Stability of compact stars (white dwarfs and neutron stars) .

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Stability of compact stars (white dwarfs and
neutron stars) .
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
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Chandrasekhar, 1931, ApJ, 74, 81
Yerevan03
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L.D.Landau, Phys. Zeit. Sov., 1932, 1, 285 On
the theory of stars.
Molecular weight2, M1.4 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.
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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
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Ideal Fermi gas of neutrons
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MASS - Total
Radius
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J.A. Wheeler, 1958. Paper read at Solway
Conference
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A.G.V. Cameron, 1959, ApJ, 130, 884
Equation of state of nonideal matter
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Cameron, 1959
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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.
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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.
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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) gtgt t(dyn).
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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.
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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.
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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
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Isentropic stars. For stars with large
isothermal core the critical mass for
pair-creation pre-SN is smaller, may be less that
100 solar mass
g/cm3
neutronization
Iron dissociation
Stability of hot neutron stars G.S.Bisnovatyi-Kog
an (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.
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Schematic cross section of a neutron star.
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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.
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Astro-ph/0305-249
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Astro-ph/02-09-257
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Neutron stars and quark matter Gordon Baym
Nucl-th/0612021
Recent observations of neutron star masses close
to the maximum predicted by nucleonic equations
of state begin to challenge our understanding of
dense matter in neutron stars, and constrain the
possible presence of quark matter in their deep
interiors.
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Neutron star crust
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Compression of cold matter during accretion
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Cooling of hot dense matter (new born neutron
star)
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Nonequilibrium layer of maximal mass
2 1029 g10-4 M Sun
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Luminosity of a single neutron star
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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 ?lt
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.
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The Astrophysical Journal, 501L89L93, 1998 July
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GRAVITATIONAL RADIATION AND ROTATION OF ACCRETING
NEUTRON STARS Lars Bildsten
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Fig. 1.Density, pressure, and nuclear abundance
in the Ca56 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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HEATING in NON-EQUILIBRIUM BETA CAPTURES
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B.-K., Seidov, 1970
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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)
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Matter is always heated during collapse
B.-K., Seidov, 1970
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K. Nakazawa et al., 1970
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3.70 MeV, 1.61 MeV
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Urca shell layer inside the star, where
e(Fermi)delta Tsuruta S., Cameron A. G. W.,
1970, ApSS, 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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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
low-amplitude 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 short-wavelength
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.
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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).