Tomoki Endo

Neutron stars are commonly considered as astronomical objects having high-density interiors and an inner core region in which various hadronic matter phases are expected. Several studies show that the inner structures affect macroscopic phenomena of the star. However, we know that the inner structures of the star strongly depend on the equation of state (EOS). The EOS of high-density matter is still not clear and several recent observations indicate restrictions to EOSs. Theoretical studies should elucidate EOSs at high density and/or high temperature. For instance, many theoretical studies have attempted to account for the rotation effect of rapidly rotating neutron stars (i.e., pulsars). Accordingly, we also apply our EOSs to rapidly rotating stars. Furthermore, neutron stars generate a strong magnetic field. Several recent studies indicate that this magnetic field exerts restrictions on the EOS. In this paper, we focus on the investigation of the inner structures and the application of our EOSs to rotating stars. We find that one of our EOSs is consistent with observations, and another is inconsistent. We also find an important relation between the radius and rotation.

The appearance of quark matter in the core of hybrid stars is a fundamental issue in such compact stars. The central density of these stars is sufficiently high such that nuclear matter undergoes a further change into other exotic phases that consist of hyperons and quarks. However, the equation of state (EOS) for the high-density matter is still not clear and several recent observations have indicated the limitations of the EOSs; theoretical studies should try to elucidate the EOSs. It is believed that the inner regions of the stars should consist of a mixed hadron-quark phase. We study the mixed hadron-quark phase, taking into account finite-size effects, and find that that the mixed phase should be restricted to a narrower region. Therefore, a quark matter phase should appear in the central region.

Hadron-quark mixed phase is expected in a wide region of the inner structure of hybrid stars. However, we show that the hadron-quark mixed phase should be restricted to a narrower region because of the charge screening effect. The narrow region of the mixed phase seems to explain physical phenomena of neutron stars such as the strong magnetic field and glitch phenomena, and it would give a new cooling curve for the neutron star.

Nonuniform structures of mixed phases at the first-order phase transition to charged kaon condensation are studied using a density functional theory within the relativistic mean-field model. Including electric field effects and applying the Gibbs conditions in a proper way, we numerically determine density profiles of nucleons, electrons, and condensed kaons. Importance of charge screening effects is elucidated and thereby we show that the Maxwell construction is effectively justified. Surface effect is also studied to figure out its effect on the density profiles.

The Coulomb interaction effect is consistently taken into account in the hadron-quark mixed phase. It. is found that the finite-size effects, such as the surface effect and the charge screening effect, greatly alter the properties of the mixed phase and restrict; its density region. In particular, the charge screening effect and the rearrangement of the charged particles are elucidated. As the Gibbs conditions, are satisfied throughout the numerical procedure, we show that the Maxwell construction becomes physically meaningful and the equation of state becomes similar to that given by the Maxwell construction.

The Coulomb screening effect and the finite-size effect such as surface tension are figured out in the hadron-quark deconfineinent phase transition. We study the mixed phase of the quark droplets immersed in hadron matter. We see that the droplet phase is mechanically unstable if the surface tension is strong enough. Once the, Coulomb potential is properly taken into account, we could effectively satisfy the condition for charge chemical equilibrium in the Maxwell construction. As a result, we suggest the Maxwell construction acquires the physical meaning effectively.

Hadron-quark混合相は複数の化学ポテンシャルが存在する系である。Maxwell構成法を敢えて適用するとGibbs条件の一つが破れてしまう為に、この系ではMaxwell構成法から得られる描像はこれまでは否定されてきた。しかしながら我々の研究により、表面張力・クーロン遮蔽効果といった"有限サイズ効果"を適切に取り扱う事によりMaxwell構成法から得られる描像はeffectiveであることが示される。この混合相は中性子星内部の系に対応し、inner core 〜 outer core領域に存在するとされている混合相は我々の研究により制限を受けることとなる。

An approximate energy expression is proposed for arbitrarily spin-polarized Fermi liquids with central two-body forces. It is explicitly expressed as a functional of spin-dependent radial distribution functions and can be used conveniently in the variational method. It includes the potential energies completely and the kinetic energies up to main parts of the three-body cluster terms. This approximation is similar to that used previously for spin-unpolarized and fully polarized matter. A notable feature of this expression is that it guarantees the necessary conditions on arbitrarily spin-polarized structure functions automatically. The Euler-Lagrange equations are derived from this energy expression and are numerically solved for arbitrarily spin-polarized liquid 3 He. The results for liquid He-3 with the HFDHE2 potential are consistent with the nearly ferromagnetic property.