there are no observational
contradictions to the
conventional neutron star model.
3. Nonequilibrium layer is formed in the neutron star crust,
during NS cooling, or during accretion onto it .
It may be important for NS cooling, glitches, and explosions.
4. Nonequilibrium electron capture is important for
matter heating in white dwarfs, SN explosions, and in
pulsations of dense stars (Urca shells).