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Table of contents
I Context
1 Neutron stars : general aspects
1.1 From theoretical predictions to observations
1.2 Birth of a neutron star
1.2.1 Pre-supernova evolution
1.2.2 Core-collapse supernova explosions
1.3 Neutron stars as magnetic dipoles
1.3.1 Rotational energy
1.3.2 Magnetic dipole radiation
1.3.3 Surface magnetic field
1.3.4 Characteristic age
1.4 A variety of neutron stars
2 A laboratory for physics
2.1 From microphysics to astrophysics
2.1.1 Structure of a neutron star
2.1.2 Equations for the stellar structure
2.2 A laboratory for microphysics
2.2.1 Mass-radius diagram
2.2.2 Observational constraints
2.3 A laboratory for gravitational physics
2.3.1 Gravitational wave emission
2.3.2 Test of gravitation theories
II Thermal evolution of neutron stars
3 Cooling of isolated neutron stars
3.1 A little bit of history
3.2 Thermal evolution modeling
14 CONTENTS
3.2.1 General relativistic heat equations
3.2.2 Modeling
3.2.3 NSCool code
3.3 A toy model
3.3.1 Thermal conductivity
3.3.2 Specific heat
3.3.3 Neutrino emission
3.3.4 Envelope model
3.3.5 Analytical solutions
3.4 Cooling history of a neutron star
3.5 Towards a more realistic model
3.5.1 Superfluidity in neutron stars
3.5.2 Heating processes
3.6 Influence of the microphysics input
3.6.1 Non superfluid stars
3.6.2 Superfluid stars
3.6.3 Influence of the envelope model
3.6.4 Influence of the equation of state
3.6.5 Minimal cooling paradigm
3.7 Observations of the temperature of isolated neutron stars
3.7.1 An observational challenge
3.7.2 Present status
3.7.3 Cassiopeia A neutron star
3.7.4 Future perspectives
3.8 Theoretical modeling versus observations
3.8.1 Modeling of the cooling of Cassiopeia A neutron star
3.8.2 Modeling of all the available data
4 Cooling of young neutron stars
4.1 Thermal evolution in the early ages
4.2 The specific heat in the crust
4.2.1 The cluster structure of the inner crust
4.2.2 Specific heat in the crust
4.2.3 Specific heat of the superfluid neutrons
4.2.4 Influence of the clusters on the critical temperature
4.2.5 Neutron specific heat in uniform matter
4.2.6 Neutron specific heat in non-uniform matter
4.2.7 Total specific heat in the crust
4.3 Cooling simulations
4.3.1 Neutron star model
4.3.2 Microphysics input
4.3.3 Fast cooling scenario
4.3.4 Slow cooling scenario
4.4 Perspectives
4.4.1 Modeling
4.4.2 Observations
5 Thermal evolution of accreting neutron stars
5.1 Observations of accreting neutron stars
5.2 Quiescent state of X-ray transients
5.2.1 Nature of the quiescent emission
5.2.2 Deep crustal heating scenario
5.2.3 Atmosphere models
5.3 Heat equation
5.4 Soft X-ray transients
5.4.1 Thermal evolution of a soft X-ray transient
5.4.2 A toy model
5.4.3 Observations & constraints on microphysics
5.5 Quasi-persistent X-ray transients
5.5.1 Observations
5.5.2 Previous modelings of the thermal relaxation
5.5.3 New model for an accreting neutron star
III Rotating elastic neutron stars
6 Rotating neutron stars
6.1 3+1 formalism
6.1.1 Spacetime foliation
6.1.2 Induced metric
6.1.3 Eulerian observer
6.1.4 Adapted coordinates
6.1.5 Extrinsic curvature
6.1.6 3+1 decomposition of the stress-energy tensor
6.1.7 3+1 Einstein equations
6.2 Circular, axisymmetric and stationary spacetimes
6.2.1 Stationarity and axisymmetry
6.2.2 Circular spacetime
