Neutron stars. 1, Eqation of state and structure / P. Haensel, A.Y. Potekhin, D.G. Yakovlev.

Format:

Book

Author/Creator:

Haensel, Paweł.

Contributor:

Potekhin, A. Y.

Yakovlev, D. G.

Series:

Astrophysics and space science library ; 326.

Astrophysics and space science library ; 326

Language:

English

Subjects (All):

Neutron stars.

Physical Description:

xxiii, 619 pages : illustrations ; 25 cm.

Other Title:

Eqation of state and structure

Place of Publication:

New York : Springer, [2007]

Summary:

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.

Contents:

1.1 Neutron stars 1

1.2 History: from prediction to discovery 2

1.3 Internal structure and processes - Theoretical outlook 11

1.3.1 Structure 11

1.3.2 The main mystery: The equation of state in neutron star cores 14

1.3.3 Neutron star models 16

1.3.4 Superfluidity 17

1.3.5 Neutrino processes 19

1.3.6 Thermodynamics and kinetics 21

1.3.7 Cooling of neutron stars 25

1.3.8 Magnetic fields 26

1.3.9 Seismology 28

1.4 Observations versus theory 28

1.4.1 Telescopes 28

1.4.2 Birth in supernova explosions. Supernova connection 31

1.4.3 Evolutionary scenarios: Three driving forces 34

1.4.4 Pulsars 34

1.4.5 Isolated neutron stars 41

1.4.6 Neutron stars in binary systems - X-ray binaries 44

1.4.7 Neutron stars in the Galaxy 49

1.5 Neutron stars as "superstars" in physics and astrophysics 50

1.6 About the rest of this book 51

2 Equilibrium Plasma Properties. Outer Envelopes 53

2.1 Plasma parameters 55

2.1.1 Overall parameters 55

2.1.2 Electrons 56

2.1.3 Ions 60

2.2 Free energy and thermodynamic quantities 63

2.2.1 Fully ionized dense plasma. The basic decomposition 65

2.3 Fully ionized plasma without electron correlations 66

2.3.1 Ideal electron gas. Fermi-Dirac integrals 67

2.3.2 Coulomb liquid of ions 72

2.3.3 Coulomb crystal 77

2.3.4 Melting 88

2.3.5 The pressure of degenerate electrons with electrostatic corrections 90

2.4 Intermediate-density regime. Electron response 91

2.4.1 Interpolation 91

2.4.2 Thomas-Fermi-like theories 92

2.4.3 Electron exchange and correlation effects 93

2.4.4 Electron polarization in ion liquid 96

2.4.5 Electron polarization in ion solid 99

2.4.6 The heat capacity 103

2.4.7 Multi-ionic mixtures 106

2.5 Low densities. Partial ionization 107

2.5.1 Ionization equilibria in the "chemical picture" 107

2.5.2 An example: Partially ionized hydrogen plasma 111

3 Structure and EOS of Neutron Star Crusts 115

3.1 The formation of the crust in a newly born neutron star 116

3.2 Ground state of the outer crust 118

3.3 Ground state of the inner crust at p [GreaterTilde] 10[superscript 14] g cm[superscript -3] 125

3.3.1 Hartree-Fock calculations 126

3.3.2 Extended Thomas-Fermi (ETF) calculations 130

3.3.3 Compressible liquid drop model (CLDM) 133

3.4 Ground state of the bottom layers of the crust 140

3.4.1 The bulk approximation 140

3.4.2 Unusual nuclear shapes 142

3.4.3 Quantum corrections to the CLDM energy 147

3.5 Reaching the crust-core interface from the core side 148

3.6 The equation of state of the neutron star crust 150

3.7 Elastic properties of neutron star crust 153

3.7.1 From bcc lattice to isotropic solid 156

3.7.2 Exotic nuclei 159

3.8 Deviations from an idealized ground state model 161

3.8.1 Crust formation in a newly-born neutron star 162

3.8.2 Accreted crust 164

4 Envelopes with Strong Magnetic Fields 167

4.1 Fully ionized plasmas 168

4.1.1 Free electron in a magnetic field 168

4.1.2 Thermodynamic functions of the ideal electron gas 170

4.1.3 Magnetic oscillations 175

4.1.4 The effects of the magnetic field on plasma ions 176

4.1.5 Weakly non-ideal Coulomb plasma 178

4.1.6 Strongly coupled Coulomb plasma 180

4.2 Bound species in strong magnetic fields 184

4.2.1 Atoms 184

4.2.2 Molecules and chains 188

4.2.3 Effects of motion 190

4.2.4 Magnetic condensation 192

4.3 Models of strongly magnetized outer envelopes of neutron stars 193

4.3.1 Strongly magnetized iron envelopes 194

4.3.2 Strongly magnetized hydrogen atmosphere 196

5 Neutron Star Cores: Nucleons and Hyperons 207

5.2 Before the discovery of pulsars: 1932-1967 208

5.3 After the discovery of pulsars: 1968-2005 213

5.3.1 Nucleons 213

5.3.2 Nucleons and hyperons 215

5.4 The properties of nuclear matter 217

5.5 The Hamiltonian 221

