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

G.S.Bisnovatyi-Kogan

Space Research Institute RAN, Moscow

Joint Institute of Nuclear Researches, Dubna1. History2. Stability criteria3. Critical states of stars: loss of dynamic stability4. Quark stars: can they exist?5. Non-equilibrium layer in the neutron star crust6. Neutron star cooling, glitches, and explosions7. Non-equilibrium matter heating in weak interactions

VIII  Winter School on Theoretical Physics

FROM NUCLEAR PHYSICS TO ASTROPHYSICS AND COSMOLOGY31 January - 7 February, 2010,  Dubna, Russia

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, 374On 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.

Harrison, K. Thorne, Vacano, J.A.Wheeler, 1965,Gravitational Theory and Gravitational Collapse.

N.A. Dmitriyev and S.A. Kholin,

“Features of static solutions of the gravity equations”

Problems of cosmogony (1963), 9, 254-262 (in Russian);

At incresing density each extremum add one unstable mode:

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, 761Critical parameters of stars.- Dynamic instability of presupernovae

neutronizationIron dissociation

Pair creation

g/cm^3

GR

Stability of hot neutron stars:G.S.Bisnovatyi-Kogan (1968),

Astrofizika, 4, 221.The mass limit of hot superdense

stable configurations

Mass of the hot “neutron” stardoes not exceed 70 Solar mass.

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

Schematic cross section of a neutron star.

J. Drake et al., astro-ph/02-04-159

The conclusion is not reliable: effective temperature may belower than spectral value, what leads to larger radius.

Astro-ph/0305-249

Astro-ph/02-09-257

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.

Neutron star crust

Compression of cold matter during accretion

Cooling of hot dense matter (new born neutron star)

=2 10^29 g=10^-4 M Sun

Nonequilibrium layer of maximal mass

Luminosity of a single neutron star

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.

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.

HEATING inNON-EQUILIBRIUM BETA

CAPTURES

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B.-K., Seidov, 1970

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

B.-K., Seidov, 1970

K. Nakazawa et al., 1970

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-KoganThe 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.

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.

Conclusions.

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).