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As discussed in Chapter 5, the fundamental problem of the EOS of neutronstar cores cannot be solved on purely theoretical basis: there is no strict theory but many theoretical models instead. Therefore, one can try to select (constrain) the true model using observations. In the present Chapter we will describe some results of this activity. The methods to constrain the EOS are numerous. The activity started just from the discovery of neutron stars in 1967 (Chapter 1). The results obtained by the time of this writing (2006) are a tremendous challenge of observational astrophysics, but look like a failure in their essence: the EOS has been only weakly constrained by observations. [ABSTRACT FROM AUTHOR]

This chapter is different from others. It deals with objects which, at the time of this writing, are hypothetical. We do not know whether strange matter and strange stars exist or not. We start with the discussion of the strange matter hypothesis (§8.3). Its history is described in §8.4. Models of strange matter are presented in §§8.5-8.8. Finally, §8.9 is devoted to other speculative self-bound phases of super-dense matter. [ABSTRACT FROM AUTHOR]

It has been recognized since the 1960s that with increasing density ρ above the standard nuclear-matter density ρ0 the matter can undergo phase transitions to states qualitatively different from the state at ρ ∼ ρ0. These high-density phases are exotic by the standards of terrestrial nuclear physics. Their possible existence above some threshold densities results from assumed specific features of strong (hadronic) interactions (pion condensation, kaon condensation) and the quark structure of baryons (quark deconfinement). [ABSTRACT FROM AUTHOR]

As we have seen in §3.5, nuclei cannot exist at densities exceeding ∼ (1.5 − 2.0) × 1014 g cm−3. At these densities the matter becomes a uniform plasma of neutrons, protons, and electrons. Up to ρ ∼ 2ρ0 its properties can be calculated in a rather reliable way using the methods of the nuclear many-body theory, which have been applied with some success for the microscopic description of ordinary nuclear structure. At such densities the only baryons present in the ground state of the matter are nucleons which are in beta equilibrium with electrons (and muons if the electron Fermi energy exceeds mμc2 = 105.7 MeV). The shell of the neutron-star core with densities ρ ≲ 2ρ0 is called the outer core. Its matter will be called the npeμ matter. At higher densities our assumption of the npeμ composition of dense matter can be invalid because the matter may contain hyperons. The derivation of the equation of state (EOS) of the matter composed of nucleons, hyperons, electrons, and muons will be the topic of the present chapter. [ABSTRACT FROM AUTHOR]

Neutron stars are relativistic objects. Their structure and evolution should be studied using the General Theory of Relativity. The importance of relativistic effects for a star of mass M and radius R is characterized by the compactness parameterrg/R given by Eq. (1.4), where rg is the Schwarzschild radius. Typically, one has rg/R ∼ 0.2 − 0.4 for a neutron star, whereas rg/R ≪ 1 for all other stars. For instance, rg/R ∼ 10-4 for white dwarfs and rg/R ∼ 10−6 for main-sequence stars of M ≃ M⊙. [ABSTRACT FROM AUTHOR]

Magnetic fields B ≳ 1012 G, typical for isolated neutron stars (§1.3.8), drastically modify many physical properties of the matter. Motion of free electrons and ions perpendicular to the field lines is quantized into Landau orbitals with a characteristic transverse scale equal to the magnetic lengtham = (ħc/eB)1/2. This brings to the scene an atomic field-strength parameter γ = (a0/am)2, where a0 is the Bohr radius. If this parameter is large, the Lorentz force acting on valence electrons in atoms exceeds the Coulomb force. The Landau energy levels of electrons are modified by relativistic effects if the field strength in the relativistic units, (4.1)$$ b = h--\omega _c /(m_e c^2 ) = B/B_r , $$ becomes b ≳ 1. Here, ωc = eB/(mec) is the electron cyclotron frequency and Br = me2}c{3}/(eħ) = 4.414 × 1013 G is often called the relativistic magnetic field. [ABSTRACT FROM AUTHOR]

After an overall introduction into the neutron star physics, we begin a systematic description of neutron star layers (Fig. 1.2). Chapters 2-4 are devoted to neutron star envelopes. These envelopes are non-uniform. The structure of an envelope for a star with the effective surface temperature ∼ 106 K is schematically shown in Fig. 2.1. We indicate characteristic densities and geometrical depths of interfaces between adjoining layers. One can distinguish the atmosphere, the ocean of ion liquid, followed by solidified layers denoted as the outer and inner crusts. At the bottom of the envelope there may be a mantle containing a liquid crystal of nonspherical nuclei (§3.7.2). These layers are already outlined in §1.3.1 and will be studied in more detail below. The properties of the atmosphere, ocean, and the upper edge of the solidified layer strongly depend on temperature. For the assumed surface temperature ∼ 106 K the internal temperature of a cooling (isolated) star would be ∼ 108 K; the main temperature gradient would occur in the ocean, while deeper layers would be nearly isothermal. When the star cools, the atmosphere and the ocean become thinner. In a sufficiently cold star they may be absent and the solidified matter will extend to the very surface. [ABSTRACT FROM AUTHOR]

After discussing the Coulomb properties of neutron star envelopes in Chapter 2, we will mainly focus on the nuclear part of the problem. Following a widespread convention we will often call an entire neutron star envelope as a crust (see a discussion on this point in the introductory part of Chapter 2). [ABSTRACT FROM AUTHOR]

Neutron stars are compact stars which contain matter of supranuclear density in their interiors (presumably with a large fraction of neutrons). They have typical masses M ∼ 1.4M⊙ and radii R ∼ 10 km. Thus, their masses are close to the solar mass M⊙ = 1.989 × 1033 g, but their radii are ∼ 105 times smaller than the solar radius R⊙ = 6.96×105 km. Accordingly, neutron stars possess an enormous gravitational energy Egrav and surface gravity g, (1.1)$$ \begin{gathered} E_{grav} \sim GM^2 /R \sim 5 \times 10^{53} erg \sim 0.2Mc^2 , \hfill \\ g \sim GM/R^2 \sim 2 \times 10^{14} cm{\text{ }}s^{ - 2} , \hfill \\ \end{gathered} $$ where G is the gravitational constant and c is the speed of light. Clearly, neutron stars are very dense. Their mean mass density is (1.2)$$ \bar \rho \simeq 3M/(4\pi R^3 ) \simeq 7 \times 10^{14} g cm^{{\text{ - 3}}} \sim (2 - 3)\rho _0 , $$ where ρ0 = 2.8 × 1014 g cm−3 is the so called normal nuclear density, the mass density of nucleon matter in heavy atomic nuclei. The central density of neutron stars is even larger, reaching (10-20) ρ0. By all means, neutron stars are the most compact stars known in the Universe. [ABSTRACT FROM AUTHOR]