6.2.3 Metric
6.2.4 Maximal slicing
6.3 Einstein equations for rotating stars
6.4 Perfect fluid
6.4.1 Circularity
6.4.2 Decomposition of the fluid velocity
6.4.3 Energy-momentum tensor
6.4.4 Fluid equilibrium
6.4.5 Global properties
6.5 (2+1)+1 formalism
6.5.1 Foliation of the t hypersurfaces
6.5.2 Induced metric
6.5.3 Adapted coordinates
6.5.4 Extrinsic curvature
6.6 Numerical resolution with LORENE
6.6.1 Spectral methods
6.6.2 LORENE library
6.6.3 Block diagram of the Nrotstar code
6.6.4 An example
6.7 Constraints on the equation of state for dense matter
6.7.1 Observations of millisecond pulsars
6.7.2 Maximum rotational frequency
6.7.3 Influence of rotation of the M − R diagram
7 Newtonian and relativistic elasticity
7.1 Solid phases in neutron stars
7.1.1 Glitches
7.1.2 Solid crust
7.1.3 Liquid or solid core ?
7.1.4 Observational consequences
7.2 Newtonian models of elastic neutron star
7.2.1 Newtonian elasticity in a nutshell
7.2.2 Models of neutron stars with a (partially) solid interior
7.3 Elasticity in General Relativity
7.3.1 Previous formulations
7.3.2 Carter & Quintana formalism
7.3.3 Karlovini & Samuelsson formalism
7.3.4 Relativistic formulation of starquakes
8 Rotating neutron stars with a solid interior
8.1 Elastic deformation of rotating stars
8.1.1 Small deformations
8.1.2 Eulerian variation
8.1.3 Lagrangian variation
8.1.4 Semi-Lagrangian variation
8.2 Rotating Elastic neutron stars
8.2.1 Metrics
8.2.2 Quasi-isotropic coordinates
8.2.3 Strain tensors
8.2.4 Relative strain tensor
8.2.5 Shear tensor
8.2.6 Energy momentum tensor of an elastic fluid
8.2.7 Circularity condition
8.2.8 Einstein equations
8.2.9 Equation for equilibrium
8.2.10 Boundary conditions
8.3 Newtonian limit
8.3.1 Equation for equilibrium
8.3.2 Boundary conditions
8.4 Numerical resolution
8.4.1 Block diagram of the Elastar code in LORENE
8.4.2 KADATH
8.5 Perspectives
IV Spin-up of accreting neutron stars
9 Formation of millisecond pulsars
9.1 Accretion in binary systems
9.1.1 Roche-lobe overflow
9.1.2 Mass transfer dynamics
9.1.3 Disk formation
9.1.4 Neutron star recycling
9.2 Evolution of neutron star binaries
9.2.1 The population of millisecond pulsars
9.2.2 The different cases of Roche lobe overflows
9.2.3 Neutron star X-ray binaries & millisecond pulsars
10 Model of accreting magnetized neutron stars
10.1 Spin-up modeling
10.1.1 Mass increase and accretion rate
10.1.2 Angular momentum evolution
10.2 Accretion disk model
10.2.1 Magneto-hydrodynamic equation
10.2.2 Inner radius of the accretion disk
10.2.3 Relativistic specific angular momentum
10.2.4 Magnetic torque
10.2.5 Total angular momentum equation
10.2.6 Degeneracy parameter
10.3 Magnetic field evolution of accreting neutron stars
10.3.1 Accretion-induced magnetic field decay
10.3.2 Model of magnetic field decay
10.4 Models of neutron stars
10.4.1 Equations of state
10.4.2 Rotating neutron star configurations
10.5 Block diagram of the Evol code
11 Application to the spin-up of neutron stars
11.1 PSR J1903+0327
11.1.1 An eccentric millisecond pulsar
11.1.2 Formation scenarios
11.1.3 Results
11.1.4 Conclusions
11.2 The extreme-mass millisecond pulsars
11.2.1 The less massive millisecond pulsar : PSR J0751+1807
11.2.2 The most massive pulsar : PSR J1614-2230
11.2.3 Modeling
11.3 Perspective : sub-millisecond pulsars
Conclusion and perspectives
