Neutron Stars 1: Equation of State and Structure / Edition 1

Neutron Stars 1: Equation of State and Structure / Edition 1

by P. Haensel, A.Y. Potekhin, D.G. Yakovlev

ISBN-10: 0387335439

ISBN-13: 9780387335438

Pub. Date: 11/03/2006

Publisher: Springer New York

With masses comparable to that of the Sun and radii of about only ten kilometers, neutron stars are the most compact stars in the Universe. They offer a unique possibility of revealing the properties of superdense matter through a comparison of theoretical models to observations. This book describes all layers of neutron stars with the emphasis on their thermodynamics


With masses comparable to that of the Sun and radii of about only ten kilometers, neutron stars are the most compact stars in the Universe. They offer a unique possibility of revealing the properties of superdense matter through a comparison of theoretical models to observations. This book describes all layers of neutron stars with the emphasis on their thermodynamics and composition. Theories of dense matter are reviewed and used to construct neutron star models. Separate chapters are devoted to hypothetical strange quark stars and exotic phases of dense matter in neutron star cores. The effects of strong magnetic fields in neutron star envelopes are discussed and the final chapter compares neutron star models to observations.

Product Details

Springer New York
Publication date:
Astrophysics and Space Science Library Series, #326
Edition description:
Product dimensions:
9.21(w) x 6.14(h) x 1.38(d)

