Abstract
The composition of the neutron stars from its surface region, outer-core, inner-core, and to its center is still being investigated. One can only surmise on the properties of neutron stars from the spectroscopic data that may be available from time to time. A few models have suggested that the matter at the surface region of the neutron star is composed of atomic nuclei that get crushed under extremely large pressure and gravitational stress, and this leads to the creation of solid lattice with a sea of electrons, and perhaps some protons, flowing through the gaps between them. Nuclei with high mass numbers, such as ferrous, gold, platinum, uranium, may exist in the surface region or in the outer-core region. It is found that the structure of the neutron star changes very much as one goes from the surface to the core of the neutron star. The surface region is extremely hard and very smooth. Surface irregularities are hardly of the order of 5 mm, whereas the interior of the neutron star may be superfluid and composed of neutron-degenerate matter. However, the neutron star is highly compact crystalline systems, and in terrestrial materials under pressure, many examples of incommensurate phase transitions have been discovered. Consequently, the properties of incommensurate crystalline neutron star have been studied. The composition of the neutron stars in the super dense state remains uncertain in the core of the neutron star. One model describes the core as superfluid neutron-degenerate matter, mostly, composed of neutrons , and a small percentage of protons and electrons More exotic forms of matter are possible, including degenerate strange matter. It could also be incommensurate crystalline neutron matter that could be BCC or HCP. Using principles of quantum statistical mechanics, the specific heat and entropy of the incommensurate crystalline neutron star has been calculated assuming that the temperature of the star may vary between to . Two values for the temperature T that have been arbitrarily chosen for which the calculations have been done are and . The values of specific heat and entropy decrease as the temperature increases, and also, their magnitudes are very small. This is in line with the second law of thermodynamics.
Highlights
The composition of the neutron stars from its surface region, outer-core, inner-core, and to its center is still being investigated
A few models have suggested that the matter at the surface region of the neutron star is composed of atomic nuclei that get crushed under extremely large pressure and gravitational stress, and this leads to the creation of solid lattice with a sea of electrons, and perhaps some protons, flowing through the gaps between them
The composition of the neutron star with 90% neutrons and 10% protons is assumed to be a crystalline state resulting in incommensurate crystallization of the neutron star. In this manuscript, calculations have been done for the entropy and specific heat of the neutron star
Summary
The inner crust and core have very high temperatures, of order of 107 K to 1010 K ; extremely high density results in extremely high gravitational field or stress, and extremely high pressure; and all put together can result in a crystalline structure of the neutron star with 90% neutrons and 10% protons It is not known exactly whether the outer crust and the inner crust are BCC or HCP and there are suggestions that the proton fraction could be more than 10%. It is well known that in the crystalline state or a quantum solid, the system is intrinsically restless, and the energy it possesses is the zero-point energy that is calculated using the Heisenberg’s Uncertainty principle [15,16] In this manuscript, the crystalline state is assumed to be incommensurate such that the number of neutrons Nn is less than the number of sites ( N s ) and the number of protons ( N p ) is less than N s.
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