Dispersion and decay of collective modes in neutron star cores

Abstract

We calculate the frequencies of collective modes of neutrons, protons and electrons in the outer core of neutron stars. The neutrons and protons are treated in a hydrodynamic approximation and the electrons are regarded as collisionless. The coupling of the nucleons to the electrons leads to Landau damping of the collective modes and to significant dispersion of the low-lying modes. We investigate the sensitivity of the mode frequencies to the strength of entrainment between neutrons and protons, which is not well characterized. The contribution of collective modes to the thermal conductivity is evaluated.

Application of superconducting-superfluid magnetohydrodynamics to nuclear “pasta” in neutron stars

“…In the mean field models of nuclear matter one usually assumes θ α = 0 [37]. Variation of S with respect to the four-vector potential (A 0 , A) leads to Maxwell equations…”

“…In order to estimate (δ F 1cm 2 ×d n ) z , it is assumed that the baryon density inside the slab is 0.16 fm −3 , and thus, n np ∼ −3.692 × 10 −3 fm −3 [37]. The perturbation of the velocity lag v p − v n which is assumed to be ∼ 1 cm s −1 in typical conditions, around its' equilibrium zero value, is related to δ w: v p − v n = (n p n n ) −1 (det n αβ )δ w, and one finds v p − v n = 1.501δ w. For the order of magnitude estimates it is assumed that (n n0 − n o n0 )/n n0 ∼ 1, which is expected to provide error of the order of 50%.…”

“…This approximation may be removed for various electron many-body regimes using the linear response theory [37]. While the relativistic contributions to the total mass density provide rather small quantitative corrections [47], the nucleon-nucleon interactions provide qualitatively new effects such as magnetization of neutron vortices [44], the mode mixing and avoided crossing [37] (still, the relativistic contributions are essential from the perspective of the gravitational interaction). Here, the focus is on physics due to the nuclear interactions, thus the relativistic corrections are neglected to a good first approximation.…”

Long-wavelength phonons in the crystalline and pasta phases of neutron-star crusts

“…This approximation requires that the wavelength of the modes is large compared to the Thomas-Fermi screening length. In doing so, we miss the damping of the modes which is to a large extent generated by the electrons [10].…”

Photons in dense nuclear matter: Random-phase approximation

“…Alternatively, one may consider a periodic lattice of positively charged ions. In the first case, the spectrum of excitation includes (quasi-) particle-hole excitations and collective modes which are both modified by the uniform charge background [15] [28]. This is the scenario relevant for homogeneous matter in the core of neutron stars.…”