Two-fluid models of superfluid neutron star cores

Abstract

Both relativistic and non-relativistic two-fluid models of neutron star cores are constructed, using the constrained variational formalism developed by Brandon Carter and co-workers. We consider a mixture of superfluid neutrons and superconducting protons at zero temperature, taking into account mutual entrainment effects. Leptons, which affect the interior composition of the neutron star and contribute to the pressure, are also included. We provide the analytic expression of the Lagrangian density of the system, the so-called master function, from which the dynamical equations can be obtained. All the microscopic parameters of the models are calculated consistently using the non-relativistic nuclear energy density functional theory. For comparison, we have also considered relativistic mean field models. The correspondence between relativistic and non-relativistic hydrodynamical models is discussed in the framework of the recently developed 4D covariant formalism of Newtonian multi-fluid hydrodynamics. We have shown that entrainment effects can be interpreted in terms of dynamical effective masses that are larger in the relativistic case than in the Newtonian case. With the nuclear models considered in this work, we have found that the neutron relativistic effective mass is even greater than the bare neutron mass in the liquid core of neutron stars.Comment: 24 pages, 15 figures, accepted for publication in MNRA

Post-glitch exponential relaxation of radio pulsars and magnetars in terms of vortex creep across flux tubes

“…Temperature evolution is chosen as given by equation (15). Microscopic parameters related to effective masses are taken from Chamel (2008). The toroidal field is considered to reach its maximum intensity at a region with R = 0.8R * .…”

“…Since m * p /mp < 1, proton mass current is inversely directed with the neutron velocity field. Chamel (2008) has shown that effective to bare mass ratio for Douchin & Haensel (2001) and Akmal et al (1998) equations of state changes in the range m * p /mp ≈ 0.9 − 0.4 throughout the entire core depending upon the nucleon-nucleon interactions which in turn depends on the density.…”

Seismology of adolescent neutron stars: Accounting for thermal effects and crust elasticity

“…a radius in the range of 11.5 ± 1.2 km. Fortunately, the SLy4 equation of state [34,42] satisfies these criteria. This model also suits our purposes by involving the simplest reasonable composition.…”

“…To model the star's core, we use the numerical fit to the SLy4 EoS proposed by Chamel [34,42]. This is a zero temperature EoS which accounts for the presence of a mixture of superfluid neutrons and superconducting protons in the core, and includes the entrainment effect.…”

“…We also need a comprehensive formalism for modelling dynamics which accounts for all the desired parameters. Progress on the first of these issues was recently made by Chamel [34], who provided the first ever consistent equation of state including entrainment. The second problem has been explored in basic models [35], to the point where there are no technical stumbling blocks preventing more realistic studies.…”