Table of Contents

List of Figures     xiii
List of Tables     xix
Introduction     xxi
Overview     1
Neutron stars     1
History: from prediction to discovery     2
Internal structure and processes - Theoretical outlook     11
Structure     11
The main mystery: The equation of state in neutron star cores     14
Neutron star models     16
Superfluidity     17
Neutrino processes     19
Thermodynamics and kinetics     21
Cooling of neutron stars     25
Magnetic fields     26
Seismology     28
Observations versus theory     28
Telescopes     28
Birth in supernova explosions. Supernova connection     31
Evolutionary scenarios: Three driving forces     34
Pulsars     34
Isolated neutron stars     41
Neutron stars in binary systems - X-ray binaries     44
Neutron stars in the Galaxy     49
Neutron stars as "superstars" in physics and astrophysics     50
About the rest of this book     51
Equilibrium Plasma Properties. Outer Envelopes     53
Plasma parameters     55
Overall parameters     55
Electrons     56
Ions     60
Free energy and thermodynamic quantities     63
Fully ionized dense plasma. The basic decomposition     65
Fully ionized plasma without electron correlations     66
Ideal electron gas. Fermi-Dirac integrals     67
Coulomb liquid of ions     72
Coulomb crystal     77
Melting     88
The pressure of degenerate electrons with electrostatic corrections     90
Intermediate-density regime. Electron response     91
Interpolation     91
Thomas-Fermi-like theories     92
Electron exchange and correlation effects     93
Electron polarization in ion liquid     96
Electron polarization in ion solid     99
The heat capacity     103
Multi-ionic mixtures     106
Low densities. Partial ionization     107
Ionization equilibria in the "chemical picture"     107
An example: Partially ionized hydrogen plasma     111
Structure and EOS of Neutron Star Crusts     115
The formation of the crust in a newly born neutron star     116
Ground state of the outer crust      118
Ground state of the inner crust at p [GreaterTilde] 10[superscript 14] g cm[superscript -3]     125
Hartree-Fock calculations     126
Extended Thomas-Fermi (ETF) calculations     130
Compressible liquid drop model (CLDM)     133
Ground state of the bottom layers of the crust     140
The bulk approximation     140
Unusual nuclear shapes     142
Quantum corrections to the CLDM energy     147
Reaching the crust-core interface from the core side     148
The equation of state of the neutron star crust     150
Elastic properties of neutron star crust     153
From bcc lattice to isotropic solid     156
Exotic nuclei     159
Deviations from an idealized ground state model     161
Crust formation in a newly-born neutron star     162
Accreted crust     164
Envelopes with Strong Magnetic Fields     167
Fully ionized plasmas     168
Free electron in a magnetic field     168
Thermodynamic functions of the ideal electron gas     170
Magnetic oscillations     175
The effects of the magnetic field on plasma ions     176
Weakly non-ideal Coulomb plasma     178
Strongly coupled Coulomb plasma     180
Bound species in strong magnetic fields     184
Atoms     184
Molecules and chains     188
Effects of motion     190
Magnetic condensation     192
Models of strongly magnetized outer envelopes of neutron stars     193
Strongly magnetized iron envelopes     194
Strongly magnetized hydrogen atmosphere     196
Neutron Star Cores: Nucleons and Hyperons     207
Introduction     207
Before the discovery of pulsars: 1932-1967     208
After the discovery of pulsars: 1968-2005     213
Nucleons     213
Nucleons and hyperons     215
The properties of nuclear matter     217
The Hamiltonian     221
Phenomenological nucleon-nucleon interaction     221
Three-body interaction     223
Relativistic corrections and three-body interaction     225
Meson-exchange nucleon-nucleon interaction     226
Three-and more-nucleon interactions     230
The hyperon interactions     231
Solving the many-body problem - an overview     233
Energy of nucleon matter     235
Brueckner-Bethe-Goldstone (BEG) theory      235
Green's Function Theory     240
Variational method     243
Relativistic mean-field model     246
Effective energy density functionals     253
Energy of hyperon-nucleon matter     254
Brueckner-Bethe-Goldstone theory     254
Relativistic mean-field model     256
The equation of state of the outer core     257
Calculating the equation of state     257
The nuclear symmetry energy and the proton fraction     259
Equation of state and composition     260
Inner core: minimal model - nucleons and leptons     263
Equation of state of the [Mu] matter     263
Proton fraction and direct Urca threshold     265
Adiabatic index     266
Hyperons in the inner core     267
Hyperonic composition     268
Hyperon softening of equation of state     273
Superluminal and ultrabaric equations of state     275
Effect of baryon superfluidity on equation of state     279
Effect of strong magnetic field on equation of state     279
Neutron Star Structure     281
Equations of hydrostatic equilibrium     281
Baryon number, mass and chemical potential. Binding energy of neutron stars     284
Proper mass and gravitational energy     287
Constructing neutron star models     287
Introductory remarks     287
Equation of state     289
Masses and stability of neutron stars     290
Stellar oscillations and stability     290
Stability criteria based on the mass-radius diagram     293
Neutron stars and white dwarfs     294
A variety of neutron star models     296
Maximum masses of neutron stars     297
The nature of the maximum mass of neutron stars     298
The upper bound on the maximum mass     301
Low-mass neutron stars and the minimum mass     302
Radii and surface redshifts     303
Circumferential radii     304
Radii of low-mass neutron stars     306
Gravitational redshifts     308
The upper bound on gravitational redshift and the lower bound on neutron star radius     308
The upper bound on surface gravity     309
Apparent radii     311
Binding energy     313
