## Crust formation in a newlyborn neutron star

Let us consider a newly born neutron star. Crystallization during its cooling is first-order phase transition in a Coulomb plasma. Just after the temperature falls below the local melting temperature Tm(p) at a given density p (Fig. 3.17), the matter becomes an overcooled liquid. This state is metastable, and the crystallization is expected to start at T < Tm (p) via the formation of nucleation seeds and subsequent crystal growth. A possible scenario of crystallization at p 8 x 1013 g cm3 was...

## E1 The causal limit EOS with a

It is convenient to introduce the dimensionless variables, P , - P - 1 , 5 , m , nb , (E.2) where r0 c y Gps, M0 psr3, and ns is the value of the baryon number density at the stellar surface p ps. These variables allow one to rewrite the relativistic equations of hydrostatic equilibrium, Eqs. (6.7)-(6.8), in a dimensionless form. Using the thermodynamic relation nb 2P + 11 2 (2R - 1)1 2 . (E.4) Non-rotating stars. The dimensionless Tolman-Oppenheimer-Volkoff and mass-balance equations read The...

## The equation of state of the neutron star crust

In the present section we discuss the EOS of the outer and inner crusts, built of cold catalyzed matter. The EOS in the outer crust is rather well established. We suggest to use the HP EOS given in Table A.1 of Appendix A. It is similar to the older BPS EOS. In some pressure intervals the two EOSs give a few percent difference in p, resulting from the difference in nuclides present at those pressures. As soon as one leaves the region of experimentally known nuclei, the EOS of cold catalyzed...

## Nnp

Where we use the short-handed notation, given by Eq. (5.36), for the integration over momentum states below the Fermi surface. The central quantity of the independent pair approximation is the in-medium T-matrix, which describes two-nucleon scattering in a nucleon medium. In the momentum representation, the T-matrix for an NN' nucleon pair satisfies the integral equation (PiP2 TNN' (n + in) pip2) (PlP2 VNN> PlP2) dfci dk2 (Zn)3 (z f x Ann'(ki, k2, Q + ir )(kik2 TNN'(fi + in) PiP2) , (5.48)...

## The main mystery The equation of state in neutron star cores

The pressure of the matter in neutron star interiors is mainly produced by highly degenerate fermions and can be calculated assuming T 0. It is the bulk property of the matter, provided by entire Fermi seas of fermions. The EOS in a neutron star crust has been calculated with an accuracy, sufficient to construct neutron star models, although some theoretical problems are unsolved (Chapters 2-4). The theory is based on reliable experimental data on atomic nuclei, nucleon scattering, and on the...

## The Crab Nebula and the moment of inertia of the Crab pulsar

The AD 1054 supernova remnant, the Crab Nebula, was discovered by amateur astronomer John Bevis in 1731 and rediscovered by Charles Messier in 1758. John Duncan found in 1921 that the nebula is expanding (see Duncan 1939). Now it is probably the most often observed nebula in the sky. Optical observations of its filaments indicate that filaments are accelerated. This acceleration as well as the nebula emission are powered by the Crab pulsar which was discovered in the center of the nebula in...

## The heat capacity

To illustrate the temperature dependence of thermodynamic quantities, let us outline the main features of the heat capacity of the Coulomb plasma. In Fig. 2.7 we show the temperature dependence of the electron and ion heat capacities calculated per one ion at constant volume . The left panel shows various contributions to CV for the iron plasma at p 108 g cm-3. In this case, the plasma parameters are xr 3.626, TF 1.627 x 1010 K, that is, the electrons are relativistic and strongly degenerate T...