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. 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.