5.5.1 Phenomenological nucleon-nucleon interaction 221

5.5.2 Three-body interaction 223

5.5.3 Relativistic corrections and three-body interaction 225

5.6 Meson-exchange nucleon-nucleon interaction 226

5.6.1 Three-and more-nucleon interactions 230

5.7 The hyperon interactions 231

5.8 Solving the many-body problem - an overview 233

5.9 Energy of nucleon matter 235

5.9.1 Brueckner-Bethe-Goldstone (BEG) theory 235

5.9.2 Green's Function Theory 240

5.9.3 Variational method 243

5.9.4 Relativistic mean-field model 246

5.9.5 Effective energy density functionals 253

5.10 Energy of hyperon-nucleon matter 254

5.10.1 Brueckner-Bethe-Goldstone theory 254

5.10.2 Relativistic mean-field model 256

5.11 The equation of state of the outer core 257

5.11.1 Calculating the equation of state 257

5.11.2 The nuclear symmetry energy and the proton fraction 259

5.12 Equation of state and composition 260

5.13 Inner core: minimal model - nucleons and leptons 263

5.13.1 Equation of state of the [Mu] matter 263

5.13.2 Proton fraction and direct Urca threshold 265

5.13.3 Adiabatic index 266

5.14 Hyperons in the inner core 267

5.14.1 Hyperonic composition 268

5.14.2 Hyperon softening of equation of state 273

5.15 Superluminal and ultrabaric equations of state 275

5.16 Effect of baryon superfluidity on equation of state 279

5.17 Effect of strong magnetic field on equation of state 279

6 Neutron Star Structure 281

6.1 Equations of hydrostatic equilibrium 281

6.2 Baryon number, mass and chemical potential. Binding energy of neutron stars 284

6.3 Proper mass and gravitational energy 287

6.4 Constructing neutron star models 287

6.4.2 Equation of state 289

6.5 Masses and stability of neutron stars 290

6.5.1 Stellar oscillations and stability 290

6.5.2 Stability criteria based on the mass-radius diagram 293

6.5.3 Neutron stars and white dwarfs 294

6.5.4 A variety of neutron star models 296

6.5.5 Maximum masses of neutron stars 297

6.5.6 The nature of the maximum mass of neutron stars 298

6.5.7 The upper bound on the maximum mass 301

6.5.8 Low-mass neutron stars and the minimum mass 302

6.6 Radii and surface redshifts 303

6.6.1 Circumferential radii 304

6.6.2 Radii of low-mass neutron stars 306

6.6.3 Gravitational redshifts 308

6.6.4 The upper bound on gravitational redshift and the lower bound on neutron star radius 308

6.6.5 The upper bound on surface gravity 309

6.6.6 Apparent radii 311

6.7 Binding energy 313

6.7.1 Approximate formulae 315

6.7.2 Neutron star models with M [TildeTilde] M[subscript min] 317

6.8 Basic internal structure of neutron stars 318

6.9 Universal structure of the outer envelope 319

6.9.1 The structure of magnetic envelopes 322

6.10 Moment of inertia for slow rigid rotation 323

6.10.1 Dragging of local inertial reference frames and moment of inertia 323

6.10.2 Moment of inertia versus M 324

6.10.3 Crustal moment of inertia 326

6.10.4 Moment of inertia versus M and R 326

6.10.5 Approximate formula for I[subscript max] 328

6.11 Elastic shear strain, non-axial deformations, and gravitational radiation 328

6.11.1 Elastic strain and neutron stars with M [TildeTilde] M[subscript min] 330

6.11.2 Non-axial deformation of solitary pulsars and gravitational waves 330

6.12 Rotating neutron stars 333

6.12.1 Space-time metric and the equations of stationary motion 334

6.12.2 Stationary configurations of rotating neutron stars 335

6.12.3 Spinning low-mass neutron stars 341

6.12.4 Maximum mass and minimum rotation period 343

6.12.5 Rapid differential rotation and maximum mass 343

6.12.6 Approximate formulae for P[subscript min] 345

6.12.7 The causal upper bound on the mass of spinning neutron stars 345

6.12.8 The lower bound on rotation period 346

6.12.9 From the upper bound on z[subscript surf] to the lower bound on the rigid-rotation period 346

6.12.10 Rapid rotation and

gravitational-radiation instabilities 347

7 Neutron Stars with Exotic Cores 351

7.2 Exotic phases - an overview 351

7.2.1 Meson condensates 352

7.2.2 Deconfinement of quarks 352

7.2.3 Mixed-phase state 353

7.2.4 Crystallization 353

7.2.5 Exotic self-bound states of superdense matter 354

7.3 Pion condensation 354

7.4 Kaon condensation 361

7.5 Quark matter 364

7.6 Mixed-phase state 373

7.7 Solid cores of neutron stars 378

