Fig. 7-15 Schematic picture of the internal structure of a neutron star The outer crust retains nuclei arranged in a lattice. In the inner crust with higher densities, electron capture increases the number of neutron-rich nuclei. Neutrons then drip from the nuclei and form a "neutron sea" at a density 4×1011g/cm3. The outer core consists of neutron/proton liquids. Much deeper inside the star, there appears an inner core, where hyperons, mesons, and quarks are predicted to exist.

Fig. 7-16 Lambda Lambda pairing gap at the Fermi surface of Lambda hyperons in background neutron matter This figure shows the Lambda Lambda pairing gap in background neutron matter that imitates the interior of neutron stars. The horizontal axis represents the density of Lambda hyperons and the vertical axis the strength of superfluidity. The ascending sequence associated with each curve of the background densities rhoN corresponds to the density variation inside a neutron star from its surface to its core. These curves indicate that the higher the density, the weaker the superfluidity.

A neutron star, mainly made up of neutrons as its name suggests, is a compact and dense astronomical object with a radius of ca. 10 km and a mass ca. 1.5 times that of the sun (Fig. 7-15). Neutron stars are produced by supernova explosions and cool by emitting neutrinos in their early stages. Since differences in the internal composition of neutron stars lead to differences in their emissivity of neutrinos and cooling rate, observation of the surfaces of neutron stars is an important probe into their interior. The cores of neutron stars are so dense that there probably exist hadrons (collective name for baryons and mesons) other than nucleons, such as hyperons (baryons with a strangeness quantum number) and even quarks, the constituent elements of hadrons. Neutron stars having these particles cool faster than those without them. However, this might result in "too fast" a cooling of neutron stars. For this reason, we need a regulator that suppresses such cooling in order to rationalize observational data. One candidate mechanism is a superconducting/superfluid state for the interior matter of neutron stars. Baryons such as neutrons might pair up to form Cooper pairs in a fashion similar to the superconductivity of an electron system. Thereby, the energy of the system may become lower in a paired condition than that of the system with baryons unpaired, and thus, such a state may be realized. Past studies have made it clear that the emissivity of neutrinos is suppressed and therefore neutron stars cool more slowly in a superconducting/superfluid state. One important clue to understanding the interior of neutron stars composed of hadrons would be knowledge of the properties of dense hadronic matter. We have therefore studied Lambda hyperon superfluidity in dense hadronic matter composed of nucleons and Lambda hyperons using the relativistic Hartree-Bogoliubov model, which fulfills the requirements of special relativity. As a result, we have shown that the higher the background nucleon density rhoN is, the less likely Lambda hyperon superfluidity becomes (Fig. 7-16). This is because the meson that mediates interactions between both nucleons and Lambda hyperons makes the (relativistic Dirac) effective mass of Lambda hyperons smaller with increasing rhoN, even if the density of Lambda hyperons is fixed. This is a novel result obtained exclusively with the relativistic model, whereas the first studies of Lambda hyperon superfluidity were done with nonrelativistic models. We have concluded that there is little possibility that Lambda hyperon superfluidity very much suppresses the emissivity of neutrinos in a region where Lambda hyperons exist (rhoN > 2 rho0), considering both the above result and a recent experiment implying that the Lambda Lambda interaction is much weaker than was thought earlier. Consequently, we are now studying superconductivity/superfluidity with other hyperon pairs and interspecies pairs to pursue other promising mechanisms to retard the cooling.

Reference T. Tanigawa et al., Possibility of Lambda Lambda Pairing and Its Dependence on Background Density in a Relativistic Hartree-Bogoliubov Model, Phys. Rev. C, 68(1), 015801 (2003).

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