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Structure and properties of neutron stars and quark stars

Present level of knowledge and research activity

(at the beginning of the project)

Among very recent observations of very compact objects that can be candidates of neutron stars, some cases appear to be extremely compact so that the possibility of having a neutron star can be excluded, and the models of quark stars must be taken seriously. In the most compact quark stars, constituted from strange quark matter, the trapped null geodetics, relevant both for trapped gravitational waves and trapped neutrinos, must exist.

The theory of neutron stars and quark stars is highly developed at present [1,2]. To study the thermal structure and the cooling problem, we need four coupled differential equations; an equation of state, the general-relativistic TOV-equation for hydrostatic equilibrium in gravitational field, an equation for conservation of mass-energy, and an equation for the energy transport inside the star (dependent on the heat capacity and emission of photons and neutrinos). In a young, hot neutron star, the cooling process will be dominated by emission of neutrinos, and later by emission of photons. By simultaneous integration of the four equations, we may obtain temperature, pressure, density, and luminosity as functions of stellar radius and time.

The equation of state will be directly related to the internal structure of the star, and as well as the total mass, radius, moment of inertia, and thermal properties. In neutron stars, we may find “cosmic” superfluidity by neutrons or superconductivity by protons, i.e., singlet-pairing or triplet-pairing at different densities. The superfluidity will not have much effect on the equation of state and the total mass and radius, but a rather strong effect on the heat capacity and the cooling problem. Also, the neutrino production may be suppressed in superfluid regions.

The existence of pion condensation, kaon condensation, or quark matter in the inner core of a neutron star, would also change the equation of state and the heat capacity and the emission of neutrinos. We then have to find the critical densities for phase transitions to such “special” states of matter, to see if such transitions are possible inside the star.

Strong magnetic fields in neutron stars should change the opacity and the conductivity, and thereby the temperature gradient and the cooling rate. We get, for instance, “cylinder symmetry” and anisotropic effects in a strong magnetic dipole field.

If we can determine experimentally (by observations) the surface temperature and the age of neutron stars, for instance in supernova remnants, we can fit theoretical cooling curves (for different internal structures) to observations (boundary conditions), to obtain information about the internal structure. The cooling rate or the “thermal evolution” of the star can then give us information about the temperature and the heat capacity and thereby about the possible existence of various “exotic” phases of matter in the interior of a neutron star.

[1] N.K. Glendenning Compakt Stars: Nuclear Physics, Particle Physics, and General Relativity Springer-Verlag, New York 1997
[2] F. Weber, Pulsars as Astrophysical Laboratories for Nuclear and Particle Physics IoP Publishing, Bristol and Philadelphia 1999

Basic ideas of our research plan in the proposed area

The effects of strong gravitational field and microphysics are mixed in a direct and natural way when we determine properties of compact stars, i.e., neutron stars, quark stars, and hybrid stars (neutron stars with a quark core). The General Relativity implies equations of structure, the equation of state of matter is given by the particle physics. Therefore, testing properties of compact stars means testing the particle theory models. The theory of compact stars is highly developed at present, however, there remains an a very interesting and open question, namely, of existence and properties of extremely compact stars having radius R<3M that admit existence of bound null geodesics. The existence of such extremely compact stars is admitted by detailed models of both neutron stars and quark stars and is indicated by observational data coming from some galactic sources. In such stars, trapped modes of gravitational waves and trapped neutrinos could appear. The existence of neutrinos trapped by the strong gravitational field of extremely compact stars could lead to very interesting and observable effects. First, it will lower the expected neutrino luminosity of the stars. Second, and more important, is the fact that it can influence the structure of the star during its cooling. It can even lead to a “two-temperature” regime in the cooling process, whose influence on the internal structure of the extremely compact stars could be very strong and maybe some “self-organized” structures could be created in some layers inside such stars. We want to study in detail the cooling process of the extremely compact stars and an interesting possibility of the existence of “two-temperature” regime of the cooling process and its implications, both theoretical and observational. We shall use sophisticated models of the interior of the compact stars, based on various equations of state determined from elementary particle physics, focusing on various forms of quark matter. In the outermost shell (crust), there is a possibility to study interactions of electrons with lattices in the extreme physical conditions by means of quantum many-body physics (theory).