Tatsuyuki Takatsuka

HADRON-QUARK CROSSOVER AND MASSIVE HYBRID STARS WITH STRANGENESS

Using the idea of smooth crossover from hadronic matter with hyperons to quark matter with strangeness, we show that the maximum mass (M max) of neutron stars with quark matter cores can be larger than those without quark matter cores. This is in contrast to the conventional softening of the equation of state due to exotic components at high density. The essential conditions for reaching our conclusion are that (1) the crossover takes place at relatively low densities, around three times the normal nuclear density and (2) the quark matter is strongly interacting in the crossover region. From these, the pressure of the system can be greater than that of purely hadronic matter at a given baryon density in the crossover density region and leads to M max greater than 2 solar mass. This conclusion is insensitive to the different choice of the hadronic equation of state with hyperons. We remark upon several implications of this result to the nuclear incompressibility, the hyperon mixing, and the neutrino cooling.

Confronting Neutron Star Cooling Theories with New Observations

With the successful launch of Chandra and XMM/Newton X-ray space missions combined with the lower energy band observations, we are now in the position where careful comparison of neutron star cooling theories with observations will make it possible to distinguish among various competing theories. For instance, the latest theoretical and observational developments appear to exclude both nucleon and kaon direct Urca cooling. In this way we can now have realistic hopes for determining various important properties, such as the composition, degree of superfluidity, equation of state, and stellar radius. These developments should help us obtain better insight into the properties of dense matter.

Hyperon-Mixed Neutron Star Matter and Neutron Stars ∗)

Effective Σ − n and Σ − Σ − interactions are derived fromthe G-matrix calculations for {n+Σ − } matter and employed in the investigation of hyperon mixing in neutron star matter. The threshold densities ρt(Y ) at which hyperons start to appear are between 2ρ0 and 3ρ0 (where ρ0 is the normal nuclear density) for both Λ and Σ − , and their fractions increase rapidly with baryon density, reaching 10% already for ρ � ρt+ρ0. The mechanism of hyperon mixing and single-particle properties, such as the effective mass and the potential depth, are analyzed taking into account the roles of YN and NN interactions. The resulting equation of state is found to be too soft to sustain the observed neutron star mass Mobs =1 .44M� .W e discuss the reason for this and stress the necessity of the “extra repulsion” for YN and YY interactions to resolve this crucial problem. It is remarked that ρt(Y ) would be as large as 4ρ0 for neutron stars compatible with Mobs. A comment is given regarding the effects on the Y -mixing problem from a less attractive ΛΛ interaction, newly suggested by the NAGARA event.

Superfluidity in Neutron Star Matter and Symmetric Nuclear Matter

Nucleon superfluids which are realized in neutron star interior and symmetric nuclear matter are studied with use of realistic nuclear forces, in the density domain from the subnuclear region to about 3ρ_0 (ρ_0 being the nuclear density). It is shown that characteristic aspects of nuclear forces manifest themselves in the appearance of several kinds of nucleon superfluids, which strongly depends on the density ρ. In this chapter emphasis is put on the pairing correlations where strong noncentral (tensor and spin-orbit) forces play important roles. A theoretical framework applicable to the nonzero angular-momentum pairing including the coupling due to tensor force is given by extending the usual BCS-Bogoliubov theory for the ^1S_0 pairing (the zero angular-momentum one). This formulation has been applied to the ^3P_2+^3F_2 pairing in neutron matter (the dominant component of neutron stars) and the ^3S_1+^3D_1 pairing in symmetric nuclear matter. In the former case, although spin-orbit force mainly contributes to the ^3P_2 attraction, the tensor coupling with the ^3F_2 component assists to realize the ^3P_2 superfluid. In the latter case, the tensor coupling to the ^3D_1 component plays a vital role to realize the ^3S_1 superfluid with a large energy gap. Results of the energy gaps calculated for such nonzero angular-momentum pairings, as well as those for the ^1S_0 pairing, are shown. We have found the realization of the following nucleon superfluids; the neutron ^3P_2 superfluid and the proton ^1S_0 one in the fluid core of neutron stars at ρ≃(0.7∼3)ρ_0, the neutron ^1S_0 superfluid in the inner crust of neutron stars at ρ≃(10^−3∼0.5)ρ_0, and the ^3S_1 superfluid in symmetric nuclear matter at a wide range of ρ including ρ_0, contrary to the ^1S_0 one realized at ρ≲ρ_0/2. The properties of these superfluids and their implications are also discussed.