7.7.1 Physical origins and models 378

7.7.2 Elastic shear moduli 381

7.8 Nucleation of exotic high-density phase 381

7.8.1 Pion condensation 385

7.8.2 Kaon condensation 386

7.8.3 Quark deconfinement 388

7.8.4 The nucleation of a mixed normal-exotic phase 390

7.9 Phase transitions and neutron star structure 391

7.9.1 Linear response to a phase transition in the neutron star center 391

7.9.2 Moderate softening without any density jump 393

7.9.3 Strong softening without any density jump: The third family of compact stars 394

7.9.4 Moderate softening with density jump 395

7.9.5 Strong softening with density jump: The third family of compact stars 396

7.9.6 The proof of the inequality M*(A)< M(A) 397

7.9.7 Nonequilibrium first-order phase transition and its consequences 398

7.9.8 Large-amplitude corequake and collapse 399

7.10 Changes in stellar parameters due to a corequake 401

7.10.1 Estimates of [Delta]R, [Delta]I, and [Delta]E in corequakes 402

7.11 Mixed-phase core and neutron star corequakes 403

8 Strange Matter and Strange Stars 407

8.2 Units 407

8.3 The strange matter hypothesis 408

8.4 Strange matter - history 409

8.5 The simplest "toy" MIT Bag Model 411

8.6 The Bag Model with massive strange quarks and QCD interactions 413

8.7 Other models of strange quark matter 415

8.8 The equation of state of strange matter 416

8.8.1 The linear approximation of the EOS 416

8.8.2 The adiabatic index of strange matter 417

8.8.3 The effect of quark superconductivity on the EOS 417

8.9 Even stranger matter 419

8.10 Strange stars - history 421

8.11 Bare strange stars 423

8.12 The nonexistence of quark stars with heavy quarks 426

8.13 Scaling properties 428

8.14 The surface of a bare strange star with electrons 430

8.15 The surface of a bare strange star without electrons 432

8.16 Strange stars with the crust 433

8.16.1 The minimum radius of strange stars with the crust 434

8.17 Apparent radii of strange stars 435

8.18 The surface gravity of strange stars 437

8.19 The conversion of neutron stars into strange stars 438

8.20 Even stranger stars of abnormal matter and Q-stars 439

8.21 Rotating strange quark stars 440

8.21.1 Uniformly rotating strange stars 441

8.21.2 The crust of rotating strange stars 446

8.21.3 Maximum mass and maximum spin frequency of strange stars 450

8.21.4 Instabilities in rotating strange stars 451

9 Theory Versus Observations 455

9.1 Masses of neutron stars in binary systems 456

9.1.1 X-ray binaries 456

9.1.2 Double neutron star binaries 467

9.1.3 Pulsar - white dwarf binaries 481

9.1.4 Pulsars in binaries with non-degenerate stars 487

9.1.6 From November 2005 to August 2006 and beyond 489

9.2 Gravitational surface redshift 490

9.3 Neutron star radii 491

9.3.1 Thermal emission of isolated neutron stars 492

9.3.2 X-ray emission from accreting neutron stars in binaries 496

9.3.3 Final remarks on radius measurements 498

9.4 Millisecond and submillisecond pulsars 499

9.5 The Crab Nebula and the moment of inertia of the Crab pulsar 501

9.5.1 The energy balance of the Crab pulsar and its nebula 502

9.5.2 Observational evaluations of the Crab Nebula parameters 503

9.5.3 Bound on the moment of inertia 504

9.6 Neutrinos from Supernova 1987A and binding energy of neutron stars 506

9.7 Pulsar glitches and crustal moment of inertia 508

9.8 Pros and cons of the existence of strange stars 511

9.8.1 Con: Macroglitches of radio pulsars 511

9.8.2 Con: Strangelets in galaxies 513

9.8.3 Pro: Too small radii for some neutron stars 514

9.8.4 Pro: Submillisecond pulsars 515

A Tables of EOSs in Neutron Star Crust 517

B Analytical Models of Nuclear Density Profiles 521

B.1 Steplike profile model 521

B.2 Smooth Composition Model 522

B.2.1 Spherical nuclei in the inner crust 523

B.2.2 Spherical nuclei in the outer crust 524

B.2.3 Exotic nuclei 524

C Analytical Representations of Unified EOSs 527

C.1 Representation convenient for non-rotating stars 528

C.2 Representation convenient for rotating stars 530

C.3 Adiabatic index 532

D Semi-Analytical EOSs in Neutron Star Cores 533

E Scaling of Stellar Models for Linear EOSs 537

E.1 The causal limit EOS with a = 1 537

E.2 The case of a< 1 541.

Notes:

Includes bibliographical references (pages [543]-595) and index.

ISBN:

9780387335438

0387335439

OCLC:

75964765