Approximate formulae     315
Neutron star models with M [TildeTilde] M[subscript min]     317
Basic internal structure of neutron stars      318
Universal structure of the outer envelope     319
The structure of magnetic envelopes     322
Moment of inertia for slow rigid rotation     323
Dragging of local inertial reference frames and moment of inertia     323
Moment of inertia versus M     324
Crustal moment of inertia     326
Moment of inertia versus M and R     326
Approximate formula for I[subscript max]     328
Elastic shear strain, non-axial deformations, and gravitational radiation     328
Elastic strain and neutron stars with M [TildeTilde] M[subscript min]     330
Non-axial deformation of solitary pulsars and gravitational waves     330
Rotating neutron stars     333
Space-time metric and the equations of stationary motion     334
Stationary configurations of rotating neutron stars     335
Spinning low-mass neutron stars     341
Maximum mass and minimum rotation period     343
Rapid differential rotation and maximum mass     343
Approximate formulae for P[subscript min]     345
The causal upper bound on the mass of spinning neutron stars     345
The lower bound on rotation period     346
From the upper bound on z[subscript surf] to the lower bound on the rigid-rotation period     346
Rapid rotation and gravitational-radiation instabilities     347
Neutron Stars with Exotic Cores     351
Introduction     351
Exotic phases - an overview     351
Meson condensates     352
Deconfinement of quarks     352
Mixed-phase state     353
Crystallization     353
Exotic self-bound states of superdense matter     354
Pion condensation     354
Kaon condensation     361
Quark matter     364
Mixed-phase state     373
Solid cores of neutron stars     378
Physical origins and models     378
Elastic shear moduli     381
Nucleation of exotic high-density phase     381
Pion condensation     385
Kaon condensation     386
Quark deconfinement     388
The nucleation of a mixed normal-exotic phase     390
Phase transitions and neutron star structure     391
Linear response to a phase transition in the neutron star center     391
Moderate softening without any density jump     393
Strong softening without any density jump: The third family of compact stars      394
Moderate softening with density jump     395
Strong softening with density jump: The third family of compact stars     396
The proof of the inequality M*(A)< M(A)     397
Nonequilibrium first-order phase transition and its consequences     398
Large-amplitude corequake and collapse     399
Changes in stellar parameters due to a corequake     401
Estimates of [Delta]R, [Delta]I, and [Delta]E in corequakes     402
Mixed-phase core and neutron star corequakes     403
Strange Matter and Strange Stars     407
Introduction     407
Units     407
The strange matter hypothesis     408
Strange matter - history     409
The simplest "toy" MIT Bag Model     411
The Bag Model with massive strange quarks and QCD interactions     413
Other models of strange quark matter     415
The equation of state of strange matter     416
The linear approximation of the EOS     416
The adiabatic index of strange matter     417
The effect of quark superconductivity on the EOS     417
Even stranger matter     419
Strange stars - history     421
Bare strange stars     423
The nonexistence of quark stars with heavy quarks     426
Scaling properties     428
The surface of a bare strange star with electrons     430
The surface of a bare strange star without electrons     432
Strange stars with the crust     433
The minimum radius of strange stars with the crust     434
Apparent radii of strange stars     435
The surface gravity of strange stars     437
The conversion of neutron stars into strange stars     438
Even stranger stars of abnormal matter and Q-stars     439
Rotating strange quark stars     440
Uniformly rotating strange stars     441
The crust of rotating strange stars     446
Maximum mass and maximum spin frequency of strange stars     450
Instabilities in rotating strange stars     451
Theory Versus Observations     455
Masses of neutron stars in binary systems     456
X-ray binaries     456
Double neutron star binaries     467
Pulsar - white dwarf binaries     481
Pulsars in binaries with non-degenerate stars     487
Summary of neutron star mass measurements     488
From November 2005 to August 2006 and beyond     489
Gravitational surface redshift     490
Neutron star radii     491
Thermal emission of isolated neutron stars     492
X-ray emission from accreting neutron stars in binaries     496
Final remarks on radius measurements     498
Millisecond and submillisecond pulsars     499
The Crab Nebula and the moment of inertia of the Crab pulsar     501
The energy balance of the Crab pulsar and its nebula     502
Observational evaluations of the Crab Nebula parameters     503
Bound on the moment of inertia     504
Neutrinos from Supernova 1987A and binding energy of neutron stars     506
Pulsar glitches and crustal moment of inertia     508
Pros and cons of the existence of strange stars     511
Con: Macroglitches of radio pulsars     511
Con: Strangelets in galaxies     513
Pro: Too small radii for some neutron stars     514
Pro: Submillisecond pulsars     515
Appendices     517
Tables of EOSs in Neutron Star Crust     517
Analytical Models of Nuclear Density Profiles     521
Steplike profile model     521
Smooth Composition Model     522
Spherical nuclei in the inner crust     523
Spherical nuclei in the outer crust     524
Exotic nuclei     524
Analytical Representations of Unified EOSs     527
Representation convenient for non-rotating stars     528
Representation convenient for rotating stars     530
Adiabatic index     532
Semi-Analytical EOSs in Neutron Star Cores     533
Scaling of Stellar Models for Linear EOSs     537
The causal limit EOS with a = 1     537
The case of a< 1     541
Bibliography     543
List of Symbols     597
List of Abbreviations     605
Subject Index     607

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