Hadron–quark crossover and massive hybrid stars

On the basis of the percolation picture from the hadronic phase with hyperons to the quark phase with strangeness, we construct a new equation of state (EOS) with the pressure interpolated as a function of the baryon density. The maximum mass of neutron stars can exceed

Thermal Evolution of Hyperon-Mixed Neutron Stars

2M_{\odot }

Effective YN and YY Interactions and Hyperon-Mixing in Neutron Star Matter Y ≡ Λ Case

if the following two conditions are satisfied: (i) the crossover from hadronic matter to quark matter takes place at around three times the normal nuclear matter density, and (ii) the quark matter is strongly interacting in the crossover region and has a stiff equation of state. This is in contrast to the conventional approach, assuming the first-order phase transition in which the EOS always becomes soft due to the presence of the quark matter at high density. Although the choice of the hadronic EOS does not affect the above conclusion for the maximum mass, the three-body force among nucleons and hyperons plays an essential role in the onset of hyperon mixing and the cooling of neutron stars.

Occurrence of Hyperon Superfluidity in Neutron Star Cores

With the impressive amount of data that have poured out from Chandra and XMM/Newton X-ray space missions, as well as the lower energy band observations, we are now in the position where careful comparison of neutron star thermal evolution theories with observations will help us to distinguish among various competing theories. For instance, the latest theoretical and observational developments probably will contradict with the direct Urca cooling of neutron stars without some exotic particles. In this paper, we investigate one of the remaining possible fast cooling scenarios—direct Urca cooling of neutron stars in the hyperon-mixed phase. We conclude that this cooling scenario is a valid process if hyperon superfluidity is not too weak.

Nucleon Superfluidity in Neutron Star Core with Direct URCA Cooling

Effective ΛN and ΛΛ interactions in dense hyperonic nuclear matter are constructed on the basis of the G-matrix calculation with Nijmegen hard-core potentials. With these effective interactions, the mixing of Λ in neutron star matter and the equation of state are analyzed. The Λ-mixed phase is shown to appear in neutron star cores with a baryon number density ρ > ρt(Λ) � (3 − 5)ρ0, where ρt(Λ) is the threshold density for the Λmixing and ρ0 is the normal nuclear matter density. The density ρt(Λ) depends not only on the ΛN but also on the NN interactions. The three-body force introduced in the NN interaction to reproduce the proper nuclear saturation properties enhances the Λ-mixing and drastically softens the equation of state. The resulting equation of state is not consistent with the observed neutron star mass Mobs =1 .44M� . It is found that this crucial problem can be resolved by the introduction of a three-body repulsion also for the ΛN and ΛΛ interactions. The finite-temperature effect on the Λ-mixing is found to be large, especially at lower densities and is expected to affect the properties of neutron stars at birth.

Baryon Superfluidity and Neutrino Emissivity of Neutron Stars

proach. Numerical results for the equation of state (EOS) with the mixing ratios of the respective components and the hyperon energy gaps including the temperature dependence are presented. These are meant to serve as physical inputs for Y -cooling calculations of NSs. By paying attention to the uncertainties of the EOS and the YY interactions, it is shown that both Λ and Σ − are superfluid as soon as they appear although the magnitude of the critical temperature and the density region where superfluidity exists depend considerably on the YY pairing potential. Considering momentum triangle condition and the occurrence of superfluidity, it is found that a so-called “hyperon cooling”(neutrino-emission from direct Urca process including Y ) combined with Y -superfluidity may be able to account for observations of the colder class of NSs. It is remarked that Λ-hyperons play a decisive role in the hyperon cooling scenario. Some comments are given regarding the consequences of the less attractive ΛΛ interaction recently suggested by the “NAGARA event” 6He.