Low-energy collective excitations in the neutron star inner crust

Abstract

We study the low-energy collective excitations in the inner crust of the neutron star, where a neutron superfluid coexists with a Coulomb lattice of nuclei. The dispersion relation of the modes is calculated systematically from a microscopic theory including neutron band structure effects.These effects are shown to lead to a strong mixing between the Bogoliubov-Anderson bosons of the neutron superfluid and the longitudinal crystal lattice phonons. In addition, the speed of the transverse shear mode is greatly reduced as a large fraction of superfluid neutrons are entrained by nuclei. Not only does the much smaller velocity of the transverse mode increase the specific heat of the inner crust, it also decreases its electron thermal conductivity. These results may impact our interpretation of the thermal relaxation in accreting neutron stars. Due to strong mixing, the mean free path of the superfluid mode is found to be greatly reduced. Our results for the collective mode dispersion relations and their damping may also have implications for neutron star seismology.

Neutron Stars—Cooling and Transport

“…At ρ ≈ 10 12 − 10 14 g cm −3 the conductivity due to superfluid phonons was estimated to be significantly larger than that due to lattice phonons and comparable to electron conductivity when T ≈ 10 8 K. The authors found that this mode of heat conduction could limit the anisotropy of temperature distribution at the surface of highly magnetized neutron stars. However, new studies of the low-energy collective excitations in the inner crust of the neutron star (Chamel 2012;Chamel et al 2013), including neutron band structure effects, show that there is a strong mixing between the Bogoliubov-Anderson bosons of the neutron superfluid and the longitudinal crystal lattice phonons. In addition, the speed of the transverse shear mode is greatly re-duced as a large fraction of superfluid neutrons are entrained by nuclei.…”

Density Functional Approach to Superfluid Phonon in Inner Crust of Neutron Stars

“…The former has amplitude around the surface region r ≈ 3 − 8 fm of the cluster while the latter does not penetrate into r < 7fm, hence the overlap integral could become small. This might lead to a SPH-LPH coupling weaker than that evaluated in macroscopic approaches [2,[5][6][7][8], where this effect is not taken into account.…”

“…Many of the previous studies of the SPH in the inner crust have been performed in the framework of the macroscopic effective theory or the hydrodynamical approaches [2,[5][6][7][8]. However, inhomogeneity of inner crust matter may affect the character of the SPH and the coupling to the lattice phonon, and therefore nuclear many-body approaches are required to provide microscopic information on SPH in the inner crust.…”

“…Aguilera et al [2] pointed out that the SPH may play a role of another heat carrier besides electrons. An important point is that the SPH couples to the lattice phonon (LPH), and the coupling governs mean free path of this mode and the thermal conductivity [2,[5][6][7][8]. The thermal conductivity by SPH can be comparable to that by electrons under strong magnetic field and at low temperature [2].…”

Magnetar giant flare oscillations and the nuclear symmetry energy

“…Since the quasi-free neutrons are superfluid, assuming the traction vanishes at the crust-core boundary may also be a good approximation. An additional impact of the superfluid is that some fraction, f ent , of the quasi-free neutrons are entrained with the nuclei [36,37]. We assume zero traction at the crust-core transition and leave a more complete description of matter at the highest densities to future work.…”