Coexistence of Anderson-Bogoliubov phonon and quadrupole cluster vibration in the inner crust of neutron stars

Abstract

Background: Low-lying collective excitations of inner crust matter in neutron stars are expected to have impact on observables such as the quasi-periodic oscillation in giant flares and the cooling of inner crust in transient phenomena. Coupling between Anderson-Bogoliubov superfluid phonon (AB phonon) in superfluid neutron gas and collective excitations of nuclear clusters is a key issue. Purpose: We intend to predict the nature of low-lying excitation modes of superfluid inner crust matter with focus on quadrupole excitations around a spherical nuclear cluster. We study how the AB phonon of neutron superfluid and possible quadrupole shape vibration of clusters are affected by the inhomogeneous structure of inner crust matter. Methods: The coordinate-space Hartree-Fock-Bogoliubov method and the quasiparticle randomphase approximation formulated in a spherical Wigner-Seitz cell are adopted to describe neutron superfluidity and low-lying collective excitations. We perform systematic numerical calculations for quadrupole excitations by varying the neutron chemical potential and the number of protons in a cell. Results: The calculated results indicate emergence of both AB phonon and quadrupole shape vibration of the cluster with small mixing between the two collective modes. The quadruple AB phonon is similar to that in uniform superfluid apart from small admixture of the shape vibration of cluster. The excitation energy and the collectivity of the cluster vibration mode shows strong and oscillatory dependence on the neutron chemical potential (the neutron gas density), leading to softening and instability in certain situations. This is caused by the resonance shell effect where unbound but resonant single-particle states of neutrons play a central role. Conclusions: The AB phonon of superfluid neutron gas and the quadrupole shape vibration of nuclear cluster coexist in inner crust. The coupling between the AB phonon and the quadrupole shape vibration is weak. The collectivity of the quadrupole shape vibration is governed by the resonance shell effect, and it suggests that emergence of deformed nuclear clusters is possible at any layer of inner crust.

Time-dependent extension of the self-consistent band theory for neutron star matter: Anti-entrainment effects in the slab phase

“…2(b). It is to mention here that if superfluidity is present, which is neglected in the present work, it would prevent the system from exciting until the motion exceeds certain critical velocity for breaking Cooper pairs, whereas additional collective excitation modes, the Anderson-Bogoliubov phonons, may be present [50,51].…”

Proximity Effect of Pair Correlation in the Inner Crust of Neutron Stars with Hartree–Fock–Bogoliubov Theory

“…Since the method is an extension of that is used in Refs. [15,16], we describe it briefly with emphasis on new aspects which are introduced in the present study.…”

Properties of a quantum vortex in neutron matter at finite temperatures

“…Besides, longitudinal lattice vibrations are mixed with the low-energy collective excitations of the superfluid so that their combined contribution to the crustal specific heat may become comparable to or even larger than that of electrons [65,66]. The superfluid excitations may be also coupled to nuclear-shape vibrations [67,68]. The latter become energetically favorable in the inner crust due to significant decrease of the nuclear surface tension, which is expected to drop by an order of magnitude as compared to normal nuclei.…”