Two-component Superfluid Hydrodynamics of Neutron Star Cores

Abstract

We consider the hydrodynamics of the outer core of a neutron star under conditions when both neutrons and protons are superfluid. Starting from the equation of motion for the phases of the wave functions of the condensates of neutron pairs and proton pairs we derive the generalization of the Euler equation for a onecomponent fluid. These equations are supplemented by the conditions for conservation of neutron number and proton number. Of particular interest is the effect of entrainment, the fact that the current of one nucleon species depends on the momenta per nucleon of both condensates. We find that the nonlinear terms in the Euler-like equation contain contributions that have not always been taken into account in previous applications of superfluid hydrodynamics. We apply the formalism to determine the frequency of oscillations about a state with stationary condensates and states with a spatially uniform counterflow of neutrons and protons. The velocities of the coupled sound-like modes of neutrons and protons are calculated from properties of uniform neutron star matter evaluated on the basis of chiral effective field theory. We also derive the condition for the two-stream instability to occur.

Andreev–Bashkin effect in superfluid cold gases mixtures

“…In this respect, the quantities we suggest to focus on to find experimental evidence of the presence of entrainment are much more suitable than trying to directly detect the current induced by one component on the other. It is worth mentioning that a recent experiment [52] was able to record the dynamics of both superfluid and normal fractions of a weakly interacting Bose-Bose mixture, as well as the finite temperature polarisabilities. We believe that experiments such as this one pave the way towards the detection of subtle superfluid effects such as the AB drag.…”

“…Despite its introduction was inspired by the problem of 3 He and 4 He superfluid mixtures, the low miscibility of these two fluids makes this system hardly achievable in experiments. The AB mechanism has instead recently found applications in the domains of astrophysics and of cold atom systems.…”

Dispersion and decay of collective modes in neutron star cores

“…Chamel and Haensel showed that values of n np obtained from Skyrme interactions had a large spread [24], and in Ref. [14] the result for the SLy4 Skyrme interaction,…”

“…For the nucleon contributions to the quantities E αβ we use the results of Hebeler et al [10], which were earlier employed in calculations of mode frequencies at long wavelengths [14]. In our numerical calculations we use values of E nuc αβ based on chiral effective field theory, because we regard these as the best available.…”

“…Rather we shall include the Coulomb interaction between electrons and protons explicitly. For frequencies small compared with the pairing gaps and for wavelengths large compared with the coherence lengths, the neutrons and protons may be described by hydrodynamics (see [14] and references therein), and the Hamiltonian for the system is thus…”